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A peer-reviewed version of this preprint was published in PeerJ on 4 January 2019.

View the peer-reviewed version (peerj.com/articles/5565), which is the preferred citable publication unless you specifically need to cite this preprint.

Marjanović D, Laurin M. 2019. Phylogeny of limbed reassessed through revision and expansion of the largest published relevant data matrix. PeerJ 6:e5565 https://doi.org/10.7717/peerj.5565 1

1 Reproducibility in : reevaluation of the 2 largest published morphological data matrix for 3 phylogenetic analysis of Paleozoic limbed vertebrates 4 5 David Marjanović1, Michel Laurin2 6 7 1 Science Programme “ and Geoprocesses”, Museum für Naturkunde (Leibniz 8 Institute for Evolutionary and Biodiversity Research), Berlin, ; ORCID: 0000-0001- 9 9720-7726 10 2 Centre de Recherches sur la Paléobiologie et les Paléoenvironnements (CR2P), Centre 11 national de la Recherche scientifique (CNRS)/Muséum national d’Histoire naturelle 12 (MNHN)/Université Pierre et Marie Curie (UPMC; Sorbonne Universités), Paris, France; 13 ORCID: 0000-0003-2974-9835 14 15 Corresponding author: 16 David Marjanović1 17 Museum für Naturkunde, Invalidenstraße 43, D-10115 Berlin, Germany 18 E-mail address: [email protected]

1 PeerJ Preprints | https://doi.org/10.7287/peerj.preprints.1596v3 | CC BY 4.0 Open Access | rec: 15 Jan 2018, publ: 15 Jan 2018 2

19 Abstract 20 21 The largest published phylogenetic analysis of early limbed vertebrates (Ruta M, Coates MI. 22 2007. Journal of Systematic Palaeontology 5:69–122) recovered e.g. , 23 and (in some trees) as paraphyletic and found the “temnospondyl 24 hypothesis” on the origin of (TH) to be more parsimonious than the 25 “lepospondyl hypothesis” (LH) – though only, as we show, by one step. 26 We report thousands of misscored cells, most of them due to typographic and similar 27 accidental errors. Further, some characters are duplicated; some have only one described 28 state; for some, most taxa were scored after presumed relatives. Even continuous characters 29 were unordered, the effects of ontogeny were not sufficiently taken into account, and data 30 published after 2001 were mostly excluded. 31 After these issues are improved – we document and justify all changes to the matrix –, 32 but no characters are added, we find (Analysis R1) much longer trees with e.g. monophyletic 33 Caudata, Diadectomorpha and (in some trees) Seymouriamorpha; either 34 crownward or rootward of Acanthostega; either crownward or rootward of 35 ; the LH is 9 steps shorter than the TH (R2; constrained) and 12 steps shorter 36 the “ hypothesis” (PH – R3; constrained). Brachydectes () is not found 37 next to Lissamphibia; instead, the sister-group of Lissamphibia is a large that includes 38 adelogyrinids, urocordylid “nectrideans” and aïstopods. 39 Adding 56 OTUs to the original 102 increases the resolution. The added taxa range in 40 completeness from complete articulated to an incomplete lower jaw. Even though 41 the lissamphibian-like temnospondyls , and Tungussogyrinus and 42 the extremely peramorphic are added, the difference between LH 43 (R4) and TH (R5) rises to 10 steps, that between LH and PH (R6) to 15; the TH also requires 44 several more regains of lost bones than the LH. 45 Most bootstrap values are low, and plummet when taxa are added. Statistically, the TH 46 (R2, R5) is not distinguishable from the LH or the PH; the LH (R1) and the PH (R3) may be 47 distinguishable from each other under the original taxon sample at p ≥ 0.04. A test for the 48 upper bound of the p value is not available. 49 Bayesian inference (Analysis EB, same settings as R4) mostly agrees with R4. High 50 posterior probabilities are found for Lissamphibia (1.00) and for the LH (0.92); however, 51 many branches remain weakly supported, and most are short, as expected from the small 52 character sample. 53 We discuss phylogeny, approaches to coding, methods of phylogenetics (Bayesian 54 inference vs. equally weighted vs. reweighted parsimony), some character complexes, and 55 prospects for further improvement of this matrix. In its present state, even after our changes, 56 the matrix cannot provide a robust assessment of the phylogeny of early limbed vertebrates; 57 sufficient improvement, however, will be laborious but not difficult. 58

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59 Table of contents 60 61 Introduction 5 62 Aims 6 63 Accuracy of analysis procedure 6 64 Accuracy of the matrix of RC07 8 65 The effects of different methods of analysis 10 66 Phylogeny of early limbed vertebrates 11 67 Phylogenetic background 12 68 Abbreviations 15 69 Nomenclature 16 70 Taxonomic nomenclature 16 71 Phylogenetic nomenclature 17 72 Anatomical nomenclature 18 73 Material and methods 18 74 Treatment of characters 18 75 Character interdependence; redundant characters 18 76 Ordering of multistate characters 19 77 Continuous characters 19 78 Inapplicable characters and mergers 20 79 “Ontogeny discombobulates phylogeny” (Wiens, Bonett & 80 Chippindale, 2005) 22 81 Deleted, recoded and split characters 23 82 Modifications to individual cells 25 83 The albanerpetid neck 29 84 Treatment of OTUs 30 85 /Protorothyris 30 86 Dendrerpetidae 30 87 31 88 The roof of Brachydectes 32 89 Taxa added as parts of existing OTUs 32 90 Taxa added as new OTUs for a separate set of analyses 33 91 Taxa that were not added 49 92 Phylogenetic analyses 51 93 Maximum-parsimony analyses 51 94 Robustness analyses 52 95 Exploratory Bayesian analysis 53 96 Results 54 97 Reanalysis of the matrix of Maddin, Jenkins & Anderson (2012) 54 98 Reanalysis of the matrix of Pardo, Small & Huttenlocker (2017) 57 99 Reanalyses of the matrix of Ruta & Coates (2007) 58 100 Analyses of our revised matrix 63 101 Analysis R1 63 102 Analysis R2 65 103 Analysis R3 67 104 Analysis R4 69 105 Analysis R5 72 106 Analysis R6 72 107 Bootstrap analyses B1 and B2 75 108 Analysis EB 79

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109 Discussion 81 110 Bayesian inference and parsimony in comparison 82 111 Reweighting and equal weighting in comparison 84 112 Persisting problems with the character sample 85 113 Phylogenetic relationships 87 114 taxa and Whatcheeriidae 88 115 More mysteries 89 116 Colosteidae 92 117 The interrelationships of Anthracosauria, , 118 Caerorhachis, Gephyrostegidae, Casineria and 119 Temnospondyli 93 120 The “Parrsboro jaw” 97 121 Anthracosaurian phylogeny 98 122 Temnospondyl large-scale phylogeny 98 123 Stereospondylomorpha 105 124 Dissorophoidea 105 125 Other added temnospondyls 107 126 Chroniosuchia 109 127 Solenodonsaurus 111 128 Seymouriamorpha 111 129 Amniota and Diadectomorpha 112 130 113 131 The lepospondyl problem 113 132 The interrelationships of the “microsaurs” 120 133 Added “microsaurs” 122 134 Lissamphibian origins 123 135 Lissamphibian phylogeny 127 136 Characters 128 137 Surprising reversals 128 138 Other recently discussed characters that are included in this 139 matrix 132 140 Preaxial polarity in limb development 133 141 Other characters that are potentially important for the origin of 142 lissamphibians but not considered in this matrix 135 143 Conclusions 138 144 Phylogeny 136 145 Phylogenetics 138 146 Errata in some of our previous publications 139 147 Errata caused by the lack of page proofs at PLOS ONE 140 148 Acknowledgments 140 149 References 142 150 Supplementary Information 173 151 Appendix 1: Changes to the matrix of RC07 175 152 Appendix 2: Revised matrix 336 153 154

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155 Introduction 156 157 This ancient inhabitant of the coal swamps of Nova Scotia, was, in short, as we often find to be 158 the case with the earliest forms of life, the possessor of powers and structures not usually, in the 159 modern world, combined in a single . It was certainly not a , yet its bony scales, and 160 the form of its vertebræ, and of its teeth, might, in the absence of other evidence, cause it to be 161 mistaken for one. We call it a batrachian, yet its dentition, the sculpturing of the bones of its 162 skull, which were certainly no more external plates than the similar bones of a , its ribs, 163 and the structure of its limbs, remind us of the higher ; and we do not know that it ever 164 possessed , or passed through a larval or fish-like condition. Still, in a great many important 165 characters, its structures are undoubtedly batrachian. It stands, in short, in the same position with 166 the Lepidodendra and Sigillariæ under whose shade it crept, which though placed by palæo- 167 botanists in alliance with certain modern groups of plants, manifestly differed from these in 168 many of their characters, and occupied a different position in . In the coal period, the 169 distinctions of physical and vital conditions were not well defined—dry land and water, 170 terrestrial and aquatic plants and , and lower and higher forms of and vegetable 171 life, are consequently not easily separated from each other. 172 – Dawson (1863: 23–24) about acadianum 173 174 Homoplasy Is even More Common than I, or perhaps Anyone, Has ever Imagined 175 – section headline in Wake (2009: 343) 176 177 What is required is a more complete discussion of the character coding of previous data matrices, 178 and a thorough reanalysis based on those matrices. This would enable a well-founded discussion 179 of lissamphibian origins in light of a supermatrix based on all the current and pertinent data. 180 – Sigurdsen & Green (2011: 459) 181 182 Giant morphological data matrices are increasingly common in cladistic analyses of 183 phylogeny, reporting numbers of characters never seen or expected before. However, the concern 184 for size is usually not followed by an equivalent, if any, concern for character 185 construction/selection criteria. Therefore, the question of whether quantity parallels quality for 186 such influential works remains open. 187 – Simões et al. (2016a: abstract) 188 189 Not too surprisingly, as it is yet a youthful paradigm shift, modern phylogenetic systematics is 190 still evolving to improve on the lack of precision, rigour and objectivity it inherited from the pre- 191 cladistic period. Furthermore, transforming a descriptive science (morphological description) 192 bounded by language as a means of outlining empirical observations into hopefully objectively 193 delimited characters and character-states is a difficult task; every effort to do so is to be 194 commended, while at the same time rigorously scrutinized and improved upon. 195 – Simões et al. (2016a: 215) 196 197 Phylogenetic trees are hypotheses that attempt to explain a data matrix. Much work has gone, 198 to great success, into the methods for generating and testing phylogenetic hypotheses from a 199 given data matrix; and a matrix of molecular data can, apart from the problem of alignment, 200 be largely taken for granted as a set of observed facts. But molecular data are not always 201 available. In many cases phylogeneticists have to rely on morphological data – and a matrix 202 of morphological data is a matrix of hypotheses. The characters, their states, and the 203 relationships between the states are hypotheses that rely on hypotheses about , 204 about independent evolution from other characters, about ontogeny and even preservation 205 (especially in the case of ); the terminal taxa (OTUs) are hypotheses that rely on 206 hypotheses of monophyly, ontogeny and again preservation; and even given all these, each 207 in a data matrix is still a hypothesis that relies on hypotheses of homology, ontogeny and 208 preservation – some are close enough to observed facts, others less so. In addition, 209 morphological data matrices can only be compiled by hand – there is no equivalent to 210 sequencer machines or alignment programs. This makes human error inevitable.

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211 Consequently, morphological data matrices must not be taken for granted as sets of objective 212 data; the hypotheses of which they consist must be identified and carefully tested. 213 The analysis by Ruta & Coates (2007 – hereinafter RC07) has played a large role in 214 shaping current ideas on the phylogeny and early evolution (Late Devonian to , 215 with a few younger taxa) of the limbed vertebrates, including the origins of and 216 lissamphibians. Being based on the largest matrix so far applied to this problem, its results 217 have been widely treated as a consensus and even used as the basis for further work in 218 evolutionary biology (Bernardi et al., 2016; MacIver et al., 2017). However, several 219 conflicting phylogenetic results have persisted in other analyses based on different matrices 220 (Vallin & Laurin, 2004; Marjanović & Laurin, 2008, 2009; Sigurdsen & Green, 2011; Pardo 221 et al., 2017; Pardo, Small & Huttenlocker, 2017: fig. 2, S7, S6). Although the large 222 differences in character sampling between any two of these analyses may be the greatest 223 contribution to their discrepancies (Pardo et al., 2017), it is also possible that some of the 224 differences between these trees may be a function of taxon sampling, analytical parameters 225 like ordering, choice of optimization criterion (parsimony or Bayesian inference), correlation 226 between characters (due to different treatments of ontogeny and heterochrony or other sources 227 of large-scale convergence, or to outright duplication of characters), or accidental misscores 228 (Vallin & Laurin, 2004; Wiens, Bonett & Chippindale, 2005; Tykoski, 2005; Pawley, 2006; 229 Marjanović & Laurin, 2008, 2009, 2013a; Sigurdsen & Green, 2011; Langer et al., 2017). We 230 have aimed to test this complex of hypotheses rigorously by reevaluating the matrix of RC07 231 in detail, and by adding taxa for a separate set of analyses. 232 233 Aims 234 235 We investigated the following questions. 236 237 Accuracy of analysis procedure 238 239  Did RC07 find all of the most parsimonious trees (MPTs) that follow from their 240 matrix? 241 242 This may seem trivial, but Matsumoto et al. (2013) reported that the software PAUP* 4.0b10 243 found three times as many MPTs as TNT 1.0 did when used on their matrix; conversely, 244 Schoch (2013: 682) reported that PAUP 3.1 did not find any trees as short as those recovered 245 by TNT; Baron, Norman & Barrett (2017) found only 93 of 16,632 MPTs, having neglected 246 to run a second round of tree bisection and reconnection on their TNT trees (Watanabe, 247 2017a, b; Langer et al., 2017: supplementary information: 26); and Skutschas & Gubin (2012) 248 found that the “parsimony ratchet”, a procedure for reducing calculation time (Ruta, Coates & 249 Quicke, 2003), did not find any trees less than 35 steps longer than the MPTs. RC07 used the 250 parsimony ratchet. We therefore repeated their analysis without using the ratchet (Analysis 251 O1 – see Table 1 and Fig. 1). 252 253  Did Maddin, Jenkins & Anderson (2012) find all of the most parsimonious trees 254 (MPTs) that follow from their matrix, and what are their topologies? 255  Did Pardo, Small & Huttenlocker (2017) find all of the MPTs that follow from their 256 matrix, and what are their topologies? 257 258 Maddin, Jenkins & Anderson (2012) published the first phylogenetic analysis that found a 259 animal (Gerobatrachus) to be a lissamphibian. At least this is the position 260 Gerobatrachus has in the majority-rule consensus tree – the authors did not report the strict

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261 consensus of the trees they found, and they did not comment on any most parsimonious 262 topologies that did not fit the majority-rule consensus. Several important analysis settings 263 remain unpublished as well. Given the extreme relevance of a possible lissamphibian in the 264 Early Permian, we reanalyzed their matrix. 265 Similarly, Pardo, Small & Huttenlocker (2017) published the first two phylogenetic 266 analyses that found the extant to have two separate origins among the 267 temnospondyls, turning most temnospondyls (Gerobatrachus, , …) 268 into lissamphibians. This occurs in their Bayesian analysis (fig. 2 = S7A) and in the majority- 269 rule consensus of their parsimony analysis (fig. S7B); the authors did not comment on any 270 most parsimonious topologies that did not fit the majority-rule consensus. Noting that none of 271 the nodes between and + Karauridae occurs in 100% of the MPTs 272 (Pardo, Small & Huttenlocker, 2017: fig. S7B), and remembering that even the figure “100%” 273 in majority-rule consensus trees is sometimes rounded up, we reanalyzed that matrix as well 274 (not the unpublished one that resulted in fig. S6). 275 276 Table 1: Overview of analysis settings and results concerning lissamphibian origins. See 277 Table 3 for results concerning other questions. Steps were counted in PAUP* (Swofford, 278 2003), partial uncertainty was distinguished from polymorphism. ”Parsimony” refers to 279 equally weighted maximum parsimony, “bootstrap” to equally weighted maximum parsimony 280 bootstrap, “Bayesian” to Bayesian inference. 281 Matrix Taxon Analysis Method Constraint Steps Result Figures sample RC07 RC07 O1 parsimony none 1621 TH 2 (102 O2 against TH1 1622 LH 9 revised OTUs) R1 none 2182 LH 10, 11 R2 against LH2 2191 TH3 12 R3 for PH 2194 PH 13 B1 bootstrap none 2295 LH 18 expanded R4 parsimony none 3011 LH 14 (158 R5 against LH2 3021 TH 15, 16 OTUs) R6 for PH 3026 PH 17 B2 bootstrap none 3089 LH 19 EB Bayesian none (3075)4 LH 20, 21 282 283 1 This constraint is aimed at enforcing the LH, but it is also compatible with the (never 284 proposed) “inverse polyphyly hypothesis”, where the salientians would be lepospondyls and 285 the gymnophionomorphs (represented by ) would be temnospondyls. 286 2 This constraint is aimed at enforcing the TH, but it is also compatible with the PH. 287 3 A highly unusual version of the TH, see Results, Discussion and Table 3. 288 4 This is the parsimony treelength calculated for this topology by PAUP*. The more 289 appropriate Bayesian treelength is not comparable to the other lengths presented here. 290 291  What is the difference in tree length between the MPTs of RC07, which find 292 Lissamphibia nested among the temnospondyls (Fig. 1), and the shortest trees 293 compatible with their matrix that are constrained to place Lissamphibia among the 294 “lepospondyls”? 295

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296 RC07 reported that this difference is both nine steps (p. 85) and 15 steps (p. 86). The first 297 resulted from using the whole tree of Laurin (1998a) as a constraint, which is of course not 298 the only possibility for where and how Lissamphibia could be placed among the 299 “lepospondyls”. RC07 did not publish the constraint they used for the second; we therefore 300 created one and used it in a second analysis of their matrix (Analysis O2). 301 302 Accuracy of the matrix of RC07 303 304 Analogously to the problem of alignment in molecular analyses, morphological analyses 305 begin with the construction of a dataset, where characters need to be defined in ways that 306 prevent them from being redundant. (When the state of a character is predictable from the 307 state of another character, the characters are redundant for the purposes of phylogenetic 308 analysis; to use redundant characters amounts to counting the same character at least twice, 309 doubling or multiplying its influence on the results.) Observations need to be interpreted in 310 terms of these characters, and then these interpretations need to be inserted in the data matrix 311 by hand. In our own practice, we have every once in a while caught ourselves making 312 typographic errors, being momentarily confused about which state is 0 and which is 1 313 (because of faulty memory as well as conflicting conventions on how to assign such numbers 314 – 0 can for instance mean “absent” or “presumably plesiomorphic”), inserting the right value 315 in the wrong column or line, and committing similar blunders; additionally, we have on 316 occasion misinterpreted the descriptive literature and its illustrations (line drawings, but even 317 photographs, can give misleading three-dimensional impressions), overlooked poorly known 318 publications, had language barriers or conflicting terminologies prevent us from being sure if 319 a published sentence said one thing or the opposite, or simply relied on the then current state 320 of research that was later overturned when the next publication came out. It stands to reason 321 that these things also happen to other people. 322 Following the reevaluations by Marjanović & Laurin (2008, 2009: supplementary 323 information) of the matrices by McGowan (2002) and Anderson et al. (2008a), those by 324 Sigurdsen & Green (2011) of the matrices by Vallin & Laurin (2004), RC07 and Anderson et 325 al. (2008a) and the one by Langer et al. (2017) of the matrix by Baron, Norman & Upchurch 326 (2017), we scrutinized the matrix of RC07 in the light of the following questions: 327 328 ↓ Figure 1: Strict consensus of the MPTs (length: 1621 steps including polymorphisms) 329 found by RC07 and by our unconstrained reanalysis of their unchanged data matrix 330 (Analysis O1; see Table 1). The topology is identical to RC07: fig. 5, 6. Names of extant 331 taxa are in boldface in this and all following tree figures. In this figure and all following ones, 332 Albanerpetidae and Dendrerpetidae are each a single OTU (called “” and 333 “Dendrerpeton” by RC07). The name Edopoidea (and, in some other figures, 334 Eutemnospondyli) is placed under the assumption that Mastodonsaurus (not included in any 335 of our analyses) would be closest to Eryops as found by Schoch (2013); “Dissorophoidea 336 (S13)” is placed according to Schoch’s (2013) definition, “Dissorophoidea (YW00)” is placed 337 according to the definition by Yates & Warren (2000), and “Dissorophoidea (content)”, only 338 shown where different from Dissorophoidea (YW00), is the smallest clade that has the 339 traditional contents of that taxon (trematopids, Broiliellus, amphibamids/branchiosaurids, 340 Micromelerpeton). The origin of digits cannot be narrowed down to a single internode in this 341 and several other figures. For easier orientation, Ichthyostega, Baphetes and Eryops are 342 written in purple. The color scheme of the background boxes is consistent across all figures. 343 Occasional abbreviations: Gymnophio., Gymnophionomorpha; Liss., Lissamphibia; micr. or 344 microbr., microbrachomorphs; Ph., . All “microsaurs” are underlain in the same 345 shade of gray, but some (in some figures) are not labeled as such due to lack of space.

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origin of digits Tulerpeton Colosteus Greererpeton Colosteidae Acherontiscus Adelospondylus adelospondyls Adelogyrinus Adelogyrinidae Dolichopareias Ossinodus Whatcheeria Whatcheeriidae Pederpes Eucritta Baphetes Baphetoidea Megalocephalus Chenoprosopus Edopoidea Cochleosaurus Isodectes Neldasaurus Dvinosauria Amphibia Capetus Balanerpeton Dendrerpetidae Eryops Acheloma Trematopidae Phonerpeton Dissorophoidea (YW00) Ecolsonia Broiliellus brevis Micromelerpeton Dissorophoidea (S13) Leptorophus Schoenfelderpeton Platyrhinops Eoscopus crown-group “amphibamids” Albanerpetidae Eocaecilia Gymnophionomorpha “caudates” Lissamphibia Valdotriton Batrachia Notobatrachus Vieraella Caerorhachis Silvanerpeton Anthracosauria Embolomeri Pholiderpeton scutigerum Pholiderpeton attheyi Anthracosaurus “gephyrostegids” Bruktererpeton Utegenia Ariekanerpeton Leptoropha “seymouriamorphs” Microphon Solenodonsaurus Tseajaia “diadectomorphs” Paleothyris/Protorothyris Westlothiana Asaphestera Saxonerpeton Odonterpeton Microbrachomorpha Hyloplesion Hapsidopareion Pelodosotis Ostodolepididae Rhynchonkos/Aletrimyti/Dvellecanus “microsaurs” Euryodus Gymnarthridae Stegotretus Pantylidae Brachydectes Lysorophia Scincosaurus Batrachiderpeton Diplocaulidae Holospondyli Diploceraspis Ptyonius Urocordylidae 9 Lethiscus Oestocephalus Aïstopoda Phlegethontia 10

346  Are there enough redundant characters in the matrix of RC07 to change the resulting 347 trees? 348  Are there enough accidental misscores in the matrix of RC07 to change the resulting 349 trees? 350 351 The second question (the only one investigated by Langer et al., 2017) accounts for the bulk 352 of the work we present here. All changes to the matrix, most of which are of this kind, are 353 documented and justified in Appendix 1, the commented character list, which comprises more 354 than half of the text of the present publication. The revised matrix is presented in human- 355 readable form as Appendix 2, where the changes are highlighted in color, and in NEXUS 356 format as Data S1. 357 In all likelihood, accidental misscores should be a good approximation to random 358 noise. Such noise is expected to produce many weak false signals which cancel each other out 359 instead of accumulating into a challenge to the true signal. However, when the true signal is 360 weak to begin with (perhaps due to a character sample which is small enough to cause 361 accidental sampling bias) and one or a few strong false signals are already present (due to 362 large-scale evolutionary convergence or redundant characters), random noise added to the true 363 and false signals may change the balance from slightly in favor of the true signal to slightly in 364 favor of a false signal – or indeed from one false signal to another, so that efforts to reduce the 365 strength of the first false signal will not make the true signal stand out. 366 Our methods for identifying and attempting to deal with redundant characters – in 367 many cases a hard problem on which we expect future advances – are explained below 368 (Material and methods: Treatment of characters). This includes ontogeny-related characters: 369 taxa known only from immature or paedomorphic individuals will predictably have 370 “immature” states of many characters, with dramatic consequences for the resulting trees such 371 as clustering of these taxa into spurious (Wiens, Bonett & Chippindale, 2005). Our 372 approach to this difficult problem, modified from the recommendation of Wiens, Bonett & 373 Chippindale (2005: 96), was independently proposed by Tykoski (2005), Pawley (2006: 206) 374 and Marjanović & Laurin (2008); it was explained in more detail by Marjanović & Laurin 375 (2013a) and is presented again below (Material and methods: Treatment of characters: 376 “Ontogeny discombobulates phylogeny”). The changes made to the matrix for this reason are 377 likewise documented and justified in Appendix 1. 378 Due to the high calculation times, we were unable to test these questions separately. 379 As mentioned, Sigurdsen & Green (2011) have performed their own reevaluation of 380 the matrix of RC07. That work, however, had a very limited scope (see Marjanović & Laurin, 381 2013a, for discussion). We have incorporated most, though not all, of the changes to 382 individual cells suggested in it (as discussed under the respective characters in Appendix 1). 383 Unlike Sigurdsen & Green (2011), we have not deleted characters of unclear value. 384 385 The effects of different methods of analysis 386 387  Does a Bayesian analysis of our revised matrix support a different tree than the 388 parsimony analyses? 389 390 All of the analyses mentioned above used the nonparametric method somewhat misleadingly 391 called “parsimony” or “maximum parsimony”. For comparison, we also applied Bayesian 392 inference to our revised matrix. The behavior of Bayesian inference under the conditions of 393 this matrix are not well understood, and Bayesian analyses are time-consuming; we therefore 394 ran only one analysis (under the same conditions as R4 and B2: enlarged taxon sample, no 395 constraints) which we consider exploratory (Analysis EB). According to recent simulations,

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396 Bayesian inference has advantages over parsimony (Wright & Hillis, 2014; O’Reilly et al., 397 2016, 2017; Puttick et al., 2017; but see Brown et al., 2017, and Goloboff, Torres & Arias, 398 2017); in particular, it is much less sensitive to long-branch attraction, which may be a 399 concern with some of the “weirder” taxa in our sample like adelospondyls, aïstopods or 400 indeed lissamphibians. 401 402 Phylogeny of early limbed vertebrates 403 404 The matrix of RC07 is the largest published one that concerns the phylogeny of early (roughly 405 Paleozoic) limbed vertebrates other than amniotes. If we have come satisfactorily close to 406 solving the problems presented above, our modified matrix should therefore be better suited 407 to investigating the following questions, among others, than any other matrix published so far, 408 even though it cannot treat all of them in sufficient depth. Compare Fig. 1: 409 410  Are lissamphibians temnospondyls, “lepospondyls” or (diphyletically) both? 411 o How strong is the support for each of these hypotheses? 412  Are the albanerpetids lissamphibians, and if so, what are their closest relatives? 413  Do the traditional diadectomorphs form a clade? 414  Do the traditional “microsaurs” form a clade (including or excluding any 415 lissamphibians)? 416  Do the traditional “lepospondyls”, or some of them, form a clade (including or 417 excluding any lissamphibians)? 418  Do the traditional seymouriamorphs form a clade? 419  Are the traditional seymouriamorphs or any traditional “lepospondyls”, especially 420 “microsaurs”, closer to Amniota? 421  What can be said about temnospondyl phylogeny? 422  Is Anthracosauria or Temnospondyli closer to Amniota? 423  What are the phylogenetic positions of Solenodonsaurus, Gephyrostegus, 424 Bruktererpeton, Caerorhachis, Silvanerpeton and Tulerpeton (all have been connected 425 to anthracosaur origins at one point or another)? 426  Are Adelogyrinidae and Acherontiscus “lepospondyls” or close to the colosteids? 427  Is Colosteidae or Whatcheeriidae closer to the tetrapod crown-group? 428  Is Ichthyostega or Acanthostega closer to the tetrapod crown-group? 429  What happens to the above questions when taxa are added? 430 o What is the phylogenetic position of Chroniosuchia and several other taxa? 431 o Are the traditional diadectomorphs amniotes, or are they the closest relatives of 432 Amniota? 433 o Is Casineria close to origins? 434 435 These questions are presented in more detail in the “Phylogenetic background” section below 436 and in the Discussion (section “Phylogenetic relationships”). To avoid another duplication of 437 the number of analyses, we added taxa but no characters; adding characters will be part of 438 future work. However, we discuss a few characters – both inside and outside the present 439 matrix – that have recently been connected to lissamphibian origins (Discussion: Characters: 440 subsections other than the first). 441 442 443 444

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445 Phylogenetic background 446 447 The early phylogeny of the limbed vertebrates contains a number of open questions on which 448 there is either no consensus, or the existing consensus is weakly supported. Most famously, 449 the origin of the modern amphibians (Lissamphibia and its possible member or sister-group 450 Albanerpetidae – see below on that name) remains a vexing problem (Fig. 2). From the late 451 19th century to now, the modern amphibians have been considered temnospondyls by some 452 (Fig. 2C – “temnospondyl hypothesis”, abbreviated as TH below; most recently found by: 453 RC07; Sigurdsen & Green, 2011; Pardo, Small & Huttenlocker, 2017: fig. S6; Pardo et al., 454 2017), lepospondyls by others (Fig. 2D – “lepospondyl hypothesis”, abbreviated as LH 455 below; Vallin & Laurin, 2004; Pawley, 2006: appendix 16; Marjanović & Laurin, 2008, 2009, 456 2013a), and polyphyletic by yet others (Fig. 2E – “polyphyly hypothesis”, abbreviated as PH 457 below; Carroll, 2007; Huttenlocker et al., 2013), with Salientia being nested among the 458 temnospondyls, Gymnophionomorpha among the lepospondyls, and Caudata either in the 459 lepospondyls (all early works) or in the temnospondyls (works published in the 21st century). 460 This particular question has far-reaching implications for the interpretation of most of 461 our taxon sample. For example, the seymouriamorphs – considered close to amniote origins 462 for most of the 20th century, though known to have gilled juveniles and possibly neotenes – 463 indeed lie on the amniote stem under the TH (Fig. 1); from phylogenetic bracketing, it follows 464 that the unfossilized parts of their anatomy and behavior were more amniote-like than found 465 in lissamphibians and lay within the range of other crown-group in the absence of 466 evidence to the contrary. Under the PH, the seymouriamorphs lie on the common stem 467 of amniotes and to the exclusion of batrachians (salientians + caudates); the last 468 common ancestor of the extant amphibians was thus the last common ancestor of all crown- 469 group tetrapods, and its features should be expected to have persisted in the seymouriamorphs 470 unless there is evidence to the contrary. Under the LH, in contrast, the seymouriamorphs are 471 (most likely, see below) stem-tetrapods, bracketed by extant tetrapods on only one side, and 472 may have been much less similar to extant tetrapods than the TH or the PH predict. Likewise, 473 the diverse temnospondyls are stem-amphibians under the TH (Fig. 1, 2C), bracketed by 474 lissamphibians and amniotes among extant taxa; under the PH (Fig. 2E), they belong to the 475 batrachian stem, bracketed by extant amphibians on both sides, so that a great many features 476 found among extant amphibians should be expected to have been shared by temnospondyls 477 (validating a large amount of existing literature and artwork); under the LH, however (Fig. 478 2D), they are not crown-group tetrapods at all, but lie fairly far rootward on their stem and 479 should be expected to be unlike anything alive today in an unknown but large number of 480 aspects. (The new version of the TH by Pardo, Small & Huttenlocker, 2017: fig. 2, S7 but not 481 S6, makes much the same predictions as the PH in this regard because it turns most 482 temnospondyls into lissamphibians.) 483 Among other more or less open questions are the phylogenies of Temnospondyli (e.g. 484 Pawley, 2006; Ruta, 2009; Dilkes, 2015a; Pardo, Small & Huttenlocker, 2017), 485 “Lepospondyli” (RC07; Huttenlocker et al., 2013; Marjanović & Laurin, 2013a; Pardo, Small 486 & Huttenlocker, 2017: fig. S6) and Devonian limbed vertebrates (e.g., Ahlberg & Clack, 487 1998; Clack et al., 2012a; Pardo et al., 2017), as well as the relative positions of 488 Anthracosauria and Temnospondyli (Laurin & Reisz, 1999; RC07; Pardo et al., 2017) and the 489 position of Diadectomorpha inside or next to Amniota (Berman, Sumida & Lombard, 1992; 490 Berman, 2013), not to mention the positions of confusing (Andrews & Carroll, 1991; 491 Smithson et al., 1994; Clack, 2001; Ruta, Milner & Clack, 2002; Vallin & Laurin, 2004; 492 RC07) or fragmentary taxa (Smithson, 1980; Paton, Smithson & Clack, 1999; 493 Bolt & Lombard, 2006; Clack et al., 2012b, 2016; Sookias, Böhmer & Clack, 2014).

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494 495 496 Figure 2: Hypotheses on the origin(s) of the extant amphibians, and their compatibility 497 with molecular and morphological data. The names Amphibia and Lissamphibia do not 498 apply in E. A: Consensus of all recent molecular studies (e.g. Pyron, 2014: supplementary file 499 amph_shl.tre; Irisarri et al., 2017). B: Part of the consensus of all recent morphological 500 studies (e.g. our results, RC07, and references in both); modern amphibians not shown. C: 501 Extant amphibians added to B according to the “temnospondyl hypothesis”; note 502 compatibility with A. D: “Lepospondyl hypothesis” mapped to B; note compatibility with A. 503 E: “Polyphyly hypothesis” mapped to B; note lack of compatibility with A. In earlier versions 504 of the “polyphyly hypothesis”, Caudata often lies next to Gymnophionomorpha instead of 505 Salientia; in that case, the name Batrachia does not apply (or becomes a synonym of the 506 tetrapod crown-group). 507 508 Molecular data are of limited use for tackling these questions: of all tetrapodomorphs 509 (tetrapods and everything closer to them than to ), only , , caecilians 510 and amniotes still have living members (Fig. 2). Thus, molecular data cannot test, say, 511 whether Amniota is closer to Anthracosauria or to Temnospondyli, or if the many disparate 512 taxa classified as “Lepospondyli” constitute a clade, a grade, or a wastebasket. When it comes 513 to the origins of the extant amphibians, molecular data can distinguish the PH (Fig. 2E) from 514 the other hypotheses, because the PH predicts that the extant amphibians are paraphyletic with 515 respect to Amniota, while the other two hypotheses of course predict monophyly under recent 516 conceptions of the affinities of temnospondyls, lepospondyls and amniotes (Fig. 2B; Laurin, 517 2002; see also Marjanović & Laurin, 2007, 2013a); but molecular data cannot distinguish the 518 two monophyly hypotheses, because too many relevant taxa have been extinct for too long. 519 Finding the extant amphibians monophyletic with respect to Amniota (Fig. 2A), analyses of 520 molecular data support both monophyly hypotheses equally (Fig. 2A, C, D); only 521 paleontological data can distinguish them. Existing analyses of paleontological data, however, 522 disagree greatly on this question (see above; Fig. 2C–E) as well as on others. To some extent, 523 no doubt, this is due to the many differences in their taxon and character samples. Another

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524 possible reason, however, are problems in datasets of the kinds presented above. When such 525 misscores and miscodings are removed from matrices – without, as far as possible, changing 526 the taxon or character sample –, do the results change? 527 The largest published morphological data matrix that has been applied to the problems 528 of the phylogeny of limbed vertebrates in general and the origin of the modern amphibians in 529 particular is that by RC07; it supported the TH and is often cited for this result. Here we 530 reevaluate this matrix in to test, and explain within the limitations of the dataset, to what 531 degree this result – and others that together constitute the consensus tree of RC07 (fig. 5, 6; 532 our Fig. 1) – continues to follow from their dataset after a thorough effort to improve the 533 accuracy of the scoring and reduce character redundancy has been carried out to the best of 534 our current knowledge. 535 Naturally, this effort will not suffice to solve the question of lissamphibian origins or 536 any other of the many controversies in the phylogeny of early limbed vertebrates. A quick 537 look at matrices such as those of Ruta (2009), Sigurdsen & Green (2011), Maddin, Jenkins & 538 Anderson (2012), Sookias, Böhmer & Clack (2014), Dilkes (2015a), Clack et al. (2016), 539 Pardo, Small & Huttenlocker (2017) or Pardo et al. (2017), or at reinvestigations of anatomy 540 such as those of Witzmann (2007, 2010, 2013), Bolt & Lombard (2010), Mondéjar- 541 Fernández, Clément & Sanchez (2014), Dilkes (2015a) or Pardo et al. (2017) and references 542 therein will demonstrate that many characters which are known to carry phylogenetic signal 543 for the present taxon sample remain absent from this matrix; this even includes some of the 544 very few (41) characters used by McGowan (2002). Adding them (as well as yet more taxa) 545 will be part of future work, and may well lead to trees with a different topology. However, we 546 think the present work forms a necessary step towards solving any of those problems. Further 547 progress may come from larger matrices – if and only if the increase in the number of cells is 548 not accompanied by a proportional decrease in the care that goes into scoring them (Simões et 549 al., 2016a). 550 Originally we did not intend to add any taxa to the matrix, just as we have not added 551 any characters. However, soon after the work of RC07 was published, the intriguing 552 amphibamid temnospondyl Gerobatrachus was described and was argued to add strong 553 support to the PH (Anderson et al., 2008a). Phylogenetic analyses that included 554 Gerobatrachus in different versions of the same matrix have supported the PH (Anderson et 555 al., 2008a), the LH (Marjanović & Laurin, 2009), or more recently the TH (Maddin & 556 Anderson, 2012; Maddin, Jenkins & Anderson, 2012); the latter work even found 557 Gerobatrachus to be nested within Lissamphibia (partially replicated by Pardo, Small & 558 Huttenlocker, 2017: fig. S6B, S7B; trivially replicated by Pardo, Small & Huttenlocker, 2017: 559 fig. 2, S7A, where most temnospondyls are lissamphibians; not replicated by Pardo, Small & 560 Huttenlocker, 2017: fig. S6A or by Pardo et al., 2017, where Gerobatrachus and 561 Lissamphibia are sister-groups as in Maddin & Anderson, 2012). Clearly, Gerobatrachus is 562 too important to be left out. Following the example of Marjanović & Laurin (2008) and 563 Langer et al. (2017), we have therefore performed a separate series of analyses (R4–R6, B2) 564 for which we added Gerobatrachus to the matrix; at that opportunity, for the same series of 565 additional analyses, we added a further 55 OTUs as detailed and justified in Material and 566 methods: Taxa added as new OTUs for a separate set of analyses, bringing the total from 102 567 to 158. 568 In the Discussion section, we explore the relationships of certain taxa and the 569 distributions of certain character states in the light of our findings and other recent 570 publications. By presenting the current areas of uncertainty (some expected, some 571 unexpected), we hope to highlight opportunities for future research. 572 573

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574 Abbreviations 575 576 AMNH: properly AMNH DVP or AMNH FARB – Department of Vertebrate or 577 Collection of Fossil Amphibians, Reptiles and at the American Museum of Natural 578 History, New York. 579 BEG: Vertebrate Paleontology Laboratory, The University of at Austin (formerly 580 Bureau of Economic Geology). 581 BPE: bootstrap percentage given the expanded taxon sample (bootstrap analysis B2). 582 BPO: bootstrap percentage given the original taxon sample (bootstrap analysis B1). 583 CG78: Carroll & Gaskill (1978). 584 ci: consistency index (in lowercase to make the numbers stand out). 585 CM: Carnegie Museum of Natural History, Pittsburgh. 586 LH: “lepospondyl hypothesis” on the origin of lissamphibians. 587 hi: homoplasy index. 588 MB.Am.: “” in the vertebrate paleontology collection of the Museum für 589 Naturkunde, Berlin. 590 MCZ: properly MCZ VPRA – “” or “amphibian” in the vertebrate paleontology 591 collection of the Museum of Comparative Zoology, Harvard University, Cambridge 592 (Massachusetts). 593 MGUH: Geologisk Museum, Statens Naturhistoriske Museum, Københavns Universitet, 594 Copenhagen (“Museum Geologicum Universitatis Hafniensis”). 595 MNHN: Muséum national d’Histoire naturelle, Paris. 596 MNN MOR: Moradi collection of the Musée national du Niger, currently kept at the Burke 597 Museum, University of Washington, Seattle. 598 MPT: most parsimonious tree. 599 NHMW: Naturhistorisches Museum Wien, Vienna. 600 NMS: National Museum of , Edinburgh. 601 NSM: Nova Scotia Museum, Halifax. 602 OTU: operational taxonomic unit (a line in a data matrix). 603 PH: “polyphyly hypothesis” on the origin of “lissamphibians”. 604 PIN: Paleontological Institute of the Academy of Sciences of the Russian Federation, 605 Moscow. 606 PP: posterior probability in percent given the expanded taxon sample (exploratory Bayesian 607 analysis EB). 608 PU-ANF: “amphibian” specimens from Puertollano (Spain) in the vertebrate collection of the 609 Department of Paleontology, Geology division, Universidad Complutense, Madrid; formerly 610 kept at the Museum für Naturkunde, Berlin. 611 rc: rescaled consistency index. 612 RC07: Ruta & Coates (2007). 613 ri: retention index. 614 TH: “temnospondyl hypothesis” on the origin of lissamphibians. 615 TMM: Vertebrate Paleontology Laboratory, The University of Texas at Austin (formerly 616 Texas Memorial Museum). 617 USNM: National Museum of Natural History, Smithsonian Institution, Washington (DC). 618 YPM: Yale Peabody Museum, New Haven (Connecticut). 619 Abbreviations not listed here that consist of at least three letters, at least one space and 620 a number designate characters, following the practice of RC07; see Appendix 1. Note that 621 merged characters keep the abbreviations of all their constituents: e.g., PREMAX 1-2-3 622 (character 1) is built from the three characters PREMAX 1, PREMAX 2 and PREMAX 3 of 623 RC07, and MAX 5/PAL 5 (character 22) consists of MAX 5 and PAL 5 of RC07.

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624 Nomenclature 625 626 A few remarks are necessary to explain our use of certain terms. 627 628 Taxonomic nomenclature 629 630 Without mentioning the fact that they were doing so, Averianov & Sues (2012: 466) corrected 631 the spelling of Albanerpetontidae Fox & Naylor, 1982, to Albanerpetidae. We follow this in 632 analogy to several corrections by Martín, Alonzo-Zarazaga & Sanchiz (2012) as discussed by 633 Marjanović & Laurin (2013b: 543), who did not know of Averianov & Sues (2012) and 634 therefore incorrectly claimed that “no other spelling [than Albanerpetontidae] has ever been 635 used”, as well as in analogy to several further corrections by Schoch & Milner (2014). 636 Assuming that this correction is a “justified emendation”, the name Albanerpetidae must 637 continue to be attributed to Fox & Naylor, 1982 (International Commission on Zoological 638 Nomenclature, 1999: articles 19.2, 29). 639 Likewise, the spelling Hapsidopareiontidae must be corrected to Hapsidopareiidae 640 Daly, 1973: there is no basis for -ont- in Homeric Greek παρήϊον (“cheek”) (Perseus Digital 641 Library, accessed 5 November 2017). This name has been used so rarely that the question of 642 common usage does not arise. 643 There is little if any room for doubt about the fact that the species name Trihecaton 644 howardinus is automatically emended to T. howardinum Vaughn, 1975 (International 645 Commission on Zoological Nomenclature, 1999: article 31.2 = 34.2), because Trihecaton 646 (meaning “300”; a numeral, not a noun) is – if anything – neuter. 647 There is no room for doubt about the fact that the same Article emends 648 Madygenerpeton pustulatus to Madygenerpeton pustulatum Schoch, Voigt & Buchwitz, 2010. 649 Previously, Tryphosuchus contained T. paucidens (type species) and T. kinelensis, and 650 Konzhukovia contained K. vetusta (type species) and K. tarda. Pereira Pacheco et al. (2016) 651 found T. paucidens and K. vetusta as sister-groups, which together formed the sister-group of 652 K. tarda. Consequently, Pereira Pacheco et al. (2016) wondered if T. paucidens should be 653 referred to Konzhukovia. This is not possible: Tryphosuchus Konzhukova, 1955, has priority 654 over Konzhukovia Gubin, 1991, which only the International Commission on Zoological 655 Nomenclature could overturn. The fact that Pereira Pacheco et al. (2016) considered T. 656 paucidens a nomen dubium has no bearing on this: first, to declare a name a nomen dubium is 657 a taxonomic (subjective) act, not a nomenclatural (objective) one; second, a taxon name does 658 not automatically become a nomen dubium if the name of its type subtaxon is one. 659 Konzhukovia and Tryphosuchus were previously included in Tryphosuchinae Golubev, 660 1995 (type : Tryphosuchus), within Melosauridae Fritsch, 1885 (type genus: 661 Melosaurus). Pereira Pacheco et al. (2016: fig. 5) confirmed that Konzhukovia and 662 Tryphosuchus form a clade to which Melosaurus does not belong. However, because they 663 found this clade to lie closer to than to Melosaurus, they did not refer it to 664 Melosauridae; instead, “we erect the new family Konzhokoviidae [sic!] fam. nov. to replace 665 Tryphosuchinae” (p. 251). This, too, is not valid without an Opinion by the Commission. By 666 means of the Principle of Coordination (Article 36.1), when the name Tryphosuchinae was 667 created at the subfamily rank, the name Tryphosuchidae at the family rank was automatically 668 created at the same time; it must be attributed to Golubev, 1995, and therefore has priority 669 over Konzhukoviidae. (We should note that Konzhukoviidae is so spelled in the title, the 670 abstract, and five times in the text, of which two are marked “fam. nov.”, including the one at 671 the beginning of the “Systematic palaeontology” section; the misspelling Konzhokoviidae 672 occurs five times in the text as well, three of which are marked “fam. nov.”.) Because

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673 Konzhukoviidae is (trivially) not in common usage, the exception constituted by Article 35.5 674 does not apply. 675 The genus and species names Diploradus austiumensis Clack & T. R. Smithson in 676 Clack et al., 2016, were explained as follows (Clack et al., 2016: 3): “Genus from diplo 677 (Greek) ‘double’ and radus (Greek) ‘row’ referring to the double coronoid row. Species 678 from austium (Latin) ‘mouth of a river or stream’ referring to Burnmouth.” We have not been 679 able to find a word similar to “radus” in the Greek or for that matter Latin dictionaries in the 680 Perseus Digital Library (“Dictionary Entry Lookup” and “English-to-[Language] lookup” in 681 the “General Search Tools” http://www.perseus.tufts.edu/hopper/search accessed 5 November 682 2017). The closest in form and meaning appears to be Latin , originally meaning “staff, 683 rod”. (The one language we have found where rad means “row” is Slovak.) A form austium 684 does not seem to exist; the word meaning “opening”, “door”, “river mouth” is ostium – 685 although some confusion between au and o already set in in Classical times (as in the names 686 Claudius and Clodius), this does not seem to have happened for ostium, which is derived from 687 os meaning “mouth”. Further, -um is an ending (nominative singular), not part of the stem of 688 this word. In short, the species name should have been ostiensis. Most likely the name cannot 689 be corrected; Article 32 (International Commission on Zoological Nomenclature, 1999) is 690 worded very strictly. We hope, however, that similar cases can be avoided in the future. 691 692 Phylogenetic nomenclature 693 694 Because of the length of this paper and because the International Code of Phylogenetic 695 Nomenclature (“PhyloCode”) has not yet taken effect, we refrain from proposing new clade 696 names or definitions. Having, however, noticed that the names Adelogyrinidae and 697 Adelospondyli currently refer to the same taxon, we follow RC07: 81 (but not fig. 5) and 698 Coates, Ruta & Friedman (2008: fig. 2: “Adelospondyli”) in informally referring to a clade 699 composed of Acherontiscus and Adelogyrinidae as “adelospondyls” for brevity, always 700 excluding the historically included lysorophians. 701 We have previously proposed and defined the name Gymnophionomorpha 702 (Marjanović & Laurin, 2008: 152–154, fig. 3) as applying to the largest clade that contains 703 tentaculata L., 1758, but not Rana temporaria L., 1758, Salamandra salamandra 704 (L., 1758), inexpectatum Estes & Hoffstetter, 1976, Brachydectes newberryi 705 Cope, 1868, Rhynchonkos stovalli (Olson, 1970), Batropetes fritschi (Geinitz & Deichmüller, 706 1882) or craddocki (Langston & Olson, 1986). To the list of external specifiers we 707 propose to add Plagiosaurus depressus Jaekel, 1914, Brachyops laticeps Owen, 1854, and 708 Pelorocephalus mendozensis Cabrera, 1944, to keep Gymnophionomorpha from 709 encompassing Eryopiformes on the pertinent trees of Pardo, Small & Huttenlocker (2017: fig. 710 2, S7). 711 As in a previous paper (Marjanović & Laurin, 2013a), where we failed to make this 712 explicit, we use “modern amphibians” for Lissamphibia and its possible member or sister- 713 group Albanerpetidae. 714 Several names for temnospondyl clades, including Temnospondyli itself, have been 715 given very different definitions by Yates & Warren (2000) and Schoch (2013). We have 716 generally applied the definitions by Yates & Warren (2000). The important exceptions are 717 Dissorophoidea and Stereospondylomorpha, which we use in the text for clades containing all 718 those OTUs that have traditionally been regarded as members of clades with these names and 719 exclude most or all OTUs that have traditionally not been regarded as members. For 720 Dissorophoidea, we indicate both definitions and our usage in the tree figures (our usage 721 usually, but not always, coincides with the definition by Yates & Warren, 2000). 722

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723 Anatomical nomenclature 724 725 Consistently or nearly so, RC07 (as also Pardo, Szostakiwskyj & Anderson, 2015) exchanged 726 the terms “skull roof” and “skull table”. The former refers to the dermatocranium except its 727 ventral side (the palate); the latter refers to the dorsal side of the skull roof, often demarcated 728 from the lateral sides by distinct edges. 729 RC07 (and Ruta, Coates & Quicke, 2003) also almost consistently used “mesial” when 730 they were aiming at “medial”. This appears to be a common British practice; internationally, 731 however, it is “medial” that means “toward the sagittal plane at a right angle to it”, while 732 “mesial” belongs to toothrow nomenclature and means “toward the symphysis along the 733 curvature of the jaw”, the opposite of the poorly chosen term “distal”. Many instances of 734 “mesial” apply to the lower jaw and actually mean “lingual”, “proximal at a 90° angle to the 735 curvature of the jaw”, the opposite of “labial”; only at the symphysis is mesial medial. 736 We have tried to rectify these issues in the annotated character list (Appendix 1). 737 However, we use the pairs “anterior – posterior” and “cranial/rostral – caudal” 738 interchangeably (despite a preference for the latter) because there is, in our taxon sample, no 739 danger of confusion. 740 Our ambiguous usage of “orbit” (Marjanović & Laurin, 2008, 2013a) confused Pardo 741 & Anderson (2016), who claimed that we had first thought that Brachydectes had very large 742 eyes which filled its orbitotemporal fenestrae (ascribed to our 2008 paper) and that we had 743 later amended this view (ascribed to 2013a); in reality, we explicitly stated (2008: 194–195) 744 that we considered the “orbits (or ‘orbitotemporal fenestrae’ as they are sometimes called in 745 salientians and caudates)” to have “presumably” contained jaw muscles in Brachydectes, not 746 just the eyeballs, and we implied no changes in the later paper (Marjanović & Laurin, 2013a: 747 239, 241). – In the present work we consistently speak of “orbitotemporal fenestrae” to mean 748 skull openings that appear to have contained the eyes as well as jaw muscles, regardless of the 749 inferred homologies of these openings. 750 751 Material and methods 752 753 The data matrices were edited in successive versions of Mesquite up to 3.31 (Maddison & 754 Maddison, 2017); this program was also used to display and visually compare trees and to 755 optimize characters on them. 756 757 Treatment of characters 758 759 Character interdependence; redundant characters 760 761 Characters in a data matrix for phylogenetic analysis are interdependent when a state of a 762 character (other than “unknown”) is predictable – without prior knowledge of phylogeny – 763 from the state of another character. Because phylogenetic analysis operates on the assumption 764 that all characters are independent of each other, the presence of interdependent characters in 765 a matrix amounts to counting the same apomorphy at least twice, which can distort the 766 resulting tree topology and will almost inevitably distort at least some of its support values. 767 While this fact seems to be universally acknowledged in principle, we find (Marjanović & 768 Laurin, 2008, 2009, 2013a; and below) that it is underappreciated in practice. 769 Different kinds of character interdependence require different amounts of effort to 770 detect. O’Keefe & Wagner (2001: 657; and references therein) distinguished “logical 771 correlations among characters” from “[b]iological correlations”; Pardo (2014: 52–60) 772 distinguished four kinds of interdependence. We call Pardo’s first three kinds, which include

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773 logical interdependence, “redundancy” and biological interdependence “correlation” 774 hereinafter. 775 It can be very difficult to determine whether characters are correlated; studies of 776 development genetics are sometimes, perhaps often, required (Kangas et al., 2004; Harjunmaa 777 et al., 2014). We expect, therefore, that all of our best efforts will be unable to completely 778 eliminate character interdependence from any morphological matrix. However, many cases of 779 redundant characters are much more obvious; and although RC07 noticed and removed 780 several cases from the preceding version (Ruta, Coates & Quicke, 2003), we present a 781 considerable number of additional cases in Appendix 1. We have merged each pair (or 782 multiple) of redundant characters that we identified into a single character. 783 784 Ordering of multistate characters 785 786 RC07 (p. 78), like Ruta, Coates & Quicke (2003: 271), followed the widespread practice (e.g. 787 Sigurdsen & Green, 2011; Schoch, 2013; stated but unexplained preference of Simões et al., 788 2016a: 211; Pardo et al., 2017; Pardo, Small & Huttenlocker, 2017) of treating all multistate 789 characters as unordered. Following another widespread practice, they did not spell out any 790 reasons for this decision. Presumably they adhered to the common assumption (already 791 identified and discussed by Slowinski, 1993) that ordering a character is to make an 792 assumption, while “leaving” it unordered means not to make an assumption – which is 793 incorrect (Slowinski, 1993). In particular, potentially continuous (clinal) characters should be 794 ordered, because the basic assumption behind ordering – that it is easier to change from any 795 state to a similar state than to a less similar one – has already been used to partition the 796 observed spread of data into discrete states in the first place; it would be incoherent to reject 797 this assumption in one place but not the other (Slowinski, 1993; Wiens, 2001). This also holds 798 for certain meristic characters (Wiens, 2001). As advocated by Slowinski (1993), Wiens 799 (2001) and Baron, Norman & Barrett (2017: supplementary information: 4–9), we have 800 ordered many, but not all, multistate characters; see Appendix 1 for discussion of each case. 801 Two characters (numbers 32, 134: PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1, EXOCC 2-3- 802 4-5/BASOCC 1-5) have part of their state range ordered (e. g. Slowinski, 1993: fig. 1a, d); 803 this is accomplished by creating stepmatrices (Appendix-Tables 2, 4). We have marked these 804 decisions in the name of each multistate character by adding “(ordered)”, “(unordered)” or 805 “(stepmatrix)” to its end. 806 The consequences of ordering potentially continuous characters are largely 807 unpredictable. Empirically, ordering such characters can reveal additional signal and thus 808 increase the resolution of the consensus tree (Slowinski, 1993; Fröbisch & Schoch, 2009a; 809 Grand et al., 2013; Simões et al., 2016a: fig. 2b, 3b, 4; Baron, Norman & Barrett, 2017: fig. 1, 810 extended data fig. 4); on the other hand, and even at the same time, it can also reveal 811 previously hidden character conflict and thus decrease the resolution, showing that the 812 original resolution was not supported by the data (Slowinski, 1993; Marjanović & Laurin, 813 2008; Baron, Norman & Barrett, 2017: fig. 1, extended data fig. 4). Both of these results are 814 congruent with the finding of the simulation studies by Grand et al. (2013) and Rineau et al. 815 (2015) that ordering clinal characters decreases the rate of artefactual resolution and increases 816 the power to detect real clades. 817 818 Continuous characters 819 820 Due to the limits of available computation power, we have not been able to analyze 821 continuous characters “as such” (as recommended by Simões et al., 2016a; Brocklehurst, 822 Romano & Fröbisch, 2016; and references therein), but have broken them up into a small

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823 number of discrete states. Such characters were ordered if multistate (see above). Where 824 RC07 had defined reproducible state limits that did not render the characters parsimony- 825 uninformative, we have not changed them; in the cases of PREMAX 7 and SKU TAB 1, 826 which we have wholly recoded (see below: “Deleted, recoded and split characters”), we 827 divided the observed range into several equal parts (not many – Bardin et al., 2014) at round 828 numbers because there are no gaps in the distribution. This is an obvious opportunity for 829 future improvement. See Brocklehurst, Romano & Fröbisch (2016) for further discussion. 830 831 Inapplicable characters and mergers 832 833 Perhaps the eventual solution will be to write new algorithms for computer programs that will 834 allow the characters to be coded independently but that will consider interactions between 835 characters and count steps in some characters only on those portions of the tree on which they 836 are applicable. 837 – Maddison (1993: 580) 838 839 Character-taxon matrices and their accompanying character lists should be viewed as formatted 840 data, and not just a table of observations. That is, they should be constructed with an 841 understanding of how that information will be interpreted by the algorithm that is receiving 842 them. For many multistate characters, authors should consider how character state information is 843 (or is not) distributed to other transformation series. The problem with ‘0’ being used as a catch- 844 all for anything that simply ‘isn’t 1’ should be borne in mind when using binary characters (see 845 discussion below). 846 – Brazeau (2011: 494) 847 848 Maddison (1993) concluded that addressing this problem would require modification of 849 phylogenetic software; 25 later, there are still few signs of progress on this problem. 850 – Brazeau, Guillerme & Smith (2017: 5) 851 852 It is a common situation that a character is inapplicable to part of a taxon sample: when, say, 853 the ectopterygoid bone in the palate is absent, it does not have a shape, and it is not toothed or 854 toothless. Strong & Lipscomb (1999) reviewed the methods for dealing with such cases: 855  Reductive coding: inapplicable scores are treated as missing data, using the symbols 856 “?” or “-”. (The latter designates a gap in a molecular sequence, which is treated either 857 as missing data – the default setting in available software – or as a fifth nucleotide/21st 858 amino acid – which is absence coding, see below.) 859  Composite coding: characters that are inapplicable to any OTU are merged with the 860 characters they depend on, producing multistate characters. For instance, 861 “ectopterygoid toothed (0); toothless (1)” might be merged with “ectopterygoid 862 present (0); absent (1)” as the unordered multistate character “ectopterygoid toothed 863 (0); toothless (1); absent (2)”. 864  Nonadditive binary coding: the presence or absence of each character state is treated 865 as a binary character of its own that can be scored for all OTUs. For example, “toothed 866 ectopterygoid: present (0); absent (1)” and “toothless ectopterygoid: present (0); 867 absent (1)” can be scored for all OTUs – taxa that lack an ectopterygoid have state 1 of 868 both of these characters. 869  Absence coding: inapplicability is coded as an additional state of each concerned 870 character. 871 As Strong & Lipscomb (1999) pointed out, absence coding creates redundant characters by 872 counting each condition that makes characters inapplicable several times, once for each 873 character that it makes inapplicable. Absence coding must therefore be avoided. 874 Nonadditive binary coding runs the same risk. In the example given above, an OTU 875 cannot have state 0 of both characters: having state 0 of one unfailingly predicts state 1 of the

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876 other. The characters are thus redundant. (See “Errata in some of our previous publications” 877 below for a real example from RC07.) It also treats nonhomologous conditions as the same 878 state, which runs the risk of creating spurious apomorphies which may increase artefactual 879 resolution (Brazeau, 2011, and references therein); Strong & Lipscomb (1999: 368–369) went 880 so far as to state that “non-additive binary coding denies homology and the hierarchical 881 relationships between states. The result are and character interpretations that are 882 absurd and inaccurate representations of our observations.” Brazeau (2011: 495) further 883 performed a reductio ad absurdum by asking what would happen if molecular data were 884 coded as, e.g., “adenine at site 121: absent (0); present (1)”, where state 0 would treat 885 guanine, cytosine, thymine, and the absence of site 121 (a deletion) as identical and primarily 886 homologous for no defensible reason. 887 Composite coding eliminates the redundancy that is sometimes created by nonadditive 888 binary coding. Furthermore, it has the advantage over reductive coding that it prevents 889 contradictory optimization of ancestors. With reductive coding, an ancestor may be optimized 890 as having a toothed ectopterygoid and at the same time as having no ectopterygoid at all 891 (Brazeau, Guillerme & Smith, 2017, and references therein); composite coding makes this 892 impossible and may thus make arguably nonsensical trees less parsimonious. However, 893 composite coding is not always feasible to its full extent. In our example, if the character that 894 represents the presence of the ectopterygoid is merged with the character that describes its 895 dentition, what is to become of size and shape? Merging all of the affected characters would 896 often yield a huge multistate character that would, in many cases, require a complex 897 stepmatrix and be difficult to interpret in evolutionary terms (as already noted by Maddison, 898 1993), not to mention adverse effects on calculation times (pers. obs.). 899 RC07 used reductive, composite and nonadditive binary coding in different cases. The 900 numerous occurrences of nonadditive binary coding may be a side effect of taking characters 901 from diagnoses and synapomorphy lists (Bardin, Rouget & Cecca, 2014), where they are 902 usually presented in the form of a single (presumedly derived) state, while the other states are 903 not mentioned. We have greatly reduced the amount of nonadditive binary coding. There are a 904 few cases we have left for the time being; these are cases where the effort needed to rectify 905 the situation would probably be out of proportion to the gain in phylogenetic signal. Examples 906 are PREMAX 4, “Premaxilla with flat, expanded anteromedial dorsal surface and elongated 907 along its lateral margin but not along its medial margin, when observed in dorsal aspect: 908 absent (0); present (1)”, PASPHE 11, “Basipterygoid processes of the basisphenoid shaped 909 like anterolaterally directed stalks, subtriangular to rectangular in ventral view and projecting 910 anterior to the insertion of the cultriform process: absent (0); present (1)”, TIB 6, “Outline of 911 medial margin shaped like a distinct, subsemicircular embayment contributing to 912 interepipodial space and the diameter of which is less than one-third of bone length: absent 913 (0); present (1)”, and TRU VER 30, “Transverse processes stout and abbreviated, the length 914 of which is less than 30% of neural arch height: absent (0); present (1)”. We would need to 915 survey the range of morphologies and in some cases their considerable ontogenetic 916 transformations – see below – in detail in order to determine how many characters, let alone 917 how many states, should be distinguished within state 0 of each of these. All these characters 918 should, however, be reinvestigated in the future. 919 In a few cases we have changed fully reductive to partially composite coding. This 920 includes, for instance, the following characters of RC07: 921 140. ECT 1: Separately ossified ectopterygoid: present (0); absent (1). 922 141. ECT 2: Ectopterygoid with (0) or without (1) fangs […]. 923 142. ECT 3: Ectopterygoid without (0) or with (1) small teeth (denticles) […]. 924 143. ECT 4: Ectopterygoid longer than/as long as (0) or shorter than (1) palatine. 925 144. ECT 5: Ectopterygoid with (0) or without (1) row of teeth (3+) […].

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926 145. ECT 6: Ectopterygoid/ contact: present (0); absent (1). 927 146. ECT 7: Ectopterygoid narrowly wedged between palatine and pterygoid: no (0); 928 yes (1). 929 The presence (ECT 1) and size of the ectopterygoid (ECT 4) are now a single character, to 930 which we have added an additional state (ultimately from McGowan, 2002): 931 115. ECT 1-4: Ectopterygoid at least as long as palatine (0); at least about a third as 932 long as but shorter than palatine (1); at most about a third as long as palatine (2); 933 absent (3) (ordered). 934 The interpretation of ECT 1 and ECT 4 as parts of a potentially continuous character fits the 935 observation that taxa with very small ectopterygoids tend to be the closest relatives of those 936 with no ectopterygoids and nested among taxa with middle-sized ones: absence, in this 937 particular case, seems to be in effect a length of zero. ECT 2, ECT 3 and ECT 5, however, are 938 unaffected; they continue to be scored as unknown for OTUs that lack ectopterygoids. 939 Restudy of the literature and a specimen has shown that states ECT 6(1) and ECT 7(1) can 940 only be scored for at most one OTU each (Appendix 1); this makes the characters ECT 6 and 941 ECT 7 parsimony-uninformative, so we have deleted them (see below). 942 To make our mergers more transparent, we have created abbreviations for merged 943 characters from those of all their constituents: e.g., PREMAX 1-2-3 (character 1) is built from 944 the three characters PREMAX 1, PREMAX 2 and PREMAX 3 of RC07, and MAX5/PAL5 945 (character 22) consists of MAX 5 and PAL 5 of RC07. The extreme case is VOM 5-10/PTE 946 10-12-18/INT VAC 1 (character 105), assembled from the six characters VOM 5, VOM 10, 947 PTE 10, PTE 12, PTE 18 and INT VAC 1 of RC07. 948 Too recently for us to use, Brazeau, Guillerme & Smith (2017) published a new 949 approach to dealing with reductively coded inapplicability in phylogenetics software. We are 950 looking forward to further developments of its implementation. However, we strongly 951 disagree that so-called “neomorphic characters” should be scored as having the presumedly 952 plesiomorphic state when they are inapplicable. This requires identifying the plesiomorphic 953 state in advance, which increases the danger that the phylogenetic analysis will conform to 954 one’s preconceptions just as much as an all-zero outgroup would. It is also much less easy 955 than Brazeau, Guillerme & Smith (2017: 23) implied when they stated that in their analysis 956 “every inapplicable token in each neomorphic character was replaced with the token 957 corresponding to the presumed non-derived condition (typically ‘absent’)” – for example, our 958 matrix contains many characters for the presence or absence of bones that are, in our taxon 959 sample, plesiomorphically present and are apomorphically lost several times, while different 960 taxon samples (e.g. vertebrates generally, or actinopterygians) would support the opposite 961 polarization or none at all. Further, this method creates redundancy just like absence coding 962 does: in the example by Brazeau, Guillerme & Smith (2017: table 1), absence of the tail 963 unfailingly predicts absence of eyespots on the tail. 964 965 “Ontogeny discombobulates phylogeny” (Wiens, Bonett & Chippindale, 2005) 966 967 Heterochrony can result in misleading scores if only morphologically immature (juvenile or 968 paedomorphic) individuals of some taxa are known, which can result in large-scale character 969 correlation that can strongly distort phylogenetic trees (Wiens, Bonett & Chippindale, 2005). 970 We have tried to deal with this problem as described by Marjanović & Laurin (2008) and in 971 more detail by Marjanović & Laurin (2013a), modified from the recommendation of Wiens, 972 Bonett & Chippindale (2005: 96) and independently proposed by Tykoski (2005: 276): in 973 OTUs known only from apparently immature or paedomorphic individuals, observed states 974 are scored as unknown if they are restricted to immature stages in non-paedomorphic close 975 relatives of the OTU in question. Pawley (2006: 206) appears to have used the same

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976 approach: “If it was possible that a derived […] characteristic may be absent in a particular 977 specimen due to the morphogenetic immaturity of the specimen, then the character state was 978 coded ‘?’, to avoid confusing morphogenetic immaturity with the plesiomorphic state.” The 979 ontogeny of most of our OTUs and their closest relatives is insufficiently well known; despite 980 this, and in spite of the additional complications discussed by Marjanović & Laurin (2013a), 981 we think that this approach offers the greatest chance to escape character correlation caused 982 by heterochrony. Each of the rather few cases is discussed in Appendix 1 and marked in blue 983 in Appendix 2. 984 985 Deleted, recoded and split characters 986 987 Our matrix has only 277 characters, a strong decrease from the 339 of RC07. For the most 988 part, this is due to our mergers of redundant characters and does not entail a loss of 989 information (detailed in Appendix 1). The characters IFN 1, ILI 10, ISC 1, DOR FIN 1 and 990 BAS SCU 1, however, were parsimony-uninformative in the matrix of RC07 and remain so 991 after our corrections (all of them documented and justified in Appendix 1); we have deleted 992 them rather than carrying these currently useless characters along and inflating the character 993 count (see Marjanović & Laurin, 2013a, for discussion). The characters PREFRO 6, PREFRO 994 9, LAC 6, NOS 1, VOM 11, PAL 6, ECT 6, ECT 7, BASOCC 6 and DEN 1 were parsimony- 995 informative as scored by RC07, but this is no longer the case after our corrections (likewise 996 documented and justified in Appendix 1), so we have deleted them as well. (For LAC 6 and 997 VOM 11, one of the two states turns out not occur in the original taxon sample at all, and only 998 once or never in the expanded taxon sample.) Conversely, the character ANG 3 was 999 parsimony-uninformative in RC07, but is parsimony-informative in our matrix even for the 1000 original taxon sample (see Appendix 1); we have kept it (though merged it with ANG 2, now 1001 character 161). 1002 Characters INT FEN 1 and TEETH 3 were composites of two independent characters 1003 each; we have split INT FEN 1 into the redefined INT FEN 1 (character 84) and the new 1004 MED ROS 1 (character 85), and TEETH 3 into the redefined TEETH 3 (character 183) and 1005 the new TEETH 10 (character 190). Similarly, we have reversed the merger of PIN FOR 1 1006 and PIN FOR 2 of Ruta, Coates & Quicke (2003), our characters 91 and 92, into PIN FOR 2 1007 of RC07. We have also partitioned several characters into more states than before. 1008 Character PREMAX 7, a ratio of two measurements, was parsimony-uninformative as 1009 defined (one of the two original states is limited to an OTU that was scored as unknown by 1010 RC07), but not as described or scored; we have measured all OTUs, defined new state limits 1011 (as discussed in Appendix 1: character 3), and rescored the entire taxon sample. SKU TAB 1, 1012 another ratio, was defined and described in contradictory ways, neither of which matched the 1013 scores; we have treated it the same way (see Appendix 1: character 95). The measurements, 1014 sources, calculations and state changes are presented and compared to the original and revised 1015 scores in Data S2; the ratios, sources and state changes are also shown in Appendix-Tables 1 1016 (for PREMAX 7) and 3 (for SKU TAB 1). 1017 PTE 15 is not reproducible; we have not figured out, either from the description or 1018 from the scores, what the difference between the two states was meant to be (see Appendix 1). 1019 The most likely meaning would be a duplicate of PTE 14 (character 123); we have deleted 1020 PTE 15. 1021 Similarly, TAB 4 was described in a confusing way (see Appendix 1). Most likely, it 1022 is either a duplicate of PAR 7 (character 36) or is scored in a way that strongly contradicts its 1023 definition. (It concerns the position of the suture between the tabular and the squamosal – 1024 most OTUs do not have such a suture, but were scored as known nonetheless.) We have 1025 deleted it as well.

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1026 Table 2: List of specimens used by D. M. to change scores in the matrix (as cited in 1027 Appendix 1) or to score added taxa. The OTUs are in the same order as in the matrix, which 1028 is unchanged from the non-alphabetical version of the matrix file of RC07 for the shared taxa 1029 (Acanthostega through Tseajaia). Specimens that do not contradict any scores of RC07 or the 1030 literature on the added taxa (Iberospondylus through Casineria) are not listed except in cases 1031 of polymorphism; a few such specimens are mentioned in the text. *, type specimen of the 1032 type species; **, type and only known specimen of the only known species. 1033 OTU Specimens Acanthostega TMM 41766-1 (cast of MGUH VP 6033*, formerly “A. 33”) Ichthyostega AMNH 23100; MCZ 3361; TMM 41224-2 (all of them casts of MGUH VP 6055, formerly “A. 55”) Greererpeton TMM 41574-1 Edops MCZ 1378, 1769, 1781, 1782, 6489, 6493, 7126, 7128, 7136, 7143, 7158, 7162, 7197, 7258, 7259, 7264, 7274; USNM 23309 Chenoprosopus CM 34909; USNM 437646 Isodectes CM 81430, 81512; MCZ 6044 (cast of USNM 4481); unnumbered MCZ cast of AMNH 6935 before etching; USNM 4471, 4474, 4555 Trimerorhachis AMNH 4565*, 4572; TMM 40031-80, 40031-81, 40998-39 Eryops AMNH 4180, 4183, 4186, 4189*, 4673, 23529; MCZ 1126, 1129, 1536, 2588, 2638, 2682, 2766; TMM 31225-33, 31226-12, 31227-11, 31227- 14, 40349-20; USNM uncatalogued “Texas ’84 #40”, “Texas ’86 #77” Phonerpeton AMNH 7150; MCZ 1414, 1419*, 1485, 1548, 1771, 2313, 2474; USNM 437796 Ecolsonia CM 38017, 38024 Broiliellus brevis MCZ 3272 Doleserpeton AMNH 24969, 29466, 29470; BEG 40882-25 Platyrhinops AMNH 2002 Eocaecilia MNA V8066* (Museum of Northern ; formerly MCZ 9010) Karaurus unnumbered MNHN cast1 of PIN 2585/2** Triadobatrachus MNHN.F.MAE126** (natural mold and cast)1 Archeria MCZ 2049, other MCZ specimens2 Gephyrostegus MB.Am.641; TMM 41733-1 (cast) Seymouria BEG 30966-176 Diadectes AMNH 4352, 4839; BEG 31222-56 Paleothyris TMM 45955-2 (cast of MCZ 3482) Batropetes B. palatinus: MB.Am.1232 (including casts) Tuditanus CM 29592 Stegotretus CM 34901 (all others were on loan) Asaphestera NMC 10041 (National Museum of ; currently on loan to J. Anderson, University of Calgary) Microbrachis MB.Am.840 Hyloplesion NHMW 1983/82/54, other NHMW specimens Odonterpeton USNM 4465+4467**3 Scincosaurus MB.Am.29 Diceratosaurus AMNH 6933*; CM 25468, 26231, 29593, 29876, 34617, 34656, 34668, 34696, 34670, 67157, 67169, 72608, 81504, 81507, 81508; MB.Am.776, MB.Am.778 Ptyonius MCZ 3721 (cast of “AMNH 6871 (85466)”)

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Sauropleura CM 25312 Lethiscus MCZ 2185** Phlegethontia USNM 17097 Tseajaia CM 38033 Nigerpeton MNN MOR 69* (including unpublished intercentrum and unprepared skull fragments), 70, 82, 83, 108 Saharastega MNN MOR 73** (including two unpublished pieces) Iberospondylus PU-ANF 2, 14*, 154 Caseasauria Eothyris: MCZ 1161**; Oedaleops: unnumbered MCZ cast of UCMP 35758* (University of California Museum of Paleontology) Sparodus NHMW 1899/0003/0006 (Fig. 3, 4) Carrolla TMM 40031-54** MB.Am.1346 Chelotriton MB.Am.45 (natural mold and cast) Trihecaton CM 47681*, 47682 (probably part of the same individual) St. Louis tetrapod MB.Am.1441** (natural mold and cast) Casineria NMS G 1993.54.1** (part and counterpart; Fig. 5–7) 1034 1035 1 Observed together with M. L. 1036 2 All were used to score the same characters. 1037 3 The apparently unpublished specimens CM 81525 and CM 81526 are also labeled 1038 Odonterpeton, and are kept together with a note by Donald Baird (dated 1991) which says 1039 that further small skeletons attributed to Brachydectes may belong to Odonterpeton as well. 1040 More likely, CM 81525 – a limbless without a trace of limbs or girdles, whose skull 1041 is only preserved as an indistinct impression – is instead a juvenile aïstopod with ribs that are 1042 not yet k-shaped, and the disarticulated CM 81526 is a juvenile Brachydectes after all (D. M., 1043 pers. obs.; J. Pardo, pers. comm. after seeing photos taken by D. M.); a more detailed study is 1044 in preparation. 1045 4 All three were observed together with Rodrigo Soler-Gijón; additionally, they had been 1046 studied earlier by M. L. (Laurin & Soler-Gijón, 2001, 2006). 1047 1048 Modifications to individual cells 1049 1050 We have changed scores that contradict the descriptive literature or our observations of 1051 specimens. While we have not systematically compared every single score to the literature or 1052 specimens, our attention was not limited to particular taxa or characters; we ended up making 1053 changes to the scoring of all taxa, and of all characters that remain in the matrix (as well as 1054 several that we deleted as parsimony-uninformative, see above) except 96 (FONT 1), 150 1055 (PSYM 4) and 187 (TEETH 7). All modifications (including those made by Damien Germain 1056 [2008a: chapter V], except where we found them unjustified) are documented and justified in 1057 Appendix 1, with citations of the literature and/or specimens we used to rescore each cell. For 1058 the sake of brevity, the original scores (RC07) are usually not mentioned there, only our 1059 modified ones are; scores we did not change are not mentioned in Appendix 1 except where 1060 they could be controversial. 1061 “This has not been a literature-based exercise”, wrote Ruta, Coates & Quicke (2003: 1062 292) in their conclusions; and while they and RC07 did have to rely on the literature to score 1063 some taxa (if only because the taxon sample is simply too large for anyone to visit all relevant 1064 specimens within realistic time and budget constraints), both of their publications contain lists 1065 of specimens they had studied firsthand. Strangely, however, the results of almost none of 1066 these observations are mentioned in the papers; there is no way of extracting information on

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1067 which characters are described or illustrated incorrectly in the literature or which ones are 1068 visible in the fossils but not presented in a publication (so that scoring from the literature 1069 would produce spurious missing data). We must insist that a data matrix is not an appropriate 1070 place to publish new observations: in a matrix there is no way to tell if a surprising score is a 1071 new observation or just a typographic error, a momentary confusion of contradictory 1072 conventions about which state is called 0 and which is called 1, or one of a number of other 1073 very common problems (see above and Marjanović & Laurin, 2013a, for discussion). For 1074 each of the scores we have changed based on our observations of specimens, we have 1075 therefore documented the change and referred to the numbers of specimens that show the 1076 states we have scored. Only the specimens that have led us to changing a score (or several) 1077 are listed in Table 2; specimens that agree with the scores of RC07 are therefore only listed 1078 when other specimens of the same OTU show another state and we have consequently scored 1079 polymorphism. 1080 In the end we have probably compared almost all cells in the matrix to the literature 1081 and/or to specimens. Shying away from the inordinate amount of time this work ended up 1082 taking, we initially concentrated our efforts on characters and OTUs relevant to lissamphibian 1083 origins, as determined, mostly, by optimizations on trees in Mesquite (Maddison & Maddison, 1084 2017). Soon, though, we branched out to characters with subjectively suspicious state 1085 distributions (it goes without saying that many turned out to be entirely or partially correct), 1086 characters we did not immediately understand, characters we recoded while merging them 1087 with others and taxa that had been redescribed (recently or sometimes not so recently). 1088 Furthermore, we investigated characters that supported conflicting or unusual hypotheses of 1089 relationships apart from lissamphibian origins, and the taxa implicated in these; examples are 1090 Seymouriamorpha and Diadectomorpha, both surprisingly found to be paraphyletic by RC07, 1091 and Adelogyrinidae and Acherontiscus, found for the first time to clade with colosteids rather 1092 than “lepospondyls” by RC07. Finally, we checked the scores of OTUs that temporarily did 1093 strange things in preliminary analyses of ours, like Tulerpeton, Edops, Trimerorhachis or 1094 Ossinodus (unsurprisingly, some of this strangeness has remained). Whenever we investigated 1095 a character, we usually verified its scores for all OTUs, and whenever we investigated an 1096 OTU, we verified its scores for all characters except as restricted below. 1097 For the following OTUs – and quite possibly others – we have compared most or all 1098 cells to the literature (see below for specimens): 1099  Panderichthys (Boisvert, 2005, 2009; Brazeau & Ahlberg, 2006; Boisvert, Mark- 1100 Kurik & Ahlberg, 2008; Ahlberg, 2011 – occiput, extremities and girdles) 1101  Ventastega (Ahlberg, Lukševičs & Lebedev, 1994; Ahlberg et al., 2008; Lukševičs, 1102 Ahlberg & Clack, 2003) 1103  Acanthostega (Coates, 1996; Porro, Rayfield & Clack, 2015) 1104  Ichthyostega (skull roof: Clack & Milner, 2015; lower jaw: Ahlberg & Clack, 1998; 1105 Clack et al., 2012a; : Jarvik, 1996; Callier, Clack & Ahlberg, 2009; Ahlberg, 1106 2011; Pierce, Clack & Hutchinson, 2012; vertebrae: Pierce et al., 2013) 1107  Tulerpeton (Lebedev & Coates, 1995) 1108  Crassigyrinus (Panchen, 1985; Panchen & Smithson, 1990; Clack, 1998) 1109  Whatcheeria (Lombard & Bolt, 1995, 2006) 1110  Baphetes (Milner & Lindsay, 1998; Milner, Milner & Walsh, 2009 – only previously 1111 missing data and explicitly stated contradictions to older literature) 1112  Eucritta (Clack, 2001) 1113  Edops (Romer & Witter, 1942) 1114  Chenoprosopus (Hook, 1993; Reisz, Berman & Henrici, 2005 – previously missing 1115 data, including all postcranial material, and data mentioned as having been hitherto 1116 misinterpreted)

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1117  Cochleosaurus (Sequeira, 2004, 2009) 1118  Neldasaurus (Chase, 1965) 1119  Trimerorhachis (Pawley, 2007; Milner & Schoch, 2013) 1120  Dendrerpetidae (Carroll, 1967; A. R. Milner, 1980, 1996; Godfrey, Fiorillo & Carroll, 1121 1987; Holmes, Carroll & Reisz, 1998; Robinson, Ahlberg & Koentges, 2005 – 1122 especially to make sure no polymorphisms were overlooked; see below and Schoch & 1123 Milner, 2014) 1124  Eryops (appendicular skeleton: Pawley & Warren, 2006) 1125  Acheloma (Maddin, Reisz & Anderson, 2010; Polley & Reisz, 2011 – mostly filled in 1126 previously missing data) 1127  Broiliellus (Carroll, 1964; Schoch, 2012) 1128  Platyrhinops (Clack & Milner, 2010; remaining missing data filled in from Hook & 1129 Baird, 1984, and from Werneburg, 2012b, where not likely ontogeny-dependent) 1130  Doleserpeton (Sigurdsen, 2008; Sigurdsen & Bolt, 2009, 2010; Sigurdsen & Green, 1131 2011: appendix 2) 1132  Micromelerpeton (Boy, 1972, 1995; Schoch, 2009b) 1133  Apateon, Leptorophus, Schoenfelderpeton (Boy, 1972, 1986, 1987; Werneburg, 1991; 1134 Schoch & Fröbisch, 2006; Schoch & Milner, 2008; Fröbisch & Schoch, 2009b) 1135  Albanerpetidae (Estes & Hoffstetter, 1976; Fox & Naylor, 1982; Gardner, 2001; 1136 McGowan, 2002; Gardner, Evans & Sigogneau-Russell, 2003; Venczel & Gardner, 1137 2005; Maddin et al., 2013a; note that we follow this latter reference in interpreting the 1138 “cultriform process of the parasphenoid” [McGowan, 2002: fig. 13] as a hyobranchial 1139 element, contra Marjanović & Laurin, 2008) 1140  Eocaecilia (Jenkins, Walsh & Carroll, 2007) 1141  Triadobatrachus (Rage & Roček, 1989; Roček & Rage, 2000; Sigurdsen, Green & 1142 Bishop, 2012; Ascarrunz et al., 2016) 1143  Valdotriton (Evans & Milner, 1996) 1144  Karaurus (Ivachnenko, 1978) 1145  Caerorhachis (Ruta, Milner & Coates, 2002) 1146  Bruktererpeton (Boy & Bandel, 1973) 1147  Gephyrostegus (Carroll, 1970; Godfrey & Reisz, 1991; Klembara et al., 2014) 1148  Eoherpeton (Panchen, 1975; Smithson, 1985) 1149  Proterogyrinus (Holmes, 1980, 1984) 1150  Archeria (Romer, 1957; Holmes, 1989) 1151  Solenodonsaurus (Laurin & Reisz, 1999; Danto, Witzmann & Müller, 2012 – mostly 1152 filled in previously missing data) 1153  Kotlassia (Bystrow, 1944; Bulanov, 2003) 1154  Diadectes (Case, 1910, 1911; Case & Williston, 1912; Olson, 1947; Moss, 1972; 1155 Berman, Sumida & Lombard, 1992; Berman, Sumida & Martens, 1998; Berman et al., 1156 2004) 1157  Limnoscelis (Fracasso, 1983; Berman & Sumida, 1990; Reisz, 2007; Berman, Reisz & 1158 Scott, 2010; Kennedy, 2010) 1159  Westlothiana (Smithson et al., 1994) 1160  Batropetes (Glienke, 2013, 2015) 1161  Rhynchonkos (CG78; Szostakiwskyj, Pardo & Anderson, 2015) 1162  Microbrachis (CG78; Vallin & Laurin, 2004; Olori, 2015) 1163  Hyloplesion (CG78; Olori, 2015) 1164  Brachydectes (Wellstead, 1991; Pardo & Anderson, 2016)

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1165  Acherontiscus (Carroll, 1969b) 1166  Adelospondylus, Adelogyrinus, Dolichopareias (Andrews & Carroll, 1991) 1167  Scincosaurus (Milner & Ruta, 2009) 1168  Diplocaulus (postcranium and lower jaw: Williston, 1909; Douthitt, 1917) 1169  Diploceraspis (mostly postcranium and lower jaw: Beerbower, 1963) 1170  Lethiscus (Wellstead, 1982; Anderson, Carroll & Rowe, 2003; Pardo et al., 2017) 1171  Oestocephalus (Carroll, 1998a; Anderson, Carroll & Rowe, 2003; Anderson, 2003a) 1172  Phlegethontia (Anderson, 2002, 2007a) 1173  Notobatrachus (Estes & Reig, 1973; Báez & Basso, 1996; Báez & Nicoli, 2004, 2008) 1174  Vieraella (Estes & Reig, 1973; Báez & Basso, 1996) 1175  Ossinodus (Warren & Turner, 2004; Warren, 2007; Bishop, 2014) 1176  Pederpes (Clack & Finney, 2005) 1177  Orobates (Berman et al., 2004; Nyakatura et al., 2015: digital model) 1178  Ariekanerpeton (Laurin, 1996a; Klembara & Ruta, 2005a, b) 1179  Leptoropha (Bulanov, 2003) 1180  Microphon (Bulanov, 2003, 2014) 1181  Tseajaia (Moss, 1972; Berman, Sumida & Lombard, 1992) 1182  Utegenia (Laurin, 1996b; Klembara & Ruta, 2004a, b) 1183 Parts of the above list have puzzling implications. For instance, Ruta, Coates & Quicke 1184 (2003) cited Ahlberg, Lukševičs & Lebedev (1994) as their source for scoring Ventastega, but 1185 only used that publication to code not much more than half of the bones that are described and 1186 illustrated in that work; large parts of the skull, e.g. almost the entire palate, were scored as 1187 entirely unknown by Ruta, Coates & Quicke (2003) and RC07 for reasons that we could not 1188 determine. This goes so far that in some instances some of the bones belonging to a skull 1189 fragment were scored while others sutured to them in the same fragment were not. 1190 RC07 cited the paper by Sequeira (2004), but only for its phylogenetic analysis, not 1191 for its redescription of the skull of Cochleosaurus based on “several large, presumably adult, 1192 ” (Sequeira, 2004: abstract) – all previous descriptions “were based almost entirely on 1193 small, subadult […] specimens” (ibid.). RC07 thus perpetuated the outdated scores of 1194 Cochleosaurus by Ruta, Coates & Quicke (2003). 1195 Ruta, Coates & Quicke (2003) cited Boy & Bandel (1973) as their source for the 1196 scoring of Bruktererpeton. That publication is written in German, which may explain some of 1197 the differences between it and the scoring by Ruta, Coates & Quicke (2003) and RC07. 1198 (Fortunately, German is D. M.’s native language.) Some of the figures, however, contradict 1199 the matrix by RC07 as well. 1200 Despite the overlap in authors, many discrepancies exist between the matrix by RC07 1201 and the detailed redescriptions of Caerorhachis (Ruta, Milner & Coates, 2002 – not cited by 1202 RC07, but cited as “2001”, the of publication originally intended by the journal, by Ruta, 1203 Coates & Quicke, 2003), Silvanerpeton (Ruta & Clack, 2006 – not cited, not even as “in 1204 press”), Ariekanerpeton (Klembara & Ruta, 2005a, b – not cited, although personal 1205 observations are cited) and Utegenia (Klembara & Ruta, 2004a, b – cited). 1206 Ruta, Coates & Quicke (2003) scored Kotlassia after the description by Bystrow 1207 (1944); RC07 did not change this. Bystrow explicitly synonymized Kotlassia and 1208 Karpinskiosaurus and did not document for all parts of his description on which specimen(s) 1209 they were based. Bulanov (2003) disagreed with Bystrow and separated the two taxa again, 1210 considering them rather distant relatives, but he merely mentioned the existence of postcrania 1211 of Kotlassia (the entire monograph describes only the cranial anatomy of a wide range of 1212 seymouriamorphs). Similarly, Klembara (2011) redescribed only the skull of 1213 Karpinskiosaurus. A useful description of the postcrania of either taxon does not exist as far

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1214 as we know. We have accepted the scores by RC07 at face value for the time being and scored 1215 all postcranial characters of Karpinskiosaurus, a taxon we have added to the matrix (see 1216 below), as unknown, except for those few that Bystrow (1944) explicitly commented on. 1217 For the following taxa we have compared most or all cells to specimens (fossils or 1218 casts) which are, where necessary, mentioned under the respective characters in Appendix 1: 1219  Ichthyostega (palate only) 1220  Edops (as Romer & Witter [1942] noted, the sutures on the only known adult skull 1221 roof – that of MCZ 1378 – are for the most part extremely difficult to trace, so we 1222 have accepted their interpretations wherever D. M. was unable to confirm them; D. M. 1223 did not detect any contradictions) 1224  Isodectes (postcranium only) 1225  Ecolsonia (previously missing data only) 1226  Triadobatrachus 1227  Karaurus (everything except the palate, which is not reproduced by the cast we had 1228 access to) 1229 Diceratosaurus is about to undergo redescription by Jason Anderson’s lab, D. M. and Florian 1230 Witzmann; we have not preempted that work, but only changed the scores of characters of 1231 particular interest based on D. M.’s observations of specimens, mostly filling in missing data 1232 – and often confirming the redescription by Jaekel (1903). 1233 The complete list of specimens we have used to change scores in the matrix forms 1234 Table 2. We cannot provide a list of all specimens we have seen; however, whenever D. M. 1235 visited a collection, he saw all or almost all specimens that are broadly relevant to this study. 1236 One exception to this is the NMS, where the collection is kept in a building on the other side 1237 of the city and specimens that are not on exhibit are brought to the museum building only on 1238 request; the only NMS specimen D. M. has seen is Casineria (which we added to the matrix 1239 as described below). The other exception is the Anderson lab at the University of Calgary, 1240 which currently houses many important specimens of which D. M. has only taken the time to 1241 study a referred specimen of Asaphestera in any detail. 1242 1243 The albanerpetid neck 1244 1245 Though this concerns very few characters, our coding of the albanerpetids (a single OTU as in 1246 RC07) assumes our reinterpretation of their unique atlas-axis complex. As in , this 1247 complex accommodated dorsoventral and lateral movements of the head at separate joints. 1248 Traditionally (e.g. Estes & Hoffstetter, 1976; Fox & Naylor, 1982), this complex is 1249 considered to consist of the atlas (a complete consisting of a centrum and fused, fully 1250 formed, full-size neural arch), the axis (a centrum that lacks any trace of a neural arch), and 1251 the third vertebra (again a complete vertebra consisting of a centrum and fused, fully formed, 1252 full-size neural arch). The “axis” is commonly sutured to the “third vertebra”. Dorsoventral 1253 movements of the head occurred between the skull and the atlas, lateral ones between the atlas 1254 and the “axis”. By comparison to amniotes and “microsaurs”, we think it is more 1255 parsimonious to interpret the “axis” as only the intercentrum of the axis, even though 1256 intercentra are otherwise unknown in albanerpetids, while the “third vertebra” would be the 1257 pleurocentrum and neural arch of the axis. Comparison to temnospondyls is more difficult; in 1258 both Doleserpeton (Sigurdsen & Bolt, 2010) and Gerobatrachus (Anderson et al., 2008a), the 1259 only dissorophoids with pleurocentrum-dominant vertebrae, the axis is very incompletely 1260 preserved, but the relative sizes of pleuro- and intercentra elsewhere in the column are at least 1261 not incompatible with our interpretation. 1262 1263

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1264 Treatment of OTUs 1265 1266 Paleothyris/Protorothyris 1267 1268 One OTU of RC07 is (explicitly) a composite of Paleothyris acadiana and Protorothyris 1269 archeri. Protorothyris is, according to the only phylogenetic analysis that has included it so 1270 far (Müller & Reisz, 2006), more closely related to Petrolacosaurus – another OTU in this 1271 matrix – than to Paleothyris; Paleothyris could even be more closely related to Captorhinus – 1272 also included in this matrix – than to either Protorothyris or Petrolacosaurus. 1273 Still, these two species are morphologically similar, and most of their differences 1274 could not be scored in our matrix, so we have not made a special effort to weed out scores 1275 based on Protorothyris. Our changes to this OTU, however, are exclusively based on the 1276 description of Paleothyris by Carroll (1969a) and D. M.’s observations of Paleothyris 1277 specimens, especially TMM 45955-2 (a cast of MCZ 3482, which is on display and was not 1278 accessible at the time), cursorily confirmed against MCZ 3473, MCZ 3475, MCZ 3477, MCZ 1279 3481 (the holotype), MCZ 3483, MCZ 3486, MCZ 3487, MCZ 3488, MCZ 3490, MCZ 3492 1280 and the apparently uncatalogued unlabeled specimen B-17 (also kept at the MCZ). Some of 1281 these changes are from known to unknown, so they likely concern characters whose state is 1282 known in the more completely preserved Protorothyris but not in Paleothyris. 1283 1284 Dendrerpetidae 1285 1286 Milner (1996) revised the specimens from (Nova Scotia, Canada) that were at that 1287 time included in Dendrerpeton acadianum (following Carroll, 1967), but had originally been 1288 described as several genera with many species. “The majority of specimens are still 1289 attributable to Dendrerpeton acadianum but three other forms are represented by one or two 1290 specimens each. These are Dendrerpeton confusum sp. nov., based on a single large skull, 1291 Dendrerpeton helogenes (Steen) comb. nov., based on two specimens, and an indeterminate 1292 cochleosaurid, based on a set of cranial fragments” (Milner, 1996: abstract). One of the 1293 specimens newly referred to D. helogenes was the well preserved skull that had been 1294 described by Godfrey, Fiorillo & Carroll (1987) as D. acadianum. “Subsequently HOLMES et 1295 al. [ = Holmes, Carroll & Reisz] (1998) described an exquisitely preserved skeleton of a 1296 temnospondyl from Joggins and referred it to Dendrerpeton acadianum. By doing so, they 1297 lumped all the Joggins material together again. In this work, it is argued that the Joggins 1298 material includes two distinct genera, Dendrerpeton sensu MILNER 1996 and Dendrysekos 1299 (Dendrerpeton helogenes of MILNER 1996), which differ in a number of characters. The 1300 specimens of GODFREY et al. [ = Godfrey, Fiorillo & Carroll] (1987) and HOLMES et al. 1301 (1998) are referable to Dendrysekos. This effectively means that Dendrysekos rather than 1302 Dendrerpeton has formed the outgroup in many recent cladistic analyses of temnospondyls.” 1303 (Schoch & Milner, 2014: 25) 1304 Ruta, Coates & Quicke (2003) did not cite Milner (1996). Their “Dendrerpeton 1305 acadianum” OTU, kept unchanged by RC07 (who did not cite Milner [1996] either), is in part 1306 based on their personal observations of specimens, of which at least some – notably the 1307 lectotype – really do belong to D. acadianum according to Milner (1996) and Schoch & 1308 Milner (2014). However, Ruta, Coates & Quicke (2003) also used and cited the descriptions 1309 by Godfrey, Fiorillo & Carroll (1987) and Holmes, Carroll & Reisz (1998). Assuming that the 1310 personal observations were in fact used to score the taxon and not merely to cursorily confirm 1311 the literature, this OTU is thus a chimera of Dendrerpeton acadianum and Dendrysekos 1312 helogenes.

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1313 Schoch & Milner (2014) continued to maintain that Dendrerpeton and Dendrysekos 1314 are sister-groups; for this reason, we have not split the OTU for the time being, but merely 1315 renamed it Dendrerpetidae, the name recommended by Schoch & Milner (2014), and 1316 compared it to the literature to make sure no polymorphisms had been overlooked (see above 1317 and Watanabe, 2015). In future work, however, it may be a good idea to treat all dendrerpetid 1318 species separately (including Dendrerpeton rugosum from Jarrow in : A. R. Milner, 1319 1980; Schoch & Milner, 2014): Ruta (2009) added Dendrerpeton confusum to a 1320 temnospondyl matrix derived from the matrix of RC07 and found that it was not the sister- 1321 group of the “D. acadianum” OTU. We have not done this yet because the present matrix 1322 most likely does not contain enough characters to place them accurately with respect to each 1323 other. 1324 (Whether the “D. acadianum” OTU of Ruta [2009] included any other dendrerpetids is 1325 unclear to us. The matrix of Ruta [2009] is a slight modification of that of Ruta & Bolt 1326 [2006]. The latter’s appendix 1 lists all OTUs, except D. confusum, and the literature sources 1327 used to score them. For “D. acadianum”, these are Carroll, 1967; A. R. Milner, 1980, 1996; 1328 Godfrey, Fiorillo & Carroll, 1987; and Holmes, Carroll & Reisz, 1998. In addition, this OTU 1329 is marked with an asterisk for having “been examined directly by one or both authors (using 1330 either casts or original specimens)”; which specimens those are is not mentioned, but 1331 presumably they are the same as those consulted by Ruta, Coates & Quicke [2003]. However, 1332 given the absence of D. confusum from this appendix, we wonder if the appendix was written 1333 before Ruta & Bolt decided to separate the two Dendrerpeton OTUs; if so, it is possible that 1334 the “D. acadianum” OTU really is just D. acadianum and not a chimera.) 1335 Balanerpeton has sometimes (Pawley, 2006; Clack et al., 2012b; Dilkes, 2015a), but 1336 not always (Milner & Sequeira, 1994; Ruta, 2009), been found as the sister-group of 1337 “Dendrerpeton”; we therefore follow Schoch & Milner (2014) in not including it in the 1338 Dendrerpetidae OTU. 1339 1340 Rhynchonkos 1341 1342 Szostakiwskyj, Pardo & Anderson (2015) have shown that previous conceptions of 1343 Rhynchonkos (e.g. CG78; considered to contain a single species) were chimeric. They 1344 restricted Rhynchonkos to its holotype, a skull with lower jaw. The other skulls were referred 1345 to the new taxa Aletrimyti and Dvellecanus; a further lower jaw turned out to belong to none 1346 of the three. Szostakiwskyj, Pardo & Anderson (2015) did not mention the postcranial 1347 material that had been referred to Rhynchonkos (e.g. CG78). A poorly preserved but largely 1348 articulated presacral skeleton (CG78: fig. 67) belongs to the same specimen as the referred 1349 skull of Aletrimyti (Szostakiwskyj, Pardo & Anderson, 2015: 5). We therefore wondered 1350 whether to restrict our Rhynchonkos OTU to Rhynchonkos or instead to Aletrimyti (the type 1351 material of which is also slightly better preserved than that of Rhynchonkos). J. Pardo (pers. 1352 comm. 2015) has, however, pointed out that the postcranial material needs to be revisited. We 1353 have therefore restricted the Rhynchonkos OTU to the type material of Rhynchonkos and 1354 scored all postcranial characters as unknown. 1355 We considered adding Aletrimyti and Dvellecanus as separate OTUs to our analyses 1356 with added taxa. Most likely, however, this would require also adding several at least 1357 superficially similar “microsaurs” (Nannaroter, Tambaroter, Huskerpeton, Proxilodon) and 1358 several characters; we prefer to leave this to future work. 1359 RC07 had scored a few characters that remain unknown for all of the specimens 1360 referred to Rhynchonkos by CG78. An example is CAU FIN 1 (our character 277), for which 1361 they scored state 1, the absence of lepidotrichia in the tail – only the most proximal tail

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1362 vertebrae are represented in the previously attributed material (CG78: 103–104, 109–110, fig. 1363 67–72)! This is, incidentally, a common issue that affects several other OTUs (Appendix 1). 1364 1365 The skull roof of Brachydectes 1366 1367 Wellstead (1991) reconstructed several unusual features in the skull roof of Brachydectes. We 1368 previously tried (Marjanović & Laurin, 2008, 2013a) to resolve these problems by 1369 reinterpreting the homologies of the bones that Wellstead (1991) had identified. For example, 1370 the supposed do not meet in Wellstead’s reconstruction, but are separated by a 1371 contact between the suproccipital and the parietals; we suggested that they were tabulars 1372 instead, while the supposed tabulars would be postorbitals (thought absent by Wellstead), and 1373 postparietals would be absent. As a byproduct, this would restore normal spatial relationships 1374 to the posttemporal foramen identified by Wellstead (1991). 1375 Based on new material and μCT scans, Pardo & Anderson (2016) have now shown 1376 that Wellstead (1991) overlooked a few sutures and misjudged certain 3D relationships; our 1377 reinterpretation of Wellstead’s reconstruction is therefore moot. In particular, Wellstead 1378 correctly identified the postparietals, which do, however, meet in the midline in most or all 1379 specimens for a variable part of their length; there is no posttemporal foramen at all; and 1380 postorbitals are, like in lissamphibians, absent. We have updated the scores of Brachydectes 1381 following Pardo & Anderson (2016). 1382 Note also that the reconstruction of Batropetes by Carroll (1991), which Marjanović & 1383 Laurin (2008, 2013a) used for comparison to Brachydectes, differs in several respects from 1384 the ones by Glienke (2013, 2015), which we have used here to score Batropetes. 1385 1386 Taxa added as parts of existing OTUs 1387 1388 We have interpreted almost all OTUs as genera (or larger taxa in the cases of Albanerpetidae 1389 and Dendrerpetidae) rather than species. This has allowed us to fill in some missing data and 1390 to approach more plesiomorphic morphotypes. We do not think the polymorphisms this has 1391 occasionally introduced are a problem; quite the opposite – they are a better representation of 1392 the scope of the matrix. With the exceptions of Megalocephalus (Milner, Milner & Walsh, 1393 2009), Broiliellus (Schoch, 2012; Holmes, Berman & Anderson, 2013; Dilkes, 2015b), 1394 Oestocephalus (Anderson, 2003a) and of course Pholiderpeton, the monophyly of the few 1395 genera in this matrix that are not monospecific is fairly obvious, at least with respect to the 1396 other OTUs in this matrix, and has not been disputed in the literature. Pholiderpeton was 1397 already coded as two separate OTUs (Ph. scutigerum, Ph. attheyi) by RC07 and indeed Ruta, 1398 Coates & Quicke (2003). Megalocephalus is, if at all, only paraphyletic with respect to 1399 Kyrinion (Milner, Milner & Walsh, 2009) which is not included in this matrix (we have 1400 refrained from adding it because it would, given the present character sample, provide almost 1401 no new information on baphetid morphodiversity and thus baphetid relationships); also, we 1402 have not used any information from ?M. lineolatus, but only from the type species M. 1403 pachycephalus. We have not used information from any species referred to Broiliellus other 1404 than the one used by RC07, B. brevis – which is, incidentally, not the type species of 1405 Broiliellus and might therefore end up outside that taxon. In the figures and Appendix 2, we 1406 explicitly call this OTU “Broiliellus brevis”. We also ignored the incompletely preserved 1407 ?Oestocephalus nanus (Boyd, 1982), which is likely closer to Phlegethontia than to 1408 Oestocephalus (Anderson, 2003a), and the well preserved and stunningly well prepared but 1409 inadequately described ?O. guettleri (Krätschmer, 2006) and have – no doubt like RC07 – 1410 restricted ourselves to the type species, O. amphiuminus. Because information about the 1411 specimen called Scincosaurus spinosus was unavailable to us, we only used the type species,

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1412 S. crassus (used by RC07). Further, while the monophyly of Micromelerpeton has not been 1413 doubted, we have ended up using only M. credneri (the type species, used by RC07) because 1414 the other species do not add any information, being known from fewer individuals which are 1415 all skeletally immature. 1416 Milner & Schoch (2013) found that all recognized species of Trimerorhachis except T. 1417 sandovalensis form a clade which may or may not be the sister-group of T. sandovalensis to 1418 the exclusion of Neldasaurus. Because Neldasaurus is an OTU in this matrix, we have not 1419 used information from ?T. sandovalensis to score the Trimerorhachis OTU. We considered 1420 adding ?T. sandovalensis as an OTU to our analyses with added taxa, but its scores would 1421 hardly differ from the Trimerorhachis OTU at all. – Because Milner & Schoch (2013) 1422 presented a phylogeny of the four species in the undoubted Trimerorhachis clade, we have 1423 avoided scoring Trimerorhachis as polymorphic and instead tried to identify the 1424 plesiomorphic condition (as we have done with Albanerpetidae and Batropetes); this concerns 1425 very few characters, however. 1426 1427 Taxa added as new OTUs for a separate set of analyses 1428 1429 Several theoretical considerations suggest that taxon exemplars should be as diverse as possible 1430 […] [five references]. Importantly, a recent study based on simulations of true phylogenies 1431 (Salisbury & Kim, 2001) indicates that dense and random taxon sampling increases the 1432 probability of retrieving correctly the plesiomorphic condition of characters as well as the 1433 ancestral state near the tree root. Furthermore, Salisbury & Kim’s (2001) simulations show that 1434 in the analysis of small clades, estimates of ancestral states are strongly affected by 1435 topology and by the number of descendent [sic] branches in progressively more distal internal 1436 nodes. 1437 – Ruta, Coates & Quicke (2003: 255) 1438 1439 Also, taxon removal because of incomplete preservation and missing character scores may be 1440 undesirable, because such taxa may have a positive effect on cladogram resolution […] [five 1441 references]. 1442 – Ruta, Coates & Quicke (2003: 257) 1443 1444 We recommend the inclusion of as many fossils as possible in any phylogenetic analysis. 1445 – Conrad & Norell (2015) 1446 1447 Analogously to that of Marjanović & Laurin (2008b, 2009), the most important of the aims of 1448 the present work is to find out which hypothesis on the origin of the modern amphibians the 1449 matrix by RC07 supports if we keep, as far as possible, its taxon and character sample intact. 1450 However, the Early Permian (Cisuralian) Gerobatrachus was described too late (Anderson et 1451 al., 2008a) to be included in the matrix of RC07, yet it is highly relevant because the 1452 phylogenetic analysis included in its description supported the PH. Being a temnospondyl 1453 with many similarities to lissamphibians, Gerobatrachus may also be considered to support 1454 the TH over the LH; indeed, the analysis by Maddin, Jenkins & Anderson (2012) found it to 1455 be the oldest known lissamphibian while supporting the TH. However, this is based on a 1456 further development of the matrix by Anderson et al. (2008a) that did not take the 1457 reevaluations by Marjanović & Laurin (2009) and Sigurdsen & Green (2011) into account; 1458 and Marjanović & Laurin (2009) found the LH despite including Gerobatrachus. Following 1459 the example of Marjanović & Laurin (2008), we have therefore added Gerobatrachus to the 1460 present matrix in order to test if it changes the results. 1461 At this opportunity we also added the following taxa: 1462  Chroniosuchia is an enigmatic clade that has long been known from fragmentary 1463 remains. Only recently has more complete material been published, without, however, 1464 clarifying the phylogenetic position of the group. These animals have occasionally

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1465 (e.g. Laurin, 2000; Klembara, Clack & Čerňanský, 2010) been considered 1466 embolomeres (thus anthracosaurs) mainly because of their embolomerous centra, but 1467 their confusing mosaic of character states is compatible with a number of other 1468 phylogenetic positions as well; indeed, Klembara et al. (2014) recovered them as the 1469 sister-group to a gephyrostegid-seymouriamorph clade, Witzmann & Schoch (2017) 1470 found them in three positions (next to Anthracosauria, Silvanerpeton or a clade 1471 containing Gephyrostegus, seymouriamorphs, amniotes and “microsaurs” among 1472 others), and Schoch, Voigt & Buchwitz (2010) and Buchwitz et al. (2012) even found 1473 them to be lepospondyls. Moreover, the two chroniosuchians we added could 1474 influence the positions of the embolomeres, Gephyrostegus, Bruktererpeton, 1475 Silvanerpeton, perhaps Caerorhachis, and possibly Solenodonsaurus in our tree. 1476 o is by far the most thoroughly described representative (Clack & 1477 Klembara, 2009; Klembara, Clack & Čerňanský, 2010) of the clade, with most 1478 of the skeleton being preserved.– The specimens described and figured by 1479 Clack & Klembara (2009) did not preserve much of the lower jaws; Clack & 1480 Klembara (2009: 21) therefore stated that they had scored the reconstruction 1481 by Ivachnenko & Tverdochlebova (1980) in their phylogenetic analysis. This 1482 reconstruction (Ivachnenko & Tverdochlebova, 1980: drawing 1б) would 1483 allow unambiguous scoring of our characters 147 (PSYM 1) and 155 (SPL 2), 1484 which Clack & Klembara (2009) scored as unknown, and 156 (SPL 3-4), 1485 which they scored as having our state 1 or 2. However, we have kept only the 1486 scores of Clack & Klembara (2009) because all of the drawings in Ivachnenko 1487 & Tverdochlebova (1980) are reconstructions which often do not indicate 1488 which parts are actually known; the characters in question concern those parts 1489 of the lower jaw that are most likely to be incompletely preserved or 1490 crisscrossed by fractures (as chroniosuchian dermal bones usually are). We 1491 should note that the reconstruction of the skull proper in all three views 1492 (dorsal, ventral, lateral: drawings 1а, б, в) differs appreciably from those of 1493 Clack & Klembara (2009) and Klembara, Clack & Čerňanský (2010) in the 1494 shape and proportions of the skull, the course of some sutures, and the size, 1495 shape and relative positions of all openings, in two cases even their presence. 1496 The text (Ivachnenko & Tverdochlebova, 1980: 22) only briefly describes the 1497 chroniosuchian lower jaw in general, without mentioning which information is 1498 based on Chroniosaurus or Chroniosuchus, and does not refer to the characters 1499 in question. Specimen drawings or photos of the lower jaw of any 1500 chroniosuchian have never been published to our knowledge, except for part of 1501 the labial side of that of Chroniosaurus in Clack & Klembara (2009: fig. 2) 1502 which does not provide further information. 1503 o Bystrowiella, originally described from rather limited postcranial material 1504 (Witzmann, Schoch & Maisch, 2008), has recently become another well- 1505 understood chroniosuchian following the discovery of cranial as well as further 1506 postcranial material (Witzmann & Schoch, 2017). As a bystrowianid, it breaks 1507 the potentially long branch of the chroniosuchid Chroniosaurus. 1508  Further temnospondyls other than stereospondylomorphs: 1509 o Micropholis is an amphibamid, which means that the TH and the PH consider 1510 it close to the ancestry of some or all extant amphibians. It is the only 1511 dissorophoid known to have two widely spaced occipital condyles (like the 1512 modern amphibians), and it shares the Early age of the oldest known 1513 lissamphibians (the stem-salientians Triadobatrachus and Czatkobatrachus), 1514 unlike the Cisuralian Doleserpeton and Gerobatrachus or the

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1515 Amphibamus. Growth series spanning most of the skeleton are known (Schoch 1516 & Rubidge, 2005). – It is particularly surprising that RC07 did not add 1517 Micropholis to their matrix; they speculated that it might “turn out to occupy a 1518 more derived position than Doleserpeton on the amphibian stem group” 1519 (RC07: 86) because of its stratigraphic position. 1520 o Nigerpeton was described (Steyer et al., 2006; Sidor, 2013) as a cochleosaurid 1521 edopoid temnospondyl. The edopoids are thought to be close to the base of 1522 Temnospondyli – indeed, some analyses of temnospondyl phylogeny have 1523 used one or more edopoids as the outgroup or part thereof (e.g. Schoch & 1524 Witzmann, 2009a, b) – so we expected an influence on the position of 1525 Temnospondyli and on the interrelationships of its largest constituent groups. 1526 The skull and lower jaw have been described, though their surface is mostly 1527 badly preserved. D. M. has seen all known specimens – including postcranial 1528 material – and compared all scores to them; in Appendix 1 we report a number 1529 of previously unpublished observations. 1530 o Saharastega, of which likewise the entire skull is known, though the 1531 preservation of the surface is again bad (Damiani et al., 2006), has had an 1532 unstable phylogenetic position close to the root of Temnospondyli. Based on a 1533 few character states that are rather odd for a temnospondyl, it has even been 1534 suggested to be a seymouriamorph, though not in the peer-reviewed literature 1535 (Yates, 2007). It almost certainly is a temnospondyl, but, as for Nigerpeton, we 1536 expected an influence on the relationships and the large-scale phylogeny of the 1537 temnospondyls. In addition, this is of course an opportunity to clarify the 1538 position of Saharastega itself. – D. M. has seen the only known specimen and 1539 compared all scores to it; in Appendix 1 we report a number of previously 1540 unpublished observations. 1541 o Iberospondylus is a rather early temnospondyl known from most of the skull 1542 and various postcranial remains, preserving an unusual combination of 1543 plesiomorphies and apomorphies such as the dissorophoid-like dorsal process 1544 on the quadrate. The eight phylogenetic analyses that have included it so far 1545 (Laurin & Soler-Gijón, 2001, 2006; Pawley, 2006: fig. 44; Schoch & 1546 Witzmann, 2009a, b; Dilkes, 2015a; Pardo, Small & Huttenlocker, 2017: fig. 2, 1547 S7) have given seven different results, and two of them were based on very 1548 small matrices. The present matrix, large as it is, is an opportunity to clarify 1549 the position of Iberospondylus; as the latter does not seem to belong to any of 1550 the large recognized temnospondyl clades, the interrelationships of these 1551 clades could also be influenced. – Both of us have studied all three specimens. 1552 o Tungussogyrinus has occasionally been considered a caudate, which would be 1553 highly interesting considering its age. Werneburg (2009) 1554 redescribed it as the sister-group to all other branchiosaurids, but noted 1555 similarities to lissamphibians, especially one apomorphy shared with Salientia 1556 that is coded in this matrix. It might thus bolster the TH or certain versions of 1557 the PH. – RC07 (p. 86) mentioned Tungussogyrinus together with Micropholis. 1558 o Acanthostomatops (Witzmann & Schoch, 2006a) is a Cisuralian zatracheid 1559 temnospondyl thought to lie close to Dissorophoidea and/or Eryops. As 1560 pointed out but not tested by Witzmann & Schoch (2006a), it may thus 1561 influence temnospondyl phylogeny as well as the position of Lissamphibia. 1562 o Palatinerpeton is a temnospondyl known from an incompletely preserved, 1563 immature skeleton (Boy, 1996). Endowed with an unusual combination of 1564 characters and suggested to be a stereospondylomorph (Schoch & Milner,

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1565 2000) or in a trichotomy with Stereospondylomorpha and an - 1566 Zatracheidae-Parioxys clade (Boy 1996; see “Taxa that were not added”, 1567 below, for Parioxys), it has the potential to influence temnospondyl phylogeny. 1568 o Erpetosaurus, redescribed by Milner & Sequeira (2011) on the basis of many 1569 flattened specimens that range from skull fragments to incomplete articulated 1570 skeletons, is a dvinosaurian temnospondyl, thought to be most closely related 1571 to Isodectes in the taxon sample of RC07. We have added it in order to confuse 1572 things – in other words, to test the robusticity of this matrix against homoplasy: 1573 Erpetosaurus shows a confusing mix of unexpected plesiomorphies and 1574 unexpected similarities to colosteids (among others). It further has some 1575 potential to clarify the relationships of the few dvinosaurs included here. 1576 o Mordex was neglected for a long time because it is mostly known from larvae 1577 that were confused with , Platyrhinops and other dissorophoids 1578 from the same site. Recently, however, it has been understood as the oldest 1579 known trematopid (Milner & Sequeira, 2003; Milner, 2007; Werneburg, 1580 2012b); Milner (2007) called it “most similar to Ecolsonia” (tentatively 1581 confirmed by Schoch, 2012, and Schoch & Milner, 2014), which implies that 1582 adding Mordex to the present analysis will influence the phylogenetic position 1583 of Ecolsonia. Although it is not very well known – the largest specimen is an 1584 incomplete skull roof, the others are all much smaller and incompletely 1585 ossified (Werneburg, 2012b) –, it differs from all other taxa in this matrix. 1586 o Branchiosaurus used to be the name given to almost all skeletally immature 1587 temnospondyls from the Czech Pennsylvanian, as well as occasionally the 1588 Pennsylvanian and Cisuralian of other places. Building on and greatly 1589 expanding the work of Milner & Sequeira (2003), Werneburg (2012b) tried to 1590 sort out this confusion and provided a preliminary redescription of the type 1591 species, B. salamandroides from the Czech Republic. This redescription 1592 confirms that Branchiosaurus differs in several features from all other 1593 branchiosaurids (see Milner & Schoch, 2008); some of these features are coded 1594 in the present matrix. Branchiosaurus is further necessary to test the 1595 phylogenetic position of Tungussogyrinus (see above). – As Werneburg 1596 (2012b) noted, B. fayoli from Commentry and “B. aff. fayoli” from Montceau- 1597 les-Mines (both France) need to be redescribed before it can be assessed 1598 whether they form a clade with B. salamandroides; we have therefore not used 1599 any information from them. 1600  “Microsaurs”: 1601 o Utaherpeton was a surprising omission by RC07, given the facts that it is 1602 among the oldest known “microsaurs” and has been considered a 1603 “microsaur” (Carroll, Bybee & Tidwell, 1991; Carroll & Chorn, 1995; 1604 Anderson, 2001; Anderson et al., 2008a) or the sister-group of Microbrachis 1605 and thus a basal member of the “microsaur”-lysorophian-lissamphibian clade 1606 (Vallin & Laurin, 2004); in more recent analyses it fell out close to a 1607 “nectridean”-aïstopod-lysorophian-lissamphibian clade (Marjanović & Laurin, 1608 2009: Electronic Supplementary Material 2) or as a “lepospondyl” outside the 1609 major groups (Pardo, Small & Huttenlocker, 2017: fig. S6, and references 1610 therein). Similarities to the “nectrideans” were already noted in the original 1611 description (Carroll, Bybee & Tidwell, 1991). A variety of interesting effects 1612 on lepospondyl intra- and perhaps even interrelationships could be expected 1613 from its addition to the present matrix based on the two descriptions (Carroll, 1614 Bybee & Tidwell, 1991; Carroll & Chorn, 1995). – We have tentatively

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1615 accepted the referral by Carroll & Chorn (1995) of the specimen they 1616 described to Utaherpeton. Carroll & Chorn (1995) did not offer any evidence 1617 for this referral other than the fact that their specimen is a “microsaur” from 1618 the same locality as Utaherpeton, and did not discuss or even mention the 1619 question. However, the unusual proportions of the hindlimb mentioned in the 1620 diagnosis by Carroll et al. (1991) do appear to fit, the difference in the shape of 1621 the interclavicle may well be ontogenetic, and while the figures do not make 1622 clear if either specimen has precisely 26 presacral vertebrae as described, they 1623 do not rule out that both at least have the same or almost the same count. 1624 o The “Goreville microsaur”, too, is among the oldest known “microsaurs”. 1625 Although it was deliberately not named by Lombard & Bolt (1999), it differs 1626 from all other OTUs in this matrix, so we do not see a reason not to include it; 1627 its somewhat unusual combination of plesio- and apomorphic character states 1628 (noted in its description) could change the topology of the tree. Eight badly 1629 preserved specimens, amounting to most of the skeleton, are known. 1630 o Sparodus is another “microsaur” that is not obviously deeply nested in one of 1631 the universally recognized clades, showing affinities to both Pantylidae and 1632 Gymnarthridae but having fewer apomorphies than the undisputed members of 1633 both (and being older than most of them). Thus, it may clarify the relationships 1634 of one or both of these clades. Furthermore, “microsaur” phylogeny is so 1635 unstable that any addition of a taxon may drastically change it once again; 1636 changes in “microsaur” phylogeny moreover affect the other lepospondyls, and 1637 with them the positions of the modern amphibians. – Personal observation by 1638 D. M. of NHMW 1899/0003/0006 (Fig. 3, 4), the referred specimen described 1639 by Carroll (1988), shows that Carroll’s (1988: fig. 1) drawing and 1640 reconstruction of the skull are probably optimistic, unless the sutures are better 1641 visible on the latex cast Carroll used (which we have not seen) than on the 1642 fossil itself. However, this concerns very few characters. 1643 o Carrolla is a brachystelechid “microsaur” known only from a skull with lower 1644 jaw. Few differences between it and Batropetes (the brachystelechid that was 1645 already included in the matrix) are known, and few of those concern characters 1646 in the present matrix, but the redescription by Maddin, Olori & Anderson 1647 (2011) based on high-resolution computed tomography has made a large 1648 amount of information available. This is especially important because it allows 1649 us to better test the results by Vallin & Laurin (2004), who found 1650 Brachystelechidae to be the sister-group of Lysorophia + Lissamphibia, as well 1651 as the results by Maddin, Jenkins & Anderson (2012), who found the 1652 brachystelechids to be nested in a clade (Recumbirostra) that contains all the 1653 other “microsaurs” with a snout tip that protrudes beyond the premaxillary 1654 toothrow (state PREMAX 8(1) in the present matrix). – D. M. has seen the 1655 only known specimen and was consequently able to score some characters that 1656 concern externally visible anatomy and were insufficiently addressed by 1657 Maddin, Olori & Anderson (2011); these are described in Appendix 1. 1658 1659 ↓ Figure 3: NHMW 1899/0003/0006 (formerly 1899-III-6), a specimen referred to 1660 Sparodus validus. For an interpretative drawing, see Carroll (1988: pl. XII), which, however, 1661 makes the vertebrae appear much flatter than they are and omits the unusually well preserved 1662 scales. Some of the scales are only visible as striations in the matrix (see Fig. 4), which is 1663 usual in other “microsaurs” and in micromelerpetid temnospondyls; but most retain thick 1664 bone. Photo taken by D. M.

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1665 1666 1667 Figure 4: Ventral view of the palate and lingual view of the left lower jaw of the 1668 Sparodus specimen shown in Fig. 3. Carroll (1988: fig. 1A) provided an interpretative 1669 drawing of a latex cast. The photograph was taken by holding a digital camera to an ocular of 1670 a binocular microscope. Abbreviations: l., left; r., right; .c, largest caniniform tooth (on the 1671 maxilla); .t, tusk (one of two per bone); cor, unidentified coronoid; d, dentary; hu, humerus; j, 1672 jugal; mx, maxilla; orb, orbit; pal, palatine; pmx, premaxilla; po, postorbital; pof, postfrontal; 1673 sc, scales preserved as striations. Photo taken by D. M. 1674 1675 o Crinodon is a “microsaur” that is rich in plesiomorphies. Known from a well- 1676 preserved dermatocranium and partial lower jaws (CG78) – parts of the body 1677 that the present craniocentric matrix is well equipped to deal with –, it may 1678 help shed light on “microsaurian” intra- and interrelationships. CG78 classified

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1679 it as a tuditanid, but the two “tuditanids” in the present matrix (Tuditanus and 1680 Asaphestera) were not found as sister-groups by RC07, leaving us wondering 1681 whether the diagnostic characters of “Tuditanidae” might all be 1682 symplesiomorphies or homoplasies. 1683 o Trihecaton is a large “microsaur” known from an articulated skeleton that 1684 lacks the skull (apart from the maxilla, whose dorsal edge is not prepared), part 1685 of the lower jaw, most of the distal limbs and much of the tail – although 1686 further preparation would probably reveal additional bones. Presumably 1687 because most of the skull is unknown, Trihecaton has never featured in a 1688 phylogenetic hypothesis since CG78 gave it its own family in 1689 Tuditanomorpha; yet, it differs from all other OTUs in this matrix, so we see 1690 no reason to continue its exclusion from phylogenetic analyses. D. M. coded 1691 Trihecaton directly from the two known specimens (which most likely belong 1692 to the same individual); it is possible that additional preparation has been done 1693 since the description by CG78. 1694 o Quasicaecilia, known from an isolated skull without lower jaws (except an 1695 articular fragment), was redescribed by Pardo, Szostakiwskyj & Anderson 1696 (2015). It is a very small brachystelechid that may contribute to resolving the 1697 relationships of brachystelechids, other burrowing “microsaurs”, lysorophians 1698 and lissamphibians; additionally or alternatively, it could highlight the effects 1699 of miniaturized taxa on phylogenetic analyses. 1700 o Llistrofus is very similar to Hapsidopareion in the original taxon sample, but 1701 while Bolt & Rieppel (2009) found very few differences in their redescription 1702 of the skull, they also found very few synapomorphies. The postcranium is 1703 scored after CG78. 1704  The diadectomorphs (in the present matrix: Diadectes, Orobates, Tseajaia, 1705 Limnoscelis) are usually thought to lie on the amniote stem. It has, however, been 1706 proposed (Berman, Sumida & Lombard, 1992; Berman, 2013) that they are actual 1707 amniotes – in particular, the closest known relatives of Synapsida, thus part of 1708 Theropsida, the sister-group of Sauropsida (Goodrich, 1916). Surprisingly, all 1709 unquestioned amniotes in the matrix by RC07 – Petrolacosaurus, Paleothyris, 1710 Captorhinus – are sauropsids; the lack of unambiguous theropsids means that the 1711 original taxon sample is unable to test the mentioned hypothesis, even though its large 1712 amount of non-amniote OTUs would have made it very well suited for such a purpose. 1713 The two OTUs we have added help to solve this problem. Furthermore, they 1714 might further influence diadectomorph monophyly – which was not found by Ruta, 1715 Coates & Quicke (2003), Pawley (2006), RC07, or even Germain (2008a). 1716 o We have included Eothyris, Oedaleops and Eocasea as a single OTU called 1717 Caseasauria. Eothyris is known from an isolated, almost complete skull and 1718 lower jaw (Reisz, Godfrey & Scott, 2009); Oedaleops is known from a less 1719 complete skull and lower jaw, additional skull fragments, vertebrae, ribs, and 1720 girdle and limb elements (Reisz, Godfrey & Scott, 2009; Sumida, Pelletier & 1721 Berman, 2014; we follow the latter in not including the ilium tentatively 1722 referred by Langston, 1965); Eocasea is known from a skeleton lacking the 1723 girdle, the , the distal part of the tail and most of the skull 1724 (Reisz & Fröbisch, 2014). The overlapping parts of these three taxa score 1725 almost identically in our matrix; where they disagree, we have simply scored 1726 polymorphism (and noted this in Appendix 1), because the relationships of 1727 these taxa to each other and to the herbivorous members of Caseidae, which 1728 are not considered here, remain unclear (Reisz, Godfrey & Scott, 2009;

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1729 Sumida, Pelletier & Berman, 2014; Reisz & Fröbisch, 2014; Brocklehurst, 1730 Romano & Fröbisch, 2016; though see Brocklehurst et al., 2016).– Some data 1731 of Eothyris not presented in the cited publications were filled in by D. M. by 1732 observation of the holotype; they agree with the conditions in Oedaleops 1733 (Reisz, Godfrey & Scott, 2009) and Eocasea (Reisz & Fröbisch, 2014). We did 1734 not consider Callibrachion or Datheosaurus, which are poorly preserved and 1735 incompletely ossified (Spindler, Falconnet & Fröbisch, 2015), or the very 1736 recently (re)described Vaughnictis (Brocklehurst et al. 2016); they should be 1737 taken into account in future analyses, however, because all the analyses by 1738 Brocklehurst et al. (2016: fig. 10, 11) fully resolved the phylogenetic positions 1739 of all taxa mentioned in this paragraph. 1740 o Supplementing the Caseasauria OTU is Archaeovenator, the oldest known 1741 varanopid and sister-group to all other varanopids, known from a largely 1742 complete, mostly articulated skeleton described by Reisz & Dilkes (2003) and 1743 recently found nearly as close to the origin of Synapsida as Caseasauria (Reisz 1744 & Fröbisch, 2014: appendix S5; Brocklehurst et al., 2016). 1745  Lissamphibians: 1746 o Liaobatrachus is an Early salientian known from plentiful, very 1747 well preserved articulated skeletons (Dong et al., 2013). Although it was found 1748 to form a trichotomy with the two component clades of the crown-group of 1749 frogs, which means it is not very close to the root of Salientia, it may still 1750 influence the position of Salientia in particular and Lissamphibia in general, 1751 because few of the more stemward salientians are well preserved. 1752 o Beiyanerpeton is a recently described (Gao & Shubin, 2012) neotenic 1753 salamandroid of apparently Late age, in any case older than its Early 1754 Cretaceous relative Valdotriton which was already included in the matrix. It is 1755 the only known lissamphibian, extant or extinct, to possess grooves for the 1756 lateral-line organ on the skull. Among the lissamphibians in the matrix, it is the 1757 only one known to possess opisthotics that are not fused to the prootics or 1758 exoccipitals (or otherwise absent). These factors make it important enough to 1759 add it to this matrix (which contains both of these characters), even though its 1760 paedomorphosis makes some characters difficult to interpret for purposes of 1761 phylogenetics (see Gao & Shubin, 2012: supplementary information). 1762 o The even older (Late or ) Pangerpeton was found by Jia & Gao 1763 (2016a) to be a stem-hynobiid salamander, similarly close to the root of 1764 Urodela as Beiyanerpeton and Valdotriton. Several features of the only known 1765 skeleton (which lacks most of the tail, but is accompanied by a body outline) 1766 suggest that it had undergone , although it remained aquatic 1767 (Wang & Evans, 2006). Indeed, in having the jaw joints and the occiput in the 1768 same vertical transverse plane, it is more peramorphic than Beiyanerpeton, 1769 Valdotriton and even Karaurus. The skeleton is preserved in ventral view, so 1770 that most of the skull roof remains unknown, and it is unfortunate that the 1771 photos (even in the PDF version) have such low resolution that, for example, 1772 the ribs are entirely invisible and had to be scored from sparse remarks in the 1773 text that were not meant for comparison with our taxon sample. Still, 1774 Pangerpeton does not score redundantly with any other OTU in this matrix. 1775 o Even more peramorphic than Pangerpeton is Chelotriton. Scoring of this late 1776 pleurodeline salamandrid () is based mostly on MB.Am.45 1777 (Marjanović & Witzmann, 2015). This specimen exhibits peramorphic traits 1778 that are otherwise rare or even entirely unknown in salamanders (in a few

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1779 cases even in lissamphibians as a whole), such as very long ribs, some of 1780 which are ventrally curved, and jaw joints that lie far caudal of the occiput. In 1781 1981, it was misidentified as a “Dissorophid temnospondyl” “?Amphibamus” 1782 on a label. MB.Am.45 is indeed strikingly amphibamid-like in appearance, 1783 with some similarity also to certain diplocaulid “nectrideans”. We have added 1784 Chelotriton to the matrix to see the effects, if any, of its unexpected 1785 peramorphic features on caudate and lissamphibian intra- and 1786 interrelationships. For this purpose, we took MB.Am.45 (scored mostly from 1787 the silicone cast MB.Am.45.3) at face value wherever possible rather than 1788 scoring polymorphism; missing data were filled in from the less extremely 1789 peramorphic Chelotriton individuals described and figured by Roček & 1790 Wuttke (2010) and Schoch, Poschmann & Kupfer (2015). 1791  Undoubted colosteids: 1792 o Deltaherpeton is one of the oldest known colosteids, represented by a skull 1793 roof and lower jaw (Bolt & Lombard, 2001, 2010). It shows a few 1794 plesiomorphies as well as several unique features that are absent or not 1795 preserved in Colosteus and Greererpeton. Bolt & Lombard (2010) drew 1796 attention to this fact, but then undertook only a comparison instead of a 1797 phylogenetic analysis to justify their conclusion that “[t]he morphology of 1798 Deltaherpeton and the revised data presented for colosteids do not clarify the 1799 relationship of colosteids to other early tetrapods” (Bolt & Lombard, 2010: 1800 abstract). Indeed, there are characters that indicate a very rootward position of 1801 Colosteidae (as found by RC07), but others support a position more 1802 crownward than those of Whatcheeriidae and Crassigyrinus (as found by Ruta, 1803 2009, if we assume that the temnospondyls would be close to or within the 1804 crown), and a few have led to the traditional concept of colosteids as 1805 temnospondyls (as the sister-group to all other members of that clade). 1806 o Pholidogaster has been known for over 150 years; it was redescribed by 1807 Romer (1964) and, after additional preparation of the skull and , 1808 Panchen (1975). Its identity as a colosteid has not been questioned since the 1809 latter publication; and yet, to the best of our knowledge, it has never been 1810 included in a phylogenetic analysis. Although it is generally less well known 1811 than Colosteus, Greererpeton and Deltaherpeton, it scores differently from all 1812 three in our matrix; unlike in any known specimen of the other three colosteids 1813 (Bolt & Lombard, 2010), the septomaxilla and parts of its surroundings are 1814 preserved. Its age, close to that of Deltaherpeton, makes it a particularly 1815 interesting potential source of information on the phylogeny and affinities of 1816 Colosteidae. 1817  Karpinskiosaurus is a seymouriamorph that may help clarify seymouriamorph 1818 phylogeny and the affinities of Seymouriamorpha. The skulls of the type species, K. 1819 secundus, including an adult, non-paedomorphic one, were redescribed by Klembara 1820 (2011); according to the same work, the type specimen of K. ultimus requires revision, 1821 so this species is not considered here. Much of the axial skeleton was illustrated and 1822 commented on by Bystrow (1944). 1823  Anthracosaurs: 1824 o Holmes & Carroll (2010) have described a small but adult (or nearly so) 1825 incomplete skeleton of an anthracosaur (embolomere) from Joggins (Late 1826 Carboniferous). Unfortunately, NSM 994 GF 1.1 cannot be assigned to a 1827 named genus, because it does not overlap with diagnostic parts of the only 1828 known anthracosaur from the same site, Calligenethlon; however, because it is

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1829 considerably more complete than any specimen which can be assigned to 1830 Calligenethlon (all of which are slightly smaller and possibly less mature), we 1831 have added it to this matrix. Being an unusually small anthracosaur, it 1832 improves our representation of anthracosaur diversity and may contribute to 1833 the clarification of anthracosaurian intra- and interrelationships. 1834 o Palaeoherpeton is less well known than the originally included anthracosaurs, 1835 but the material was very thoroughly described by Panchen (1964) and scores 1836 differently from any other OTU in our matrix. We have therefore included it in 1837 the hope that it will contribute to resolving the phylogeny of anthracosaurs. 1838 o Neopteroplax, an anthracosaur described by Romer (1963) from a largely 1839 complete skull with lower jaw, has been mostly ignored ever since. In spite of 1840 having a skull shape quite similar to that of Pholiderpeton attheyi, however, 1841 Neopteroplax shows a number of features that are unusual for embolomeres; it 1842 makes an interesting addition to the question of anthracosaur phylogeny and 1843 affinities. We consider the referral of isolated jaw fragments and centra (not 1844 clear if pleuro- or intercentra) from a younger, very distant site to 1845 Neopteroplax (Romer, 1963: 451) highly doubtful; for the centra in particular 1846 it requires a rather long chain of inference from a single potentially diagnostic 1847 feature (the distance between the teeth). The jaw fragments would not add any 1848 information to our scoring of Neopteroplax; we have ignored the centra to 1849 avoid creating a chimera. 1850  Aïstopods: 1851 o The skull of Coloraderpeton was redescribed by Anderson (2003a) and 1852 reinterpreted from μCT data by Pardo et al. (2017). Like Lethiscus (Pardo et 1853 al., 2017), it preserves unexpected plesiomorphies; among those not known in 1854 Lethiscus are an at least mostly enclosed mandibular lateral-line canal and a 1855 bone that is most parsimoniously interpreted as a preopercular. Unfortunately, 1856 information on the postcranium is very scarce in publications (Carroll, 1998b; 1857 Anderson, 2003a; Anderson, Carroll & Rowe, 2003), and D. M. only briefly 1858 saw the specimens (at the CM) years before we decided to add Coloraderpeton 1859 to the matrix. 1860 o Pseudophlegethontia (Anderson, 2003b) may fill the morphological gap 1861 between Phlegethontia and the other aïstopods; we have reinterpreted a few 1862 characters (as detailed in Appendix 1) in the light of Lethiscus and 1863 Coloraderpeton (Pardo et al., 2017). 1864  Mississippian enigmas: 1865 o Sigournea is known only from an isolated lower jaw (Bolt & Lombard, 2006). 1866 Although similarities to the baphetoids, especially Spathicephalus (see below), 1867 and to the equally mysterious jaw material called Doragnathus (see below) 1868 have been noted (Bolt & Lombard, 2006; Milner, Milner & Walsh, 2009), 1869 these conjectures have only been tested twice in a phylogenetic analysis. 1870 Sookias, Böhmer & Clack (2014) found it in the whatcheeriid region of the 1871 tree (more rootward than Baphetes, the only included baphetoid). That analysis 1872 did not include Doragnathus and had a generally insufficient taxon and, likely, 1873 character sample to address this question. Clack et al. (2016), who included 1874 Doragnathus, found Sigournea to be a colosteid (unweighted parsimony) or in 1875 several places in the grade between the more rootward whatcheeriids and the 1876 more crownward colosteids (Bayesian inference, as well as parsimony with 1877 various degrees of reweighting). Our matrix contains enough lower-jaw and

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1878 tooth characters to show that Sigournea is distinct from any other taxon for 1879 which more than a few such characters can be scored. 1880 o Doragnathus is another mysterious animal known only from lower jaws and 1881 parts of upper jaws. It has only once before (Clack et al., 2016) been included 1882 in a phylogenetic analysis, even though it was described quite some time ago 1883 (Smithson, 1980), and even though it differs from Sigournea, Spathicephalus 1884 (see below) and all other potential relatives in characters that are included in 1885 the present matrix. As recommended by Smithson & Clack (2013), we have 1886 not scored the isolated postcranial material that was found at the same site and 1887 may or may not belong to the same taxon (described and illustrated by 1888 Smithson & Clack, 2013). 1889 o Spathicephalus is a baphetoid known from skull and lower-jaw material with 1890 several strange autapomorphies (Baird, 1962; Beaumont & Smithson, 1998). 1891 Still, in a few characters it may be more plesiomorphic than at least Baphetes 1892 and Megalocephalus, which may help test baphetoid relationships (see Milner, 1893 Milner & Walsh, 2009); it may also influence the positions of Sigournea and 1894 Doragnathus. 1895 o MB.Am.1441, the “St. Louis tetrapod”, is a natural mold of a skull with lower 1896 jaws in ventral view that was described by Clack et al. (2012b). The 1897 description noted several similarities to colosteids, but also to temnospondyls, 1898 and ultimately did not commit to either hypothesis of relationships; the 1899 phylogenetic analysis in that paper, which used a very small taxon sample and 1900 a rather repetitive character sample, found it to be the sister-group of a novel 1901 (Ptyonius, (Adelogyrinus, Greererpeton)) clade, which together with the “St. 1902 Louis tetrapod” formed the sister-group to the only two included 1903 temnospondyls – an unusual arrangement as well. The matrix presented here 1904 may be better suited to resolving the relationships of MB.Am.1441, which D. 1905 M. was able to study firsthand (both the natural mold, MB.Am.1441.1, and the 1906 silicone cast, MB.Am.1441.2). Despite the small number of characters that can 1907 be scored, the “St. Louis tetrapod” differs from all other OTUs in this matrix. 1908 o Perittodus, Diploradus and Aytonerpeton are three of the many new taxa that 1909 were briefly presented by Clack et al. (2016). Their middle Tournaisian age 1910 lies in Romer’s Gap, which is a temporal as well as morphological gap 1911 between the Devonian and the post-Tournaisian limbed vertebrates. Perittodus 1912 is mostly known from a very plesiomorphic, at most “Ichthyostega-grade” 1913 lower jaw; Diploradus has a lower jaw reminiscent of Sigournea and 1914 Doragnathus, but also preserves fragments of the rest of the skeleton; 1915 Aytonerpeton is known from scattered postcrania as well as a snout which 1916 resembles the “St. Louis tetrapod” and preserves the youngest anterior tectal 1917 identified in any limbed vertebrate. 1918  Devonian enigmas: 1919 o Ruta, Coates & Quicke (2003: 262) listed Metaxygnathus among Devonian 1920 taxa that are “known mainly from lower jaw rami and/or incomplete 1921 postcranial remains” and “are omitted” from their matrix, presumably because 1922 they are so incompletely known. As with Sigournea and Doragnathus, 1923 however, the isolated lower jaw ramus called Metaxygnathus differs from all 1924 other lower jaws (isolated or not) in this matrix. Indeed, one character, ANG 3, 1925 seems to have been deliberately included to potentially hold Acanthostega and 1926 Metaxygnathus together in “future, expanded versions of our matrix” (RC07: 1927 103). Our source was the redescription by Ahlberg & Clack (1998).

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1928 o Ymeria is an “Ichthyostega-grade” animal known from premaxillae, a palate in 1929 dorsal view and lower jaws (plus shoulder girdle remains that are too 1930 fragmentary to be scored in this matrix). It was found one node rootward of 1931 Ichthyostega in those analyses by Clack et al. (2012a) and Sookias, Böhmer & 1932 Clack (2014) that had enough resolution to tell. 1933 o Densignathus, much like Metaxygnathus, is known only from lower-jaw 1934 material (Daeschler, 2000; Ahlberg, Friedman & Blom, 2005) and was listed 1935 among the excluded taxa by Ruta, Coates & Quicke (2003: 262), but differs 1936 from all other lower jaws in the matrix. 1937 o Elginerpeton has been described, from successively greater amounts of 1938 isolated material and jaw fragments, as a Devonian animal close to the origin 1939 of limbs (Ahlberg, 1995, 1998; Ahlberg & Clack, 1998; Ahlberg, Friedman & 1940 Blom, 2005). It could serve to establish character polarities for the other 1941 Devonian OTUs. Following Ahlberg, Friedman & Blom (2005) and Ahlberg 1942 (2011), we have included the postorbital bone and the postcranial material 1943 described by Ahlberg (1998), except for the supposed humerus. 1944  Temnospondyl phylogeny is a vexing question; most mathematically possible 1945 permutations of Edopoidea (which may not be a clade; Pawley, 2006: chapter 6), 1946 Capetus, Dendrerpetidae + Balanerpeton (together mono- or paraphyletic), 1947 Dvinosauria, Eryopidae, Stereospondylomorpha and Dissorophoidea have been 1948 supported by recent phylogenetic analyses, and a few taxa have been found close to 1949 Eryopidae or as early stereospondylomorphs. This was, in part, discussed by Ruta, 1950 Coates & Quicke (2003) (as well as by Pawley, 2006: chapter 5; Ruta, 2009; Schoch, 1951 2013; Dilkes, 2015a; and references in all five). It is strange, then, that the matrices of 1952 Ruta, Coates & Quicke (2003) and RC07 do not contain a single possible 1953 stereospondylomorph despite the presence of representatives of all other clades listed 1954 above. We have therefore added: 1955 o Sclerocephalus, variously considered an eryopid relative and/or a 1956 stereospondylomorph, is known from complete articulated skeletons and was 1957 redescribed by Meckert (1993; shoulder girdle and only) and Schoch 1958 & Witzmann (2009a); D. M. compared some scores to the specimen 1959 MB.Am.1346 (a skull roof in dorsal view, a left lower jaw in medial and a 1960 right lower jaw in lateral view). Because Sclerocephalus is a weakly supported 1961 clade of four species (Schoch & Witzmann, 2009a) – ignoring the poorly 1962 known ?S. stambergi, whose phylogenetic position is even less clear 1963 (Klembara & Steyer, 2012) –, we have only considered the type species, S. 1964 haeuseri, which also happens to be the best-known one. It is known from 1965 several borderline amphibious and eryopid-like, as well as strictly aquatic, 1966 vaguely embolomere-like morphs (Schoch, 2009a). 1967 o Cheliderpeton vranyi, the type species of Cheliderpeton, was redescribed by 1968 Werneburg & Steyer (2002). Like Sclerocephalus, it has variously been 1969 considered an eryopid relative or a stereospondylomorph. The present matrix 1970 may be able to decide this question. Further, Werneburg considered 1971 Cheliderpeton an intasuchid, Steyer preferred to consider it an archegosaurid 1972 (Werneburg & Steyer, 2002); this question is testable in this matrix insofar as 1973 Cheliderpeton may form an exclusive clade with (see below) or 1974 not. Growth series of the skull roof and a few other bones are known. We have 1975 not been able to use information from the putative second species, Ch. 1976 lellbachae, which “[i]n most respects […] resembles Sclerocephalus haeuseri” 1977 and needs to be (re)described (Schoch & Witzmann, 2009b: 122).

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1978 o Glanochthon was variously referred to Archegosaurus, Actinodon, 1979 Sclerocephalus or Cheliderpeton till Werneburg & Steyer (2002) recognized it 1980 as distinct from all four and Schoch & Witzmann (2009b) redescribed it. (For 1981 example, it appears as “Cheliderpeton latirostre” in the analysis by Ruta, 1982 2009.) Found to be closer to Archegosaurus and Stereospondyli than 1983 Cheliderpeton and Sclerocephalus by Schoch & Witzmann (2009b), the two 1984 species (G. latirostris, G. angusta; Schoch & Witzmann, 2009b) are known 1985 from growth series of many skulls (including lower jaws: Boy, 1993) and most 1986 of the postcranium except, apparently, the tail. 1987 o Archegosaurus is known from complete articulated skeletons and was 1988 redescribed by Witzmann (2006: head skeleton) and Witzmann & Schoch 1989 (2006b: postcranium). Together with the other potential archegosaurids, all of 1990 which are much less completely known, it is considered a close relative of 1991 Stereospondyli. We have not used information from Memonomenos, which 1992 was often referred to Archegosaurus in earlier times but belongs elsewhere in 1993 the tree (Schoch & Milner, 2000: fig. 52; Schoch & Witzmann, 2009b). 1994 o Platyoposaurus, known from rich cranial and postcranial material (Efremov, 1995 1932; Konzhukova, 1955; Gubin, 1991), is superficially very similar to 1996 Archegosaurus and was found as its sister-group by Pardo, Small & 1997 Huttenlocker (2017: fig. 2, S7), but may actually be closer to Stereospondyli 1998 (Schoch & Witzmann, 2009b; Pereira Pacheco et al., 2016). 1999 o Konzhukovia has been allied to Archegosaurus and to Stereospondyli in 2000 various sources. Gubin (1991: drawings 6, 15) illustrated and described the 2001 well preserved type skull of the type species, K. vetusta; we have not used 2002 other information except for two comments on the same species by Pereira 2003 Pacheco et al. (2016: appendix 2). First, further information on K. vetusta is 2004 not available (Gubin [1991: fig. 2 of plate II] only showed a small photo of an 2005 additional skull fragment of K. vetusta and merely mentioned the existence of 2006 a lower-jaw fragment and postcranial fragments); second, the referral of K. 2007 tarda and a fortiori K. sangabrielensis to Konzhukovia is doubtful (as 2008 discussed above in the Nomenclature section); third, K. sangabrielensis is only 2009 known from a partial skull that hardly seems to differ from K. vetusta in 2010 characters included in this matrix, while Gubin (1991: fig. 1 of plate II) only 2011 showed small photos of a skull of K. tarda and merely mentioned the existence 2012 of another skull. The diagnoses of the three species do not differ in characters 2013 that the present matrix contains, and the illustrations apparently do not either 2014 (except for the lateral-line grooves of K. sangabrielensis, which K. vetusta 2015 actually shares: Pereira Pacheco et al., 2016: appendix 2). 2016 o is within a few internodes of the origin of Stereospondyli 2017 according to all recent analyses. It is known from complete skeletons that are 2018 unusually well ossified for a stereospondyl. The postcranium was recently 2019 described by Pawley & Warren (2005) and Hewison (2008), and the skull and 2020 lower jaw by Jeannot, Damiani & Rubidge (2006) and Hewison (2007). 2021 Shishkin, Rubidge & Kitching (1996) showed that various proportions of the 2022 skull roof of Lydekkerina are paedomorphic, a hypothesis further supported for 2023 other characters by Hewison (2007); this probably does not affect any 2024 characters in this matrix. Miniaturization by progenesis may explain the well 2025 ossified endochondral bones. 2026 o was recently identified as a rhinesuchid stereospondyl (Eltink 2027 et al., 2016) after being thought to lie close to Archegosaurus by Schoch &

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2028 Milner (2000). Almost the entire skeleton is known (Barberena, 1998; Dias & 2029 Schultz, 2003; Eltink & Langer, 2014; Eltink et al., 2016). 2030

2031 2032 2033 Figure 5: Caudal trunk vertebrae of NMS G 1993.54.1cp, the holotype of Casineria kiddi 2034 (counterpart plate), in partly right lateral, partly interior view. The neural arches end 2035 dorsally in an ossification front marked by black material (pyrite or another iron sulfide?) just 2036 dorsal to the level of the postzygapophyses, indicating that the individual was immature; the 2037 pleuro- and intercentra are reminiscent of those of the anthracosaur Proterogyrinus and the 2038 temnospondyl Neldasaurus (Chase, 1965), although their precise shapes are difficult to 2039 determine because the vertebrae are split lengthwise and probably recrystallized. 2040 Abbreviations: ic, intercentrum; nsp, neural spine; pc, pleurocentrum; poz, postzygapophysis; 2041 prz, prezygapophysis. The scale bar is approximate. Photo taken by D. M. 2042 2043 2044

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2045 2046 2047 2048 2049 2050 2051 Figure 6: Left 2052 forelimb of 2053 NMS G 2054 1993.54.1cp, 2055 the holotype 2056 of Casineria 2057 kiddi (coun- 2058 terpart plate), 2059 in plantar 2060 view. The 2061 carpus is un- 2062 ossified except 2063 for what may 2064 be a poorly 2065 ossified distal 2066 carpal 1. The 2067 inset shows 2068 phalanx IV-5 2069 at a higher 2070 magnification 2071 (length ap- 2072 proximately 1 2073 mm); note that 2074 the tip, al- 2075 though curved 2076 plantarly, is 2077 blunt, unlike in 2078 amniotes and 2079 contrary to 2080 Paton, Smith- 2081 son & Clack 2082 (1999). 2083 Abbreviation: 2084 mc, meta- 2085 carpal. The 2086 scale bar is 2087 approximate. 2088 Photos taken 2089 by D. M. 2090 2091 2092 2093

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2094  The “Parrsboro jaw” is an incomplete impression of a lower jaw of Pennsylvanian age, 2095 consistently called NSM 987GF65 in the original description (Godfrey & Holmes, 2096 1989) but NSM 987GH65 in the partial redescription (Sookias, Böhmer & Clack, 2097 2014). It has a unique combination of characters and differs from all other OTUs in 2098 this matrix, which may therefore have the potential to resolve the relationships of this 2099 mysterious fragment that has warranted redescription but defied the phylogenetic 2100 analysis of Sookias, Böhmer & Clack (2014: fig. 5A). 2101  Casineria is generally thought to be close to the origin of amniotes or at least 2102 seymouriamorphs (Paton, Smithson & Clack, 1999; Clack et al., 2012b, 2016; 2103 Witzmann & Schoch, 2017: fig. 16). In stark contrast, Pawley (2006: 207) reported 2104 that it scored identically to Caerorhachis in her matrix, apart from the (quite different) 2105 distribution of missing data, and considered them “indistinguishable based on the 2106 available evidence” (Pawley, 2006: 195, 239), pointing out further that the supposedly 2107 amniote-like features of Casineria have a wider distribution. In her phylogenetic 2108 analysis, it came out as a temnospondyl (in a trichotomy with Caerorhachis and a 2109 clade formed by all other temnospondyls). D. M. has seen the only known specimen. 2110 We present new photos (Fig. 5–7), interpretations and comparisons to the 2111 redescription of Caerorhachis (Ruta, Milner & Coates, 2002) in the Discussion (The 2112 interrelationships of Anthracosauria, Silvanerpeton, Caerorhachis, Gephyrostegidae, 2113 Casineria and Temnospondyli); notably, we identify what seems to be a postbranchial 2114 lamina on the cleithrum (Fig. 7). 2115

2116 2117 2118 Figure 7: Right cleithrum of NMS G 1993.54.1cp, the holotype of Casineria kiddi 2119 (counterpart plate), in caudal view, showing postbranchial lamina (compare fig. 70-2.4 2120 of Pawley, 2006). Total length about 11.5 mm. Photo taken by D. M. 2121 2122 Taxa that were not added 2123 2124 We have not added taxa that likely could not be handled by the character sample of the 2125 present matrix (e.g. too deeply nested taxa, such as any further baphetoids, cochleosaurids, 2126 eryopids, dvinosaurs, dissorophids, stereospondylomorphs, “microsaurs”, amniotes or 2127 lissamphibians beyond those we did add, or taxa too far outside the clade of limbed 2128 vertebrates). Still, a few taxa would have been intuitive candidates for addition, but we have 2129 left them out for the following reasons: 2130 Because of the state of preparation of the specimens, the original description of the 2131 enigmatic and interesting “anthracosaur” Eldeceeon (Smithson, 1994) is very preliminary and 2132 contains little information; following the discovery of additional specimens, Eldeceeon is 2133 being redescribed according to Ruta & Clack (2006) and Clack & Milner (2015). 2134 Although Madygenerpeton is only the second chroniosuchian for which a thorough 2135 description exists, we have not included it because it seems to lie at the tip of a long branch. 2136 According to the first phylogenetic analysis of Chroniosuchia ever performed (Schoch, Voigt 2137 & Buchwitz, 2010), it is highly nested within that clade as the sister-group of Chroniosaurus, 2138 so that its seemingly plesiomorphic aquatic adaptations are probably reversals and would

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2139 likely, perhaps together with the many other autapomorphies that Madygenerpeton has, distort 2140 the tree in general and the position of Chroniosaurus in particular. Indeed, Madygenerpeton 2141 lacks traces of the lateral-line organ (Schoch, Voigt & Buchwitz, 2010; D. M., pers. obs.) 2142 which would be expected to be present in a primarily aquatic vertebrate; the dorsal rims of the 2143 eye sockets are raised high above the skull table, implying a crocodile-like predator that 2144 looked for terrestrial prey rather than staying underwater, an interpretation further 2145 corroborated by the nostrils which are apparently raised above the roof of the snout. In 2146 temnospondyls, for example, the nostrils are always well below eye level, and, with the 2147 borderline exception of Glaukerpeton (Werneburg & Berman, 2012), the eye sockets are 2148 never noticeably raised (D. M., pers. obs., and see below). The second analysis that included 2149 Madygenerpeton (Buchwitz et al., 2012) found it as the sister-group to all other 2150 chroniosuchians, but – much like its predecessor – had a very small sample of outgroups. 2151 Conversely, the present matrix undersamples characters relevant to chroniosuchian 2152 phylogeny: the osteoderms and the antorbital fenestra, for example, are not coded. Indeed, a 2153 test run failed to find Madygenerpeton as a chroniosuchian. Only osteoderms and the 2154 mentioned skull roof (with distorted parts of the palate) are known of Madygenerpeton. 2155 The temnospondyl Parioxys ferricolus, variously allied to Eryops and/or 2156 Dissorophoidea and more specifically found as the sister-group of Iberospondylus by Pawley 2157 (2006: chapter 5), is most likely a chimeric taxon (J. Pardo, pers. comm. 2012). The lectotype 2158 (AMNH 4309) is covered by a crust that would be difficult to prepare away and completely 2159 obscures the sutures as well as most other details (D. M., pers. obs. 2013; Schoch & Milner, 2160 2014: 77), and referred specimens (AMNH 2445 and almost all of the MCZ material) are 2161 being restudied by M. Ruta (D. M., pers. obs. of loan slips in 2013). “Preparation of USNM 2162 material has revealed many similarities to ” (a dissorophid like Broiliellus; Schoch & 2163 Milner, 2014: 77); it remains to be seen if the same will hold true of the lectotype. – AMNH 2164 7118, the type and only known specimen of P. bolli, consists only of encrusted (D. M., pers. 2165 obs. 2013) assorted postcrania, and whether it (or any other material currently assigned to 2166 Parioxys) can be referred to Parioxys awaits investigation. 2167 Onchiodon is well known, but so similar to the even better known Eryops (Werneburg, 2168 2007a) that it would most likely not add any new information to this matrix. Pretty much the 2169 same holds for the less well known Glaukerpeton (Werneburg & Berman, 2012). The rest of 2170 Eryopidae – and also the diversity within Eryops – is very poorly understood and currently 2171 undergoing revision (Werneburg, 2007a, 2012a; Werneburg & Berman, 2012; Schoch & 2172 Milner, 2014; Rasmussen, Huttenlocker & Irmis, 2016). 2173 Comparison to character lists in Fröbisch & Reisz (2012), Schoch (2012), Maddin et 2174 al. (2013b) and Holmes, Berman & Anderson (2013) shows that many characters relevant to 2175 dissorophoid phylogeny are lacking from this matrix. Adding these characters and a better and 2176 more even sample of dissorophoid temnospondyls – micromelerpetids (in our matrix 2177 represented only by Micromelerpeton), dissorophids (Broiliellus brevis), trematopids 2178 (Ecolsonia, Acheloma, Phonerpeton; Mordex) and amphibamids (Amphibamus, Eoscopus, 2179 Doleserpeton, Platyrhinops, three “branchiosaurids”; Gerobatrachus, Micropholis, two more 2180 “branchiosaurids”) – will be part of future work. As Schoch (2012), Werneburg (2012b), 2181 Maddin et al. (2013b) and Holmes, Berman & Anderson (2013) pointed out, some of these 2182 taxa need to be (or are being) redescribed, and some material probably even needs additional 2183 preparation, which is in many cases as difficult to do as for Parioxys (see above). In 2184 particular, as mentioned above, we have not used information from species currently referred 2185 to Broiliellus other than B. brevis. 2186 Kirktonecta (Clack, 2011b), “the oldest known microsaur”, is so poorly preserved (and 2187 prepared – it is split through the bone like Eldeceeon) that it would not differ from several 2188 other OTUs in this matrix if we added it.

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2189 The characters in which Czatkobatrachus differs from Triadobatrachus (Evans & 2190 Borsuk-Białynicka, 2010) are not represented in this matrix. It would be possible to code 2191 Czatkobatrachus for a few characters that are unknown in Triadobatrachus, but in all of 2192 these, Czatkobatrachus has the state expected (under all hypotheses) for the ancestral 2193 lissamphibian and the ancestral salientian, so it is not relevant here. 2194 “Several other taxa [of Mesozoic salamanders] (e.g., Laccotriton, Sinerpeton, and 2195 Jeholotriton) are excluded from this analysis because they are anatomically uncertain and are 2196 currently under taxonomic revision” (Gao & Shubin, 2012: supplementary information: 3). 2197 This revision is ongoing (Jia & Gao, 2016b). 2198 Adding Chinlestegophis (Pardo, Small & Huttenlocker, 2017) to our matrix would 2199 currently be pointless in the absence of stereospondyls (other than Lydekkerina and 2200 Australerpeton in the expanded taxon sample) and characters pertinent to stereospondyl 2201 phylogeny. 2202 2203 Phylogenetic analyses 2204 2205 Maximum-parsimony analyses 2206 2207 These analyses were conducted in PAUP* 4.0b10 (Swofford, 2003) on a desktop computer 2208 with an Intel® Core™2 Duo processor (2.67 GHz) and 3.87 GB of usable RAM. Test runs in 2209 PAUP* 4.0a158 (Swofford, 2017) were sometimes slower and sometimes found fewer MPTs. 2210 Alpha versions of PAUP* 4.0 up to a158 were, however, used to generate initial tree figures 2211 for further processing from the results of all phylogenetic and robustness analyses. 2212 We did not use any additional weighting procedures (such as reweighting, see 2213 Discussion: Reweighting); each character contains at least one state transition that costs one 2214 step, and there are no state transitions that cost less. 2215

2216 2217 2218 Figure 8: Topological constraints used in Analyses R2, R3, R5 and R6 (see Table 1). 2219 These are backbone constraints: the OTUs not mentioned in the constraints were free to be 2220 positioned anywhere within the constraint tree (including at its root), and the polytomies were 2221 allowed to be resolved in all mathematically possible ways. A: Constraint against the LH, 2222 allowing both TH and PH; used in Analyses R2 and R5 (both of which found the TH). 2223 Whether Lepospondyli is extinct depends on the unconstrained positions of the caudates. B: 2224 Constraint for the PH, used in Analyses R3 and R6. 2225 2226 Six analyses (Table 1) of our modified matrix were conducted with (Analyses R4–R6) 2227 and without the added taxa (Analyses R1–R3), and with and without backbone constraints. 2228 The first constraint (Fig. 8A), used in Analyses R2 and R5, forced the dissorophoid 2229 temnospondyl Doleserpeton to be closer to the three salientians (Triadobatrachus, 2230 Notobatrachus, Vieraella; their monophyly with respect to Doleserpeton was specified, but 2231 not their relationships to each other) than the lysorophian lepospondyl Brachydectes, making 2232 the LH impossible but allowing both the TH and the PH. The second constraint (Fig. 8B), 2233 used in Analyses R3, R6 and R9, only allowed the PH by additionally forcing the 2234 gymnophionomorph Eocaecilia to be closer to Brachydectes than to Doleserpeton. Both

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2235 constraints contain Eusthenopteron in the outgroup position. In order to find all optimal 2236 islands and all optimal trees within each island, each heuristic search used 10,000 addition- 2237 sequence replicates (with random addition sequences), each of which was restricted to 50 2238 million rearrangements by tree bisection and reconnection (25 million turned out to be too 2239 few to find all MPTs in some cases). This limit was hit in almost all replicates of the analyses 2240 with added taxa and close to two thirds of the replicates in the analyses without added taxa. 2241 Analysis R1 took 25:58:25 of calculation time, Analysis R6 lasted for 47:25:19. 2242 We also reanalyzed (Analysis O1; Table 1) the original, unmodified matrix of RC07 2243 without any constraints to test whether their procedure for reducing calculation time (the 2244 “parsimony ratchet”; see Ruta, Coates & Quicke, 2003) had overlooked any MPTs. This was 2245 deemed important because, when Skutschas & Gubin (2012) applied the same procedure to 2246 their own matrix which was small enough for a branch-and-bound analysis, it found a single 2247 tree that was no less than 35 steps longer than the MPTs found by branch-and-bound – a 2248 method which is guaranteed to find all MPTs. (To our surprise, Skutschas & Gubin [2012] 2249 reported the length difference without commenting on it and without discarding the crassly 2250 suboptimal tree or offering a reason why it should be retained in consideration.) Calculation 2251 time with 5,000 addition-sequence replicates and up to a hundred million rearrangements per 2252 replicate was 21:48:07. 2253 On p. 85, RC07 reported that constraining their analysis to find a topology fully 2254 congruent with that of Laurin (1998a) – a version of the LH – required “the addition of a mere 2255 nine steps” and yielded 60 suboptimal trees. On the next page, however, they wrote: “Using 2256 our own data, the 720 suboptimal trees placing lissamphibians with lepospondyls are 15 steps 2257 longer than the most parsimonious trees from the original analysis.” (RC07 did not publish 2258 the constraint they used to obtain this result.) To resolve this contradiction, we reanalyzed 2259 (Analysis O2; Table 1) the original, unmodified matrix of RC07 under a backbone constraint 2260 that required the salientians to be closer to Brachydectes than to Doleserpeton. 2261 Eusthenopteron was again included in the constraint in the outgroup position. The salientians 2262 are Triadobatrachus, Notobatrachus and Vieraella; their monophyly with respect to 2263 Doleserpeton was specified, but not their relationships to each other (Fig. 8A with the 2264 positions of Brachydectes and Doleserpeton exchanged). Calculation time was 23:48:00. 2265 Maddin, Jenkins & Anderson (2012) reported the majority-rule consensus of their 2266 MPTs, but not the strict consensus, and did not explicitly discuss any MPTs that disagreed 2267 with the majority. Out of curiosity, we therefore repeated their analysis without modifying 2268 their matrix or applying any constraints. Because Maddin, Jenkins & Anderson (2012) did not 2269 report what settings they had used, we ran 1,000 unlimited addition-sequence replicates. 2270 Calculation time was 03:58:40.9. 2271 Pardo, Small & Huttenlocker (2017: fig. S7B) reported the majority-rule consensus of 2272 their MPTs, but did not discuss any MPTs that disagreed with the majority. Out of curiosity, 2273 we therefore repeated their analysis, too, without modifying their matrix or applying any 2274 constraints. Because Pardo, Small & Huttenlocker (2017) did not report what settings they 2275 had used, we ran 1,000 unlimited addition-sequence replicates. Calculation time was 2276 02:19:13. 2277 2278 Robustness analyses 2279 2280 José Grau (Museum für Naturkunde, Berlin) kindly performed two parsimony bootstrap 2281 analyses on our modified matrix (Table 1), one each for the original (Analysis B1) and for the 2282 expanded taxon sample (Analysis B2). Both were carried out on an Intel® Xeon® CPU E5- 2283 4667 v4 (2.20 GHz, 512 GB of available RAM) using PAUP* 4.0a158 for Unix/Linux 2284 (Swofford, 2017), and used 1,000 bootstrap replicates consisting of 500 addition-sequence

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2285 replicates which were limited to 50 million rearrangements each. To keep this within a 2286 reasonable timeframe, J. Grau divided each analysis into 100 runs of 10 bootstrap replicates, 2287 which were run on a total of 50 processors by means of GNU parallel v20130522, followed 2288 by concatenation and calculating the majority-rule consensus to obtain the final bootstrap tree. 2289 To maximize the amount of visible information, we included not only clades with bootstrap 2290 values of 0.5 and above in the bootstrap trees, but also clades with lower bootstrap values that 2291 do not contradict any of those with higher ones (PAUP* setting: contree all /majrule=yes 2292 le50=yes; equivalent to bootstrap keepall=yes for a non-parallel analysis). 2293 The total running time for each bootstrap run was between 27 and 38 hours; the 2294 consensus took around 40 minutes to compute. Each bootstrap run produced between 30,111 2295 and 114,768 trees; the consensus was calculated from a total of 6,870,699 trees. 2296 In order to test whether the differences between MPTs from different analyses with the 2297 same taxon sample and the same reversibility coding are statistically significant, we ran the 2298 tests implemented in PAUP*: a Kishino-Hasegawa test, a Templeton test and a winning-sites 2299 test. The p value we report for each is the probability (Kishino-Hasegawa) or approximate 2300 probability (Templeton, winning sites) of finding a more extreme test statistic; the null 2301 hypothesis is that the differences between the two tested trees are indistinguishable from 2302 random. The MPTs used for these tests are part of the data file (Data S1) and were chosen to 2303 differ as little as possible from each other topologically. 2304 Eduardo Ascarrunz (pers. comm.) and the reviewer Michael Buchwitz kindly notified 2305 us of problems with our first (2015) applications of these tests. Goldman, Anderson & 2306 Rodrigo (2000) and Planet (2006) have shown that all three tests, as implemented in PAUP* 2307 and elsewhere, are inappropriate to use for our questions and indeed for the vast majority of 2308 the questions they have been applied to in the phylogenetics literature. To the best of our 2309 knowledge, better tests are not available for practical purposes. Thus, we cannot reject the 2310 abovementioned null hypothesis in any case. However, the error caused by using these tests is 2311 one-sided: the p values found by better tests are always greater than the p values found by the 2312 inappropriately used one-tailed tests – greater by an amount that cannot be estimated in 2313 advance (Goldman, Anderson & Rodrigo, 2000). This allows us to look at the problem from 2314 the other side and distinguish the cases where the null hypothesis can certainly not be rejected 2315 from those where it remains rejectable: when the inappropriate tests do not reject the null 2316 hypothesis, we can be certain that a better test would not reject it either, but when the 2317 inappropriate tests do reject the null hypothesis, the null hypothesis may or may not be 2318 rejected by a better test. 2319 PAUP* performs two-tailed versions of all three tests; we report p values from the 2320 one-tailed versions, derived by halving the p values put out by PAUP* (Goldman, Anderson 2321 & Rodrigo, 2000; Planet, 2006). 2322 2323 Exploratory Bayesian analysis 2324 2325 As a preliminary test of whether the method of analysis has an impact on our results, J. Grau 2326 kindly ran an unconstrained Bayesian-inference analysis on our revised matrix including the 2327 added taxa (Analysis EB; Table 1). He used MrBayes 3.2.6 (Huelsenbeck et al., 2015) in 2328 parallel on 16 AMD Opteron™ 6172 processors (2.1 GHz), using 16 GB of RAM. Instead of 2329 the usual two, we chose to use four simultaneous runs; all other settings remained at the 2330 factory defaults, notably the specification of the first quarter of the generations as burn-in. 2331 Calculation time was 20 hours and 6 minutes. 2332 MrBayes cannot handle stepmatrices. We therefore had to split the two characters with 2333 stepmatrices into two to three characters each, which were ordered or unordered. The results 2334 of this nontrivial task are documented in Appendix 1 under characters 32 and 134; the scores

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2335 of the new characters are wholly predictable from those of the stepmatrix characters used for 2336 all other analyses, and are therefore not presented separately except in the matrix file (Data 2337 S3). The total number of characters for this analysis was 280. 2338 The average standard deviation of the split frequencies decreased to 0.05 between six 2339 and seven million generations into the analysis. Because it had not reached stationarity, we 2340 extended the analysis in the hope of reaching the recommended value of 0.01; after some 2341 twenty million generations of fluctuation around 0.013, we ended the analysis after a total of 2342 40 million generations (including ten million of burn-in). Convergence was achieved 2343 according to two other metrics: the plot of the logarithm of probability against generation 2344 number (excluding the burn-in) did not show a trend, and the potential scale reduction factor 2345 (PSRF) of the tree length was 1.000 as recommended. 2346 2347 Results 2348 2349 A very brief overview and comparison of our results is presented as Table 3; the results of 2350 statistical tests for lack of distinguishability of topologies are reported below and shown in 2351 Table 4. 2352 2353 Reanalysis of the matrix of Maddin, Jenkins & Anderson (2012) 2354 2355 Maddin, Jenkins & Anderson (2012) reported having found 34 MPTs of 1450 steps, and 2356 stated that 274 of the 308 characters in their matrix were parsimony-informative. We find that 2357 274 is instead the number of MPTs; PAUP* reports that 280 of the 308 characters are 2358 parsimony-informative. The MPTs have 1449 steps, and their indices, too, are slightly better 2359 than reported (ci = 0.3527, hi = 0.7191, ri = 0.6544, rc = 0.2308); the ci and hi excluding 2360 parsimony-uninformative characters, not reported by Maddin, Jenkins & Anderson (2012), 2361 are 0.3252 and 0.6748. The number of trees that are 1450 steps long, incidentally, is not 34, 2362 but 159,650. 2363 However, the identical strict and Adams consensus we find is practically identical to 2364 the majority-rule consensus of Maddin, Jenkins & Anderson (2012: fig. 4). The only 2365 differences are the following: Utaherpeton emerges as the sister-group to all other 2366 lepospondyls rather than to Holospondyli (a clade that includes Brachydectes, the aïstopods 2367 and the nectrideans); Microbrachis and Adelogyrinus are not sister-groups forming the sister- 2368 group to the clade that contains all remaining “microsaurs” except Utaherpeton, but are 2369 successively closer to Holospondyli, within which the “nectrideans” no longer form a clade 2370 and Scincosaurus is the sister-group to (Urocordylidae (Diplocaulidae (Brachydectes, 2371 Aïstopoda))) rather than to Diplocaulidae alone; within Diplocaulidae, Diceratosaurus is 2372 closer to (Diplocaulus + Diploceraspis) than to (Keraterpeton + Batrachiderpeton). All other 2373 differences concern lack of resolution in our strict consensus: Tuditanus and Asaphestera 2374 form a trichotomy with the clade formed by all “microsaurs” not mentioned above; Pantylus, 2375 Stegotretus, Gymnarthridae, Ostodolepididae and (Rhynchonkos + Batropetes) form a 2376 polytomy; Temnospondyli has a basal polytomy between Eryops, (Balanerpeton + 2377 Dendrerpeton), Trematopidae (itself unresolved) and the clade of the remaining 2378 dissorophoids, and finally Greererpeton forms a trichotomy with Temnospondyli and the rest 2379 of the ingroup. The position of Gerobatrachus within Lissamphibia is not affected. 2380 The majority-rule consensus of our trees resolves these polytomies identically to 2381 Maddin, Jenkins & Anderson (2012: fig. 4), except that the polytomy encompassing most 2382 “microsaurs” remains unresolved. 2383

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2384 Table 3: Summary and comparison of analysis results. See Table 1 for the settings of these analyses and for the numbers of the figures that 2385 represent the trees. The “modern amphibians” column gives the closest one or two relatives of the clade of modern amphibians (TH, LH) or of 2386 the two clades of modern amphibians (PH); the Batrachia column indicates whether Caudata and Salientia form a clade to the exclusion of 2387 Eocaecilia; the Kotlassia column states whether Kotlassia is crownward of, rootward of or a member of Seymouriamorpha; the Limnoscelis 2388 column states whether Limnoscelis is crownward of, rootward of or a member of Diadectomorpha; the last column states whether Ichthyostega is 2389 rootward or crownward of Acanthostega and Ventastega. Note that whenever Amniota is closer to Temnospondyli than to CAS, Caerorhachis is 2390 found as a temnospondyl. Brachystelechidae contains Batropetes, *Carrolla and *Quasicaecilia. OTUs unique to the expanded taxon sample are 2391 marked with an asterisk. Abbreviations: #, symbol of the analysis (as used in the text and in Tables 1, 4); AS, Anthracosauria and Silvanerpeton 2392 (Caerorhachis is found as a temnospondyl); CAS, Caerorhachis, Anthracosauria and Silvanerpeton; Diad., Diadectomorpha; Seym., 2393 Seymouriamorpha; T, Temnospondyli; (U, A), a clade formed exclusively by Urocordylidae and Aïstopoda. Numbers in curly braces are 2394 bootstrap percentages, shown in boldface if 50 or higher, except for Analysis EB, where they are posterior probabilities (in %), shown in 2395 boldface if 75 or higher. 2396 # Modern amphibians Batrachia Albanerpetidae Amniota Kotlassia Limnoscelis adelospondyls Ichthyostega closest to: closer to: closest to: O1 TH: Doleserpeton yes Eocaecilia CAS crownward rootward Colosteidae crownward O2 LH: Holospondyli yes Lissamphibia CAS crownward rootward Colosteidae crownward R1 LH: (adelospondyls yes Batrachia 1) CAS; 2) 1) rootward; Diad. (U, A) 1) crownward; (U, A)) T 2) Seym. 2) rootward R2 TH: Phlegethontia1 yes Lissamphibia T rootward Diad. 1 1) crownward; 2) rootward R3 PH: Doleserpeton; no2 Caudata 1) CAS; 2) 1) rootward; Diad. (U, A) 1) crownward; (adelospondyls (U, T 2) Seym. 2) rootward A))2 B1 LH {84}3: yes {77} Batrachia {53} AS {12} Seym. {28} Diad. {59} Holospondyli + crownward (Brachydectes + crownward {35; {47} Batropetes) {20}4 25}5 R4 LH: (Brachydectes + yes Batrachia CAS Seym. crownward (U, A) crownward Brachystelechidae) R5 TH: Doleserpeton or no Eocaecilia CAS Seym. crownward (U, A) crownward *Gerobatrachus R6 PH: Doleserpeton; yes6 Valdotriton CAS Seym. crownward (U, A) crownward

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Aïstopoda6 B2 LH {213, 257}: yes {54} Lissamphibia T {6} Seym. {30} Diad. {24} all other crownward of (Brachydectes + {67} amphibians {20; Ventastega Brachystelechidae) 10}5 {11} and {15}4 Acanthostega {10} EB LH {92}: (*Carrolla yes {81} Batrachia {55} T {48} Seym. {99} Diad. {96} (“U”, A) {48; 69; crownward of + *Quasicaecilia) 86}8 Ventastega and {88}4 Acanthostega {both 76} 2397 2398 1 An entirely novel arrangement where Lissamphibia and the strangest “lepospondyls” are nested among the dvinosaurian temnospondyls, closest 2399 to Trimerorhachis; see text and Fig. 11. 2400 2 Salientia (as constrained) is nested within Temnospondyli (next to Doleserpeton), while Eocaecilia (as constrained), Caudata and 2401 Albanerpetidae are nested within Lepospondyli. 2402 3 Dissorophoidea. 2403 4 20 (B1) and 15 (B2) are the bootstrap percentages of the smallest clade that contains Batropetes, Brachydectes and Lissamphibia, which has a 2404 PP of 92; (Batropetes + Brachydectes) respectively (Brachystelechidae + Brachydectes) have 37 (B1) or 23 (B2), while (Lissamphibia 2405 (*Carrolla, *Quasicaecilia)) has a PP of 88. 2406 5 The highest bootstrap percentage that keeps the adelospondyls away from Colosteidae is 35 (B1) or 20 (B2), the highest that keeps them away 2407 from (U, A) is 25 (B1) or 10 (B2). 2408 6 Salientia (as constrained) and Caudata including Albanerpetidae are nested within Temnospondyli (next to Doleserpeton), while Eocaecilia (as 2409 constrained) is nested within Lepospondyli. 2410 7 Amphibamidae (not including *Micropholis). 2411 8 The urocordylids come out as paraphyletic (PP = 65). The PP of the adelospondyls being the sister-group of (Ptyonius (Urocordylus 2412 (Sauropleura, Aïstopoda))) is 48, the PP of that clade + *Utaherpeton is 69, the highest PP that keeps them away from Colosteidae is 86. 2413

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2414 Table 4: Summary of parsimony support for hypotheses on lissamphibian origins. See 2415 Table 1 for analysis settings. The second column subtracts the MPT length found by the 2416 second analysis in each line from that found by the first. The rightmost column summarizes 2417 the p values from the one-tailed Kishino-Hasegawa, Templeton and winning-sites tests (listed 2418 in the text; our use of the tests is discussed in Materials and methods: Robustness analyses). 2419 Bootstrap values of 0.5 or higher are given in boldface, as are p values that do not certainly 2420 fail to reject the null hypothesis at the (arbitrary) 0.05 level; the null hypothesis is that the 2421 topology differences cannot be distinguished from random variations. Note that a cutoff value 2422 of 0.1 instead of 0.05 would have given the same results, except that the Templeton and the 2423 winning-sites test distinguish R4 and R6 at a minimum of p = 0.0565 and p = 0.0966. 2424 Conversely, a cutoff value of 0.03 would have rejected the comparison of R1 and R3 2425 according to the Kishino-Hasegawa (p = 0.0352) and Templeton (p = 0.0362) tests; a cutoff 2426 value of 0.01 would have rejected all. 2427 Analyses Difference Highest bootstrap Difference in topology in number support for difference in indistinguishable from of steps topology random at p = 0.05? O1 (TH), O2 (LH) 1 not tested certainly (p > 0.44) R1 (LH), R2 (TH) 9 0.47 (Isodectes + certainly (0.225 > p > Neldasaurus) 0.133) R1 (LH), R3 (PH) 12 0.84 (Dissorophoidea) not certainly (0.035 > p > 0.017) R2 (TH), R3 (PH) 3 0.84 (Dissorophoidea) certainly (p > 0.4) R4 (LH), R5 (TH) 10 0.40 (Doleserpeton + certainly (0.227 > p > *Gerobatrachus) 0.183) R4 (LH), R6 (PH) 15 0.67 (modern amphibians) certainly (0.133 > p > 0.056) R5 (TH), R6 (PH) 5 0.67 (modern amphibians) certainly (p > 0.31) 2428 2429 Reanalysis of the matrix of Pardo, Small & Huttenlocker (2017) 2430 2431 We confirm that the temnospondyl/lissamphibian matrix published by Pardo, Small & 2432 Huttenlocker (2017) yields 882 MPTs of 1514 steps. Of the 345 characters, 322 are 2433 parsimony-informative. Indices were not reported; we find ci without uninformative 2434 characters = 0.2548, hi without uninformative characters = 0.7452, ri = 6858, rc = 0.1812. All 2435 nodes marked “100” on the majority-rule consensus tree (Pardo, Small & Huttenlocker, 2017: 2436 fig. S7B) occur in the strict consensus. Judging from inspection of the first, the last and every 2437 25th MPT (1, 25, 50, 75, 100 … 800, 825, 850, 875, 882), the following deviations from the 2438 majority-rule consensus are equally parsimonious: 2439 Some MPTs support the textbook version of the TH, where the modern amphibians 2440 form an exclusive clade which is the sister-group of Gerobatrachus within Dissorophoidea. 2441 Rileymillerus is always a stereospondyl, but Chinlestegophis can alternatively be a 2442 gymnophionomorph within Lissamphibia. In both topologies, Karauridae is the sister-group 2443 of Urodela, and Caudata as a whole lies next to Salientia. 2444 Other MPTs show Lissamphibia as (Gymnophionomorpha (Karauridae (Urodela, 2445 Salientia))), forming the sister-group of (Rileymillerus + Chinlestegophis) within 2446 Stereospondyli. 2447 In MPTs that distribute the extant amphibians as the majority-rule consensus does, the 2448 paedomorphic Kokartus can be the sister-group of Karaurus as shown, or lie one node more 2449 rootward.

57 58

2450 is the sister-group of Broiliellus or of Cacops in all inspected trees, 2451 Phonerpeton that of Acheloma or Ecolsonia. Amphibamus and Platyrhinops often switch 2452 places. Other than this and the positions of the modern amphibians, the Zatracheidae- 2453 Lapillopsis-Dissorophoidea clade is always resolved as in the majority-rule consensus; 2454 Apateon is never the sister-group of Micromelerpetidae as it is in the Bayesian tree (Pardo, 2455 Small & Huttenlocker, 2017: fig. 2 = S7A). 2456 On the eryopiform side, the clade of Uranocentrodon, Rhineceps and Broomistega is 2457 resolved in all three ways in different trees; Broomistega never leaves this clade, unlike in the 2458 Bayesian analysis. Edingerella, and the capitosaur clade are variably arranged 2459 but always form a grade of two or three clades. Sangaia can be one node closer to 2460 Rileymillerus than the trematosaur/metoposaur clade (as shown), in which case it is 2461 sometimes the sister-group of Laidleria, or one node farther away. Within the 2462 trematosaur/metoposaur clade, Trematolestes has two positions and has four. 2463 The remainder of the tree has a backbone (Siderops (Batrachosuchus, Plagiosauridae)). 2464 Rileymillerus (optionally together with Chinlestegophis, in that case further optionally the rest 2465 of Gymnophionomorpha or Lissamphibia) can lie outside this clade, which then also contains 2466 Laidleria next to Plagiosauridae as in the Bayesian tree, or in it, next to Plagiosauridae as in 2467 the majority-rule consensus; in the latter case Laidleria lies outside this whole clade (alone as 2468 shown, or together with Sangaia), and Batrachosuchus can switch places with Siderops. The 2469 resolution seen in the Bayesian tree does not occur in any of the inspected MPTs. 2470 2471 Reanalyses of the matrix of Ruta & Coates (2007) 2472 2473 Our unconstrained reanalysis of the original, unmodified matrix (Analysis O1) found 324 2474 MPTs, as RC07 did; their strict consensus (Fig. 1) is identical to that reported by RC07 (fig. 2475 5, 6). Their length is 1621 steps when we distinguish polymorphism from partial uncertainty 2476 (both occur in the matrix; PAUP* setting: pset mstaxa=variable), but 1584 steps – as reported 2477 by RC07 – when we treat both as partial uncertainty (pset mstaxa=uncertain). The indices we 2478 find are slightly different from those reported by RC07, and differ again depending on the 2479 treatment of polymorphism: when polymorphism is treated as uncertainty, the ci excluding 2480 the parsimony-uninformative characters is 0.2281 rather than 0.22, the ri is 0.6768 rather than 2481 0.67 and the rc is 0.1564 rather than 0.15; when polymorphism and uncertainty are 2482 distinguished, the ri is unaffected, but the ci excluding the parsimony-uninformative 2483 characters rises to 0.2458 and the rc becomes 0.1683. 2484 Our analysis constrained for the LH (Analysis O2) found 60 most parsimonious trees. 2485 Their strict consensus (Fig. 9) is quite unlike what RC07 reported on p. 86, and also unlike 2486 that of Laurin (1998a) which they used as a constraint on p. 85: we find Lissamphibia as the 2487 sister-group of Albanerpetidae, both of which together form the sister-group to Holospondyli 2488 (“nectrideans” including aïstopods). All of these together are found as the sister-group of 2489 Brachydectes; in other words, lepospondyl topology is identical to that in the shortest trees, 2490 except for the addition of Lissamphibia + Albanerpetidae next to Holospondyli, and except 2491 for the loss of resolution in Urocordylidae. The resolution of Temnospondyli is greatly 2492 improved. The length of these suboptimal trees is 1622 steps (1585 when polymorphism is 2493 treated as uncertainty); ci excluding the parsimony-uninformative characters = 0.2280 2494 (polymorphism treated as uncertainty) or 0.2457 (polymorphism and uncertainty 2495 distinguished), ri = 0.6766, rc = 0.1562 or 0.1681. 2496 In short, the matrix of RC07 supports the temnospondyl hypothesis over the 2497 lepospondyl hypothesis by one single step, rather than either nine or fifteen steps as originally 2498 claimed (RC07: 85, 86).

58 Eusthenopteron Panderichthys Ventastega Acanthostega Ichthyostega Tulerpeton origin of digits Colosteus Greererpeton Colosteidae Acherontiscus Adelospondylus adelospondyls Adelogyrinus Adelogyrinidae Dolichopareias Crassigyrinus Ossinodus Whatcheeriidae Whatcheeria Pederpes Eucritta Baphetes Baphetoidea Megalocephalus Capetus Edops Edopoidea Chenoprosopus Cochleosaurus Dvinosauria Isodectes Temnospondyli Neldasaurus Trimerorhachis Balanerpeton Eutemnospondyli Dendrerpetidae Eryops Acheloma Phonerpeton Trematopidae Dissorophoidea (YW00) Ecolsonia Broiliellus brevis Platyrhinops Dissorophoidea (S13) Eoscopus “amphibamids” Amphibamus Doleserpeton Micromelerpeton Apateon Leptorophus Branchiosauridae Schoenfelderpeton Caerorhachis Silvanerpeton Eoherpeton Anthracosauria Proterogyrinus Archeria Embolomeri Pholiderpeton scutigerum Pholiderpeton attheyi Anthracosaurus Gephyrostegus “gephyrostegids” Bruktererpeton Utegenia Discosauriscus Ariekanerpeton Leptoropha “seymouriamorphs” Microphon Seymouria Kotlassia Solenodonsaurus Tseajaia Limnoscelis “diadectomorphs” Orobates Diadectes Captorhinus Paleothyris/Protorothyris Sauropsida Petrolacosaurus tetrapod crown-group Westlothiana Tuditanus Asaphestera Saxonerpeton Batropetes Amphibia Odonterpeton Microbrachis Microbrachomorpha Hyloplesion Hapsidopareion Micraroter Pelodosotis Ostodolepididae Rhynchonkos/Aletrimyti/Dvellecanus “microsaurs” Cardiocephalus Euryodus Gymnarthridae Pantylus Pantylidae Stegotretus Brachydectes Lysorophia Albanerpetidae modern Eocaecilia Gymnophionomorpha amphibians Karaurus Caudata Liss- Valdotriton Batrachia amphibia Triadobatrachus Notobatrachus Salientia Vieraella Scincosaurus Keraterpeton Diceratosaurus Holospondyli Batrachiderpeton Diplocaulidae Diplocaulus Diploceraspis Ptyonius Sauropleura Urocordylidae Urocordylus 59 Lethiscus Oestocephalus Aïstopoda Phlegethontia 60

2499 ↑ Figure 9: Strict consensus of the MPTs (length: 1622 steps including polymorphisms) 2500 found by our constrained reanalysis of the unchanged matrix of RC07 (Analysis O2). 2501 The constraint forced the lysorophian “lepospondyl” Brachydectes to be closer to the three 2502 salientians (Triadobatrachus, Notobatrachus, Vieraella) than the dissorophoid temnospondyl 2503 Doleserpeton; this allowed only the LH (Fig. 8A with the positions of Brachydectes and 2504 Doleserpeton exchanged). 2505 2506 To test this result, we manually drew a most parsimonious rooted tree and a rooted tree 2507 that fulfills the constraint in Mesquite (Maddison & Maddison, 2017), which does not take 2508 ancestors into consideration. Mesquite reported the exact same lengths (distinguishing 2509 polymorphism from partial uncertainty, as Mesquite always does). 2510 This result is perhaps not as surprising as it may seem. Although they only published 2511 the values for seven nodes, RC07 (appendix 4 – p. 122) did conduct a bootstrap and a decay 2512 analysis. While Lissamphibia (bootstrap percentage = 67, Bremer index = 8) and most of the 2513 nodes within it are well supported, the sister-group relationship of Lissamphibia and 2514 Doleserpeton has a Bremer index of 1 and “no boots[t]rap support compatible with a 50% 2515 majority-rule consensus”, and the sister-group relationship of both of these to Amphibamus 2516 has a Bremer index of 2 and “no bootstrap support in a 50% majority-rule consensus”. Values 2517 for more rootward nodes were not reported, but are not likely to be any higher given the 2518 limited resolution of this part of the tree (Fig. 1). 2519 Unsurprisingly, unconstrained and constrained trees are statistically indistinguishable: 2520 p = 0.4500 (Kishino-Hasegawa and Templeton tests), p = 0.5000 (winning-sites test). 2521 Data S4 contains the unmodified matrix, the constraint, our other analysis settings, a 2522 most parsimonious tree (1621 steps) and a tree that fulfills the constraint (1622 steps). 2523 Executing it in PAUP* repeats our constrained analysis. 2524 2525 2526 2527 ↓ Figure 10: Representation of some of the MPTs (length: 2182 steps) from Analysis R1, 2528 performed on our revised matrix – specifically the ones where Anthracosauria is 2529 rootward of Temnospondyli. The remaining MPTs from R1, where Anthracosauria is 2530 crownward of Temnospondyli, are shown in the next figure. The taxon sample was 2531 unchanged from RC07; no constraint was enforced. 2532 This tree, like those in the following figures, aims to represent all of the information 2533 contained in the MPTs, more than any consensus tree can. The uninterrupted part of the tree 2534 (black lines), polytomies excepted, is present in all MPTs represented in this figure as a 2535 backbone on which the branches connected only by colored underlays have varying positions; 2536 all nodes underlain in color are absent from the strict consensus. The cyan underlay in this 2537 figure connects the two positions of Ichthyostega that occur in different MPTs: one node more 2538 rootward, or one node more crownward, than Ventastega and Acanthostega; the green 2539 underlay connects the two positions of Capetus in the upper inset, the blue one the two of the 2540 (Neldasaurus + Isodectes) clade, the yellow one the two of Doleserpeton. 2541 In this and the following figures, branches with only two neighboring positions in 2542 different MPTs are indicated with blue lines: for example, the clade of all seymouriamorphs 2543 except Kotlassia is the sister-group of Kotlassia or of the tetrapod crown-group. Trichotomies 2544 that are resolved in all three possible ways in different MPTs (none in this figure) are shown 2545 in the usual way (without a blue line). 2546 Equally parsimonious alternatives that would be confusing if shown on the same tree 2547 are shown in the insets to the left, concerning in this case Temnospondyli and Caerorhachis, 2548 which may or may not (with equal parsimony) be a temnospondyl.

60 Eusthenopteron Panderichthys Ichthyostega Ventastega Acanthostega Ossinodus Whatcheeria Whatcheeriidae Pederpes Tulerpeton Crassigyrinus

origin of digits Colosteus Greererpeton Colosteidae Baphetoidea Eucritta Baphetes – see below for alternative position – Megalocephalus Caerorhachis Eoherpeton Proterogyrinus Anthracosauria Archeria Embolomeri Pholiderpeton scutigerum Pholiderpeton attheyi Anthracosaurus Silvanerpeton Bruktererpeton Gephyrostegus Gephyrostegidae Neldasaurus Isodectes Dvinosauria Trimerorhachis Balanerpeton Temnospondyli Dendrerpetidae Capetus – see below for Eryops Edops alternative resolutions – Chenoprosopus Edopoidea Cochleosaurus Ecolsonia Acheloma Trematopidae Phonerpeton Broiliellus brevis Dissorophoidea Micromelerpeton (YW00) Apateon Dissorophoidea (S13) Leptorophus Branchiosauridae Schoenfelderpeton Eoscopus Platyrhinops Amphibamidae Amphibamus Doleserpeton Solenodonsaurus Kotlassia Seymouria Discosauriscus Ariekanerpeton Seymouriamorpha Utegenia Temnospondyli Leptoropha Microphon Eryops Limnoscelis Chenoprosopus Tseajaia Diadectomorpha Cochleosaurus “edopoids” Diadectes Edops Orobates Capetus Captorhinus Balanerpeton Paleothyris Sauropsida Dendrerpetidae Petrolacosaurus Trimerorhachis Westlothiana Neldasaurus Dvinosauria tetrapod Microbrachis Isodectes Hyloplesion “microbrachomorphs” 1 crown- Odonterpeton Acheloma Trematopidae Phonerpeton group Saxonerpeton

(YW00) Dissorophoidea Ecolsonia Amphibia Hapsidopareion Broiliellus brevis Rhynchonkos Micromelerpeton Cardiocephalus oidea (S13) Dissoroph- Gymnarthridae Branchiosauridae Euryodus Eoscopus Micraroter Ostodolepididae Platyrhinops “microsaurs” 1 Pelodosotis Amphibamus Tuditanus Tuditanidae Doleserpeton Asaphestera Pantylus Stegotretus Pantylidae Temnospondyli Scincosaurus Keraterpeton Caerorhachis Diceratosaurus Neldasaurus Batrachiderpeton Diplocaulidae Isodectes Dvinosauria Diplocaulus Trimerorhachis “microsaur” 2 Diploceraspis Balanerpeton Holo- Batropetes “microbrachomorph” 2 Dendrerpetidae spondyli Brachydectes Capetus Lysorophia Eryops adelospondyls Acherontiscus Edops Adelospondylus Chenoprosopus Edopoidea Adelogyrinus Adelogyrinidae Cochleosaurus Dolichopareias Ecolsonia Ptyonius Acheloma Trematopidae Sauropleura Urocordylidae Phonerpeton Urocordylus Micromelerpeton Lethiscus Dissoroph- Apateon Oestocephalus Aïstopoda Branchio- oidea (YW00) Leptorophus Phlegethontia sauridae Schoenfelderpeton Eocaecilia Gymnophionomorpha Dissoroph- Broiliellus brevis Albanerpetidae oidea (S13) Lissamphibia Platyrhinops Karaurus Caudata Eoscopus Valdotriton Amphibamidae Batrachia Amphibamus 61 Triadobatrachus Doleserpeton Notobatrachus Salientia Vieraella Eusthenopteron Panderichthys Ichthyostega Ventastega Acanthostega Ossinodus Whatcheeria Whatcheeriidae Pederpes Tulerpeton Crassigyrinus origin of digits Colosteus Greererpeton Colosteidae Eucritta Baphetes Megalocephalus Baphetidae Edops Chenoprosopus “edopoids” Cochleosaurus Temnospondyli Eryops Capetus Trimerorhachis Neldasaurus Dvinosauria Dissorophoidea Isodectes (YW00) Dendrerpetidae Balanerpeton Acheloma Trematopidae Phonerpeton Ecolsonia Broiliellus brevis Dissorophoidea Eoscopus (content) Doleserpeton Amphibamus Amphibamidae Dissorophoidea (S13) Platyrhinops Micromelerpeton Apateon Leptorophus Branchiosauridae Schoenfelderpeton Caerorhachis Eoherpeton Archeria Anthracosauria Proterogyrinus Pholiderpeton scutigerum Embolomeri Pholiderpeton attheyi Anthracosaurus Silvanerpeton Bruktererpeton Gephyrostegus Gephyrostegidae Solenodonsaurus Kotlassia Seymouria Discosauriscus Ariekanerpeton Seymouriamorpha Utegenia Leptoropha Microphon Limnoscelis Tseajaia Diadectes Diadectomorpha Orobates Captorhinus Paleothyris Sauropsida Petrolacosaurus Westlothiana tetrapod crown-group Microbrachis Hyloplesion “microbrachomorphs” 1 Odonterpeton Saxonerpeton Hapsidopareion Amphibia Rhynchonkos Cardiocephalus Gymnarthridae Euryodus Micraroter Ostodolepididae “microsaurs” 1 Pelodosotis Tuditanus Tuditanidae Asaphestera Pantylus Stegotretus Pantylidae Scincosaurus Keraterpeton Diceratosaurus Batrachiderpeton Diplocaulidae Diplocaulus “microsaur” 2 Diploceraspis Holospondyli Batropetes “microbrachomorph” 2 Brachydectes Lysorophia adelo- Acherontiscus Adelospondylus spondyls Adelogyrinus Adelogyrinidae Dolichopareias Ptyonius Sauropleura Urocordylidae Urocordylus Lethiscus Oestocephalus Aïstopoda Phlegethontia Eocaecilia Gymnophionomorpha Albanerpetidae Lissamphibia Karaurus Caudata Valdotriton Batrachia 62 Triadobatrachus Notobatrachus Salientia Vieraella 63

2549 ↑ Figure 11: Representation of those MPTs from Analysis R1 where Anthracosauria lies 2550 crownward of Temnospondyli. See legend of Fig. 10 for more information. Note the 2551 additional position of Ichthyostega (immediately crownward of Ventastega and rootward of 2552 Acanthostega) and the fixed position of Caerorhachis (outside of Temnospondyli, though 2553 close to it). Dark blue underlay: Platyrhinops (3 positions); yellow: Kotlassia (3 positions); 2554 red: (Leptoropha + Microphon) (3 positions). 2555 2556 Analyses of our revised matrix 2557 2558 Note that the tree lengths we report throughout are those given by PAUP* (distinguishing 2559 polymorphism from partial uncertainty). Mesquite consistently reports one fewer step for 2560 trees from Analyses R1–R3 (original taxon sample; see Table 1) and one or two fewer steps 2561 for trees from Analyses R4–R6 (expanded taxon sample); apparently, the programs handle the 2562 stepmatrices differently. (As mentioned, PAUP* and Mesquite report the same lengths for the 2563 MPTs of Analyses O1 and O2.) 2564 2565 Analysis R1 2566 2567 The unconstrained analysis of our presumably improved matrix without added taxa yielded 2568 1120 MPTs with a length of 2182 steps (a drastic increase over the 1621 steps required by the 2569 unmodified matrix of RC07), a ci of 0.2181 (likewise revealing increased character conflict), 2570 a hi of 0.8327, a ri of 0.62118, and a rc of 0.1355. 2571 Figures 10 and 11 presents the similarities and differences between the MPTs, based 2572 on inspection of the strict consensus and the first, the 25th, the 75th, the 125th, the last and 2573 every 50th MPT (1, 25, 50, 75, 100, 125, 150, 200 … 1000, 1050, 1100, 1120) in Mesquite. 2574 They show that, in all MPTs, Panderichthys is the most rootward member of the ingroup as in 2575 RC07. More crownwards, however, the positions of Ichthyostega, Ventastega and 2576 Acanthostega are not fully resolved: Ventastega can be the sister-group of Acanthostega or 2577 one node more rootward; Ichthyostega can be more crownward than both, more rootward than 2578 both, or (Fig. 11) between the two when they are not sister-groups. This partial departure from 2579 more traditional ideas (e.g. Coates, 1996; RC07) appears to be mostly or entirely due to new 2580 information on Ichthyostega; the rootward position has been considered a strong possibility 2581 for several years (see Discussion: Phylogenetic relationships: Devonian taxa and 2582 Whatcheeriidae). Interestingly, a Ventastega-Acanthostega clade is only recovered when 2583 Ichthyostega lies crownward of it. 2584 The next more crownward branch is the Mississippian Whatcheeriidae (resolved as in 2585 RC07), followed crownward by the Devonian Tulerpeton. Contrary to the findings of Clack & 2586 Klembara (2009) and Ruta (2009), these two taxa never fall out as sister-groups. Next more 2587 crownward is Crassigyrinus, followed by Colosteidae (which was instead rootward of 2588 Whatcheeriidae in RC07). 2589 Crownward of these, the MPTs share a consistent backbone, which is a Hennigian 2590 comb of – from rootward to crownward – Baphetidae, Anthracosauria, Silvanerpeton, 2591 Gephyrostegus, Solenodonsaurus, Seymouriamorpha, and then the crown-group consisting of 2592 Amphibia, Diadectomorpha and Sauropsida (Fig. 10, 11). Parts of this arrangement 2593 contradicts the findings of RC07 (Fig. 1); the position of Solenodonsaurus is altogether novel. 2594 In different MPTs, Temnospondyli is either rootward of Anthracosauria (one node 2595 crownward of Baphetidae) as in RC07, or crownward of Anthracosauria (one node rootward 2596 of Solenodonsaurus). These two positions are part of two classes of topologies that have 2597 limited overlap other than the mentioned backbone and the almost complete resolution of the 2598 tetrapod crown-group.

63 64

2599 When Temnospondyli is rootward of Anthracosauria (Fig. 11), Eucritta is one node 2600 rootward of Baphetidae; Edops is the sister-group of all other temnospondyls, which form a 2601 Hennigian comb of Cochleosauridae, Eryops, Capetus, Dvinosauria, Dendrerpetidae and 2602 Dissorophoidea, where Balanerpeton can be the sister-group of either of the last two. 2603 Caerorhachis is one node rootward of the anthracosaurs (RC07); within the latter, 2604 Pholiderpeton scutigerum is the sister-group of either (Proterogyrinus + Archeria) or (Ph. 2605 attheyi + Anthracosaurus), both unlike in RC07. Bruktererpeton is either the sister-group of 2606 Gephyrostegus (e.g. Klembara et al., 2014) or one node more rootward (never crownward as 2607 in RC07 or Witzmann & Schoch, 2017), both lying rootward of Solenodonsaurus and 2608 crownward of Silvanerpeton; the traditional seymouriamorphs show a remarkable diversity of 2609 mono- and paraphyletic arrangements, though never the one found by RC07. 2610 When Temnospondyli is crownward of Anthracosauria (Fig. 10), Eucritta is a non- 2611 baphetid baphetoid (RC07; Ruta, 2009; Milner, Milner & Walsh, 2009; Witzmann & Schoch, 2612 2017). Caerorhachis is one node rootward of the anthracosaurs in some MPTs (Fig. 10: main 2613 tree and upper inset), in which case Dissorophoidea forms the sister-group to all other 2614 temnospondyls (among which Dvinosauria is highly nested), or to all except Dvinosauria, or 2615 to all except (Isodectes + Neldasaurus), in which latter case Trimerorhachis is the sister- 2616 group of a highly nested (Balanerpeton + Dendrerpetidae) clade. In the other MPTs (Fig. 10: 2617 lower inset), Caerorhachis is the sister-group of all other temnospondyls (Pawley, 2006; also 2618 suggested by Godfrey, Fiorillo & Carroll, 1987), among which Dvinosauria is sister to the 2619 remainder, followed by Dissorophoidea. Edops is far from the temnospondyl root in both 2620 cases. Anthracosauria is resolved as in RC07; Bruktererpeton and Gephyrostegus are sister- 2621 groups and lie one node rootward of Temnospondyli; the traditional seymouriamorphs form a 2622 monophyletic Hennigian comb, except that Kotlassia is either one node rootward of 2623 Seymouriamorpha or a member of it (the sister-group to the rest) – a subset of the resolutions 2624 in the other of topologies. 2625 In both cases (Fig. 10, 11), the dissorophoid Ecolsonia can emerge as a trematopid 2626 (Ruta, 2009; Maddin et al., 2013b; Holmes, Berman & Anderson, 2013; Dilkes, 2015a) or one 2627 node closer to all other dissorophoids (RC07). 2628 All MPTs support the LH. Lissamphibia is highly nested among the “lepospondyls”; 2629 within Temnospondyli, Amphibamidae is monophyletic and highly nested. 2630 The tetrapod crown-group consists of Amphibia (the lissamphibian total group, here 2631 including all “lepospondyls”) and the sister-groups Diadectomorpha and Sauropsida. 2632 Sauropsida is resolved as in RC07; Diadectomorpha is resolved as (Limnoscelis (Tseajaia 2633 (Orobates, Diadectes))) as in Reisz (2007), Kissel (2010) and Berman (2013) and further 2634 supported by Berman, Reisz & Scott (2010). 2635 Westlothiana is the most rootward amphibian, unchanged from RC07, even though we 2636 have changed many of its scores. Like in RC07, it is followed crownward by two “microsaur” 2637 clades, which comprise all “microsaurs” in the taxon sample except Batropetes; the 2638 composition and especially the topologies of these clades are quite different from those found 2639 by RC07, however. The larger and more rootward clade has a basal split into (Microbrachis + 2640 Hyloplesion) on one side and (Odonterpeton (Saxonerpeton (Hapsidopareion 2641 (Gymnarthridae, Ostodolepididae)))) on the other, where Rhynchonkos is the sister-group of 2642 Gymnarthridae or (Gymnarthridae + Ostodolepididae); the smaller and more crownward one 2643 is composed of Pantylidae (as in RC07) and Tuditanidae (Tuditanus + Asaphestera). 2644 Among the “microsaurs”, neither Tuditanomorpha nor Microbrachomorpha of the 2645 classification by CG78 are thus found as monophyletic, and the name Recumbirostra 2646 Anderson, 2007b, cannot be applied (see Discussion: Phylogenetic relationships: The 2647 interrelationships of the “microsaurs”). Still, the “microbrachomorphs” other than the 2648 tentatively (by CG87) referred Batropetes form a paraphyletic series: Odonterpeton is only

64 65

2649 one internode away from (Hyloplesion + Microbrachis), and three extra steps in Mesquite 2650 allow these two clades to be sister-groups. 2651 Next more crownward lie the sister-groups Scincosaurus and Diplocaulidae. Their 2652 relationship is reminiscent of Milner & Ruta (2009) or Ruta, Coates & Quicke (2003). 2653 Diplocaulidae is resolved as in RC07 or Germain (2010), except that Keraterpeton and 2654 Diceratosaurus are sister-groups. Five extra steps are needed in Mesquite to make 2655 (Scincosaurus + Diplocaulidae) the sister-group of (adelospondyls (Urocordylidae, 2656 Aïstopoda)); one more is required to make the latter clade the sister-group of Diplocaulidae 2657 alone as in RC07. 2658 The mentioned brachystelechid “microsaur” Batropetes and the lysorophian 2659 Brachydectes lie successively closer to the modern amphibians, as in Vallin & Laurin (2004); 2660 three extra steps are needed in Mesquite to render them each other’s sister-group, four steps 2661 are required to move Batropetes closer to Lissamphibia than Brachydectes. However, unlike 2662 in Vallin & Laurin (2004), the sister-group of Lissamphibia is not Brachydectes, but a clade 2663 that contains, one could say, all the strangest “lepospondyls”: the adelospondyls form the 2664 sister-group to Urocordylidae + Aïstopoda. Unlike in RC07, Adelospondylus is resolved as the 2665 sister-group to the other adelogyrinids and Lethiscus as the sister-group of the other aïstopods. 2666 To move the adelospondyls out of the “lepospondyls” and next to the colosteids, as in RC07 2667 and Witzmann & Schoch (2017), requires a single extra step in Mesquite. To have 2668 Urocordylidae + Aïstopoda follow suit (reaching a topology more similar to those of Pardo et 2669 al., 2017, and Witzmann & Schoch, 2017) requires, however, a total of ten extra steps. 2670 Lissamphibia is fully resolved as (Eocaecilia (Albanerpetidae (Caudata, Salientia))), 2671 unlike in RC07 or Vallin & Laurin (2004) but like in some other recent morphological works 2672 and, excluding the extinct Albanerpetidae, all recent molecular studies (Pyron, 2014: 2673 supplementary file amph_shl.tre; Irisarri et al, 2017; and references therein). 2674 2675 Analysis R2 2676 2677 Constraining the analysis of the original taxon sample against the lepospondyl hypothesis 2678 yielded 64 MPTs with a length of 2191 steps – nine more than in the unconstrained Analysis 2679 R1 – and a ci of 0.2173, a hi of 0.8334, a ri of 0.6191, and a rc of 0.1345. Figure 12 presents 2680 the similarities and differences between the MPTs, based on inspection of all of them in 2681 Mesquite. All MPTs have a bundle of highly unusual features. 2682 Specifically, when the salientians move closer to Doleserpeton than to Brachydectes, 2683 they drag not merely the other lissamphibians along, but also the aïstopods, urocordylids and 2684 adelospondyls; and this assemblage nests not within the amphibamids or the dissorophoids 2685 more generally, but within the dvinosaurs. The modern amphibians form the sister-group to 2686 the aïstopod Phlegethontia; all together are joined on the outside by Oestocephalus, then 2687 Lethiscus, then Urocordylidae (where Ptyonius is resolved as the sister-group to the rest), then 2688 the adelospondyls, and then the dvinosaurian temnospondyl Trimerorhachis, followed by 2689 Isodectes and then Neldasaurus. The clade that contains all non-dvinosaurian temnospondyls 2690 is still recovered as in Analysis R1, but is almost fully resolvedas in a subset of the trees from 2691 Analysis R1, with highly nested edopoids. Temnospondyli lies crownward of 2692 2693 ↓ Figure 12: Representation of all MPTs (length: 2191 steps) from Analysis R2, 2694 performed on our revised matrix. The taxon sample was unchanged from RC07. A 2695 constraint forced the three salientians (Triadobatrachus, Notobatrachus, Vieraella) to be 2696 closer to the dissorophoid temnospondyl Doleserpeton than to the lysorophian “lepospondyl” 2697 Brachydectes; this allowed both the TH and the PH. 2698 Cyan underlay as in Fig. 10 and 11.

65 Eusthenopteron Panderichthys Ichthyostega Ventastega Acanthostega Ossinodus Whatcheeriidae Whatcheeria Pederpes Tulerpeton Crassigyrinus origin of digits Colosteus Colosteidae Greererpeton Eucritta Baphetes Baphetoidea Megalocephalus Caerorhachis Eoherpeton Proterogyrinus Anthracosauria Archeria Embolomeri Pholiderpeton scutigerum Pholiderpeton attheyi Anthracosaurus Silvanerpeton Bruktererpeton Gephyrostegus Gephyrostegidae Balanerpeton Dendrerpetidae Capetus Eryops Edops Chenoprosopus Edopoidea Cochleosaurus Acheloma Phonerpeton Trematopidae Ecolsonia Dissorophoidea Broiliellus brevis (YW00) Eoscopus Doleserpeton Amphibamidae Amphibia Dissorophoidea (S13) Amphibamus Platyrhinops Micromelerpeton Apateon Leptorophus Branchiosauridae Schoenfelderpeton Neldasaurus Isodectes “dvinosaurs” Trimerorhachis Acherontiscus Adelospondylus adelospondyls Adelogyrinus Adelogyrinidae Dolichopareias Ptyonius Sauropleura Urocordylidae tetrapod crown-group Urocordylus Lethiscus Oestocephalus “aïstopods” Phlegethontia Albanerpetidae Eocaecilia Gymnophionomorpha modern amphibians Karaurus Caudata Lissamphibia Valdotriton “temnospondyls” Batrachia Triadobatrachus Notobatrachus Salientia Vieraella Solenodonsaurus Kotlassia Seymouria Discosauriscus Ariekanerpeton Utegenia Seymouriamorpha Leptoropha Microphon Limnoscelis Tseajaia Diadectes Diadectomorpha Orobates Captorhinus Paleothyris Sauropsida Petrolacosaurus Westlothiana Microbrachis Hyloplesion “microbrachomorphs” 1 Odonterpeton Saxonerpeton Hapsidopareion Rhynchonkos Cardiocephalus Euryodus Gymnarthridae Micraroter Pelodosotis Ostodolepididae “microsaurs” Tuditanus Asaphestera Tuditanidae Pantylus Pantylidae Stegotretus Batropetes “microbrachomorph” 2 Brachydectes Lysorophia Scincosaurus Keraterpeton Diceratosaurus 66 Batrachiderpeton Diplocaulidae Diplocaulus Diploceraspis 67

2699 Gephyrostegidae, Silvanerpeton, Anthracosauria and (most rootward) Caerorhachis. Eucritta 2700 is the sister-group of Baphetidae. In some trees, the (Microbrachis + Hyloplesion) clade falls 2701 out as the sister-group to all lepospondyls except Westlothiana. 2702 Other than this, the topology is consistent with trees from Analysis R1 (Fig. 10). The 2703 clade formed by Diplocaulidae and Scincosaurus does not follow the other holospondyls into 2704 Temnospondyli, but stays behind as the sister-group of (Batropetes + Brachydectes). 2705 Ichthyostega and Ecolsonia have the same positions as in Analysis R1; Kotlassia is always 2706 rootward of Seymouriamorpha; Lissamphibia and Albanerpetidae are sister-groups in all 2707 MPTs. 2708 Statistical tests find the difference between a tree from Analysis R2 and a tree from 2709 Analysis R1 insignificant at a p level of 0.05: p is 0.2248 under the Kishino-Hasegawa test, 2710 0.1854 under the Templeton test and 0.1332 under the winning-sites test (Table 4). 2711 2712 Analysis R3 2713 2714 An analysis of the original taxon sample that was constrained to be compatible with the 2715 polyphyly hypothesis yielded 736 MPTs with a length of 2194 steps – only three steps more 2716 than those from Analysis R2, 12 more than those from Analysis R1 – and a ci of 0.2170, a hi 2717 of 0.8336, a ri of 0.6184 and a rc of 0.1342. 2718 Judging from the first, the last and every 25th MPT, the different MPTs (Fig. 13) are 2719 very similar to those of R1. Salientia forms the sister-group to Doleserpeton and is nested 2720 within the amphibamid dissorophoid temnospondyls, not within the dvinosaurian 2721 temnospondyls as it is in R2. All other modern amphibians have the same positions as in R1. 2722 This version of the PH, where Salientia alone belongs to the temnospondyls while 2723 Caudata and Gymnophionomorpha are lepospondyls, has not been proposed since Carroll & 2724 Holmes (1980). To move Caudata into Temnospondyli (as the sister-group of Salientia) 2725 requires two extra steps in Mesquite; to move Caudata + Albanerpetidae into Temnospondyli 2726 costs one more step and comes at the cost of nesting this clade within Salientia (next to 2727 Notobatrachus + Vieraella). 2728 The difference between a tree from Analysis R3 and a tree from Analysis R1 is 2729 potentially significant at the level of p = 0.05 according to the statistical tests: p = 0.0352 2730 (Kishino-Hasegawa), 0.0362 (Templeton), 0.0175 (winning sites). The difference between 2731 Analyses R3 and R2 is far from significance: p = 0.4074 (Kishino-Hasegawa), 0.4255 2732 (Templeton), 0.5000 (winning sites). 2733

2734 2735 2736 Figure 13: Representation of all MPTs (length: 2194 steps) from Analysis R3, performed 2737 on our revised matrix. Only the parts different from the results of R1 (Fig. 10, 11) are 2738 shown. Outside the shown clades, the entire range of resolutions of R1 also occurs in R3. 2739 lies in the place where Lissamphibia is found in R1. The taxon sample was 2740 unchanged from RC07. A constraint forced the dissorophoid temnospondyl Doleserpeton to 2741 be closer to the three salientians (Triadobatrachus, Notobatrachus, Vieraella) than the 2742 lysorophian “lepospondyl” Brachydectes, and additionally forced the gymnophionomorph 2743 Eocaecilia to be closer to Brachydectes than to Doleserpeton; this allowed only the PH.

67 Eusthenopteron Panderichthys *Elginerpeton *Metaxygnathus Ventastega Acanthostega *Ymeria

origin of digits *Perittodus Ichthyostega Whatcheeria Whatcheeriidae Pederpes Ossinodus *Densignathus Tulerpeton Crassigyrinus Eucritta *St. Louis tetrapod *Pholidogaster Colosteidae *Aytonerpeton *Deltaherpeton Colosteus Greererpeton Baphetes Megalocephalus Lethiscus Baphetidae *Diploradus *Coloraderpeton *Sigournea Aïstopoda Phlegethontia *Doragnathus *Pseudophlegethontia *Spathicephalus Oestocephalus Edops Chenoprosopus “edopoids” *Pseudophlegethontia Cochleosaurus Phlegethontia Eryops Aïstopoda Lethiscus *Nigerpeton *Coloraderpeton *Saharastega Oestocephalus *Sclerocephalus Eutemnospondyli Eryopi- formes *Cheliderpeton *Lydekkerina Stereo- Lissamphibia *Glanochthon spondylo- *Archegosaurus Notobatrachus morpha Salientia Vieraella *Australerpeton *Liaobatrachus *Konzhukovia Triadobatrachus *Platyoposaurus *Chelotriton Capetus Karaurus Batrachia “caudates” *Beiyanerpeton *Erpetosaurus Valdotriton Trimerorhachis Dissorophoidea (YW00) Dvinosauria *Pangerpeton Neldasaurus Isodectes Albanerpetidae Balanerpeton Gymnophionomorpha Eocaecilia Dendrerpetidae *Quasicaecilia *Palatinerpeton Brachystelechidae “m.” 4 *Carrolla *Iberospondylus “microbrachomorphs” 4 Batropetes *Mordex Lysorophia Brachydectes Ecolsonia Trematopidae Rhynchonkos Acheloma Phonerpeton Hapsidopareiidae *Llistrofus Hapsidopareion *Micropholis “microbrachomorph” 3 Odonterpeton Dissorophoidea Micromelerpeton *Sparodus (content) Apateon “branchio- Saxonerpeton Leptorophus saurids” 1 *Trihecaton Schoenfelderpeton Ostodolepididae Micraroter Dissorophoidea (S13) *Acanthostomatops Pelodosotis *Branchiosaurus Cardiocephalus *Tungussogyrinus Gymnarthridae Euryodus Broiliellus brevis *Goreville microsaur “microsaurs” 3 Tuditanidae *Crinodon Eoscopus Tuditanus Platyrhinops “amphi- Asaphestera Amphibamus Temnospondyli bamids” 2 Pantylidae Pantylus Doleserpeton Stegotretus *Gerobatrachus Oestocephalus *Parrsboro jaw Phlegethontia – see above for Caerorhachis Aïstopoda Lethiscus *Pseudophlegethontia alternatives – Eoherpeton *Coloraderpeton Proterogyrinus Urocordylus Archeria Urocordylidae Ptyonius Embolomeri Pholiderpeton scutigerum Sauropleura Pholiderpeton attheyi Adelogyrinus Anthracosaurus *NSM 994 GF 1.1 Adelogyrinidae Dolichopareias Anthracosauria Adelospondylus *Palaeoherpeton Acherontiscus adelo. *Neopteroplax “microbrachomorph” 2 *Utaherpeton Holo- Silvanerpeton spondyli Diploceraspis “m.” 2 *Casineria “gephyro- Diplocaulus Bruktererpeton stegids” Diplocaulidae Batrachiderpeton Gephyrostegus Keraterpeton *Chroniosaurus Chronio- Diceratosaurus *Bystrowiella suchia Scincosaurus Solenodonsaurus Microbrachis Amphibia Leptoropha “microbrachomorphs” 1 Hyloplesion “microsaurs” 1 Microphon Seymouria Westlothiana Seymouria- Kotlassia Synapsida *Caseasauria *Karpinskiosaurus morpha *Archaeovenator Discosauriscus Limnoscelis Utegenia Diadecto- Diadectes Ariekanerpeton Orobates tetrapod morpha Tseajaia Amniota crown- Paleothyris 68 group Sauropsida Petrolacosaurus Captorhinus 69

2744 ↑ Figure 14: Representation of all MPTs (length: 3011 steps) from Analysis R4 (revised 2745 matrix, expanded taxon sample, no constraint). The insets at the left show the two 2746 remaining parsimonious alternatives to the three aïstopod topologies shown in the main tree. 2747 In this and the following figures, the names Stereospondylomorpha and Limnarchia 2748 are placed according to prevailing usage, not according to the definitions by Yates & Warren 2749 (2000) or Schoch (2013). According to the former, Stereospondylomorpha would in this 2750 analysis probably exclude *Sclerocephalus and *Cheliderpeton, possibly also *Glanochthon; 2751 all three were included in the different topology of Yates & Warren (2000: fig. 1). Limnarchia 2752 would be a synonym of Stereospondylomorpha as used here, but would exclude the originally 2753 included dvinosaurs. Stereospondylomorpha as redefined by Schoch (2013) would have the 2754 contents shown here, but this does not apply to some of the following figures. Similarly, 2755 Dvinosauria would under its original definition (Yates & Warren, 2000) be a synonym of 2756 Dissorophoidea as defined in the same work; as redefined by Schoch (2013), it would have 2757 the contents shown here, but not quite in Fig. 16. 2758 The cyan underlay connects the four positions of Ossinodus (a whatcheeriid sister to 2759 the rest, one node more crownward than Whatcheeriidae, sister to *Densignathus, or one node 2760 more crownward than it). The two positions of the “Parrsboro jaw” (see text) are connected 2761 by the red underlay. The green underlay connects the two positions of (*Nigerpeton + 2762 *Saharastega), the dark blue one the four of *Casineria, the brown one the two of 2763 *Trihecaton. 2764 2765 Analysis R4 2766 2767 From here on, the OTUs we have added are marked with an asterisk; taxa absent even from 2768 the expanded taxon sample are marked with two asterisks. 2769 An unconstrained analysis of the increased taxon sample found 401 MPTs with a 2770 length of 3011 steps, a ci of 0.1860, a hi of 0.8788, a ri of 0.6186, and a rc of 0.1150. 2771 Figure 14 presents the similarities and differences between the MPTs, based on the 2772 strict and Adams consensus trees and on the first, the last and every 10th tree. 2773 Despite containing several OTUs known only from isolated lower jaws, the Devonian 2774 area of the tree is remarkably well resolved (Fig. 14): *Elginerpeton, *Metaxygnathus, 2775 (Acanthostega + Ventastega), *Ymeria, *Perittodus, Ichthyostega, Whatcheeriidae, 2776 *Densignathus, Tulerpeton and Crassigyrinus are successively more crownward. This pattern 2777 is partially obscured by Ossinodus, which has four positions: as a whatcheeriid (the sister- 2778 group to the rest as in R1), as the sister-group of *Densignathus, or one node more 2779 crownward or more rootward than the latter. 2780 Crownward of Crassigyrinus follows a dichotomy between an unusually enlarged 2781 Temnospondyli and its sister-group, which contains the tetrapod crown-group (all MPTs 2782 support the LH). 2783 Within Temnospondyli, the sister-group of all others is Eucritta, followed by a novel 2784 and fully resolved colosteid-baphetid clade. The *“St. Louis tetrapod” (MB.Am.1441; Clack 2785 et al., 2012b) is the sister-group to all other colosteids, among which *Pholidogaster is the 2786 sister-group to (*Aytonerpeton (*Deltaherpeton (Colosteus, Greererpeton))). Within 2787 Baphetidae, Baphetes, Megalocephalus, *Diploradus and *Sigournea are successively closer 2788 to *Doragnathus and *Spathicephalus. 2789 The traditional temnospondyls form a clade which is resolved as an unusual Hennigian 2790 comb where Edops, Cochleosauridae, Eryopiformes, Capetus, Dvinosauria, (Balanerpeton + 2791 Dendrerpetidae) and *Iberospondylus are successively closer to Dissorophoidea. 2792 *Palatinerpeton has two positions as the sister-group of Dendrerpetidae or of 2793 (*Iberospondylus + Dissorophoidea). *Nigerpeton and *Saharastega form a novel clade with

69 70

2794 three novel positions: as the sister-group of Eryops, of Stereospondylomorpha or of all 2795 traditional temnospondyls except Edops and Cochleosauridae. 2796 Dissorophoidea is fully resolved. Trematopidae, including *Mordex and Ecolsonia, is 2797 the sister-group of the remainder, in which *Micropholis clusters with the “branchiosaurs” of 2798 the original taxon sample, while (*Branchiosaurus + *Tungussogyrinus) is the sister-group of 2799 *Acanthostomatops. The latter three together form the sister-group of (Broiliellus + 2800 Amphibamidae). 2801 The *Parrsboro jaw (Godfrey & Holmes, 1989; Sookias, Böhmer & Clack, 2014) is 2802 found in two very distinct positions: as the sister-group to the clade of all traditional 2803 temnospondyls, or next to Caerorhachis. 2804 Caerorhachis (and optionally the *Parrsboro jaw) is one node crownward of 2805 Temnospondyli. It is followed crownward by Anthracosauria, Silvanerpeton, Bruktererpeton, 2806 Gephyrostegus, Chroniosuchia (*Chroniosaurus, *Bystrowiella), Solenodonsaurus and 2807 Seymouriamorpha. Anthracosauria is fully resolved as in RC07, with the added taxa forming 2808 a clade (*NSM 994 GF 1.1 (*Palaeoherpeton, *Neopteroplax)) that nests with 2809 Anthracosaurus. *Casineria has four positions: one node rootward of Bruktererpeton, one 2810 node crownward of Gephyrostegus, between the two, or as the sister-group of Bruktererpeton. 2811 Just outside the tetrapod crown-group lies Seymouriamorpha, in which (Leptoropha + 2812 Microphon) and a (Seymouria (*Karpinskiosaurus, Kotlassia)) clade lie successively closer to 2813 Discosauriscidae. Within the crown, the amniote + diadectomorph clade is fully resolved; 2814 curiously, however, the added OTUs *Caseasauria and *Archaeovenator emerge as the sister- 2815 group to Limnoscelis, followed by the clade of the other diadectomorphs and then by 2816 Sauropsida – in other words, the diadectomorphs are found as amniotes, specifically as 2817 that lack the synapsid condition (Berman, 2013), but they do not form a clade 2818 (unlike in Berman, 2013). 2819 On the amphibian side of the crown, Westlothiana remains the sister-group to the 2820 remainder, which has a topology somewhat reminiscent of Vallin & Laurin (2004). Instead of 2821 having a “microsaur” grade at the base as in Analyses R1–R3, this clade shows a basal 2822 dichotomy: (Holospondyli (Microbrachis, Hyloplesion)) lies on one side, while the other 2823 branch groups the remaining “microsaurs” and Brachydectes (which is the only lysorophian 2824 even in the expanded taxon sample) with the fully resolved Lissamphibia. 2825 The basal dichotomy of Holospondyli is into a (Scincosaurus + Diplocaulidae) clade, 2826 which is fully resolved as in R1–R3, and a clade of (*Utaherpeton (adelospondyls 2827 (Urocordylidae, Aïstopoda))). Aïstopoda is poorly resolved. Moving the adelospondyls next 2828 to or into the colosteids seems not to be possible without requiring at least eight extra steps in 2829 Mesquite. 2830 On the other side of the amphibian branch, Pantylidae and Tuditanidae are sister- 2831 groups like in R1–R3; Tuditanidae is augmented by *Crinodon and the *Goreville microsaur. 2832 A (Gymnarthridae + Ostodolepididae) clade lies next to the remainder, in which 2833 Saxonerpeton, an unexpected (Odonterpeton + *Sparodus) clade, an expected 2834 (Hapsidopareion + *Llistrofus) clade, Rhynchonkos and finally a clade composed of 2835 Brachydectes and Brachystelechidae (composed of Batropetes + (*Carrolla + 2836 *Quasicaecilia); named after a synonym of Batropetes) are successively closer to 2837 Lissamphibia, unlike in R1. Within Lissamphibia, Albanerpetidae emerges as the sister-group 2838 of Batrachia. The closest relative of Salientia is the caudate *Chelotriton; together they are 2839 the sister-group to a clade formed by all other caudates, in which Karaurus is as highly nested 2840 as possible. 2841 *Trihecaton has two positions as the sister-group of (Holospondyli (Microbrachis, 2842 Hyloplesion)) or one node rootward of Saxonerpeton. 2843

70 Eusthenopteron Panderichthys *Elginerpeton *Metaxygnathus Ventastega Acanthostega *Ymeria

origin of digits *Perittodus Ichthyostega Whatcheeria Whatcheeriidae Pederpes Ossinodus *Densignathus Tulerpeton Crassigyrinus Eucritta Colosteidae as in Fig. 14 Baphetidae as in Fig. 14 Edops Chenoprosopus “edopoids” Cochleosaurus Eryops *Nigerpeton *Saharastega *Sclerocephalus

Eutemnospondyli Eryopi- *Cheliderpeton see also Fig. 16 formes *Lydekkerina Stereo- *Glanochthon spondylo- *Archegosaurus morpha *Australerpeton *Konzhukovia *Platyoposaurus Capetus *Erpetosaurus Trimerorhachis

Dissorophoidea Dvinosauria Neldasaurus Isodectes Balanerpeton Balanerpeton *Palatinerpeton Dendrerpetidae Dendrerpetidae *Palatinerpeton *Acanthostomatops *Iberospondylus *Mordex

(YW00) Ecolsonia Trematopidae tetrapod crown-group Acheloma Phonerpeton *Micropholis Micromelerpeton Apateon Eryopi- “branchio- Leptorophus saurids” 1 formes Schoenfelderpeton Eryops Dissorophoidea Broiliellus brevis *Sclerocephalus (content) Eoscopus *Nigerpeton Platyrhinops “amphi- *Saharastega Amphibamus bamids” 2 *Platyoposaurus *Gerobatrachus *Cheliderpeton Stereo- Triadobatrachus *Glanochthon spondylo- *Liaobatrachus Salientia *Archegosaurus Notobatrachus morpha Dissorophoidea (S13) *Australerpeton Vieraella Lissamphibia *Konzhukovia *Chelotriton *Lydekkerina *Pangerpeton Albanerpetidae Eocaecilia Gymnophio. Valdotriton Karaurus Procera “microsaurs” 2 *Beiyanerpeton Doleserpeton Brachystelechidae *Quasicaecilia Amphibia *Acanthostomatops *Carrolla “microbrachomorphs” 3 Batropetes *Branchiosaurus “branchio- *Tungussogyrinus saurids” 2 Lysorophia Brachydectes *Parrsboro jaw Hapsidopareiidae *Llistrofus Hapsidopareion Caerorhachis *Sparodus *Goreville microsaur Anthracosauria as in Fig. 14 “microbrachomorph” 2 Odonterpeton Silvanerpeton Pelodosotis *Casineria Ostodolepididae “gephyro- Micraroter Bruktererpeton stegids” Gephyrostegus Gymnarthridae Cardiocephalus Euryodus *Chroniosaurus Chronio- Rhynchonkos *Bystrowiella suchia Saxonerpeton Solenodonsaurus *Crinodon Leptoropha Tuditanidae Tuditanus Microphon Seymouria Asaphestera Seymouria- Kotlassia Pantylidae Pantylus morpha Stegotretus *Karpinskiosaurus Discosauriscus Holospondyli as in Fig. 14 Utegenia Ariekanerpeton “microbracho- Microbrachis Lepospondyli morphs” 1 Hyloplesion Amniota incl. Diadectomorpha “microsaurs” 1 *Trihecaton as in Fig. 14 Westlothiana 71 72

2844 ↑ Figure 15: Representation of some MPTs (length: 3021 steps) from Analysis R5 2845 (revised matrix, expanded taxon sample, constraint against the LH as in Analysis R2). 2846 The insets at the left show two equally parsimonious alternative to parts of the temnospondyl 2847 topology shown in the main tree. The remaining MPTs from R5 are represented in Fig. 16; the 2848 differences are again limited to eutemnospondyl phylogeny (Eutemnospondyli being the 2849 sister-group of Edops, as defined by Schoch, 2013). 2850 Cyan, red, green and dark blue underlays as in Fig. 14, though note a fourth position 2851 for (*Nigerpeton + *Saharastega) in the lower inset. Further underlay colors: magenta: 2852 *Palatinerpeton (3 positions); violet: *Tungussogyrinus (3); light brown: *Cheliderpeton (2); 2853 dark brown: (Eocaecilia + Albanerpetidae) (2). 2854 2855 Analysis R5 2856 2857 An analysis of the increased taxon sample with a constraint against the LH found 6778 MPTs 2858 which have 3021 steps – 10 more than the MPTs of Analysis R4 – as well as a ci of 0.1854, a 2859 hi of 0.8792, a ri of 0.6170, and a rc of 0.1144. 2860 As shown by comparison of the strict and Adams consensus trees and the first, the last 2861 and every 250th MPT (Fig. 15, 16), all of which support the TH, the constraint has not had a 2862 strong effect on the tree; most of the differences to the results of R4 consist of loss of 2863 resolution among the temnospondyls. This is in stark contrast to earlier versions of this matrix 2864 (Marjanović & Laurin, 2015, 2016) or to the differences between R1 and R2. 2865 The clade of *Nigerpeton and *Saharastega gains two new positions within 2866 Stereospondylomorpha (Fig. 15: lower inset; Fig. 16: middle inset); in one of them (Fig. 16), 2867 Dvinosauria joins it. These two clades can also form a clade or grade just crownward of 2868 Cochleosauridae, followed crownward by Eryops and then Stereospondylomorpha (Fig. 16: 2869 main tree, upper inset); or they can form a clade next to Stereospondylomorpha, which then, 2870 too, lies crownward of Eryops (Fig. 16: upper inset). The trematopids sometimes (Fig. 16) 2871 form a grade (with Ecolsonia at its crownward end as in RC07 and some MPTs of R1), 2872 *Tungussogyrinus, *Branchiosaurus and *Micropholis gain positions within the non- 2873 trematopid non-lissamphibian dissorophoid grade, *Acanthostomatops sometimes leaves it. 2874 Unlike in Analysis R2, which was performed under the same constraint, Lissamphibia is not 2875 nested among the dvinosaurs, and no “lepospondyls” are found among the temnospondyls; 2876 instead, either Doleserpeton or *Gerobatrachus, but never both together, is the sister-group of 2877 Lissamphibia. Lissamphibia is resolved with a Procera topology, where an (Albanerpetidae + 2878 Eocaecilia) clade is nested within a caudate grade or next to a caudate clade, which always 2879 excludes *Chelotriton, the sister-group to all other procerans. 2880 *Trihecaton has a single position as the sister-group of (Holospondyli (Microbrachis, 2881 Hyloplesion)). The other large lepospondyl clade is slightly rearranged from R4: the sister- 2882 group of the Brachydectes-brachystelechid clade is Hapsidopareiidae, followed by 2883 (Odonterpeton (*Goreville microsaur, *Sparodus)), then (Rhynchonkos (Gymnarthridae, 2884 Ostodolepididae)), and then Saxonerpeton followed by (Tuditanidae + Pantylidae) as in R4. 2885 The statistical tests find the difference between a tree from R5 and a tree from R4 2886 insignificant: p = 0.1831 (Kishino-Hasegawa), 0.2278 (Templeton), 0.0975 (winning sites). 2887 2888 Analysis R6 2889 2890 With a constraint for the PH, an analysis of the increased taxon sample found 1816 MPTs 2891 with 3026 steps – 5 more than those from Analysis R5, 15 more than those from Analysis R4. 2892 The MPTs have a ci of 0.1851, a hi of 0.8794, a ri of 0.6162 and a rc of 0.1140. 2893

72 73

2894 2895 2896 Figure 16: Eutemnospondyl phylogeny from those MPTs from Analysis R5 that are not 2897 represented in Fig. 15; see the legend of Fig. 15 for more information. 2898 2899 Inspection of the first, the last and every 50th MPT (we later examined every 10th MPT 2900 up to the 640th for the position of *Cheliderpeton) shows topologies mostly identical to those 2901 of R4, allowing us to greatly simplify Fig. 17. In addition to its positions in R4, the 2902 *Nigerpeton-*Saharastega clade can lie inside a rearranged Stereospondylomorpha (as in 2903 some MPTs of R5). Batrachia is nested as the sister-group to Doleserpeton, followed by 2904 *Gerobatrachus. Within Batrachia, *Chelotriton is the sister-group of Salientia. 2905 Albanerpetidae is highly nested in the clade of all remaining caudates, as the sister-group of 2906 Valdotriton. 2907 Lepospondyli is resolved much like in Analysis R1, with Eocaecilia as the sister- 2908 group of Aïstopoda; Brachydectes sometimes entersBrachystelechidae as the sister-group of 2909 Batropetes. Aïstopoda is better resolved than in R4 and R5 in that there is always a dichotomy 2910 between (Oestocephalus + Phlegethontia) and the remainder. *Trihecaton lies next to 2911 Gymnarthridae or next to Micraroter. 2912 Trees from R6 and R4 are indistinguishable at the level of p = 0.05: p = 0.1328 2913 (Kishino-Hasegawa), 0.0565 (Templeton), 0.0966 (winning sites). Unsurprisingly, trees from 2914 R6 and R5 are hardly distinguishable: p = 0.3515 (Kishino-Hasegawa), 0.3174 (Templeton), 2915 0.4538 (winning sites). 2916 2917 2918

73 Eusthenopteron Panderichthys *Elginerpeton *Metaxygnathus Ventastega Acanthostega *Ymeria

origin of digits *Perittodus Ichthyostega Whatcheeria Whatcheeriidae Pederpes Ossinodus *Densignathus Tulerpeton Crassigyrinus Eucritta Colosteidae as in Fig. 14 Baphetidae as in Fig. 14 Edops Chenoprosopus “edopoids” Cochleosaurus Eryops *Nigerpeton *Saharastega *Sclerocephalus Eutemnospondyli Eryopi- *Cheliderpeton formes *Lydekkerina Stereo- Eryopi- *Glanochthon spondylo- formes *Archegosaurus morpha Eryops *Australerpeton *Konzhukovia *Sclerocephalus *Platyoposaurus *Nigerpeton Capetus *Saharastega *Erpetosaurus *Platyoposaurus Trimerorhachis

*Cheliderpeton Dissorophoidea Dvinosauria Stereo- Neldasaurus *Glanochthon spondylo- Isodectes *Archegosaurus morpha Balanerpeton *Australerpeton Dendrerpetidae *Konzhukovia *Palatinerpeton *Lydekkerina *Iberospondylus *Mordex (YW00) Ecolsonia Trematopidae Acheloma tetrapod crown-group Phonerpeton *Micropholis Dissorophoidea Micromelerpeton (content) Apateon “branchio- Leptorophus saurids” 1 Schoenfelderpeton Dissorophoidea (S13) *Acanthostomatops *Branchiosaurus *Tungussogyrinus Broiliellus brevis Eoscopus Gymnophionomorpha Platyrhinops = Holospondyli “amphi- Amphibamus bamids” 2 Oestocephalus *Gerobatrachus Phlegethontia Doleserpeton Aïstopoda Lethiscus *Pangerpeton *Pseudophlegethontia Albanerpetidae *Coloraderpeton Valdotriton Eocaecilia Karaurus “caudates” Batrachia *Beiyanerpeton Urocordylidae as in Fig. 14 *Chelotriton Adelogyrinidae as in Fig. 14 Temnospondyli Triadobatrachus *Liaobatrachus Salientia Acherontiscus adelo. Notobatrachus “microbrachomorph” 3 *Utaherpeton Vieraella “m.” 2 *Parrsboro jaw Diplocaulidae as in Fig. 14 Caerorhachis Scincosaurus Anthracosauria as in Fig. 14 *Quasicaecilia Brachystelechidae *Carrolla Silvanerpeton Batropetes *Casineria “gephyro- Lysorophia Brachydectes “microbracho- Bruktererpeton morphs” 2 stegids” Microbrachis Gephyrostegus Hyloplesion *Chroniosaurus Chronio- Pelodosotis *Bystrowiella suchia Ostodolepididae Micraroter “microsaurs” 1 Solenodonsaurus *Trihecaton Leptoropha Cardiocephalus Microphon Gymnarthridae Seymouria Euryodus Seymouria- Kotlassia Rhynchonkos morpha *Sparodus *Karpinskiosaurus *Goreville microsaur Discosauriscus Utegenia “microbrachomorph” 1 Odonterpeton Lepospondyli Ariekanerpeton Hapsidopareiidae *Llistrofus Hapsidopareion Amniota incl. Diadectomorpha Saxonerpeton *Crinodon as in Fig. 14 Tuditanidae Tuditanus Asaphestera Pantylidae Pantylus Stegotretus 74 Westlothiana 75

2919 ↑ Figure 17: Representation of all MPTs (length: 3026 steps) from Analysis R6 (revised 2920 matrix, expanded taxon sample, constraint for the PH as in Analysis R3). 2921 Underlays as in Fig. 15. 2922 2923 Bootstrap analyses B1 and B2 2924 2925 Figures 18 and 19 present the bootstrap trees for the original and the expanded taxon samples, 2926 respectively (Analyses B1 and B2). They are fully resolved because clades with bootstrap 2927 values below 0.5 (50%) are included if they do not contradict the majority-rule consensus (see 2928 above). In Fig. 18 (Analysis B1), support is skewed towards peripheral nodes, while the 2929 “trunk” of the tree has bootstrap percentages well below 50. Still, together with many 2930 uncontroversial results, the position of Whatcheeriidae rootward of Colosteidae, 2931 Crassigyrinus and even Tulerpeton is supported (67%, 54% and 57%, respectively) as well as 2932 the membership of Ossinodus (52%), the position of Eucritta as a baphetoid (55%), 2933 Dissorophoidea sensu lato excluding Lissamphibia (84%), Ecolsonia as a trematopid (56%), 2934 Trematopidae as the sister-group to Dissorophoidea sensu stricto (55%), Amphibamidae 2935 excluding Branchiosauridae (60%), Micromelerpeton as the sister-group of Branchiosauridae 2936 (61%), Bruktererpeton and Gephyrostegus as sister-groups (53%), the monophyly of 2937 Diadectomorpha (59%) and Sauropsida (80%) as well as their sister-group relationship (68%), 2938 Microbrachis and Hyloplesion as sister-groups (67%), Lissamphibia including Albanerpetidae 2939 (65%), Batrachia + Albanerpetidae (53%), Batrachia excluding Albanerpetidae (77%), 2940 Caudata (74%) and the sister-group relationship of Scincosaurus and Diplocaulidae (56%). 2941 Further, Acanthostega as crownward of Ventastega (45%), Ichthyostega as crownward of 2942 both (47%), Balanerpeton + Dendrerpetidae (49%), Isodectes + Neldasaurus (47%), the 2943 adelospondyl clade (47%) and the sister-group relationship of Urocordylidae and Aïstopoda 2944 (43%) are each almost certainly better supported than any single alternative. In contrast, 2945 Kotlassia is found within Seymouriamorpha only in 28% of the replicates. 2946 Adding taxa (Analysis B2) slightly increases the bootstrap support of four nodes, but – 2947 unsurprisingly – generally depresses the support of almost the entire tree (Fig. 19). Of its 2948 potentially controversial branches, only the sister-group relationship of *Nigerpeton and 2949 *Saharastega (50%), that of Microbrachis and Hyloplesion (66%), that of Scincosaurus and 2950 Diplocaulidae (63%), the clade of modern amphibians (Albanerpetidae + Lissamphibia: 67%) 2951 and Batrachia (54%) are found by 50% or more of the bootstrap replicates; Lissamphibia is 2952 found in 44% of the replicates, Karaurus + *Beiyanerpeton in 46%, Chroniosuchia and 2953 Gephyrostegidae in 42% each, and the adelospondyl clade (40%) and Doleserpeton + 2954 *Gerobatrachus in 40% each. The addition of two synapsids (Synapsida: 56%) has made 2955 Limnoscelis a diadectomorph (24%) outside of Amniota (30%) and reduced the support for 2956 the monophyly of Sauropsida to 26%, although support for Amniota + Diadectomorpha is 2957 considerably higher at 44%. 2958 2959 2960 2961 2962 ↓ Figure 18: Bootstrap tree from Analysis B1 (revised matrix, original taxon sample, no 2963 constraint; compare Fig. 10). Clades with a bootstrap percentage below 50 are included if 2964 they are compatible with those above 50; percentages of 50 and above are in boldface. 2965 2966 ↓↓ Figure 19: Bootstrap tree from Analysis B2 (revised matrix, expanded taxon sample, 2967 no constraint; compare Fig. 14). See legend of Fig. 18 for more information. 2968

75 Eusthenopteron Panderichthys Ventastega Acanthostega 100 Ichthyostega 45 Ossinodus Whatcheeria 47 Whatcheeriidae 52 origin of digits 72 Pederpes Tulerpeton 80 Crassigyrinus Colosteus Colosteidae 57 95 Greererpeton Eucritta 54 Baphetes Baphetoidea 55 82 Megalocephalus Caerorhachis Trimerorhachis 67 14 35 Isodectes Dvinosauria Temnospondyli 47 Neldasaurus Eryops 40 19 Edops 27 Chenoprosopus Edopoidea Cochleosaurus 33 67 18 Capetus Balanerpeton Dendrerpetidae 15 49 30 Ecolsonia Acheloma Trematopidae Dissorophoidea (YW00) 53 Phonerpeton 84 90 Broiliellus brevis Dissorophoidea (content) 55 Platyrhinops Eoscopus Amphibamidae 35 Dissorophoidea (S13) 60 39 Amphibamus Doleserpeton 39 44 Micromelerpeton 61 Apateon 71 Leptorophus Branchiosauridae 76 Schoenfelderpeton Silvanerpeton Eoherpeton Anthracosauria 10 Pholiderpeton attheyi 54 52 57 Anthracosaurus Embolomeri Pholiderpeton scutigerum 23 Proterogyrinus 33 Archeria 12 Bruktererpeton Gephyrostegidae 53 Gephyrostegus Solenodonsaurus Kotlassia 16 26 Seymouria Leptoropha 28 90 Microphon Seymouriamorpha 31 36 Ariekanerpeton 36 Discosauriscus 23 Utegenia Limnoscelis Tseajaia 59 Diadectomorpha 22 60 Diadectes Orobates 68 77 Captorhinus Paleothyris 80 Sauropsida 84 Petrolacosaurus 19 Westlothiana tetrapod crown-group Odonterpeton 23 Microbrachis “microbrachomorphs” 1 67 Hyloplesion 26 12 Saxonerpeton Hapsidopareion Amphibia 15 Cardiocephalus Gymnarthridae 26 73 Euryodus 73 Rhynchonkos 22 Micraroter Ostodolepididae Pelodosotis 22 “microsaurs” 1 75 Tuditanus Tuditanidae 24 Asaphestera 12 Pantylus Pantylidae 92 Stegotretus 47 Acherontiscus Adelospondylus adelospondyls 76 Adelogyrinus Adelogyrinidae 2 39 Dolichopareias “microsaur” 2 Batropetes “microbrachomorph” 3 37 Brachydectes Lysorophia Gymnophionomorpha 20 Eocaecilia 19 Albanerpetidae 65 Karaurus Caudata Lissamphibia 53 77 74 Valdotriton Batrachia Triadobatrachus 90 Notobatrachus Salientia 25 96 Vieraella Scincosaurus Keraterpeton 56 43 Diceratosaurus 57 Batrachiderpeton Diplocaulidae 14 45 Diplocaulus Diploceraspis Holospondyli 100 Ptyonius 83 Sauropleura Urocordylidae 40 Urocordylus 76 43 Lethiscus 70 Oestocephalus Aïstopoda 36 Phlegethontia Eusthenopteron Panderichthys *Elginerpeton *Metaxygnathus 98 *Ymeria 42 19 Ventastega 31 Acanthostega *Perittodus 11 Ichthyostega 8 *Densignathus origin of digits 10 Ossinodus Whatcheeria Whatcheeriidae 26 14 45 Pederpes Tulerpeton 13 Crassigyrinus Eucritta 18 25 *St. Louis tetrapod *Pholidogaster Colosteidae *Aytonerpeton 17 29 35 *Deltaherpeton 48 Colosteus 3 76 Greererpeton Baphetes 22 11 31 Megalocephalus Baphetoidea *Diploradus *Spathicephalus Lissamphibia 19 *Sigournea Notobatrachus 68 30 82 35 *Doragnathus Salientia Vieraella *Liaobatrachus 87 Caerorhachis Batra- Triadobatrachus 38 31 *Parrsboro jaw chia *Chelotriton 8 Silvanerpeton 54 6 Karaurus 46 Eoherpeton Anthracosauria “caudates” *Beiyanerpeton 21 modern *Neopteroplax 25 46 20 Valdotriton amphi- *Palaeoherpeton *Pangerpeton bians 21 23 Anthracosaurus 28 Gymnophionomorpha Eocaecilia 67 *NSM 994 GF 1.1 13 Pholiderpeton attheyi Albanerpetidae 15 *Quasicaecilia “micro- 18 Pholiderpeton scutigerum Brachystelechidae 35 Proterogyrinus *Carrolla 37 saurs” 2 25 “microbrachomorphs” 3 Batropetes 31 Archeria 21 *Erpetosaurus Lysorophia Brachydectes 23 14 Trimerorhachis *Coloraderpeton 35 Dvinosauria 11 Neldasaurus Oestocephalus 25 6 29 Isodectes Aïstopoda *Pseudophlegethontia 24 63 *Nigerpeton Lethiscus *Saharastega Phlegethontia 30 1 50 4 Edops Edopoidea Ptyonius 57 Chenoprosopus Urocordylidae Urocordylus 41 15 Sauropleura 81 Cochleosaurus 9 2 Eryops Diploceraspis 100 2 Diplocaulus 39 Holo- 4 *Sclerocephalus Diplocaulidae Batrachiderpeton 58 spondyli Eryopi- 27 *Cheliderpeton *Konzhukovia Keraterpeton 43 63 formes 14 Stereo- Diceratosaurus 28 *Lydekkerina 18 spondylo- Scincosaurus 1 11 *Glanochthon morpha Micraroter 55 3 *Platyoposaurus Ostodolepididae 23 Pelodosotis 11 *Archegosaurus Rhynchonkos 26 30 *Australerpeton Cardiocephalus 65 10 *Palatinerpeton Gymnarthridae Capetus Euryodus 5 *Trihecaton Dissorophoidea 9 Balanerpeton 1 Microbrachis 66 6 (YW00) 37 Dendrerpetidae “microbrachomorphs” 2 Hyloplesion 15 *Acanthostomatops *Iberospondylus Odonterpeton 3 *Llistrofus 87 7 11 *Mordex 10 Ecolsonia Hapsidopareiidae Hapsidopareion 1 28 Trematopidae Saxonerpeton 17 38 Acheloma Tuditanus 85 Phonerpeton 37 21 *Crinodon 24 “branchiosaurids” 1 *Tungussogyrinus Tuditanidae 15 6 Asaphestera Dissorophoidea 16 *Branchiosaurus *Goreville microsaur 1 Am- (content) Broiliellus brevis Pantylus 77 phibia Eoscopus Pantylidae Stegotretus 36 14 9 13 Amphibamus *Sparodus “microsaurs” 1 25 “amphi- 8 24 Platyrhinops “microbrachomorph” 1 *Utaherpeton 10 12 Doleserpeton bamids” Westlothiana Dissorophoidea (S13) 40 *Gerobatrachus Adelogyrinus 47 *Micropholis Adelogyrinidae Dolichopareias 80 Micromelerpeton 65 6 Adelospondylus Apateon “branchi- adelospondyls Temnospondyli 27 Acherontiscus 45 Leptorophus osaur- Diadectes 73 60 Schoenfelderpeton ids” 2 52 Diadectomorpha Orobates 24 Bruktererpeton Tseajaia Gephyrostegidae 42 Gephyrostegus Limnoscelis Paleothyris 55 44 6 *Casineria Saur- 26 *Chroniosaurus Petrolacosaurus 4 *Bystrowiella Amniota opsida Captorhinus 30 Chroniosuchia 42 56 7 Solenodonsaurus Synapsida *Caseasauria 3 6 *Archaeovenator 9 Utegenia 29 tetrapod Ariekanerpeton 34 crown-group Discosauriscus 29 Seymouria- Leptoropha 86 morpha Microphon 30 Kotlassia 26 *Karpinskiosaurus 23 77 Seymouria Eusthenopteron Panderichthys *Elginerpeton *Metaxygnathus 100 58 *Ymeria 77 Ventastega Acanthostega 39 Ichthyostega 76 *Perittodus origin of digits 76 Whatcheeria Whatcheeriidae 58 50 Pederpes *Densignathus 57 70 Ossinodus Tulerpeton 57 Crassigyrinus Eucritta *St. Louis tetrapod 77 *Pholidogaster 97 *Aytonerpeton 74 50 Colosteidae 71 *Deltaherpeton 53 43 Colosteus 70 98 Greererpeton Baphetes Megalocephalus 82 *Diploradus Baphetidae 82 *Sigournea 86 87 44 *Doragnathus 36 *Spathicephalus Caerorhachis Eoherpeton Proterogyrinus Anthracosauria 97 Archeria 99 62 Pholiderpeton scutigerum 86 94 Pholiderpeton attheyi *Neopteroplax 68 Anthracosaurus Lissamphibia 58 44 62 *NSM 994 GF 1.1 Notobatrachus 58 *Palaeoherpeton 100 45 Salientia Vieraella 99 Silvanerpeton *Liaobatrachus *Parrsboro jaw Triadobatrachus 67 *Chelotriton Bruktererpeton Batrachia Gephyrostegidae 69 Karaurus 46 Gephyrostegus “caudates” *Beiyanerpeton 57 81 *Palatinerpeton *Pangerpeton 52 55 48 Balanerpeton Valdotriton 100 83 Dendrerpetidae Albanerpetidae “micro- Trimerorhachis Gymnophionomorpha Eocaecilia 88 saurs” 2 *Erpetosaurus 48 19 77 Dvinosauria *Quasicaecilia 48 45 57 Neldasaurus “brachystelechids” 71 Isodectes “microbr.” 3 *Carrolla 92 39 Batropetes 22 Capetus Edops Lysorophia Brachydectes 47 Cochleosaurus Diploceraspis 100 57 Chenoprosopus Edopoidea Diplocaulus 20 25 33 *Nigerpeton Diplocaulidae Batrachiderpeton 94 99 *Saharastega Keraterpeton 68 100 45 13 Diceratosaurus Eryops 86 14 *Sclerocephalus Scincosaurus 35 Eryopiformes *Pseudophlegethontia *Cheliderpeton 62 31 *Glanochthon Lethiscus 49 50 Stereo- 49 76 *Lydekkerina Aïstopoda Phlegethontia 100 Holo- spondylo- *Coloraderpeton 61 spondyli 57 *Archegosaurus 65 *Australerpeton morpha Oestocephalus 60 53 40 *Konzhukovia Sauropleura 81 “urocordylids” Urocordylus 96 98 *Platyoposaurus Ptyonius *Iberospondylus 48 Adelogyrinus 32 64 46 *Mordex Adelogyrinidae Adelospondylus 59 Dissoro- 94 Ecolsonia Dolichopareias adelo. 69 95 phoidea Acheloma Trematopidae 100 18 Phonerpeton Acherontiscus (YW00) 38 100 *Acanthostomatops “microbr.” 2 *Utaherpeton Dissoro- 20 34 Pantylus 93 phoidea *Branchiosaurus “br.” 1 Stegotretus Pantylidae (content) 47 Broiliellus brevis *Sparodus 88 *Gerobatrachus 48 Eoscopus Microbrachis 97 40 43 “microbr.” 1 Hyloplesion Dissorophoidea (S13) Platyrhinops “amphi- 49 Amphibamus Odonterpeton 35 49 bamids” 60 51 Doleserpeton *Llistrofus 100 *Micropholis Hapsidopareion Hapsidopareiidae 30 *Tungussogyrinus “br.” 2 Saxonerpeton 35 21 Micraroter Micromelerpeton Ostodolepididae 87 “microsaurs” 1 54 Pelodosotis 52 Temno- 55 Apateon Rhynchonkos 54 36 spondyli 53 Leptorophus “br.” 3 68 Schoenfelderpeton Gymnarthridae Cardiocephalus 64 Euryodus 96 *Casineria 27 Chroniosuchia 67 *Chroniosaurus *Trihecaton *Bystrowiella Asaphestera 73 55 Solenodonsaurus *Goreville microsaur 74 *Crinodon Tuditanidae Kotlassia 88 51 Seymouria Tuditanus 89 Am- 44 Westlothiana phi- 99 27 *Karpinskiosaurus 59 bia Discosauriscus Orobates 59 Leptoropha Diadecto- Limnoscelis 76 tetrapod 96 46 Seymouria- 91 100 Microphon morpha Diadectes 49 Tseajaia crown- morpha 47 Utegenia Captorhinus 44 group 52 Ariekanerpeton Synapsida *Caseasauria 75 Amniota *Archaeovenator 70 Sauropsida Paleothyris 55 Petrolacosaurus 79

2969 ↑ Figure 20: Topology and posterior probabilities from Analysis EB (revised matrix, 2970 expanded taxon sample, no constraint; compare Fig. 14, 19). The numbers are posterior 2971 probabilities (in %), in boldface if 75 or higher. For branch lengths see Fig. 21. 2972 Abbreviations: br., branchiosaurids; microbr., microbrachomorphs. 2973 2974 Analysis EB 2975 2976 The results of our exploratory Bayesian analysis (Fig. 20, 21) are remarkably similar to those 2977 of Analysis B2, which was conducted under the same settings. The most conspicuous 2978 difference may be how strong the support for the LH is: a node with a posterior probabilities 2979 of 92% (Fig. 20) would need to be broken to move the modern amphibians into 2980 Temnospondyli, not to mention one each with posterior probabilities of 76%, 74%, 73% and 2981 finally 64% (Dissorophoidea incl. *Iberospondylus). 2982 Posterior probabilities of 75% or higher support *Elginerpeton crownward of 2983 Panderichthys (100%) and outside the rest of the ingroup (77%), Acanthostega crownward of 2984 Ventastega (75%), Ichthyostega crownward of Acanthostega (76%), Tulerpeton crownward 2985 of all whatcheeriids and *Densignathus (77%), Colosteidae including the *St. Louis tetrapod 2986 (97%) forming an exclusive clade with Baphetidae and Eucritta (74%) which lies crownward 2987 of Whatcheeriidae and Crassigyrinus (86%) and rootward of Caerorhachis (again 86%), 2988 Eucritta in Baphetoidea (94%), *Sigournea + *Doragnathus + *Spathicephalus + 2989 *Diploradus (87%) lying next to Megalocephalus (82%) in Baphetidae (again 82%), 2990 Anthracosauria (97%), Embolomeri (99%), Proterogyrinus outside a clade of all other 2991 embolomeres (94%), Balanerpeton + Dendrerpetidae (83%), Dvinosauria (77%), *Nigerpeton 2992 + *Saharastega (99%), *Konzhukovia + *Platyoposaurus (98%) next to *Australerpeton 2993 (81%), Ecolsonia as a trematopid (94%), Phonerpeton + Acheloma (100%), Kotlassia inside 2994 Seymouriamorpha (99%), Discosauriscidae excluding Kotlassia, Seymouria and 2995 *Karpinskiosaurus (91%), Leptoropha + Microphon (100%), *Caseasauria + 2996 *Archaeovenator (75%), Diadectomorpha (96%), a clade composed of Limnoscelis and the 2997 two diadectids (76%), Tuditanidae (89%) containing the *Goreville microsaur + *Crinodon 2998 (88%), Gymnarthridae (96%), Ostodolepididae (87%), Hapsidopareion + *Llistrofus (100%), 2999 Microbrachis + Hyloplesion (97%), *Sparodus as a pantylid (88%), Pantylus + Stegotretus 3000 (93%), a “Holospondyli” clade including all “nectrideans”, “aïstopods”, adelospondyls, 3001 *Utaherpeton, Brachydectes, “brachystelechids” and modern amphibians (76%), the 3002 adelospondyl clade (100%), Adelogyrinidae (95%), Urocordylidae incl. Aïstopoda (96%), 3003 Aïstopoda (100%), Scincosaurus + Diplocaulidae (86%), Diplocaulidae (100%), Diplocaulus 3004 + Diploceraspis (100%) as the sister-group of Batrachiderpeton (94%), a clade of 3005 Brachydectes, the “brachystelechids” and the modern amphibians (92%), a novel clade 3006 formed by the modern amphibians, *Quasicaecilia and *Carrolla to the exclusion of 3007 Batropetes and Brachydectes (88%), Lissamphibia (100%), Batrachia (81%), Salientia 3008 excluding *Chelotriton (99%) and finally the salientians other than Triadobatrachus(100%). 3009 Amphibia including Westlothiana has 74% posterior probability, the clade of all remaining 3010 amphibians has 73%, the colosteid clade of *Aytonerpeton, *Deltaherpeton, Colosteus and 3011 Greererpeton has 71%, as does Isodectes + Neldasaurus; Amniota incl. Diadectomorpha has 3012 70%, as do Colosteidae + Baphetidae and Ossinodus + *Densignathus. Gephyrostegidae 3013 reaches 69%, Chroniosuchia to 67%. 3014 3015 3016 ↓ Figure 21: Branch lengths from Analysis EB. For nomenclature and branch support see 3017 Fig. 20.

79 0.034 Eucritta 0.022 *St. Louis tetrapod 0.078 0.040 0.041 *Pholidogaster 0.101 *Aytonerpeton 0.036 0.045 *Deltaherpeton 0.057 0.063 0.050 0.030 0.063 Colosteus 0.011 Greererpeton Baphetes 0.014 0.044 0.092 0.053 Megalocephalus 0.083 0.048 0.107 *Diploradus 0.048 *Sigournea 0.051 0.032 Caerorhachis 0.047 *Doragnathus 0.054 0.027 Eoherpeton 0.057 *Spathicephalus 0.030 0.027Proterogyrinus 0.028 0.032 Archeria 0.041 0.036 0.030 Pholiderpeton scutigerum 0.030 0.019Pholiderpeton attheyi 0.126 *Neopteroplax 0.038 0.037 Anthracosaurus 0.026 0.043 0.029 0.028 *NSM 994 GF 1.1 0.024 *Palaeoherpeton 0.046 0.022Silvanerpeton 0.053 *Parrsboro jaw 0.045 0.025 Bruktererpeton 0.042 0.058 Gephyrostegus *Palatinerpeton 0.033 0.045 0.054 0.027 *Iberospondylus 0.086 *Mordex 0.033 Ecolsonia 0.024 0.034 0.024 Acheloma 0.051 0.050 Phonerpeton 0.113 0.055 0.081 0.027 *Acanthostomatops *Branchiosaurus 0.036 0.076 0.062 0.023 Broiliellus brevis 0.070 0.025 *Gerobatrachus 0.024 0.039 Eoscopus 0.058 0.019 0.024 Platyrhinops 0.052 0.017 0.022 Amphibamus 0.024 Doleserpeton 0.021 0.085 0.050 0.045 0.063 *Micropholis 0.125 *Tungussogyrinus 0.017 0.050 Micromelerpeton 0.091 Crassigyrinus 0.034 0.030 Apateon 0.064 0.062 0.031 0.020 Tulerpeton 0.021 Leptorophus 0.046 0.026 0.094 Ossinodus 0.034 0.039 Schoenfelderpeton 0.106 0.032 Balanerpeton 0.065 *Densignathus Dendrerpetidae 0.088 Whatcheeria 0.040 0.049 0.081 Trimerorhachis 0.040 0.124 0.059 Pederpes *Erpetosaurus 0.050 0.020 0.097 0.030 Isodectes 0.070 0.023*Perittodus 0.029 0.045 0.019 Neldasaurus 0.021 Capetus 0.132 Ichthyostega 0.067 0.028 0.082 0.062 0.036 Edops Acanthostega 0.085 0.048 0.045 Cochleosaurus Ventastega 0.026 0.022 0.071 Chenoprosopus 0.016 *Metaxygnathus 0.081 0.129 0.037 0.083 *Nigerpeton 0.028 *Ymeria 0.015 0.060 *Saharastega 0.016 Eryops 0.098 0.037 *Sclerocephalus 0.033 *Elginerpeton 0.011 0.030 0.040 *Cheliderpeton Panderichthys 0.039 0.006 0.103 *Lydekkerina Eusthenopteron 0.027 *Glanochthon 0.031 0.021 0.030 *Archegosaurus 0.036 0.041 *Australerpeton *Casineria 0.031 0.064 0.065 0.044 0.079 *Konzhukovia 0.050 *Chroniosaurus 0.048 *Platyoposaurus 0.102 *Bystrowiella 0.077 0.040 Solenodonsaurus 0.090 0.022 Kotlassia 0.021 0.032 0.012 Seymouria 0.050 0.116 *Karpinskiosaurus 0.026 0.039 Discosauriscus 0.011Ariekanerpeton 0.023 0.038 0.016 0.064 Utegenia 0.016 0.017 Leptoropha 0.043 0.065 Microphon 0.017 0.019 Paleothyris 0.030 Petrolacosaurus 0.072 0.116 0.032 *Caseasauria 0.068 *Archaeovenator 0.028 0.064 0.024 Captorhinus 0.052 0.025 Tseajaia 0.017Diadectes 0.051 0.111 0.030 Limnoscelis 0.019 0.056 Orobates 0.065 0.070 *Utaherpeton Westlothiana Acherontiscus 0.061 0.111 0.037 0.014Dolichopareias 0.019 0.071 Adelospondylus 0.028 Adelogyrinus 0.036 0.035 0.041 Ptyonius 0.100 0.024 Urocordylus 0.051 0.033 Sauropleura 0.047 0.019 Oestocephalus 0.039 0.064 0.155 *Coloraderpeton 0.110 0.172 0.051 0.044 Phlegethontia Scincosaurus 0.074 0.045 Lethiscus 0.088 0.051 0.036 Keraterpeton 0.024 *Pseudophlegethontia 0.013 0.090 0.026 Diceratosaurus Batrachiderpeton 0.024 0.041 0.042 0.043 0.145 Diplocaulus 0.029 0.146 Diploceraspis Brachydectes 0.035 0.086 Batropetes 0.055 0.056 0.038 *Carrolla 0.040 0.029 0.087 *Quasicaecilia 0.169 Eocaecilia 0.026 0.069 Albanerpetidae 0.076 0.114 0.057 0.063 0.063 *Sparodus Valdotriton 0.060 0.035 0.064 0.059 Pantylus 0.054 *Pangerpeton 0.053 0.091 0.024 0.080 Stegotretus 0.036 Karaurus Odonterpeton 0.066 0.034 0.052 0.025 *Beiyanerpeton 0.029 Microbrachis 0.051 0.132 *Chelotriton 0.032 Hyloplesion 0.048 Triadobatrachus 0.018Saxonerpeton 0.046 0.049 0.014 0.070 *Liaobatrachus 0.013 0.018 0.032 Hapsidopareion 0.058 Notobatrachus 0.133 0.018 0.038 *Llistrofus 0.061 Vieraella 0.031*Trihecaton 0.072 0.037 Cardiocephalus 0.020 0.044 Euryodus 0.026 0.116 0.05 expected changes per character 0.041 Rhynchonkos 0.047 0.024 Micraroter 0.037 Pelodosotis 0.036 0.019 0.051 Asaphestera 0.041 Tuditanus 0.048 0.044 *Goreville microsaur 0.048 0.060 *Crinodon 81

3018 Posterior probabilities below 50% are most common in Temnospondyli and its 3019 surroundings as well as in the “microsaur backbone”. The strange finding of urocordylid 3020 is weakly supported (65%). The Ossinodus + *Densignathus clade is poorly 3021 supported as crownward of Whatcheeriidae (57%), *Perittodus as rootward of it (again 57%), 3022 and *Perittodus as crownward of Ichthyostega (58%); Chroniosuchia has weak support (55%) 3023 for its position crownward of Temnospondyli and*Casineria. Solenodonsaurus is kept 3024 together with Seymouriamorpha by a posterior probability of 51%. 3025 The longest branch is the terminal branch of Phlegethontia (0.172 expected changes 3026 per character; Fig. 21), followed by those of Eocaecilia (0.169), Brachydectes (0.146), 3027 Ichthyostega and *Chelotriton (0.132 each), *Neopteroplax (0.126), *Tungussogyrinus 3028 (0.125) and *Erpetosaurus (0.124). Internal branches with at least 0.1 expected changes per 3029 character are limited to Aïstopoda (0.155), Diplocaulus + Diploceraspis (0.145), 3030 Hapsidopareion + *Llistrofus (0.133), the ingroup except Panderichthys (0.129), 3031 Lissamphibia (0.114), the adelospondyls (0.111), , the clade of non-traditional baphetids 3032 (0.107) and Urocordylidae incl. Aïstopoda (0.100). 3033 3034 Discussion 3035 3036 Reevaluating the matrix of RC07 has revealed additional character conflict and polymorphism 3037 (on the latter’s impact see Watanabe, 2015) and greatly increased the length of the most 3038 parsimonious trees. Evidently, the MPTs found by RC07 painted an oversimplified picture of 3039 the evolution of the limbed vertebrates. 3040 The addition of taxa in Analyses R3–R6, B2 and EB has had unexpected effects that 3041 may have improved the reliability of the tree. As previously demonstrated (Mortimer, 2006; 3042 Butler & Upchurch, 2007), every OTU in a data matrix can influence the position of every 3043 other OTU in the resulting trees. 3044 Unstable areas of the tree and other phenomena highlight promising areas for future 3045 research. These include redescription of Westlothiana (currently being undertaken following 3046 the discovery of additional specimens: M. Ruta, pers. comm. 2015; Clack & Milner, 2015), 3047 **Eldeceeon (currently being undertaken, see Material and methods: Treatment of OTUs: 3048 Taxa that were not added above), the “microsaurs” Asaphestera, Tuditanus, Odonterpeton and 3049 *Trihecaton (see below), **Sauravus (the presumed sister-group of Scincosaurus), 3050 *Casineria (especially in order to determine whether it is distinguishable from Caerorhachis), 3051 *Utaherpeton (see below), and quite possibly others. 3052 3053 Bayesian inference and parsimony in comparison 3054 3055 We consider our Bayesian analysis exploratory because the behavior and performance of 3056 Bayesian inference on datasets like ours have not been studied. Firstly, the amount and 3057 distribution of missing data may be a matter of concern. We are aware of three studies of its 3058 effects on Bayesian inference: 3059 Wright & Hillis (2014) explicitly intended to study the performance of Bayesian 3060 inference with morphological data. They simulated matrices of exclusively binary characters 3061 and scored all characters that evolved at a given rate as unknown for selected taxa; this may 3062 be somewhat realistic for molecular data, where different genes (each with its own rate) may 3063 have been sequenced for different taxa in a supermatrix, but makes limited sense for 3064 morphological data, where missing data are clustered by body parts, not by rate of evolution. 3065 Wright & Hillis (2014) found that Bayesian inference outperforms parsimony under the 3066 conditions they studied.

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3067 Using contrived, simulated and empirical DNA datasets, Simmons (2011a, b) studied 3068 what happens when different taxa are scored for different characters so that some taxa have no 3069 scored characters in common at all, as may (again) happen when different genes have been 3070 sequenced for different taxa in a supermatrix. Given a matrix with non-overlapping taxa, 3071 parsimony cannot find only a single MPT which has them as sister-groups; instead, it will 3072 return consensus trees with polytomies when such taxa are not kept far enough apart by 3073 character states they share with other taxa. Parametric methods (Bayesian inference and 3074 maximum likelihood) instead try to compensate and can therefore find a single optimal tree 3075 which contains such taxa as sister-groups. Sometimes this turns out to be correct; however, 3076 Simmons (2011a, b) found that this situation routinely led parametric methods to finding 3077 strong support for wholly spurious clades – even under ideal conditions (no homoplasy, a 3078 perfectly fitting model of evolution, a perfect alignment, no rate heterogeneity). Moreover, 3079 which spurious clades were found was very sensitive to small changes in the scores of a 3080 matrix, despite the high support values. For datasets with missing data that are distributed as 3081 in his studies, Simmons (2011a, b) recommended that nodes and support values found by 3082 parametric analyses in parts of the tree that are not resolved in the strict consensus of a 3083 parsimony analysis of the same dataset should only be accepted after special scrutiny of their 3084 causes. 3085 In our matrix, missing data are clustered by body parts, so the findings of Wright & 3086 Hillis (2014) may not translate to our situation; all OTUs except *Casineria and the isolated 3087 lower jaws we added are scored at least for part of the dermal skull, so Simmons’s (2011a, b) 3088 almost opposite conclusion may not translate to our situation either. 3089 A second issue was raised by Puttick et al. (2017), who attempted to investigate the 3090 impact of tree shape (full symmetry vs. maximum asymmetry) on the performance of 3091 different methods. They found that all methods performed badly on the most basal nodes of a 3092 Hennigian comb, and that Bayesian inference performed least badly. Goloboff, Torres & 3093 Arias (2017: 14th page) showed that Puttick et al. (2017; later also O’Reilly et al., 2017) had 3094 actually tested something completely different: their symmetric tree had unitary branch 3095 length, while their asymmetric tree was ultrametric, so that the least nested terminal branches 3096 were many times longer than the internal branches (which had unitary length). Their 3097 experiment thus amounts to a test of susceptibility to long-branch attraction, not to tree shape. 3098 The trees we find are much closer to the asymmetric than to the symmetric end of the 3099 spectrum; the branch lengths, however, are much closer to unitary than to ultrametric, with 3100 short terminal branches making up the majority of the Devonian part and being scattered over 3101 the rest of the “trunk” (Fig. 21). Indeed, apart from the adelospondyls and the aïstopods, our 3102 Bayesian tree (Fig. 21) places most OTUs remarkably close to their relative stratigraphic 3103 positions. 3104 Of the four most recent studies of the performance of Bayesian inference on matrices 3105 of morphological characters, two (O’Reilly et al., 2016; Puttick, et al., 2017) did not mention 3106 the problem of missing data at all, and Goloboff, Torres & Arias (2017) omitted it from most 3107 of their comparisons of Bayesian inference to other methods. O’Reilly et al. (2017: 2nd page) 3108 stated that “our experiments do not attempt to simulate non-contemporary taxa or address the 3109 problem of missing data, qualities of palaeontological data that are of a level of complexity 3110 that is beyond the current debate.” For us, of course, this is most of the current debate; we are 3111 quite surprised that O’Reilly et al. (2017) chose to publish their statement in the journal 3112 Palaeontology, whose very name suggests non-contemporary taxa and missing data. 3113 Thirdly, it remains unknown whether Bayesian inference outperforms parsimony on 3114 datasets whose amount and distribution of homoplasy is like that of ours. For matrices with 3115 average evolutionary rates approaching three changes per character per tree, the performance 3116 of Bayesian inference and parsimony converges when the number of characters increases

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3117 toward 1000 (O’Reilly et al., 2016, 2017; Puttick et al., 2017; perhaps also Wright & Hillis, 3118 2014: fig. 6). Even with its many multistate characters, our matrix does not contain a number 3119 of states equivalent (or close) to 1000 binary characters. However, as listed above, the 3120 consistency indices are below 0.22 in all our parsimony analyses and below 0.19 for all those 3121 with the expanded taxon sample; this translates to an average of about five changes per 3122 character per tree, well outside the range studied by Wright & Hillis (2014: two to three 3123 changes). Similarly, O’Reilly et al. (2016, 2017) and Puttick et al. (2017) studied datasets 3124 with consistency indices between 0.26 and 1.0; most of this range occurs only in very small 3125 datasets. Individual characters in our matrix show a wide range of rates – some change states 3126 only once per tree, some change states 30 to 40 times on every tree, the extreme being 51 3127 (Analyses R1, R3) to 73 changes (R4) for SKU TAB 1 (character 95, five states). 3128 To keep their calculations in a feasible timeframe, O’Reilly et al. (2016, 2017) and 3129 Puttick et al. (2017) reduced all their parsimony results to the majority-rule consensus. This 3130 must have overestimated the precision of parsimony and may have underestimated its 3131 accuracy. 3132 Goloboff, Torres & Arias (2017) noted that all preceding studies had assumed a 3133 common branch length parameter for all characters to simulate their datasets, so that if one 3134 character had an increased probability of changing along a given branch, all others had 3135 proportionally increased probabilities of changing along that same branch. As Goloboff, 3136 Torres & Arias (2017) pointed out, this is highly unrealistic for morphological data; indeed, it 3137 does not fit our matrix (where different characters are stable or labile in different parts of the 3138 same tree). O’Reilly et al. (2017) responded to several criticisms by Goloboff, Torres & Arias 3139 (2017), but left this one unaddressed. 3140 Finally, ordered characters (let alone stepmatrices) were not used in any of the studies 3141 cited here, so the impact of ordering remains unknown. In Wright & Hillis (2014) and 3142 O’Reilly et al. (2016), all characters were binary; in Goloboff, Torres & Arias (2017: 5th 3143 page), interestingly, all characters had four states, which is far from realistic as well. 3144 Parametric methods of phylogenetics are generally less sensitive to long-branch 3145 attraction than the nonparametric method called “maximum parsimony” is (as inadvertently 3146 confirmed by Puttick et al., 2017, and O’Reilly et al., 2017). Long-branch attraction is not 3147 unknown in morphological data. Indeed, we suspect that long-branch attraction could be 3148 responsible for parts of our MPTs; in particular, our results concerning the placement of 3149 adelospondyls, aïstopods (Pardo et al, 2017) and perhaps urocordylids should be taken with 3150 caution, as discussed below. However, these very results are supported by Analysis EB 3151 (posterior probability of 76% for all these taxa being highly nested amphibians close to 3152 Lissamphibia, and 69% for them forming an exclusive clade with *Utaherpeton; Fig. 20), and 3153 the internal branches in that region of the tree are long but not extremely long (Fig. 21). 3154 Although we are looking forward to further developments of parametric methods and further 3155 tests of their performance with paleontological datasets, the extent to which the trees we 3156 present here are wrong will more likely be discovered through improvements to our matrix 3157 than improvements to the methods of analysis. Indeed, before we updated the scores of the 3158 aïstopod Lethiscus after Pardo et al. (2017) and added two more (*Coloraderpeton and 3159 *Pseudophlegethontia), the abovementioned posterior probabilities were 98% and 97%, 3160 respectively; this may have been a case of “garbage in, garbage out”, a law to which no 3161 method is immune. 3162 3163 Reweighting and equal weighting in comparison 3164 3165 Our review of their datasets indicates that […] Goloboff et al. (2017) […] their simulated datasets 3166 are not individually empirically realistic, with many matrices dominated by characters with very 3167 high consistency and an unrealistically small proportion of characters exhibiting high levels of

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3168 homoplasy. The datasets simulated by Goloboff et al. (2017) have qualities that strongly bias in 3169 favour of parsimony phylogenetic inference, and implied-weights parsimony in particular, as the 3170 presence of large numbers of characters that are congruent with the tree allows implied weights to 3171 increase the power of these ‘true’ congruent characters. This effect will not be possible when 3172 increased levels of homoplasy are present […]. 3173 – O’Reilly et al., 2017: 2nd–3rd page 3174 3175 Any method of phylogeny inference works when its assumptions are met. Therefore, the fact 3176 that the method variously called reweighting, implied weighting or a-posteriori weighting is 3177 logically circular (see below) is not an argument against using it when its assumptions are 3178 met; when they are, it outperforms all others (Goloboff, Torres & Arias, 2017). We think they 3179 are not met in our dataset and have therefore not used this method. 3180 Specifically, in the empirical matrices Goloboff, Torres & Arias (2017) cited and the 3181 matrices they simulated, there is an exponential or nearly exponential distribution of 3182 characters so that a plurality of characters has, on the MPTs found by unweighted parsimony, 3183 no homoplasy at all, i.e. as few steps as theoretically possible, in other words a consistency 3184 index of 1; next most common are characters with one extra step (ci = 0.5), then two and so 3185 on. In our matrix, homoplasy-free characters are much less common (Data S5). Given the 3186 original taxon sample (Analysis R1; Fig. 22A), the distribution zigzags around an exponential 3187 one, but the most common number of extra steps is one, followed by two and only then (by a 3188 large margin) by zero; when taxa (and thus homoplasy) are added (Analysis R4; Fig. 22B), 3189 the most common number is still one, then three, then two and four (equally), then nine, then 3190 eleven, then zero, five, seven and eight (all equally), then the rest vaguely approaches an 3191 exponential distribution with a wide variance. In both taxon samples, several binary 3192 characters have the maximum possible number of steps (i.e., of one state, no two occurrences 3193 are unambiguously optimized as homologous, or those that are are canceled out by reversals). 3194 Even if it retrieves an accurate topology, we think that reweighting is prone to 3195 underestimating homoplasy and overestimating the support for this topology. Accurate 3196 topologies are not the only goal of our research. 3197 (Reweighting attempts to downweight characters depending on how homoplastic they 3198 are. The circularity consists in the fact that the amount of homoplasy for each character is 3199 determined by optimizing the characters on the MPTs found by unweighted parsimony, which 3200 amounts to assuming that these trees are correct or nearly so. By downweighting characters 3201 that are incongruent with those trees, reweighting reduces character conflict and thus 3202 increases support and resolution, but not necessarily accuracy. As Goloboff, Torres & Arias 3203 [2017] emphasized, unweighted and reweighted parsimony are equally sensitive to long- 3204 branch attraction; furthermore, characters can be falsely congruent with each other for reasons 3205 other than long-branch attraction – redundancy and correlation in particular.) 3206 3207 Persisting problems with the character sample 3208 3209 Taxon and character sets are now large enough to be mined for large-scale evolutionary trends 3210 […]. 3211 – Coates, Ruta & Friedman, 2008: 572 3212 3213 As the number of analysed characters increases, the accuracy and resolution of all methods also 3214 increase […]. These results suggest that no matter which method is applied to a dataset, it should 3215 be a goal for morphological datasets to include as many characters as possible if the most accurate 3216 estimates of topology are to be obtained. 3217 – O’Reilly et al., 2017: 12th page 3218 3219 3220

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3221 3222 3223 Figure 22: Homoplasy distribution in our matrix. The number of extra steps (x-axis) is the 3224 number of observed steps (in Mesquite, on the tree in Data S1 for each analysis) minus the 3225 minimum possible number of steps, which is the number of states minus one (for ordered and 3226 unordered characters as well as for both of our stepmatrix characters). The number of 3227 characters that have each number of extra steps is plotted on the y-axis. The line between the 3228 data points is meaningless, but makes it easier to compare the distributions to an exponential 3229 curve. Compare Goloboff, Torres & Arias (2017: fig. 1(a)). A: original taxon sample 3230 (Analysis R1); the highest number of extra steps is 47, but we plot to 69 for comparison to B. 3231 B: expanded taxon sample (Analysis R4); the highest number of extra steps is 69. 3232

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3233 Our mergers of redundant characters are the largest factor in the decrease of the number of 3234 parsimony-informative characters from 333 to 277 (re-split to 280 for Analysis EB). This is 3235 less than three times the number of taxa (which is 102 in the original sample, 158 in the 3236 expanded sample). Many of the characters now have multiple states, so the total number of 3237 apomorphic character states has decreased much less than the number of characters suggests; 3238 still, the low number of characters (compared with the number of taxa) explains why the 3239 present matrix does not provide a fully resolved, robust large-scale phylogeny of the limbed 3240 vertebrates. That the number is indeed low for our taxon samples is confirmed by the low 3241 bootstrap values and by the short internal branches found in Analysis EB (Fig. 18, 19, 21). It 3242 has become common for phylogenetic analyses of a similarly large or smaller sample of 3243 extinct amniotes to have far larger numbers of characters (Godefroit et al., 2013: 101 OTUs, 3244 992 characters; Lee et al., 2014: 120 OTUs, 1251 characters; Tschopp, Mateus & Benson, 3245 2015: 81 OTUs, 477 characters; Ezcurra, 2016: 96 OTUs, 600 characters; Simões et al., 3246 2016b: 193 OTUs, 610 characters; Shelley, Williamson & Brusatte, 2016: 169 OTUs, 693 3247 characters; Baron, Norman & Barrett, 2017: 74 OTUs, 404 parsimony-informative characters 3248 [Mortimer, 2017]; Buscalioni, 2017: 97 OTUs, 425 characters; Cau et al., 2017, “first 3249 dataset”: 199 OTUs, 1314 parsimony-informative characters [pers. obs.]!). Indeed, the 3250 matrices of McGowan (2002), Vallin & Laurin (2004), RC07, and Anderson et al. (2008a) 3251 each contain characters that the three others lack, and a cursory look at those of Pardo, Small 3252 & Huttenlocker (2017 – 76 OTUs, 322 parsimony-informative characters [pers. obs.]) and 3253 Pardo et al. (2017 – 58 OTUs, 340 parsimony-informative characters) reveals that even they 3254 lack characters present in ours; the supermatrix by Sigurdsen & Green (2011), compiled from 3255 those of Vallin & Laurin (2004), RC07 and Anderson et al. (2008a), has 335 characters that 3256 are parsimony-informative even though the taxon sample is restricted to 25. Clearly, then, the 3257 present character sample could easily be greatly expanded. Therefore, we strongly doubt the 3258 first statement quoted above. 3259 Unfortunately, the character sample is not only small, it is not random. We think that 3260 postcranial characters in particular are underused in the present matrix. This is implied by its 3261 craniocentricity – 190 of the 277 characters, a bit more than two thirds, describe the skull, 3262 lower jaw or teeth. Further, the endochondral braincase (Maddin, Jenkins & Anderson, 2012; 3263 Szostakiwskyj, Pardo & Anderson, 2015; Pardo, Szostakiwskyj & Anderson, 2015; Ascarrunz 3264 et al., 2016; Pardo & Anderson, 2016; Pardo et al., 2017) is represented by only three 3265 characters (which all concern the occiput), and the hyobranchial skeleton (Witzmann, 2013) – 3266 even the much-discussed (e.g. Lombard & Bolt, 1979, 1988; Bolt & Lombard, 1985, 3267 1992; Laurin, 1998a; Schoch, 2002a; Clack, 2003b; Robinson, Ahlberg & Koentges, 2005; 3268 Witzmann, 2006; Sigurdsen, 2008) – has not been considered at all. The analyses of Pawley 3269 (2006), who added a net total of 53 postcranial characters to the 95 of the matrix of Ruta, 3270 Coates & Quicke (2003 – the preceding version of RC07) and found different results, support 3271 our suspicion that the present matrix and the resulting trees are affected by accidental 3272 sampling bias. For an overlapping taxon sample, Ruta (2011) found 157 characters from the 3273 appendicular skeleton alone, where the present matrix has 53. 3274 Being the largest one available of its kind and having been scrutinized for problems of 3275 coding and scoring, our matrix is currently the best starting point for comparisons and 3276 discussions as carried out below. Future analyses of the phylogeny of early limbed vertebrates 3277 will, however, certainly need much larger character samples to reach reliable conclusions. 3278 3279 Phylogenetic relationships 3280 3281 In this section we mention the bootstrap percentages (BPO and BPE from Analyses B1 and 3282 B2, shown in Fig. 18 and 19, respectively) that support or contradict clades found by our

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3283 analyses. Most of them are below 50, especially for the expanded taxon sample (Fig. 19); this 3284 highlights the suboptimal ratio between number of characters and number of taxa, as well as 3285 character conflict and wildcard taxa. As in Fig. 18 and 19 as well as Tables 3 and 4, bootstrap 3286 percentages of 50 and above are presented in boldface. 3287 Likewise, we mention the posterior probabilities (in %: PP from Analysis EB, shown 3288 in Fig. 20) that support or contradict clades found by our analyses. As in Fig. 20 and Table 3, 3289 PPs of 75 and above are presented in boldface. 3290 3291 Figure 23: Hypotheses on 3292 the relationships of 3293 Devonian limbed and 3294 possibly limbed 3295 vertebrates. (Whatcheeri- 3296 idae and *Perittodus, which 3297 have limbs, are only known 3298 from the Carboniferous with 3299 certainty.) Equally parsimo- 3300 nious positions of the same 3301 OTU are highlighted in 3302 color in this and the follow- 3303 ing figures. A: RC07 and 3304 references therein. B: our 3305 results from the same taxon 3306 sample as RC07 (Analyses 3307 R1–R3). Numbers below 3308 internodes are BPO, in bold- 3309 face if 50 or higher. C: our 3310 results from the expanded 3311 taxon sample (R4–R6). 3312 Numbers below internodes 3313 are BPE\PP, BPE in bold- 3314 face if 50 or higher, PP in 3315 boldface if 75 or higher. 3316 Analysis B2 places *Ymeria 3317 next to Ventastega (BPE: 3318 19), Acanthostega one node 3319 crownward of them (BPE: 3320 11) and *Densignathus one 3321 node rootward of What- 3322 cheeriidae (BPE: 13); EB 3323 places *Ymeria next to 3324 *Metaxygnathus (PP: 58), Acanthostega one node crownward of Ventastega (PP: 76) and 3325 *Perittodus one node crownward of Ichthyostega (PP: 58). 3326 3327 Devonian taxa, Whatcheeriidae and Perittodus 3328 3329 At the base of the ingroup, RC07 found the “textbook” Hennigian comb (Fig. 1, 23A): 3330 (Panderichthys (Ventastega (Acanthostega (Ichthyostega (Tulerpeton, post-Devonian 3331 clade))))). However, the position of Ichthyostega soon began to be questioned (Ahlberg et al., 3332 2008: supplementary information; Clack et al., 2012a) as more information about it was

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3333 discovered and published (Callier, Clack & Ahlberg, 2009; Ahlberg, 2011; Clack et al., 3334 2012a; Pierce, Clack & Hutchinson, 2012; Pierce et al., 2013; Clack & Milner, 2015). In our 3335 analyses of the original taxon sample (Fig. 23B), Ichthyostega is equally parsimoniously 3336 crownward of Ventastega (BPO = 47; BPE = 11; PP = 76) and Acanthostega (BPO = 47; BPE 3337 = 10; PP = 76), which are – only in this case – sometimes found as sister-groups (contradicted 3338 by a BPO of 45, a BPE of 19 and a PP of 75), or rootward of Acanthostega but still 3339 crownward of Ventastega, or rootward of both. We will not be surprised if the last of these 3340 three options will be upheld by analyses with larger character and outgroup samples, as 3341 indeed it has been (in the absence of Ventastega) in the analysis of Pardo et al. (2017). The 3342 picture of Ichthyostega as the Godzilla of (Pierce, Clack & Hutchinson, 2012; 3343 see also Coates & Clack, 1995), an animal that acquired an amphibious lifestyle wholly 3344 independently from more crownward and limbless tetrapodomorphs that lived after 3345 Romer’s Gap, may well be accurate. 3346 However, in our expanded taxon sample (Fig. 23C), the position of Ichthyostega is 3347 stabilized crownward of Ventastega, Acanthostega, *Ymeria and even the Tournaisian 3348 *Perittodus (BPE = 10; contradicting a PP of 58, which holds *Perittodus crownward). 3349 The added Devonian taxa are all poorly known, as is *Perittodus. Yet, all of them 3350 have fully resolved positions. This appears to be due to a combination of the relatively dense 3351 sample of lower-jaw characters and our taxon sample. 3352 Within this mostly Devonian grade, the Carboniferous whatcheeriids nest rootward of 3353 *Densignathus (PP = 57; against a BPE of 13). This is particularly intriguing in the light of 3354 the “whatcheeriid-grade” skull bones that were found with *Densignathus; we are much less 3355 certain than Daeschler, Clack & Shubin (2009) that they do not actually belong to 3356 *Densignathus. Ossinodus is found as a whatcheeriid in the original taxon sample (BPO = 52; 3357 BPE = 26), specifically as the sister-group to the other two as in RC07 (BPO = 72; BPE = 45). 3358 This contrasts with the topology (Pederpes (Ossinodus, Whatcheeria)) found by Pawley 3359 (2006) before the recent descriptions of further Ossinodus material (Warren, 2007; Bishop, 3360 2014). When we add taxa, Ossinodus gains three additional positions around *Densignathus 3361 (PP for the two as sister-groups = 70; against a BPE of 13). 3362 In all analyses, the Devonian Tulerpeton emerges crownward of Whatcheeriidae (BPO 3363 = 57, BPE = 18; PP = 77), neither rootward as in RC07 and Pawley (2006) nor as its sister- 3364 group as in Ruta & Bolt (2006) and the almost identical Ruta (2009) or in Clack & Klembara 3365 (2009). Creating the former topology in Mesquite adds two steps each to Analyses R1 and R4; 3366 for the latter, three extra steps need to be added to Analysis R1 and four to R4 (three are 3367 required to make Tulerpeton a member of an Ossinodus-*Densignathus clade one node 3368 crownward of Whatcheeriidae). 3369 Taken at face value, our results support the idea (Anderson et al., 2015; Clack et al., 3370 2016) that more than one clade of limbed vertebrates survived the at the 3371 Devonian-Carboniferous boundary. We eagerly await the forthcoming redescription of 3372 **Elpistostege based on a whole articulated CT-scanned skeleton (Cloutier & Béchard, 2013; 3373 Cloutier et al., 2016); the improved sample of Devonian stem-tetrapods and probably 3374 characters in the accompanying phylogenetic analysis will likely contribute to a better 3375 understanding of this part of the tree. 3376 3377 More Mississippian mysteries 3378 3379 RC07 found Colosteidae, Crassigyrinus and Whatcheeriidae to be successively more 3380 crownward (Fig. 1, 24A). Like Ruta (2009), we find them successively more rootward in all 3381 analyses (Fig. 23B, C, 24B, C; PP = 86; BPO = 67 for Colosteidae + more crownward taxa 3382 including Eucritta; BPE = 22 for Eucritta + more crownward taxa including Colosteidae).

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3383 This agrees with other recently published analyses; we attribute this to our corrections. For 3384 example, RC07 (and Ruta, Coates & Quicke, 2003) had scored Whatcheeria as lacking the 3385 preopercular bone in the skull (state PREOPE 1(1), which is shared by the colosteids and 3386 Crassigyrinus), so that its presence (PREOPE 1(0)) in Pederpes appeared as an isolated 3387 reversal. This was apparently due to a misreading of Clack (1998), who explicitly confirmed 3388 that the preopercular is present in Whatcheeria as described by Lombard & Bolt (1995) and 3389 Bolt & Lombard (2000); see character 81 (PREOPE 1) in Appendix 1 for discussion. The 3390 third sampled whatcheeriid-grade animal, Ossinodus, was scored as unknown, which was 3391 correct at the time; it is now known to have retained the preopercular as well (Warren, 2007), 3392 and we have scored it accordingly. 3393 RC07 also found Eucritta as the sister-group of Baphetes + Megalocephalus, as did 3394 Ruta (2009), Milner, Milner & Walsh (2009), Witzmann & Schoch (2017) and the original 3395 full description by Clack (2001). Given the original taxon sample, we find this as one of two 3396 options (BPO = 56). Unexpectedly, the other option is one node rootward of Baphetidae; a 3397 position comparable to this is the only one found when we increase the taxon sample (BPE = 3398 8), except in Analysis EB, which finds a (Eucritta (Baphetidae, Colosteidae)) clade with a PP 3399 of 74. 3400 Like Eucritta, *Spathicephalus has been considered a non-baphetid baphetoid 3401 (Beaumont & Smithson, 1998; Milner, Milner & Walsh, 2009; following the nomenclature of 3402 Milner, Milner & Walsh, 2009). *Spathicephalus is consistently a baphetoid in our analyses 3403 (BPE = 30; PP = 87); however, it is highly nested within Baphetidae (PP = 87; against a BPE 3404 of 31), closer to Megalocephalus than to Baphetes (PP = 82). Milner, Milner & Walsh (2009) 3405 sampled baphetids and baphetoid-related characters more densely than we did; however, it is 3406 possible that these advantages are outweighed by the disadvantages of their much smaller 3407 outgroup sample (only Acanthostega and Crassigyrinus), the fact that they did not order any 3408 characters (of the 24 characters, seven are continuous or meristic multistate characters), 3409 redundancy between characters 3 and 4, and the scoring of juvenile morphology as adult 3410 (affecting at least character 19). 3411 A further factor that may affect the position of *Spathicephalus may be the enigmatic 3412 *Doragnathus and *Sigournea, the latter known from an isolated lower jaw, the former from 3413 fragments of lower and upper jaws. Both are found as baphetoids in all analyses that include 3414 them (BPE = 30; PP = 87), indeed as baphetids closer to Megalocephalus than Baphetes is 3415 (PP = 82; against a BPE of 31), forming a clade with *Spathicephalus (BPE = 30; PP = 44) 3416 and *Diploradus (BPE = 19; PP = 87). Similarities between all these taxa have long been 3417 noted, but only tested once in a phylogenetic analysis (even apart from the fact that 3418 *Diploradus was very recently published): using a rather small character sample, Clack et al. 3419 (2016) found the three as a grade not very close to Baphetidae in some of their analyses, but 3420 widely scattered in others. Although our results remain to be tested with a larger sample of 3421 characters and of baphetoids, we think that *Doragnathus, *Sigournea and *Diploradus will 3422 likely be upheld as baphetoids, possibly as baphetids and likely as a clade with 3423 *Spathicephalus (BPE = 19; PP = 87). It is noteworthy in this respect that Smithson & Clack 3424 (2013) noted similarities to baphetoids in the isolated postcranial material from the site where 3425 *Doragnathus was found; perhaps it belongs to *Doragnathus after all. 3426 A very unexpected finding of our analyses with added taxa (Fig. 24C) is a clade 3427 composed of Colosteidae and Baphetidae (BPE = 3; PP = 70), which is furthermore a member 3428 of Temnospondyli (the sister-group to all others combined; contradicting a BPE of 20 and a 3429 PP of 86). This ties into the problem of the mutual positions of Temnospondyli and 3430 Anthracosauria discussed below. 3431 We are looking forward to the ongoing redescription of Crassigyrinus based on 3432 computed tomography. The abstract by Porro, Clack & Rayfield (2015) promises previously

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3433 unknown character states, but the only new information it makes explicit is that “all three 3434 coronoids bear teeth”; we were unable to use this information, because our matrix contains 3435 separate characters for the presence or absence of tusks, denticles and toothrows. 3436

3437

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3438 ↑ Figure 24: Hypotheses on the relationships of post-Devonian limbed vertebrates, and 3439 distribution of several character states. A: RC07; the entire clade shown here equals the 3440 “post-Devonian limbed vertebrates” of Fig. 23A. Anthr., Anthracosauria. B: our results from 3441 the original taxon sample (R1–R3). The entire clade shown here equals the “other post- 3442 Devonian limbed vertebrates” of Fig. 23B. Numbers are BPO, in boldface if 50 or higher. B1 3443 finds Caerorhachis next to the other temnospondyls, but places Temnospondyli in the more 3444 rootward of the two indicated positions and also finds Silvanerpeton next to the other 3445 anthracosaurs (BPO: 10). C: our results from the expanded taxon sample (R4–R6). The entire 3446 clade shown here equals the “other post-Devonian limbed vertebrates” of Fig. 23C. In B and 3447 C, the extant amphibians are shown indirectly as the three positions of the tetrapod crown- 3448 group; although not rendered in boldface, “(rest of) Temnospondyli” is extant in R2, R3, R5 3449 and R6, and “Lepospondyli” is extant in R1, R3, R4 and R6. Parentheses show which of these 3450 positions are found in which analyses. The numbers of these analyses are written in black if 3451 these analyses find a single position; for any position found as the single position by any 3452 analyses, the parentheses themselves are also black. Numbers are BPE\PP, BPE in boldface if 3453 50 or higher, PP in boldface if 75 or higher. 3454 The rectangles indicate state 0 (filled) or 1 (empty) of characters 31 (PAR 1 – cyan), 3455 147 (PSYM 1 – teal), 192 (CLE 2 – blue), 212 (HUM 10 – purple), 214 (HUM 12-15 – red), 3456 260 (TRU VER 8 – orange) and 277 (CAU FIN 1 – green); absence of a rectangle means 3457 missing data. Where known, Devonian limbed vertebrates have state 0 of each of these 3458 characters. 3459 Character 31: supratemporal/ suture (0) or tabular/parietal suture (1); 147: 3460 presence (0) or absence (1) of parasymphysial; 192: presence (0) or absence (1) of 3461 postbranchial lamina on cleithrum; 212: humerus not (0) waisted (1); 214: humerus L-shaped 3462 (0) or not (1); 260: absence (0) or presence (1) of fusion between left and right pleurocentra in 3463 ventral midline; 277: presence (0) or absence (1) of tail fin skeleton (supraneural radials, 3464 lepidotrichia). See Appendix 1 for more precise definitions and discussion. Note that, of all 3465 adelospondyls, character 260 is only known in Acherontiscus; the adelogyrinids share state 1 3466 if their single-piece centra are pleurocentra, but they have state 0 if their centra are intercentra, 3467 a question we cannot presently decide. Although all anthracosaurs in this matrix are unknown 3468 for character 277, we here show state 0 because of **CM 34638 (Clack, 2011a). 3469 Further derivations occur within some of the composite clades shown here: the highly 3470 nested temnospondyl Micromelerpeton is polymorphic for 31, and the diadectomorph 3471 Tseajaia has state 31(0); Pederpes (nested within Whatcheeriidae) has state 192(1); 3472 Urocordylidae and the diplocaulid Keraterpeton (“lepospondyls”) have state 212(0); 3473 Eusthenopteron, Panderichthys and the embolomeres Archeria and Pholiderpeton scutigerum 3474 have state 212(1), while Limnoscelis and Orobates (Diadectomorpha) as well as the 3475 diplocaulids Keraterpeton and Diceratosaurus have state 212(0); and the highly nested 3476 temnospondyls Doleserpeton and *Gerobatrachus have state 260(1). State 2 of the ordered 3477 character 214 is not shown (Eucritta, which has state 0 or 1, is therefore shown as unknown); 3478 all the OTUs that have this state (an extra-long humerus) are nested well within clades for 3479 which 214(1) is plesiomorphic. 3480 3481 Colosteidae 3482 3483 Given the original taxon sample, Colosteidae is consistently found in a position one node 3484 rootward of Baphetoidea (or Eucritta followed by Baphetidae) and one node crownward of 3485 Crassigyrinus (Fig. 24B), as found e.g. by Pawley (2006) and Ruta (2009) and discussed 3486 immediately above. Adding taxa (Fig. 24C) pushes them and the baphetids further 3487 crownward, where both together form a surprising clade of temnospondyls (discussed below).

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3488 Among the added taxa are two uncontroversial colosteids. Analyses R4–R6 and EB, 3489 the first phylogenetic analyses to include them, unsurprisingly find *Pholidogaster (BPE = 3490 30; PP = 50) and *Deltaherpeton (BPE = 48; PP = 71) as successively closer to Colosteus + 3491 Greererpeton (a clade with a BPE of 76 and a PP of 98). 3492 Also included in the enlarged taxon sample are *Erpetosaurus and the unnamed *St. 3493 Louis tetrapod (MB.Am.1441). The latter was described (Clack et al., 2012b) as having 3494 several similarities to colosteids, but also some to temnospondyls, while lacking several 3495 features otherwise found in colosteids; the former was most recently redescribed as a 3496 dvinosaurian temnospondyl with convergent similarities to colosteids, including features that 3497 the *St. Louis tetrapod lacks (Milner & Sequeira, 2011). In our analyses, the *St. Louis 3498 tetrapod consistently emerges as the sister-group to all other colosteids (BPE = 25; PP = 97), 3499 while *Erpetosaurus is a dvinosaur (BPE = 14, PP = 77; BPE = 20 and PP = 86 for not lying 3500 next to Colosteidae, BPE = 25 and PP = 97 for not being nested within it). 3501 One feature that may be relevant to the relationships of the *St. Louis tetrapod is not 3502 coded in this matrix: as pointed out by Clack et al. (2012b), denticle-covered platelets of 3503 dermal bone that fill the interpterygoid vacuities are only known in that specimen and in 3504 temnospondyls. We speculate that such platelets appear more or less automatically when the 3505 interpterygoid vacuities are wide enough (the *St. Louis tetrapod has the proportionally 3506 widest ones of any colosteid) and denticles are present throughout the roof of the mouth (they 3507 are entirely absent in Batropetes, *Carrolla, apparently *Quasicaecilia, Diplocaulus, 3508 Diploceraspis and lissamphibians except Eocaecilia). This character deserves further 3509 investigation. It may be relevant that Eocaecilia, which fairly clearly lacks such platelets, has 3510 denticles on the pterygoids and the parasphenoid but not on the or palatines (Jenkins, 3511 Walsh & Carroll, 2007). 3512 We have also added *Aytonerpeton, which Clack et al. (2016) described as sharing 3513 several similarities with the colosteids, but found far from Colosteidae in most of their 3514 analyses. One of these features – the premaxillary caniniform region, not coded in our matrix 3515 – represents an intermediate state between plesiomorphic homodonty and the premaxillary 3516 tusk which is found in traditional colosteids (and *Erpetosaurus), where it is accommodated 3517 by a notch in the dentary. This notch is a character in our matrix, and scored as absent for 3518 *Aytonerpeton (Clack et al., 2016) as it is for the generally similar *St. Louis tetrapod; yet, 3519 *Aytonerpeton nests surprisingly highly within Colosteidae, as the sister-group of 3520 (*Deltaherpeton (Colosteus, Greererpeton)) to the exclusion of *Pholidogaster (BPE = 35; 3521 PP = 71), which has the tusk and the notch. To test this further, it will probably be necessary 3522 to fully describe *Aytonerpeton and to reinvestigate the difficult specimens of 3523 *Pholidogaster. 3524 Whether the middle Tournaisian *Aytonerpeton, which is older than the Viséan *St. 3525 Louis tetrapod, can claim the title of oldest known colosteid depends on two other specimens: 3526 the **“Type 3 humerus” from in Nova Scotia (middle Tournaisian) and possibly 3527 **“Ribbo” from the early middle Tournaisian site of Willie’s Hole in (Old) Scotland 3528 (Anderson et al., 2015; Clack et al., 2016). 3529 3530 The interrelationships of Anthracosauria, Silvanerpeton, Caerorhachis, Gephyrostegidae, 3531 Casineria and Temnospondyli 3532 3533 Although [anthracosaurs have] long [been] associated with the amniote stem, this link appears to 3534 be increasingly tenuous. 3535 – Coates, Ruta & Friedman, 2008: 579 3536 3537 Ever since the early 20th century, Anthracosauria (which traditionally encompassed at least 3538 Embolomeri and the more recently discovered Eoherpeton) has generally been considered

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3539 closer to Amniota than Temnospondyli is. The analysis by RC07 supported this “textbook” 3540 consensus (Fig. 24A). However, both the anthracosaurs and the temnospondyls share features 3541 with Amniota, Diadectomorpha, “Lepospondyli”, Seymouriamorpha and/or Solenodonsaurus 3542 that the other taxon lacks (Fig. 24). Consequently, Temnospondyli has been found closer to 3543 Amniota than Anthracosauria is in a few phylogenetic analyses (Ahlberg & Clack, 1998; 3544 Laurin & Reisz, 1999: bootstrap tree and discussion; Pawley, 2006; Klembara et al., 2014, 3545 with poor support; some MPTs of Pardo et al., 2017). 3546 Our results are best considered inconclusive on this point. Analysis R1 finds 3547 Anthracosauria equally parsimoniously rootward (BPE = 6; PP = 48) or crownward of 3548 Temnospondyli (BPO = 12), while R2 fixes the rootward and R4–R6 the crownward position. 3549 Part of the reason may be character conflict: not only Anthracosauria and 3550 Temnospondyli have conflicting combinations of character states, but so do other taxa found 3551 in the same area of the tree (Fig. 24). 3552 Silvanerpeton, found as an anthracosaur (the sister-group to all others) by RC07 (BPO 3553 = 10; BPE = 6), lies one node more crownward (PP = 48) in all of our analyses except B1 and 3554 B2 (Fig. 24B, C). This is tenuous, however; earlier versions of our matrix (Marjanović & 3555 Laurin, 2015, 2016) show Silvanerpeton as an anthracosaur, one node more crownward or one 3556 node more rootward in different analyses or often in the same ones, indicating that its position 3557 depends on small changes to various scores as well as the taxon sample and constraints on 3558 other taxa. 3559 Caerorhachis is variously considered to be close to the origin of temnospondyls and/or 3560 anthracosaurs (Ruta, Milner & Coates, 2002, and references therein; Clack et al., 2016). RC07 3561 found Caerorhachis one node closer to Amniota than Temnospondyli and one node farther 3562 away than Anthracosauria (Fig. 1, 24A). This is the only position found by Analyses R4–R6 3563 (Fig. 24C). In Analyses R1 and R3, however, Caerorhachis can also be the sister-group to all 3564 other temnospondyls (Fig. 24B; BPO of Temnospondyli including Caerorhachis: 14), as 3565 found by Pawley (2006) and suggested earlier by Godfrey, Fiorillo & Carroll (1987). 3566 Analyses R2, B2 and EB place Caerorhachis rootward of both Temnospondyli (BPE = 6; PP 3567 = 48) and Anthracosauria (BPE = 4; PP = 44). 3568 RC07, and more recently Witzmann & Schoch (2017), found Gephyrostegus one node 3569 rootward of Bruktererpeton. In Analyses R1–R3, they form either a clade (BPO = 53; BPE = 3570 42; PP = 69) as found by Klembara et al. (2014) in their redescription of the skull of 3571 Gephyrostegus, or (in some MPTs from R1 and R3) Bruktererpeton is one node rootward of 3572 Gephyrostegus (Fig. 24B). Only the latter arrangement occurs in R4–R6 (Fig. 24C). As found 3573 by RC07 and Witzmann & Schoch (2017), Gephyrostegus and Bruktererpeton are crownward 3574 of Anthracosauria in all analyses. A sister-group relationship of Gephyrostegus (or 3575 Gephyrostegidae) to Anthracosauria, as found by Pawley (2006), does not occur (though it is 3576 only contradicted by BPO = 16; BPE = 6; PP = 48); it may be relevant that Pawley’s (2006) 3577 taxon sample lacked Silvanerpeton and Bruktererpeton. 3578 *Casineria emerges in the gephyrostegid grade (Fig. 24C): variously one node 3579 crownward of Gephyrostegus (BPE = 4 and PP = 27 for lying crownward of Gephyrostegidae, 3580 BPE = 7 and PP = 55 for lying rootward of Chroniosuchia), one node rootward of 3581 Bruktererpeton, between the two, or as the sister-group of Bruktererpeton. This is novel, but 3582 perhaps not too surprising. Originally, *Casineria was thought to lie very close to the origin 3583 of Amniota (Paton, Smithson & Clack, 1999; against a BPE of 9 and a PP of 55). Clack et al. 3584 (2012b) and Witzmann & Schoch (2017, using a very similar matrix) found it slightly more 3585 distant, i.e. as a “lepospondyl” (more precisely in a clade with Westlothiana and both of the 3586 sampled “microsaurs”; against a BPE of 13 and a PP of 55). Clack et al. (2016) increased the 3587 distance slightly farther, finding it as a seymouriamorph (against a BPE of 9 and a PP of 55) 3588 or in the same grade (against a BPE of 7 and still the same PP of 55) in all analyses. In the

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3589 meantime, Pawley (2006: 207) noted that *Casineria scored identically to Caerorhachis in 3590 her matrix, apart from the (quite different) distribution of missing data; the matrix contains an 3591 unusually large amount of postcranial characters, well suited for the headless skeleton called 3592 *Casineria. In our matrix, for which D. M. studied the only known *Casineria specimen (part 3593 and counterpart: NMS G 1993.54.1p, NMS G 1993.54.1cp) for a full day, Caerorhachis and 3594 *Casineria are likewise indistinguishable. Pawley’s (2006: fig. 62) phylogenetic analysis 3595 featured a trichotomy of *Casineria, Caerorhachis and all other temnospondyls, with strong 3596 bootstrap and Bremer support for Temnospondyli (fig. 63). Between Caerorhachis on one 3597 side and the seymouriamorph-“lepospondyl”-amniote clade on the other, the positions we find 3598 for *Casineria lie in the middle. 3599 Paton, Smithson & Clack (1999) emphasized that *Casineria had gastrocentrous 3600 vertebrae and claws, highlighting especially the latter as an amniote-like feature. Pawley 3601 (2006: 239; see also 195) remarked: “As in Caerorhachis bairdi, none of the postcranial 3602 characteristics claimed to be ‘reptiliomorph’ in Casineria kiddi are truly apomorphic for the 3603 amniote lineage. All are present in temnospondyls […], or potentially may be present in basal 3604 temnospondyls (including the five[-] manus), because they are plesiomorphic for early 3605 tetrapods.” We confirm that the vertebrae of *Casineria with their large intercentra are more 3606 reminiscent of Caerorhachis and animals in vaguely the same grade like the anthracosaur 3607 Proterogyrinus or, to a lesser degree, the temnospondyl Neldasaurus than of amniotes, 3608 seymouriamorphs or even chroniosuchians (Fig. 5); indeed, they differ from those of 3609 Caerorhachis at most in a slightly lesser degree of ossification. Although the terminal 3610 phalanges are distally pinched and curved plantarly, they are neither pointed as expected of a 3611 claw, nor rounded as incorrectly shown in the interpretative drawing by Paton, Smithson & 3612 Clack (1999: fig. 3b). Instead, their ends are squared off (Fig. 6). This shape is intriguingly 3613 similar to the outline drawings of the terminal phalanges of Caerorhachis by Holmes & 3614 Carroll (1977: fig. 13), who unfortunately did not provide more detailed illustrations or any 3615 description. These two character complexes, thus, are not obstacles to placing *Casineria far 3616 from amniote origins. Moreover, if our very tentative identification of distal carpal 1 in Fig. 6 3617 is correct, the first distal carpal began to ossify before the fourth in *Casineria, a 3618 plesiomorphic condition not found in amniotes or diadectomorphs (see below, Discussion: 3619 Characters: Preaxial polarity in limb development, for more discussion and references). 3620 Going beyond her matrix, Pawley (2006: 195, 239) called Caerorhachis and 3621 *Casineria “indistinguishable based on the available evidence”. Now that D. M. has seen the 3622 *Casineria specimen (Fig. 5–7), we can only find four differences to the thorough 3623 redescription of Caerorhachis by Ruta, Milner & Coates (2002): Caerorhachis is larger and 3624 has more elongate (but otherwise identical) ventral scales, a slightly more prominent dorsal 3625 process on the ilium and taller ossified parts of the neural spines. All four can effortlessly be 3626 ascribed to ontogeny. Indeed, the neural spines of *Casineria are capped by a black material 3627 (Fig. 5; likely pyrite or another iron sulfide) that is also found on the incompletely ossified 3628 ends of long bones (Fig. 6) and may be related to cartilage decay. (For scale ontogeny, see 3629 Witzmann [2007, 2010].) Lack of difference is not a synapomorphy; our analyses do not 3630 currently find Caerorhachis and *Casineria as sister-groups – if only, perhaps, because the 3631 skull of *Casineria is unknown and postcranial characters are underrepresented in our matrix 3632 –, and the two specimens come from close but not identical ages and localities. Still, the 3633 possibility should be seriously considered that *Casineria, once redescribed, could turn out to 3634 be either a synonym or the closest known relative of Caerorhachis. Rearranging a tree from 3635 Analysis R4 to form a clade of Caerorhachis, *Casineria and optionally the *Parrsboro jaw 3636 (see below) takes two extra steps in Mesquite, moving this clade next to the traditional 3637 temnospondyls (Pawley, 2006) takes one more; both actions contradict nodes with a BPE of 6 3638 and a PP of 48.

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3639 Character conflict in this part of the tree concerns, among others, features that are 3640 probably relevant to the origin of terrestriality (Fig. 24). At least one anthracosaur (**CM 3641 34638: Clack, 2011a; see also Holmes & Carroll, 2010) retained a dermal and endochondral 3642 tail fin skeleton (state CAU FIN 1(0) in this matrix, see character 276 in Appendix 1); 3643 unknown in Silvanerpeton (Ruta & Clack, 2006), Bruktererpeton and Gephyrostegus, it is 3644 absent in all temnospondyls that are well enough known to tell. The anthracosaur Archeria is 3645 known (Pawley, 2006: chapter 6) to retain the postbranchial lamina on the cleithrum (CLE 3646 2(0), see character 192 in Appendix 1); due to preservation and publication bias (the lamina is 3647 practically only visible in cranial or caudal view), this character is unknown in many OTUs in 3648 this matrix, but the lamina is absent in Gephyrostegus and all sufficiently well known 3649 unquestioned temnospondyls (e.g. Pawley, 2006: chapter 6). Because D. M. (pers. obs.) has 3650 identified what seems to be a postbranchial lamina quite similar to that of Archeria (depicted 3651 by Pawley, 2006: fig. 70-2.4) on the cleithrum of *Casineria, presented here in Fig. 7, we 3652 have scored *Casineria as possessing the lamina; this will require further investigation. If 3653 correct, it is a further argument for removing *Casineria from amniote origins. 3654 Anthracosauria, Silvanerpeton and Gephyrostegidae retain flat humeri (HUM 10(0)), while 3655 *Casineria (D. M., pers. obs.) shares a waisted (HUM 10(1)), twisted humerus shape with all 3656 skeletally mature temnospondyls (unknown in Caerorhachis); the anthracosaurs Eoherpeton, 3657 Proterogyrinus and *NSM 994 GF 1.1 additionally retain an L-shaped humerus (HUM 12- 3658 15(0)) where the entepicondyle is about as long (measured along its proximal margin) as the 3659 part of the humerus proximal to it, which is not seen in Archeria or Pholiderpeton scutigerum 3660 (unknown in Ph. attheyi, Anthracosaurus, *Palaeoherpeton and *Neopteroplax) or in the 3661 other taxa listed in this paragraph. Finally, pleurocentra that fuse in the ventral midline (TRU 3662 VER 8(1)) are found in all the taxa listed in this paragraph except the unquestioned 3663 temnospondyls. (Among the latter, TRU VER 8(1) does occur in Doleserpeton and 3664 *Gerobatrachus, as well as in some **brachyopid stereospondyls and some **tupilakosaurid 3665 dvinosaurs, but these are too highly nested to be relevant here [Warren, 1999; Werneburg et 3666 al., 2007; Warren, Rozefelds & Bull, 2011].) However, while state TRU VER 8(1) 3667 presumably increases the resistance of the to compression, this may be 3668 dorsoventral compression from bearing weight just as well as mediolateral compression from 3669 e.g. anguilliform swimming. Various amphibious and terrestrial temnospondyls, on the other 3670 hand, elaborated the neural arches and (in ) neomorphic osteoderms into a 3671 weight-bearing apparatus that evidently did not need extensively ossified centra; furthermore, 3672 the vertebral columns of Gephyrostegus and Bruktererpeton in particular look rather supple in 3673 reconstructions despite showing state TRU VER 8(1). 3674 A postbranchial lamina on the , not coded here, has been identified in the 3675 dvinosaur **Thabanchuia (Witzmann, 2013) and in a number of *stereospondyls: Schoch & 3676 Witzmann (2010) described it in **Plagiosuchus and **Trematolestes; D. M. has seen it on a 3677 clavicle of ** that, as of 2015, was to be catalogued by the University of Opole 3678 (); Yates & Warren (2000: fig. 7) depicted it in **Benthosuchus, **, 3679 **Lyrocephaliscus and **Koskinonodon – they only called it “anterior flange (prescapular 3680 process)”, but Florian Witzmann (pers. comm. 2015) confirms that this structure is most 3681 likely identical to the postbranchial lamina. The homology of the postbranchial laminae on the 3682 cleithrum of non-temnospondyls and the clavicle of temnospondyls remains unclear at the 3683 moment. 3684 Interestingly, the parasymphysial bone in the lower jaw (PSYM 1(0)) has the same 3685 distribution as the postbranchial lamina on the cleithrum, missing data and aïstopods excepted 3686 (Fig. 24). 3687 Noting the presence of anthracosaurs and Tulerpeton-like animals soon after the 3688 beginning of the Carboniferous, Anderson et al. (2015) drew attention to the old idea that all

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3689 or almost all limbed vertebrates are part of the smallest clade that contains Anthracosauria and 3690 Temnospondyli. “If Tulerpeton represents the earliest occurrence of embolomeres (as appears 3691 to be suggested by the close similarity between humeral and femoral morphology)” 3692 (Anderson et al., 2015: 24), the last common ancestor of anthracosaurs and temnospondyls 3693 would have lived in the Devonian. However, Anderson et al. (2015) provided no support for 3694 this complex of ideas, which contradicts the current consensus (including RC07), beyond 3695 citing Lebedev & Coates (1995); they did not mention the reanalysis and refutation of the 3696 latter by Laurin (1998b). Unsurprisingly, then, these historical hypotheses are not supported 3697 by our analyses; as discussed by Pawley (2006), the similarities between Tulerpeton and 3698 Anthracosauria are synapomorphic at that level, but were further modified by Temnospondyli 3699 and various other branches – they represent intermediate states. A fortiori, even if some or all 3700 extant amphibians are temnospondyls, there is currently no strong reason to think that the 3701 origin of the tetrapod crown-group happened in the Devonian as Anderson et al. (2015) 3702 speculated. The highest support values that keep Tulerpeton away from Anthracosauria are 3703 BPO = 67, BPE = 22 and PP = 86 (Fig. 18–20); the lack of support in the parsimony analyses 3704 of the extended taxon sample is likely due to the unstable positions of Eucritta, 3705 Temnospondyli, Caerorhachis and the *Parrsboro jaw which can all intervene between 3706 Tulerpeton and Anthracosauria. 3707 A topology somewhat similar to the above scenario was found by Klembara et al. 3708 (2014), where a weakly supported (Crassigyrinus (Whatcheeria, Anthracosauria)) clade and a 3709 weakly supported clade composed of Baphetidae and Temnospondyli were found. However, 3710 the second clade came out – likewise with weak support – as closer to Amniota than the first 3711 clade, which appeared just one node crownward of Ichthyostega. Containing 36 ingroup taxa 3712 (a quarter of them seymouriamorphs; Tulerpeton was not sampled), an all-zero outgroup 3713 (Klembara & Ruta, 2004b: 86 – see Marjanović & Laurin, 2008, for discussion of this 3714 practice) and 156 characters (many of course focused on seymouriamorphs), their matrix 3715 seems at least a priori less well suited to resolving this problem than ours. 3716 At present, the oldest known anthracosaurs date (as mentioned) from the middle 3717 Tournaisian (Anderson et al., 2015), while the oldest known temnospondyls appear only after 3718 Romer’s Gap (Balanerpeton, possibly Caerorhachis, perhaps *Casineria: Milner & Sequeira, 3719 1994; Paton, Smithson & Clack, 1999; Ruta, Milner & Coates, 2002; no temnospondyls have 3720 been identified in the middle Tournaisian material reported by Anderson et al., 2015, and 3721 Clack et al., 2016). This is congruent with the hypothesis that Temnospondyli and the 3722 tetrapod crown-group, which is likewise currently unknown before the end of Romer’s Gap, 3723 are more closely related to each other than to Anthracosauria. However, current understanding 3724 of the diversity of limbed vertebrates during Romer’s Gap is still very poor; the current 3725 absence of evidence may turn out not to be evidence of absence. 3726 3727 The “Parrsboro jaw” 3728 3729 An incomplete natural mold of a partly crushed lower jaw, the *Parrsboro jaw in our 3730 expanded taxon sample, has only two positions in our parsimony analyses (Fig. 24C): it is 3731 either the sister-group of Caerorhachis (BPE = 31; contradicting a node with a PP of 48) or 3732 that of all traditional temnospondyls (against a PP of 45). Both positions lie within the large 3733 range found by Sookias, Böhmer & Clack (2014) in their much smaller analysis. Analysis EB 3734 recovers what amounts to an intermediate position, rootward of Temnospondyli and 3735 Gephyrostegidae but crownward of Silvanerpeton. 3736 Immediately, a character comes to mind that is absent from the present matrix but 3737 would influence the position of the *Parrsboro jaw: the presence/absence of denticles on the 3738 prearticular. Presence, a plesiomorphy shared with e.g. colosteids (Bolt & Lombard, 2001), is

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3739 found in the *Parrsboro jaw and in Caerorhachis but not, to our knowledge, in (other) 3740 temnospondyls or for that matter any anthracosaur-grade animals. A denticle field that covers 3741 most of the lingual face of the prearticular (extending onto the splenial at least in 3742 Caerorhachis), instead of being restricted to the dorsal side, even seems to be entirely limited 3743 to Caerorhachis and the *Parrsboro jaw among all sarcopterygians. 3744 3745 Anthracosaurian phylogeny 3746 3747 In the analyses of the original taxon sample (R1–R3 and B1), Anthracosauria is resolved as in 3748 RC07 when it lies rootward of Temnospondyli (the only option in R2), but in two other ways, 3749 with Pholiderpeton scutigerum as the sister-group of either (Proterogyrinus + Archeria) or 3750 (Ph. attheyi + Anthracosaurus), when it lies crownward of Temnospondyli. Bootstrap support 3751 greater than 50% or a posterior probability greater than 75% exists for three nodes: 3752 Anthracosauria (not including Silvanerpeton; BPO = 54; BPE = 20; PP = 97), Embolomeri 3753 (BPO = 52; BPE = 21; PP = 99), Embolomeri except Proterogyrinus (PP = 94; against a BPO 3754 of 33 and a BPE of 31) and Pholiderpeton attheyi + Anthracosaurus excluding Ph. 3755 scutigerum (BPO = 57; PP = 68; against a BPE of 18). 3756 Adding taxa narrows these topologies down to that of RC07, even though 3757 Anthracosauria is consistently crownward of Temnospondyli in Analyses R4–R6 (against a 3758 BPE of 6 and a PP of 48); the three added OTUs form a clade (*NSM 994 GF 1.1 3759 (*Palaeoherpeton, *Neopteroplax); against a BPE of 28 and a PP of 62), which nests with 3760 Anthracosaurus (BPE = 28; PP = 58). 3761 Like RC07, we consistently find that Pholiderpeton scutigerum and Ph. attheyi are not 3762 sister-groups (BPO = 57; BPE = 25; PP = 68). A logical consequence (if para- or polyphyletic 3763 genera are to be avoided) would be to reinstate the genus name Eogyrinus Watson, 1926, for 3764 Ph. attheyi. However, we refrain from performing a taxonomic act because Pawley (2006: 3765 chapter 6) did find these two species as sister-groups using a different and larger character 3766 sample (but the same sample of possible anthracosaurs as RC07, minus Silvanerpeton), not to 3767 mention the weak support for our result. 3768 We are more confident that the traditional taxon Eogyrinidae, comprising all 3769 embolomeres except Proterogyrinus, Archeria and Anthracosaurus, is paraphyletic (BPO = 3770 57; BPE = 28; PP = 68). These taxa were only found to form a clade in the much smaller 3771 analysis of Buchwitz et al. (2012), which was focused on chroniosuchians. 3772 3773 Temnospondyl large-scale phylogeny 3774 3775 I shall refrain here from discussion of the temnospondyls, although work being done at present, 3776 by Baird and Carroll, for example, suggests progress toward sorting out true phyletic lines 3777 among the Rhachitomi in preference to the somewhat artificial grouping which I used in my 3778 1947 classification. 3779 – Romer (1964: 154) 3780 3781 More than fifty years after this hopeful statement, temnospondyl phylogeny remains poorly 3782 understood (Fig. 25). RC07, fittingly, found the base of Temnospondyli to be a polytomy of 3783 Edopoidea ( = Edops + Cochleosauridae), Dvinosauria, Balanerpeton, Dendrerpetidae and an 3784 Eryops-Dissorophoidea clade (Fig. 25A); *stereospondylomorphs were not included in the 3785 matrix. Most of the mathematically possible resolutions of this polytomy have been found in 3786 more focused but still large analyses: Pawley (2006: chapter 5; Fig. 25B) found Edops alone 3787 as the sister-group to all other temnospondyls (except Caerorhachis, see above and below), 3788 among which a (Capetus (Dendrerpetidae, Balanerpeton)) clade, Cochleosauridae, 3789 Dvinosauria, paraphyletic *stereospondylomorphs and Eryops were successively closer to

97 Caerorhachis (outgroup) Edops Capetus Dendrerpetidae 85 Balanerpeton *Saharastega Edops 82 60 Chenoprosopus Chenoprosopus 63 *Nigerpeton Cochleosaurus Cochleosaurus Dvinosauria Dvinosauria 60 100 Balanerpeton *Archegosaurus Capetus 90 *Platyoposaurus 64 Dendrerpetidae 87 *Konzhukovia Eryops 90 *Lydekkerina Dissorophoidea 88 *Sclerocephalus (content) 64 *Cheliderpeton + *Glanochthon Eryops *Acanthostomatops *Iberospondylus Dissorophoidea (content) A B 97

Neldasaurus “dvinosaurs” 1 Trimerorhachis *Lydekkerina “stereospondylomorph” 1 Isodectes “dvinosaur” 2 Edops Chenoprosopus Micromelerpeton Cochleosaurus Apateon Branchiosauridae Capetus Dendrerpetidae *Acanthostomatops Amphibamidae incl. dissorophids, trematopids Eryops Balanerpeton *Sclerocephalus Capetus 90 *Glanochthon Edops Dendrerpeton confusum *Nigerpeton Edopoidea (rest-dendrerpetid OTU) Chenoprosopus Balanerpeton Cochleosaurus *Sclerocephalus Dvinosauria “stereospondylo- *Cheliderpeton morphs” 2 Dissorophoidea (content) *Archegosaurus Eryops *Saharastega C D *Acanthostomatops

Capetus Dendrerpetidae Balanerpeton *Iberospondylus Capetus Edops *Iberospondylus Cochleosaurus 98 Eryops Chenoprosopus 55 *Sclerocephalus 98 *Nigerpeton Dendrerpetidae *Glanochthon 78 Balanerpeton *Archegosaurus *Australerpeton Dvinosauria 79 Dendrerpetidae 61 *Acanthostomatops Balanerpeton 81 Dissorophoidea (content/S13) Capetus 93 Capetus Edops *Iberospondylus Cochleosaurus Eryops Chenoprosopus 51 *Sclerocephalus *Nigerpeton 51 *Glanochthon Dvinosauria *Archegosaurus *Acanthostomatops *Australerpeton E F Dissorophoidea (content/S13)

Dvinosauria 62\100 Dendrerpetidae 92\100 66\99 Balanerpeton Capetus Dendrerpetidae (outgroup) ?\97 Edops Eryops *Nigerpeton ?\78 99\100 41 Dissorophoidea (content) ?\55 Cochleosaurus 95 ?\91 Chenoprosopus 100 Trimerorhachis ?\? *Iberospondylus *Sclerocephalus 84 *Acanthostomatops *Archegosaurus 24 ?\81 ?\91 Dissorophoidea (content/S13) *Platyoposaurus ?\99 21 18 Eryops *Konzhukovia ?\98 8 44 *Sclerocephalus ?\97 13 *Australerpeton *Archegosaurus 14 *Lydekkerina ?\100 88\100 *Platyoposaurus ?\100 *Glanochthon ?\77 *Australerpeton ?\99 *Lydekkerina G H 99

3790 ↑ Figure 25: Hypotheses on temnospondyl phylogeny since 2006. Taxa absent from our 3791 expanded taxon sample are omitted, those we added to the sample of RC07 are marked with 3792 an asterisk. Dvinosauria and Dissorophoidea are collapsed where possible. The colored 3793 rectangles (labeled in D) and the terms “Dissorophoidea (content)” and “Dissorophoidea 3794 (S13)” are consistent with Figures 2 and 10–19. The matrices of A–C are ultimately based on 3795 that of Ruta, Coates & Quicke (2003), so they – and ours (Fig. 26) – should not be considered 3796 fully independent of each other. Numbers below internodes are bootstrap percentages; those 3797 below 50 were, except in G, not published. A: strict consensus of RC07; non-temnospondyls 3798 omitted. Dissorophoidea is marked in boldface for being extant because it contains 3799 Lissamphibia; this is the only analysis shown here that included any lissamphibians. RC07 3800 (appendix 4) performed a bootstrap analysis but did not publish the results for the part of the 3801 tree shown here. B: Pawley (2006: chapter 5). “*Cheliderpeton + *Glanochthon” was a single 3802 OTU called “Cheliderpeton spp.”; the name Glanochthon had not yet been coined. 3803 *Acanthostomatops was included as part of a Zatracheidae OTU. C: Ruta (2009), strict 3804 consensus of analysis without reweighting; non-temnospondyls omitted. *Glanochthon 3805 latirostris was called by its previous name, “Cheliderpeton latirostre”. The “rest-dendrerpetid 3806 OTU” was called “Dendrerpeton acadianum”, but may have contained information from 3807 other dendrerpetids as well; see Material and methods: Treatment of OTUs: Dendrerpetidae. 3808 D: McHugh (2012); non-temnospondyl omitted. Dissorophidae (as two clades, one of which 3809 contains Broiliellus brevis) and Trematopidae (also as two clades) are nested in three different 3810 places within Amphibamidae. All bootstrap percentages of the nodes shown here are below 3811 50 and were not published. E, F: all equally parsimonious topologies (8 MPTs) from the 3812 analysis of 48 taxa in Dilkes (2015a); non-temnospondyls omitted. Note (in F) that 3813 Dendrerpetidae and Balanerpeton are sister-groups in all MPTs. To see the individual MPTs, 3814 we repeated the analysis (calculation time: 00:04:36.5), finding MPTs of the same number, 3815 length and indices as published by Dilkes (2015a). The bootstrap percentages are from Dilkes 3816 (2015a: fig. 11B), which shows an analysis where Capetus and *Iberospondylus were 3817 omitted; the topology is otherwise identical to E. G: Pereira Pacheco et al. (2016), focused on 3818 stereospondylomorphs. Two species of *Platyoposaurus and three of *Konzhukovia were 3819 included as separate OTUs. The tree by Eltink et al. (2016) is fully compatible. H: Pardo, 3820 Small & Huttenlocker (2017); non-temnospondyls and lissamphibians omitted (the MPTs 3821 differ only in the positions of the lissamphibians and **Chinlestegophis). Numbers are 3822 bootstrap percentages followed by Bayesian posterior probabilities in % (boldface if ≥ 75, not 3823 published < 50). 3824 3825 Dissorophoidea. Ruta (2009; Fig. 25C) found Edopoidea as a whole to be the sister-group to 3826 all other temnospondyls, among which Capetus, (Eryops + *Stereospondylomorpha), 3827 Dendrerpeton confusum and “D. acadianum” were successively closer to a trichotomous 3828 clade formed by Balanerpeton, Dvinosauria and Dissorophoidea; the only two 3829 *stereospondylomorphs in the matrix were *Sclerocephalus and *Glanochthon. (The OTU 3830 called “Dendrerpeton acadianum” most likely included Dendrysekos.) McHugh (2012; Fig. 3831 25D) found Neldasaurus, otherwise considered a dvinosaur, to be the sister-group of all other 3832 temnospondyls; those were divided into, on the one hand, a clade that contained the 3833 *stereospondyls and the neotenic dissorophoids inside a clade formed by the remaining 3834 dvinosaurs, and on the other hand a clade that contained (Dendrerpetidae + non-aquatic 3835 dissorophoids), (Balanerpeton + Capetus), Edopoidea and Eryops as successively closer 3836 relatives of the remaining *stereospondylomorphs. After deleting the colosteid Greererpeton 3837 from his taxon sample, Schoch (2013) recovered Edopoidea and (Balanerpeton + 3838 Dendrerpetidae) successively closer to a trichotomy of Dvinosauria, Dissorophoidea and 3839 Eryopiformes ( = Eryops + Stereospondylomorpha) – when he used TNT; PAUP 3.1 failed to

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3840 find any of the shortest trees (Schoch, 2013: 682). Dilkes (2015a) analyzed an expanded and 3841 corrected version of Schoch’s (2013) dataset. Given the full sample of 73 OTUs (Dilkes, 3842 2015a: fig. 10), he found a polytomy of Capetus, *Iberospondylus, (Dendrerpetidae + 3843 Balanerpeton), Edopoidea and a clade which contained all other temnospondyls; that clade 3844 was itself a polytomy of *Zatracheidae, Eryopidae, Dissorophoidea, a clade containing the 3845 *non-stereospondyl stereospondylomorphs and three separate clades of *stereospondyls. 3846 Deleting 25 OTUs, but not Greererpeton, resulted (Dilkes, 2015a: fig. 11A) in a single 3847 eryopiform clade that contained Eryops (the remaining eryopid) and the *non-stereospondyl 3848 stereospondylomorphs as a grade within which a single *stereospondyl clade was nested, and 3849 also revealed a (Dvinosauria (*Zatracheidae, Dissorophoidea)) clade, but continued to resolve 3850 the relationships of these clades in two very different ways (Fig. 25E, F). Only the additional 3851 deletion of Capetus and *Iberospondylus (Dilkes, 2015a: fig. 11B) made Eryopiformes 3852 consistently the sister-group of the (Dvinosauria (*Zatracheidae, Dissorophoidea)) clade, 3853 followed on the outside by (Dendrerpetidae + Balanerpeton) and finally Edopoidea as in 3854 Schoch (2013) and in Fig. 25E. Using the dendrerpetid Dendrysekos as the outgroup, Eltink & 3855 Langer (2014) found the ingroup to be divided into (Eryops + Dissorophoidea) and 3856 (Dvinosauria + *Stereospondylomorpha); theirs was a *stereospondylomorph-focused 3857 analysis where Trimerorhachis was the only included dvinosaur. The same holds for Pereira 3858 Pacheco et al. (2016; Fig. 25G) and for Eltink et al. (2016), who omitted Dissorophoidea 3859 altogether. Pardo, Small & Huttenlocker (2017: supplementary information part D; Fig. 25H) 3860 accepted most of the corrections by Dilkes (2015a – not mentioned by Pardo, Small & 3861 Huttenlocker, 2017) but added taxa, omitted others, and omitted the characters Dilkes had 3862 added. Dvinosauria emerged as the sister-group to the rest of the ingroup under both 3863 parsimony and Bayesian inference (Pardo, Small & Huttenlocker, 2017: fig. S7B and 2 = 3864 S7A, respectively); (Dendrerpetidae + Balanerpeton), Capetus, Edopoidea, *Iberospondylus, 3865 **Peltobatrachus, Eryopiformes, *Zatracheidae and **Lapillopsis (previously considered a 3866 stereospondyl) were found successively closer to Dissorophoidea in all MPTs, with the 3867 positions of Capetus and **Peltobatrachus slightly destabilized in the Bayesian analysis. 3868 This diversity of topologies appears to result in large part from the use of different 3869 outgroups. Pawley (2006) used Caerorhachis as the outgroup in chapter 5 after finding it to 3870 be in a trichotomy with *Casineria and all other temnospondyls in chapter 6 (her main 3871 analysis of the phylogeny of the limbed vertebrates). Ruta (2009) included a variety of early 3872 limbed vertebrates, but entirely omitted the taxa that form the amniote total group in the trees 3873 of RC07 (see Fig. 1), including Gephyrostegidae, Anthracosauria and Caerorhachis – the 3874 closest relative of Temnospondyli in his trees is Baphetoidea. McHugh (2012) used 3875 Greererpeton as the outgroup. Schoch (2013) chose the anthracosaur Proterogyrinus; in 3876 analyses where he included Greererpeton in the ingroup for unstated reasons, Greererpeton 3877 either fell out as the sister-group to Temnospondyli or, “in some variant analyses of the large 3878 dataset (66 taxa, ‘no swapping’ option in PAUP), Greererpeton nests with the dvinosaurs, and 3879 in another variant Greererpeton and Neldasaurus form a ‘clade’ at the very base of the tree 3880 (66 taxa, ‘no swapping’ option, TNT). Whereas this reflects similarities in the postorbital 3881 skull shared by the two taxa, it also shows that aquatic taxa with particular features are 3882 sometimes attracted despite the obvious homoplastic status of these characters (indicated by 3883 multiple conflicting evidence).” This attraction between Greererpeton and Neldasaurus 3884 replicates the result of McHugh (2012), as does, to a lesser extent, the attraction of 3885 Greererpeton to the dvinosaurs as a whole. Unfortunately, however, Schoch (2013: 693) did 3886 not report the lengths of these trees; the lack of branch-swapping means that the local optima 3887 found in each tree-building replicate were not explored any further, which makes it likely that 3888 the reported trees are suboptimal. Notably, however, Greererpeton did not have such effects 3889 in the analyses of a version of that matrix improved by Dilkes (2015a). In the next version of

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3890 the same matrix, Pardo, Small & Huttenlocker (2017: supplementary information part D) kept 3891 Proterogyrinus as the outgroup, and Greererpeton emerged as the sister-group to the rest of 3892 the ingroup, followed as mentioned by the monophyletic dvinosaurs. 3893 Our analyses of the original taxon sample (R1–R3, B1; Fig. 26A–C) consistently place 3894 the colosteids far away from Temnospondyli. Yet, of those MPTs in which Temnospondyli is 3895 crownward of Anthracosauria (which is all in R2), some (all in R2; Fig. 26A) find 3896 Dvinosauria (which has a BPO of 35) as the sister-group to all other temnospondyls (except 3897 Caerorhachis in some from R1; BPO = 40). This clade of all other temnospondyls (BPO = 3898 18) consists (against a BPO of 30) of a dichotomy of Dissorophoidea on the one side and an 3899 unusual clade on the other side in which (Balanerpeton + Dendrerpetidae), Capetus and 3900 Eryops (BPO = 19) are successively closer to a surprisingly highly nested Edopoidea 3901 (monophyletic: BPO = 26). Other MPTs from R1 and R3 (Fig. 26B) find Temnospondyli 3902 (always excluding Caerorhachis) as containing a backbone of (Dissorophoidea (Eryops 3903 (Cochleosauridae (Capetus (Trimerorhachis (Balanerpeton, Dendrerpetidae)))))) (against a 3904 BPO of 30); (Isodectes + Neldasaurus) is the sister-group of Trimerorhachis or of all other 3905 temnospondyls, among which Edops is one node closer to or one node farther from 3906 Dendrerpetidae than Capetus is. Finally, those MPTs (from R1 and R3; Fig. 26C) where 3907 Temnospondyli is rootward of Anthracosauria consistently resolve it as a Hennigian comb of 3908 (Edops (Cochleosauridae (Eryops (Capetus (Dvinosauria (Dendrerpetidae, 3909 Dissorophoidea)))))), with Balanerpeton as the sister-group of either of the last two. This 3910 position of Edops is reminiscent of Pawley (2006: chapter 5; Fig. 25B). Analysis B1, where 3911 Temnospondyli is again rootward of Anthracosauria, finds a sort of compromise topology, 3912 with Dvinosauria on the outside (BPO = 18) except for Caerorhachis, Eryops next to 3913 Edopoidea (BPO = 19), Dissorophoidea next to (Balanerpeton + Dendrerpetidae) (BPO = 30), 3914 and very weak support overall (Fig. 18). 3915 Analyses R4–R6 (Fig. 26C, D) find Temnospondyli rootward of Anthracosauria – so 3916 far rootward that Temnospondyli contains Eucritta and (Colosteidae + Baphetidae) 3917 successively closer to the clade of traditional temnospondyls (a surprising return to 20th- 3918 century classifications, contradicting a BPE of 20 and a PP of 86) and optionally the 3919 *Parrsboro jaw (see above). In keeping with its rootward position, the clade of traditional 3920 temnospondyls is resolved in R4 and R6 as in corresponding trees from R1 and R3, namely as 3921 (Edops (Cochleosauridae (Eryopiformes (Capetus (Dvinosauria ((Balanerpeton, 3922 Dendrerpetidae) (*Iberospondylus, Dissorophoidea))))))); in R5, Dvinosauria sometimes (Fig. 3923 26D) enters Stereospondylomorpha, and Eryopiformes sometimes becomes a grade (with 3924 Stereospondylomorpha closer to Dissorophoidea than to Eryops), in which latter case 3925 Dvinosauria can fall out rootward of it or as the sister-group of Stereospondylomorpha, i.e. as 3926 part of Limnarchia Yates & Warren, 2000. The corresponding bootstrap and Bayesian trees 3927 (Analyses B2, EB: Fig. 19, 20) find Temnospondyli rootward of Eucritta, Colosteidae, 3928 Baphetidae, Caerorhachis and Anthracosauria and consequently find a quite different 3929 temnospondyl topology, with an almost basal dichotomy of Dissorophoidea against most of 3930 the rest, but the highest BPE throughout the base of the temnospondyl tree is only 14 (for 3931 Dvinosauria); similarly, only five very small temnospondyl clades have PPs above 75 – 3932 Dvinosauria has 77, but (Isodectes + Neldasaurus) has 71, (Dissorophoidea (*Iberospondylus, 3933 *Mordex)) has 64, Stereospondylomorpha has 62, Dvinosauria except Trimerorhachis has 57, 3934 a novel (Edops + Cochleosaurus) clade has 47, Temnospondyli has 39, Dissorophoidea has 3935 38, Temnospondyli excluding *Palatinerpeton has 35, (Chenoprosopus (*Nigerpeton, 3936 *Saharastega)) has 33. 3937 3938

101 Caerorhachis Neldasaurus Neldasaurus 47 Isodectes Trimerorhachis Dvinosauria 14 35 Dissorophoidea (content/YW00) – Isodectes Eryops 40 Dissorophoidea (content/YW00) T. Cochleosaurus 84 Dendrerpetidae Chenoprosopus 18 49 Balanerpeton Capetus – Capetus Edops – T. Eryops Capetus Edops 19 Dendrerpetidae 27 Cochleosaurus Edopoidea Balanerpeton 67 Chenoprosopus Trimerorhachis Neldasaurus 47 Isodectes A B

Eucritta (only R4–R6) Colosteidae (only R4–R6) –/–\– –/3\70 Baphetidae (only R4–R6) *Parrsboro jaw (R4–R6) –/–\– Edops –/–\– Cochleosaurus T. 67/57\– Chenoprosopus 40/18\39 *Nigerpeton (R4–R6) 50\99 *Saharastega (R4–R6) –/–\– –\– Eryops *Nigerpeton (R4–R6) 50\99 *Saharastega (R4–R6) –/–\– 50\99 *Nigerpeton (R4–R6) *Saharastega (R4–R6) other stereospondylomorphs 14\62 incl. *Nigerpeton –/–\– + *Saharastega (R5, R6) Capetus *Erpetosaurus 14\77 Trimerorhachis –/–\– 35/11\– Neldasaurus 47/29\71 Isodectes Balanerpeton (R1, R3) –/–\– –/–\– *Palatinerpeton (R4–R6) –\– *Iberospondylus 17\64 Dissorophoidea (content) incl. 30/–\– 84/21\– *Acanthostomatops (R4, R5, R6) *Palatinerpeton (R5) Balanerpeton (R1, R3, R4–R6) –\– *Palatinerpeton (R4–R6) 49/37\83 –\– Dendrerpetidae –\– *Acanthostomatops (R5) C

Eucritta Colosteidae Baphetidae *Parrsboro jaw Edops Cochleosaurus T. Chenoprosopus *Nigerpeton *Saharastega Trimerorhachis *Erpetosaurus –\57 Neldasaurus Isodectes Eryops *Palatinerpeton *Iberospondylus Dissorophoidea (content) *Acanthostomatops Capetus Balanerpeton Dendrerpetidae *Nigerpeton *Saharastega Trimerorhachis *Erpetosaurus –\57 Neldasaurus Isodectes other stereospondylomorphs *Nigerpeton *Saharastega Neldasaurus Isodectes *Erpetosaurus Trimerorhachis D 103

3939 ↑ Figure 26: Temnospondyl phylogeny in our analyses, distribution of the intertemporal 3940 bone, and the application of the name Temnospondyli. Dissorophoidea and 3941 Stereospondylomorpha are collapsed; modern amphibians and various “lepospondyls” (see 3942 Fig. 11) are omitted. Filled rectangles indicate presence of the intertemporal (state 0 of 3943 character 32 – PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1), empty rectangles its absence 3944 (state 1, or state 2 in the case of *Erpetosaurus; see Appendix 1); the absence of a rectangle 3945 for *Palatinerpeton and the *Parrsboro jaw represents missing data. T., Temnospondyli as 3946 defined by Schoch (2013); the entire depicted clade is Temnospondyli as defined by Yates & 3947 Warren (2000). A: topology found in Analyses R1–R3 (original taxon sample) in MPTs 3948 where Temnospondyli is closer to Amniota than Anthracosauria. Only one position of 3949 Caerorhachis is shown; the other is far outside Temnospondyli. Numbers are BPO. B: 3950 additional topologies found in R1 and R3 (original taxon sample) in MPTs where 3951 Temnospondyli is closer to Amniota than Anthracosauria. Numbers are BPO of nodes absent 3952 from A. C: topologiesfound in R1 and R3 (original taxon sample) and R4–R6 (expanded 3953 taxon sample) in MPTs where Anthracosauria is closer to Amniota than Temnospondyli. Only 3954 one position of the *Parrsboro jaw is shown, the other being well outside Temnospondyli. 3955 Numbers are BPO/BPE\PP, or BPE\PP where BPO is inapplicable. D: additional topologies 3956 found in R5 (Fig. 16). Numbers are BPE\PP. 3957 3958 Dissorophoidea is never found closer to Eryops than Stereospondylomorpha is; in 3959 other words, Euskelia Yates & Warren, 2000, is always limited to Eryops (BPE of 3960 Eryopiformes = 2, PP = 14) or to (Eryops (*Nigerpeton, *Saharastega)) (against a BPE of 15 3961 and a PP of 33). 3962 We conclude that progress in resolving temnospondyl phylogeny may come from 3963 analyses that have not only dense sampling of temnospondyls and a long list of maximally 3964 independent characters, but also a large, dense sample of other taxa, because the closest 3965 relatives of Temnospondyli have not been identified and the position of Temnospondyli 3966 rootward or crownward of the anthracosaurs, most evidently, has an enormous impact on 3967 temnospondyl phylogeny. In other words, the problem of temnospondyl phylogeny cannot be 3968 solved in isolation. 3969 Schoch (2013: 689) defined the name Temnospondyli as applying to “[t]he least 3970 inclusive clade containing Edops craigi and Mastodonsaurus giganteus”. This definition may 3971 be applied to our trees – as done in Fig. 26 – by assuming that **Mastodonsaurus would 3972 group with the other *stereospondylomorphs or, in their absence, with Eryops. In Analyses 3973 R4–R6 and some MPTs from R1 and R3 (Fig. 26C, D), in other words all those where the 3974 anthracosaurs are closer to Amniota than the temnospondyls are, Temnospondyli would then 3975 have its usual contents, because Edops is found as the sister-group to all other traditional 3976 temnospondyls. Conversely, in Analyses R2, B1, B2, EB and the remaining MPTs from R1 3977 and R3 (Fig. 26A, B), Temnospondyli would always exclude Dissorophoidea; in R2, B1, B2, 3978 EB and some MPTs from R1 and R3, Temnospondyli would even contain nothing but Eryops, 3979 Stereospondylomorpha and Edopoidea (Fig. 26A). Furthermore, Capetus, Balanerpeton, 3980 Dendrerpetidae and Dvinosauria fall outside of Temnospondyli under this definition in the 3981 MPTs found by Pardo, Small & Huttenlocker (2017: fig. S7B; Fig. 25H). Therefore, we 3982 strongly recommend against using this definition, or any other minimum-clade definition with 3983 so few internal anchors, for this name. We have used the definition by Yates & Warren 3984 (2000), which applies the name Temnospondyli to the clade encompassing all organisms that 3985 are more closely related to Eryops than to the “microsaur” Pantylus. 3986 3987 3988

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3989 Stereospondylomorpha 3990 3991 Throughout the analyses with added taxa (Fig. 14–17, 26C, D), the stereospondylomorph 3992 temnospondyls – *Sclerocephalus, *Cheliderpeton, *Glanochthon, *Archegosaurus, 3993 *Platyoposaurus, *Konzhukovia, and the stereospondyls *Lydekkerina and *Australerpeton – 3994 form a clade, either alone (BPE = 14; PP = 62) or with *Nigerpeton + *Saharastega (some 3995 MPTs from R5 and R6) and Dvinosauria (some MPTs from R5), even though no characters 3996 intended to resolve stereospondylomorph phylogeny were included in the matrix. 3997 *Sclerocephalus or, in R4 and some trees from Analyses R5 and R6, a clade formed 3998 by *Sclerocephalus and *Cheliderpeton (BPE = 27; against PP = 50) is consistently found as 3999 the sister-group to the rest. Within this remainder (BPE = 11; PP = 57), those trees where 4000 *Nigerpeton and *Saharastega do not join, namely all from Analyses EB and R4 as well as 4001 some from R5 and R6, group *Konzhukovia with *Platyoposaurus with astonishing support 4002 (PP = 98), and both of them with *Australerpeton (PP = 81) and *Archegosaurus (PP = 60); 4003 Analysis EB also groups *Glanochthon with *Lydekkerina with negligible support (PP = 31); 4004 otherwise, *Lydekkerina is the sister-group of all the above. Despite keeping *Nigerpeton and 4005 *Saharastega out (BPE = 14), Analysis B2 groups *Australerpeton and *Archegosaurus 4006 (BPE = 30) with the likewise extremely long-snouted *Platyoposaurus (BPE = 11). In the 4007 remaining MPTs from R5 and R6, a clade of *Archegosaurus and *Glanochthon (or, perhaps 4008 surprisingly, (*Archegosaurus (*Cheliderpeton, *Glanochthon))) as well as a clade of 4009 *Konzhukovia and *Lydekkerina (BPE = 28) occur. 4010 *Lydekkerina and *Australerpeton are never found as sister-groups. Most likely we 4011 have exhausted the scope of the present character sample, and the stereospondylomorphs are 4012 sorted by noise more than by signal. Still, the position of *Sclerocephalus with respect to the 4013 others agrees – ignoring the dvinosaurs in Analysis R5 – with Eltink & Langer (2014), Dilkes 4014 (2015a), Pardo, Small & Huttenlocker (2017) and arguably McHugh (2012). 4015 Cisneros et al. (2015) found Dvinosauria nested within their small sample of 4016 stereospondylomorphs. We do not interpret this result as corroborating any of our own, 4017 because it could easily be due to their small sample of non-dvinosaurs in general – or to the 4018 fact that Eryops was included in the outgroup so that Eryopiformes was forced to include 4019 Dvinosauria a priori. Furthermore, Cisneros et al. (2015) did not order any characters. 4020 4021 Dissorophoidea 4022 4023 Something of a consensus on dissorophoid phylogeny has been forming. Recent analyses 4024 (Ruta, 2009; Maddin et al., 2013b; Holmes, Berman & Anderson, 2013; Dilkes, 2015a; Pardo, 4025 Small & Huttenlocker, 2017) have generally found Dissorophidae (represented here by 4026 Broiliellus brevis alone) and Trematopidae (Acheloma, Phonerpeton, Ecolsonia, *Mordex – 4027 the latter here included in a phylogenetic analysis for the first time) as sister-groups (forming 4028 Olsoniformes Anderson et al., 2008b), and many have found the traditional “branchiosaur” 4029 Micromelerpeton to have no connection to the branchiosaurids (Apateon, Leptorophus, 4030 Schoenfelderpeton, *Tungussogyrinus, *Branchiosaurus); sometimes, Micromelerpeton is 4031 placed as the sister-group to all other dissorophoids together (Maddin et al., 2013b; Dilkes, 4032 2015a). RC07, however, upheld the more traditional topology where the trematopids lie 4033 outside a clade formed by the other dissorophoids while Micromelerpeton forms the sister- 4034 group of Branchiosauridae (most recently found by both analyses presented in Pardo, Small & 4035 Huttenlocker, 2017: fig. S6, and by the Bayesian but not the parsimony analysis in their fig. 4036 S7). Further, in the dispute over whether Ecolsonia is a trematopid or a dissorophid (e.g. 4037 Berman, Reisz & Eberth, 1985), RC07 found a sort of compromise position in that Ecolsonia

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4038 came out one node closer to Broiliellus brevis and the remaining dissorophoids than to 4039 (Acheloma + Phonerpeton). 4040 This position remains a possibility for Ecolsonia in some trees from Analyses R1–3 4041 and R5. The other trees, as well as all trees from Analyses R4, R6 and EB, place Ecolsonia as 4042 a trematopid (BPO = 56; BPE = 38; PP = 94) like Ruta (2009), Maddin et al. (2013b), 4043 Holmes, Berman & Anderson (2013), Dilkes (2015a) and Pardo, Small & Huttenlocker 4044 (2017), but continue to find a clade of all non-trematopid dissorophoids (BPO = 55; BPE = 4045 14; PP = 48 excluding *Branchiosaurus and *Acanthostomatops, see below). Within that 4046 clade, Broiliellus can be the sister-group to most or all of the rest (which has the values BPO 4047 = 39, PP = 60) or to Amphibamidae alone (BPE = 9); the latter option is the only one in 4048 Analyses R4 and R6. Despite our best efforts to eliminate the effects of ontogeny on their 4049 scores, Micromelerpeton and Branchiosauridae remain sister-groups throughout the analyses 4050 with the original taxon sample (BPO = 61). This does not change when taxa are added (BPE = 4051 27, PP = 55), except that *Branchiosaurus, as it turns out, never enters “Branchiosauridae” 4052 (see below). 4053 As expected, *Mordex settles at the base of the trematopid clade (R4, R6, some MPTs 4054 from R5: (*Mordex (Ecolsonia (Acheloma, Phonerpeton))); BPE = 28) or grade (some MPTs 4055 from R5). Analysis EB finds it slightly more rootward, next to *Iberospondylus (PP = 46). 4056 Interestingly, none of our trees find all branchiosaurids to form a clade; such a clade is 4057 contradicted by a BPE of 8 and a PP of 60. *Branchiosaurus is found closer to Broiliellus + 4058 Amphibamidae (R4, R6, some MPTs from R5) or closer to the root of Dissorophoidea (the 4059 other MPTs from R5; BPE = 8; PP = 48), yet Micromelerpeton always stays with the bulk of 4060 “branchiosaurids” as described above (BPE = 27; PP = 55). *Tungussogyrinus, its somewhat 4061 froglike ilium (state ILI 9(1)) and Early Triassic age notwithstanding, nests with 4062 *Branchiosaurus in R4, R6 and some MPTs from R5 (BPE = 16), next to the three 4063 branchiosaurids from the original sample in other trees from R5, next to them plus 4064 Micromelerpeton in yet others from R5 and in EB (PP = 54), and next to Schoenfelderpeton in 4065 the remaining MPTs from R5. We think that the present matrix cannot test whether the 4066 branchiosaurids are a clade (Fröbisch & Schoch, 2009a; Maddin et al., 2013b) or a 4067 polyphyletic assemblage of larval and neotenic dissorophoids. 4068 RC07 did not determine if the conventional amphibamids in their sample 4069 (Amphibamus, Platyrhinops, Eoscopus, Doleserpeton) formed a clade with respect to 4070 Micromelerpeton and the branchiosaurids. The analyses with the original taxon sample (R1– 4071 R3) find them as a clade (BPO = 60; also containing the salientians in R3 as the sister-group 4072 of Doleserpeton). This remains the case when taxa are added (BPE = 25 and PP = 43 for a 4073 clade that also contains *Gerobatrachus). *Micropholis, however, joins this clade only in 4074 some MPTs from R5 (as the sister-group of Eoscopus, or one node rootward of 4075 *Gerobatrachus); elsewhere, it is the sister-group of the “branchiosaur” clade described 4076 above. In Analyses R4, Doleserpeton and *Gerobatrachus are sister-groups (BPE = 40; 4077 against a PP of 51); in R5, Doleserpeton and *Gerobatrachus are equally parsimoniously 4078 found as the sister-group of Lissamphibia, with the other one of the two being the next more 4079 distant relative; in R6, Doleserpeton is closer to Batrachia. All this remains to be tested with 4080 much larger samples of potential amphibamids and amphibamid-related characters, without 4081 reducing the sample of other temnospondyls. 4082 While we are quite skeptical about a close relationship of Micromelerpeton to some or 4083 all branchiosaurids (compare with Wiens, Bonett & Chippindale, 2005), the main alternative 4084 in the literature – Micromelerpetidae as the sister-group to all other dissorophoids (e.g. 4085 Schoch, 2013; Maddin et al., 2013b; Dilkes, 2015a) – does not seem to be well supported 4086 either; it never occurs in our MPTs and contradicts the bootstrap and Bayesian trees as well 4087 (BPO = 84; BPE = 27; EB = 60). The name Dissorophoidea should certainly not be defined

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4088 with Micromelerpeton as one of only two specifiers, as Schoch (2013) has done. That said, 4089 the older definition of Dissorophoidea by Yates & Warren (2000: 86) as all organisms closer 4090 to **Dissorophus than to Eryops (**Dissorophus being very closely related to Broiliellus) 4091 applies to a clade that contains, in the trees from some of our analyses, not only the traditional 4092 dissorophoids but also various other temnospondyls, like Balanerpeton, Dendrerpetidae, 4093 Capetus, Dvinosauria and, in some MPTs from R5, even Stereospondylomorpha (Fig. 16). 4094 Schoch (2013) listed dvinosaur-like character states of micromelerpetids and used 4095 them to argue for a sister-group relationship of Micromelerpetidae to the rest of 4096 Dissorophoidea (accepted without comment by Fröbisch et al., 2015) together with a sister- 4097 group relationship (or nearly so) of Dissorophoidea and Dvinosauria. A close relationship of 4098 Dvinosauria and Dissorophoidea is never found in our MPTs (contradicted only, however, by 4099 BPO = 30, BPE = 6 and PP = 64). We wonder if the similarities listed by Schoch (2013) are 4100 instead homoplastic and indicate that the micromelerpetids are a “dissorophoid version of a 4101 dvinosaur” – a clade that generally had a dvinosaur-like lifestyle as aquatic predators with 4102 more or less anguilliform locomotion but, unlike dvinosaurs, was capable of dispersing over 4103 land in the adult stage (at least in the one species, M. credneri, that is known to have had non- 4104 neotenic, skeletally mature adults in one population: Lillich & Schoch, 2007; Schoch, 2009b). 4105 This might even explain why dvinosaurs and micromelerpetids have not been found in the 4106 same sites (see Schoch & Milner, 2014; Cisneros et al., 2015): maybe micromelerpetids were 4107 competitively excluded from bodies of water that dvinosaurs could reach, but were able to 4108 diversify in inland water bodies out of the reach of dvinosaurs. 4109 In the matrix of Dilkes (2015a), a revision and extension of that by Schoch (2013), 4110 Dvinosauria and Dissorophoidea are held together exclusively or almost exclusively by 4111 paedomorphic adaptations to an aquatic lifestyle (“Node D” in Dilkes, 2015a: 81): 4112 hypobranchials ossified in adults; lack of ossification of the glenoid facet of the and 4113 of the carpals, pubis and tarsals; and weak torsion of the humerus – the remaining character 4114 state, jaw joints and occipital condyle(s) being at the same transverse level, may also belong 4115 here; it is in fact absent in the more mature known Micromelerpeton specimens (Boy, 1995; 4116 Schoch, 2009b: fig. 2a, b). While the sister-group of Dissorophoidea in the tree of Dilkes 4117 (2015a: fig. 13) is the terrestrial Zatracheidae (see below), followed by Dvinosauria on the 4118 outside, Dissorophoidea would be reconstructed as ancestrally aquatic because 4119 Micromelerpetidae is found as the sister-group to the other dissorophoids, among which 4120 Branchiosauridae is sister to an amphibious/terrestrial clade composed of Amphibamidae, 4121 Dissorophidae and Trematopidae; we consider this position of Branchiosauridae unlikely 4122 because of the evidence for a lack of a clear distinction between amphibamids and 4123 branchiosaurids (Vallin & Laurin, 2004; Fröbisch & Schoch, 2009a; Werneburg, 2012b; 4124 Maddin et al., 2013b; and references therein; these results are more or less congruent with the 4125 MPTs from our analyses with added taxa, where such a clear distinction is likewise absent). 4126 4127 Other added temnospondyls 4128 4129 *Nigerpeton was described as a cochleosaurid (Steyer et al., 2006; Sidor, 2013). This was 4130 confirmed by Pawley (2006), Schoch (2013), Dilkes (2015a) and Pardo, Small & 4131 Huttenlocker (2017); McHugh (2012) found it and Edops together to form the sister-group of 4132 Cochleosauridae (Fig. 25D). In our analyses (Fig. 26C, D), it is always found next to 4133 *Saharastega (BPE = 50; PP = 99). 4134 *Saharastega was described as a temnospondyl of rather uncertain position (Damiani 4135 et al., 2006). In dorsal view, its skull is unusual for a temnospondyl in some ways, which led 4136 Yates (2007) to suggest that it was a seymouriamorph. Its palate, however, is unremarkable 4137 for a temnospondyl and quite unlike that of any seymouriamorph; we also note that the skull

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4138 roof is very reminiscent of the temnospondyl **Macrerpeton (Schoch & Milner, 2014: fig. 4139 38B, E). Pawley (2006; Fig. 25B) found it to be the sister-group of all other cochleosaurids; 4140 McHugh (2012; Fig. 25D) recovered it as the sister-group of Zatracheidae, in this matrix 4141 represented by *Acanthostomatops (see below); Schoch (2013), followed by Dilkes (2015a), 4142 explicitly excluded it as too incomplete. 4143 The *Saharastega-*Nigerpeton clade is not found in or close to Cochleosauridae in 4144 any MPTs (Fig. 26C, D). R4 places it next to Eryops, next to Stereospondylomorpha or next 4145 to all traditional temnospondyls except Edops and Cochleosauridae; R6 adds a position inside 4146 Stereospondylomorpha, R5 a further one, where it can be joined by Dvinosauria. Analysis B2, 4147 finally, finds it as the sister-group of Edopoidea (BPE = 4), and EB places it next to the 4148 cochleosaurid Chenoprosopus (PP = 33), together forming the sister-group (PP = 25) of a 4149 novel Edops-Cochleosaurus clade (PP = 47). We hope for larger matrices and a restudy of 4150 **Macrerpeton more detailed than that by Montanari (2012: chapter II). *Saharastega and 4151 *Nigerpeton are both unusually large for Paleozoic temnospondyls, have rather long snouts, 4152 and are known almost only from skulls with unusual and not very good preservation; and 4153 while *Nigerpeton shares rare features with the cochleosaurids, a fully stereospondylous 4154 intercentrum (state TRU VER 13-14(0)) is catalogued as part of the holotype (D. M., pers. 4155 obs.). 4156 *Iberospondylus is better preserved than the above two, but no less enigmatic. In both 4157 descriptions (Laurin & Soler-Gijón, 2001, 2006) it was recovered as the sister-group to a 4158 clade that contained Eryops, **Parioxys (on which see Materials and methods: Taxa that were 4159 not added), **Zatrachys (*Zatracheidae; see below), the included dissorophoids and the 4160 stereospondylomorph *Sclerocephalus – a position identical (but for the taxon sample) to that 4161 found by Pardo, Small & Huttenlocker (2017; Fig. 25H). Pawley (2006) found 4162 *Iberospondylus as the sister-group of Dissorophoidea (Fig. 25B, together with **Parioxys); 4163 McHugh (2012) did not include or mention it; Dilkes (2015a: 69) recovered it as an edopoid 4164 or an eryopid with a reduced taxon sample (Fig. 25E, F). Our analyses all side with Pawley’s 4165 in finding *Iberospondylus (Fig. 26C, D), or in the case of EB an *Iberospondylus-*Mordex 4166 clade (with PP = 46), as the sister-group of Dissorophoidea (BPE = 17; PP = 64). 4167 *Iberospondylus and Dissorophoidea share the dorsal process on the caudoventral tip of the 4168 quadrate (state QUA 1(1)). 4169 *Acanthostomatops represents Zatracheidae, a clade with terrestrial adults long 4170 thought to lie close to Eryops and/or Dissorophoidea. Pawley (2006; Fig. 25B) found it next 4171 to (*Iberospondylus + Dissorophoidea), McHugh (2012; Fig. 25D) found it nested within 4172 Eryopidae together with *Saharastega, Dilkes (2015a: fig. 11; Fig. 25E, F) recovered 4173 (Dvinosauria (*Zatracheidae, Dissorophoidea)) in his analyses of reduced taxon samples, 4174 Pardo, Small & Huttenlocker (2017: fig. 2, S7; Fig. 25H) found (Eryopiformes (*Zatracheidae 4175 (**Lapillopsis, Dissorophoidea))) based on a closely related matrix. In our Analyses R4 and 4176 R6, and some MPTs from R5, unexpectedly, *Acanthostomatops is highly nested within 4177 Dissorophoidea, forming part of the sister-group of Broiliellus + Amphibamidae together with 4178 a *Branchiosaurus-*Tungussogyrinus clade. In other MPTs from R5, *Acanthostomatops, 4179 *Branchiosaurus and optionally *Tungussogyrinus lie one node rootward (instead of 4180 crownward) of the “branchiosaur” clade. In yet others, *Acanthostomatops is the sister-group 4181 of (Capetus (Balanerpeton, Dendrerpetidae)), together forming the sister-group to 4182 (*Palatinerpeton (*Iberospondylus, Dissorophoidea)); yet others have a (Balanerpeton 4183 (*Palatinerpeton (Dendrerpetidae, *Acanthostomatops))) clade next to *Iberospondylus + 4184 Dissorophoidea. Analysis B2 finds *Acanthostomatops alone as the sister-group of 4185 *Iberospondylus + Dissorophoidea (BPE = 11), while EB places it next to all dissorophoids 4186 except Trematopidae (PP = 34)While we never find *Acanthostomatops next to Eryops, we 4187 occasionally did so in the previous version of our matrix (Marjanović & Laurin, 2016), even

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4188 though practically all that has changed in the temnospondyl part of the matrix since then is a 4189 series of corrections to *Nigerpeton and *Saharastega. Evidently, the position of 4190 *Acanthostomatops is not strongly constrained by our character sample (Fig. 26C, D) despite 4191 concerning the least modified of all zatracheids. 4192 *Palatinerpeton is poorly known and has an unexpected combination of features. 4193 Unsurprisingly, then, it has never before been included in a large phylogenetic analysis. Boy 4194 (1996) presented a detailed phylogenetic hypothesis that put it close to Stereospondylomorpha 4195 and to an eryopid-*zatracheid-**Parioxys clade, and less close to Capetus; of all other 4196 temnospondyls, however, only Edopoidea was included in the investigation which polarized 4197 its characters with reference to non-temnospondyl outgroups. Schoch & Witzmann (2009a) 4198 found it as the sister-group of Eryopiformes, not close to *Acanthostomatops, which instead 4199 emerged as the sister-group of Dissorophoidea. Despite the dearth of data, Analyses R4 and 4200 R6 as well as some MPTs from R5 place *Palatinerpeton as the sister-group to either 4201 Dendrerpetidae (against a BPE of 37 and a PP of 83) or *Iberospondylus + Dissorophoidea 4202 (against a BPE of 11 and a PP of 64; Fig. 26C, D); the bootstrap analysis conducted under the 4203 same conditions (B2) similarly places *Palatinerpeton as the sister-group to (Capetus 4204 (Balanerpeton, Dendrerpetidae)) with a BPE of 5, all together forming the sister-group of 4205 (*Acanthostomatops (*Iberospondylus, Dissorophoidea)) with a BPE of 6, an arrangement 4206 similar to some MPTs from R5 (Fig. 26C). The remaining MPTs from R5 (also Fig. 26C) find 4207 *Palatinerpeton next to Dendrerpetidae + *Acanthostomatops. Analysis EB, in contrast, 4208 places it next to all other temnospondyls together (PP = 35; Fig. 20). *Palatinerpeton could 4209 become important for the question of temnospondyl phylogeny; a μCT scan could perhaps 4210 reveal the unexposed surfaces and fill in much of its missing data. 4211 *Erpetosaurus was originally thought to be a colosteid, but has long been recognized 4212 as an unusual dvinosaur with a few colosteid-like features and was redescribed as such by 4213 Milner & Sequeira (2011). We confirm this as discussed above under Colosteidae (BPE = 14; 4214 PP = 77) and shown in Fig. 26C, D. 4215 4216 Chroniosuchia 4217 4218 A clade composed of *Chroniosaurus and *Bystrowiella (BPE = 42; PP = 67) has a fully 4219 resolved position (Fig. 27G) one node crownward of Gephyrostegus or *Casineria 4220 (depending on the latter’s position) (BPE = 7; PP = 55) and one node rootward of 4221 Solenodonsaurus (or, in Analysis EB, of Seymouriamorpha including Solenodonsaurus; BPE 4222 = 6; PP = 44). This forms a kind of compromise between the positions found in earlier 4223 phylogenetic analyses, while disagreeing with all of them: the closely related analyses of 4224 Clack & Klembara (2009), Clack et al. (2012b) and Witzmann & Schoch (2017) found the 4225 included chroniosuchians in a polytomy with Silvanerpeton, Anthracosauria and a 4226 “gephyrostegid”-seymouriamorph-amniote-“microsaur” clade (Fig. 27D); Klembara, Clack & 4227 Čerňanský (2010) resolved them as anthracosaurs, agreeing with earlier suggestions (Laurin, 4228 2000, and references therein) that the chroniosuchians were the geologically youngest 4229 anthracosaurs; Schoch, Voigt & Buchwitz (2010) and Buchwitz et al. (2012) found them to be 4230 the sister-group of the only included lepospondyl – which Buchwitz et al. (2012) and table 1 4231 of Schoch, Voigt & Buchwitz (2010) stated to be the poorly known Asaphestera, while the 4232 text of Schoch, Voigt & Buchwitz (2010) mentioned Pantylus instead –; Klembara et al. 4233 (2014; Fig. 27E) recovered them as the sister-group of a gephyrostegid-seymouriamorph 4234 clade, though their bootstrap tree has them as the sister-group of Gephyrostegidae alone. All 4235 these analyses relied on quite small data matrices; however, unlike us, Schoch, Voigt & 4236 Buchwitz (2010) and Buchwitz et al. (2012) included more than two chroniosuchians in their 4237 analyses (the latter’s matrix building on the former’s).

108 Temnospondyli 109 78 Temnospondyli Anthracosauria 81 45 79 Seymouriamorpha Gephyrostegidae (composite OTU) 100 62 Lepospondyli Westlothiana 44 Seymouriamorpha 92 92 63 rest of Lepospondyli Westlothiana 92 68 (rest of) Amphibia (Lepospondyli) 66 Limnoscelis 58 D. Orobates 78 Solenodonsaurus 74 70 Diadectes (2 OTUs) D. Limnoscelis 55 51 Saur. Captorhinus 63 67 Diadectes 100 Paleothyris 64 A. *Synapsida (composite OTU) 100 Petrolacosaurus 72 Captorhinus B A

Amphibia (Temnospondyli) Caerorhachis Anthracosauria Caerorhachis Gephyrostegus rest of Temnospondyli Bruktererpeton Colosteidae “seymouriamorphs” not incl. 2 of 4 “lepospondyls” listed below *Chroniosuchia *Chroniosaurus Seymouria *Bystrowiella Kotlassia Silvanerpeton Solenodonsaurus (rest of) Anthracosauria Westlothiana Gephyrostegus Lepospondyli rest of Lepospondyli Bruktererpeton Tseajaia Seymouriamorpha Limnoscelis Paleothyris Orobates Saur. Diadectes *Casineria Captorhinus Westlothiana Lepospondyli? 2 of 4 “lepospondyls” Sauropsida Paleothyris C Petrolacosaurus D

14/–\– Caerorhachis (R1, R3) Temnospondyli/ (rest of) Temnospondyli/Amphibia Temnospondyli 40/18\39 94 Amphibia (extant in R2, R3) Baphetoidea 97 –/–\18 Solenodonsaurus 2 of 4 “lepospondyls” Kotlassia (R1, R2, R3) 80 Seymouriamorpha 2 of 4 “lepospondyls” 31/6\55 Kotlassia (R1, R3) 76 28/30\99 (rest of) Seymouriamorpha *Chroniosaurus 22/3\– Seymouriamorpha 26/13\74 Westlothiana 77 60 77 Lepospondyli/ rest of Lepospondyli/Amphibia G. Bruktererpeton –/–\– – Amphibia 22/–\73 (extant in R1, R3) 84 Gephyrostegus 59 Captorhinus Saur. Captorhinus 19/–\46 80/30\– Paleothyris 63 Petrolacosaurus Saur. Petrolacosaurus 69 Limnoscelis 84/55\55 D. 68/44\70 Limnoscelis Tseajaia D. Tseajaia 79 Diadectes 59/24\96 60/52\– Orobates 77/73\– Diadectes E F

40/18\39 Temnospondyli (extant in R3, R5, R6) incl. *Parrsboro jaw (R4–R6) Caerorhachis 35/21\86 31\– *Parrsboro jaw (R4–R6) Anthracosauria –/–\– 54/20\97 Silvanerpeton 12/–\– *Casineria (R4–R6) –/–\– Gephyrostegidae *Casineria (R4–R6) Bruktererpeton 53/42\69 16/6\– Gephyrostegus (R1, R3) –/–\– *Casineria (R4–R6) Gephyrostegus (R1, R3, R4–R6) –/–\– *Casineria (R4–R6) –/–\– *Chroniosuchia *Chroniosaurus 4\27 55\67 *Bystrowiella Solenodonsaurus 7\42 Kotlassia (R1, R3) 31/6\44 Seymouriamorpha Kotlassia (R1, R3, R4–R6) (rest of) Seymouriamorpha 22/3\– 28/30\99 Leptoropha + Microphon (R1, R3, R4–R6) Leptoropha + Microphon (R1, R3) –/–\– Lepospondyli/Amph. Westlothiana 26/13\74 rest of Lepospondyli/Amphibia (extant in R1, R3, R4, R6) –/–\– 22/–\73 Sauropsida Captorhinus 19/–\46 80/26\– Paleothyris A. 84/55\55 Petrolacosaurus D. Tseajaia 68/44\70 60/52\– Orobates “D.” 77/73\– Diadectes 59/–\– Limnoscelis –\– *Caseasauria (composite OTU) *Archaeovenator G 56\75 110

4238 ↑ Figure 27: Amniote relationships and distribution of the intertemporal bone. Taxa not 4239 included in our analyses are omitted; those included in the expanded but not the original 4240 taxon sample are marked with an asterisk. Several named clades are collapsed. The 4241 matrices of B, C, F and G are ultimately based on that of Ruta, Coates & Quicke (2003), so 4242 they should not be considered fully independent of each other. Numbers are bootstrap 4243 percentages. Filled rectangles indicate presence of the intertemporal (state 0 of character 32 – 4244 PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1), empty rectangles its absence (any other state); 4245 the absence of a rectangle indicates missing data. A., Amniota; D., Diadectomorpha; Saur., 4246 Sauropsida. A: Vallin & Laurin (2004). B: Pawley (2006: chapter 6). C: RC07; “rest of 4247 Lepospondyli” excludes the adelospondyls (see Fig. 1, 24A), bootstrap values were not 4248 published. D: Clack et al. (2012b; lacking *Bystrowiella) and Witzmann & Schoch (2017); all 4249 bootstrap percentages in this part of the tree are below 50 in both versions and were not 4250 published. E: Klembara et al. (2014). Bootstrap percentages below 50 were not published, but 4251 note that a sister-group relationship of Chroniosaurus and Gephyrostegidae (G.) is supported 4252 by a bootstrap value of 53%. F: topologies from our Analysis R2 and some MPTs from R1 4253 and R3, where Temnospondyli is closer to Amniota than Anthracosauria. Numbers are 4254 BPO/BPE\PP. G: topologies found in Analyses R4–R6 and the remaining MPTs from R1 and 4255 R3. Numbers below nodes are BPO/BPE\PP; the space for BPO is omitted where 4256 inapplicable. “D.” indicates Diadectomorpha for the original but not the extended taxon 4257 sample. 4258 4259 Our analyses thus place Chroniosuchia as the sister-group to a clade with terrestrial 4260 adults, with which they share various adaptations to walking and bearing weight that all more 4261 rootward clades, including the “gephyrostegids” and *Casineria, lack (with exceptions nested 4262 within the temnospondyls). 4263 4264 Solenodonsaurus 4265 4266 Solenodonsaurus was long thought to lie particularly close to Diadectomorpha + Amniota 4267 (Laurin & Reisz, 1999; Vallin & Laurin, 2004; Fig. 27A). RC07 found it just outside the 4268 smallest clade of diadectomorphs, amniotes and “lepospondyls” (Fig. 27C); we consistently 4269 find it just outside the smallest clade formed by the above and all seymouriamorphs (which 4270 has BPO = 22; BPE = 3; Fig. 27F, G), except in Analysis EB, where Solenodonsaurus is the 4271 sister-group to all other seymouriamorphs (PP = 51). 4272 Danto, Witzmann & Müller (2012), who redescribed Solenodonsaurus, unexpectedly 4273 found it to be a lepospondyl instead; however, their changes to the scores of Solenodonsaurus 4274 in the matrix of Ruta, Coates & Quicke (2003) clearly contradict their own text and/or 4275 illustrations in several cases, which are listed under the respective characters in Appendix 1. 4276 4277 Seymouriamorpha 4278 4279 Uniquely, RC07 found Seymouriamorpha to be a grade, with Seymouria and Kotlassia 4280 successively closer to a (Solenodonsaurus (Lepospondyli (Amniota, Diadectomorpha))) clade 4281 than a clade formed by the remaining seymouriamorphs (Fig. 1, 27C). In all trees, Seymouria 4282 is part of a clade with some or all other traditional seymouriamorphs; in Analyses R1 and R3 4283 (Fig. 27F, G), Kotlassia can be the sister-group of that clade or one node rootward of 4284 Seymouriamorpha (this is the only option in R2), and the (Leptoropha + Microphon) clade 4285 can be nested within it (always in R2; Fig. 27F) or lie one node crownward of it. The 4286 corresponding bootstrap tree (B1) shows (Kotlassia + Seymouria), supported by a BPO of 26, 4287 as the sister-group to all other seymouriamorphs (BPO of Seymouriamorpha = 28). The

110 111

4288 addition of *Karpinskiosaurus, however, rearranges seymouriamorph phylogeny and prevents 4289 Kotlassia, Leptoropha and Microphon from leaving (Fig. 27G): throughout Analyses R4–R6, 4290 the latter two are the sister-group of all other seymouriamorphs, among which a clade of 4291 (Seymouria (Kotlassia, *Karpinskiosaurus)) is the sister-group to the remainder 4292 (Discosauriscidae; BPE = 27). 4293 The only seymouriamorph clade with good support is (Leptoropha + Microphon) at a 4294 BPO of 88 a BPE of 85 and a PP of 100. All other bootstrap percentages, including those for 4295 Seymouriamorpha as a whole, are below 40 in both analyses; Analysis EB finds a PP of 91 4296 for Discosauriscidae and one of 99 for, as mentioned, Seymouriamorpha excluding 4297 Solenodonsaurus, while the other branches stay below a PP of 60. 4298 Neither the classification of Bulanov (2003), which was not based on a phylogenetic 4299 analysis, nor – with the exception of the Seymouria-*Karpinskiosaurus clade found in 4300 Analysis EB (PP = 27) – the results of the analysis by Klembara et al. (2014: fig. 8) are 4301 congruent with any of our results. From this and the very low support values (though see 4302 above for posterior probabilities), we conclude that at least the relationships of Utegenia, 4303 Ariekanerpeton and (Leptoropha + Microphon) to each other and to Discosauriscus remain 4304 unclear; while the matrix by Klembara et al. (2014) has a denser sampling of 4305 seymouriamorphs and of characters that are relevant to their phylogeny, our matrix has a 4306 much larger sample of non-seymouriamorphs to root the seymouriamorph tree. 4307 Curiously, Analysis B2 finds Seymouriamorpha inside the amniote-“lepospondyl” 4308 clade, as the sister-group to the diadectomorph-amniote clade (Fig. 19); in other words, 4309 Seymouriamorpha and the “lepospondyls” switch places compared to all other MPTs and and 4310 B1. If corroborated by future studies, this topology would amount to a reversal to the textbook 4311 hypothesis of the mid-late 20th century (which was still assumed, for unstated reasons, by 4312 Fröbisch & Schoch, 2009a: fig. 1, and by Berman, 2013). However, the sample of characters 4313 where seymouriamorphs and diadectomorphs share the same apomorphic state may already 4314 be exhaustive or nearly so in the present matrix, and the bootstrap support for this topology is 4315 very low (BPE = 9; contradicting a BPO of 19 and a PP of 46). 4316 4317 Amniota and Diadectomorpha 4318 4319 Uniquely, RC07 found the diadectomorphs to form a Hennigian comb with respect to the 4320 sauropsids (Fig. 1, 27D): (Tseajaia (Limnoscelis (Orobates (Diadectes (Captorhinus 4321 (Paleothyris/Protorothyris, Petrolacosaurus)))))). This was due to numerous misscores, at 4322 least some of which were evidently caused by reliance on ancient literature about badly 4323 preserved specimens. In Analyses R1–R3 we find (Fig. 27F, G) a monophyletic 4324 Diadectomorpha (BPO = 59; BPE = 24; PP = 96), resolved as (Limnoscelis (Tseajaia 4325 (Orobates, Diadectes))) like in the latest published analyses (Reisz, 2007; Kissel, 2010; 4326 Berman, 2013), as the sister-group of Sauropsida; the clade of diadectomorphs except 4327 Limnoscelis is found in all of our parsimony analyses and supported in all bootstrap analyses 4328 (BPO = 60; BPE = 52; against a PP of 76), and the (Diadectes + Orobates) clade enjoys some 4329 of the highest values in the entire trees (BPO = 77; BPE = 73; against a PP of 59). 4330 As mentioned (Material and methods: Treatment of OTUs: Taxa added as new OTUs 4331 for a separate set of analyses), the three amniotes included by RC07 are all sauropsids, so 4332 RC07 were unable to test whether the diadectomorphs are amniotes. We therefore added the 4333 synapsid OTUs *Caseasauria (composite) and *Archaeovenator, which robustly come out as 4334 sister-groups (BPE = 56; PP = 75). Surprisingly, however, diadectomorph monophyly breaks 4335 down; more precisely, throughout the parsimony analyses with added taxa, Limnoscelis never 4336 emerges as a diadectomorph (Fig. 27G). Instead, Analyses R4–R6 find both clades as 4337 amniotes, specifically recovering Amniota as (Sauropsida (Diadectomorpha (Limnoscelis

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4338 (*Caseasauria, *Archaeovenator)))); in terms of the topology found by Analyses R1–R3, 4339 *Caseasauria and *Archaeovenator are not placed next to Sauropsida (as they are in Analysis 4340 B2: BPE = 30), but next to Limnoscelis. 4341 Under the conditions of Analysis R4, only one additional step is required in Mesquite 4342 to restore Amniota and Diadectomorpha as sister-groups – at the cost of rendering 4343 Captorhinus a synapsid; moving it back to Sauropsida needs one step more. Analysis EB 4344 weakly supports a very different arrangement where Limnoscelis is a diadectid so that 4345 Tseajaia is the sister-group to all other diadectomorphs (PP = 76), Diadectomorpha is the 4346 sister-group of Captorhinus (PP = 49), and both together lie on the synapsid side of Amniota 4347 (PP = 44). All this is in stark contrast to the much stronger support for the smallest clade that 4348 contains all of the taxa mentioned in this section: BPO = 68, BPE = 44, PP = 70. The support 4349 for Captorhinus as a sauropsid depends very strongly on the taxon sample (BPO = 80; BPE = 4350 26; contradicted by a PP of 49), as does that for (Paleothyris + Petrolacosaurus) to a lesser 4351 extent: BPO = 84; BPE = 55; PP = 55. 4352 Many of the characters presented by Berman (2013) as supporting the membership of 4353 Diadectomorpha in Amniota are not parsimony-informative given his taxon sample; the 4354 others are already included in our matrix. Any satisfactory resolution of amniote origins will 4355 require a larger sample of amniotes and possibly hitherto unrecognized characters. Further, 4356 several of those features of the description of Tseajaia by Moss (1972) that were not revisited 4357 by Berman, Sumida & Lombard (1992) seem unusual in the light of more recent work on 4358 diadectomorphs and may warrant redescription. 4359 4360 Westlothiana 4361 4362 Despite numerous changes to its scores, Westlothiana stays (Fig. 27) in the position found by 4363 RC07 and Pawley (2006): it is the sister-group to all other “lepospondyls”. Although 4364 bootstrap support is low (BPO = 26) or only exists for a similar topology (BPE = 10 for 4365 Westlothiana + *Utaherpeton; BPE = 7 for both + all other amphibians except the 4366 adelospondyls; BPE = 13 for Amphibia), there is moderate Bayesian support (PP = 74). 4367 4368 The lepospondyl problem 4369 4370 […] the fact that we find throughout the Carboniferous and early [sic] Permian varied series of 4371 small, non-labyrinthodont amphibians, which I have classed as lepospondyls in a broad use of 4372 that term, presents an evolutionary problem for which we have at present no solution. 4373 – Romer (1964: 158) 4374 4375 Recent research is beginning to shed new light on the anatomy and relationships of rare and 4376 problematic forms, such as lepospondyls […] [four references]. Several issues related to 4377 lepospondyl interrelationships are likely to undergo extensive revision in the near future. 4378 Published analyses of lepospondyls reveal a disconcerting lack of agreement, to the point that 4379 almost any pattern of relationships has been proposed […] [11 references]. 4380 – Ruta, Coates & Quicke (2003: 290) 4381 4382 And what is a lepo…? 4383 – Gary Johnson, candidate for president of the USA, in a TV interview in 2016 4384 4385 For much of the 20th century, all limbed vertebrates (or nearly so) except Lissamphibia and 4386 Amniota were divided into Labyrinthodontia and Lepospondyli. When phylogenetic analysis 4387 began to be introduced in the mid-1990s, these two taxa had largely come to be seen as 4388 wastebaskets, Labyrinthodontia basically containing the large-bodied taxa and Lepospondyli 4389 the small-bodied ones (except small temnospondyls). It was expected that Labyrinthodontia 4390 would turn out to be paraphyletic and Lepospondyli to be polyphyletic. The first prediction

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4391 has held up, if perhaps less radically than expected; the latter has fared much less well, in that 4392 analyses like those of Ruta, Coates & Quicke (2003), Vallin & Laurin (2004; Fig. 28A) or 4393 Maddin, Jenkins & Anderson (2012; Fig. 28F) turned up a lepospondyl clade lying not close 4394 to Temnospondyli or Colosteidae as some had surmised, but right next to Diadectomorpha + 4395 Amniota (Fig. 27), reminiscent of the old idea of a close relationship between amniotes and 4396 “microsaurs” that Romer had so thoroughly excluded in the mid-20th century. (See, however, 4397 Pardo & Anderson [2016] and Pardo et al. [2017].) 4398 RC07 found a novel variant supported by previously neglected characters: they upheld 4399 the picture described above, except for finding that the adelospondyls (Acherontiscus and 4400 Adelogyrinidae) were not lepospondyls or anywhere near, forming instead a clade with the 4401 faraway colosteids (Fig. 1, 28D). However, several plesiomorphic scores for the 4402 adelospondyls, which kept them away from the remaining “lepospondyls” and are shared with 4403 colosteids, appear indefensible. For example, RC07 scored the adelospondyls as having 4404 partially covered lateral-line canals on the skull (state SC 1(1) for Dolichopareias, SC 1(1 or 4405 2) for Acherontiscus and Adelospondylus; state 1 is “mostly enclosed with short sections in 4406 grooves”, state 2 is “mostly in grooves with short sections enclosed”), but the grooves 4407 (Carroll, 1969b; Andrews & Carroll, 1991) appear wide and shallow and were most likely 4408 genuinely interrupted, with the lateral-line organ perhaps continuing in the skin away from the 4409 bone – rather than lying under the bone surface – or perhaps being interrupted itself. This 4410 condition, which we have scored as part of the existing state SC 1(3) – lateral-line organ 4411 entirely in grooves, not covered by bone – is best seen in *Archegosaurus (Witzmann, 2006) 4412 and was evidently also present in Proterogyrinus (Holmes, 1984), which RC07 had also 4413 misscored as having state 1 or 2. 4414 4415 4416 4417 ↓ Figure 28: Hypotheses on “lepospondyl” relationships since 2004. Various named clades 4418 are collapsed. Taxa not included in our analyses are omitted; those included in the expanded 4419 but not the original taxon sample are marked with an asterisk. A., Amphibia; HPSA13, 4420 Huttenlocker et al. (2013); L., Lepospondyli; MJA12, Maddin, Jenkins & Anderson (2012); 4421 ML09, Marjanović & Laurin (2009). A: Vallin & Laurin (2004). The other position of 4422 Westlothiana lies outside Amphibia and is not shown (see Fig. 27A). Numbers are bootstrap 4423 percentages. B: Pawley (2006: fig. 88). Numbers are bootstrap percentages from fig. 63 4424 (those below 50 were not reported), which shows an analysis that omitted the taxa written in 4425 dark green but found a congruent topology. C: Pawley (2006: fig. 91): cranial characters and 4426 data as in B, but the postcranial ones unchanged from Ruta, Coates & Quicke (2003). D: 4427 RC07. E: Milner & Ruta (2009); entire analysis except the aïstopod **Ophiderpeton. 4428 Adelospondyls and lysorophians were not included. H., Holospondyli; N., . 4429 Numbers are bootstrap percentages. F: matrices derived from that of Anderson et al. (2008a), 4430 namely: 1) ML09; 2) MJA12 as reanalyzed by us (Results: Reanalysis of the matrix of 4431 MJA12), lacking the corrections proposed by ML09 and those by Sigurdsen & Green (2011) 4432 but containing those by Maddin & Anderson (2012) and new ones; 3) HPSA13, lacking all of 4433 the proposed corrections mentioned here but containing new ones. Note that ML09 found the 4434 LH, MJA12 the TH and HPSA13 the PH, and that ML09 and HPSA13 did not find Eocaecilia 4435 in the same position. Numbers are bootstrap percentages from ML09, MJA12 and HPSA13 in 4436 this order (the latter two did not report percentages below 50). – Pardo, Small & Huttenlocker 4437 (2017: fig. S6) analyzed an unpublished matrix based on MJA12 with some updates based on 4438 HPSA13; the MPTs and the Bayesian tree are almost fully congruent with this tree, especially 4439 with MJA12, and neither bootstrap values nor posterior probabilities were published.

113 Westlothiana Westlothiana A. Aïstopoda (composite OTU) 114 Brachydectes ? A. 41 Adelogyrinidae (composite OTU) adelospondyls Nectridea (composite OTU) Nectridea Urocordylidae 58 (Holospondyli) 98 Microbrachis A. 100 Scincosaurus 14 28 *Utaherpeton 63 99 Diplocaulidae Pantylus 93 22 Lethiscus 29 Cardiocephalus (Gymnarthridae) Aïstopoda Oestocephalus Rhynchonkos 42 Phlegethontia Brachystelechidae (composite OTU) 31 92 modern amphibians Lysorophia (composite OTU) 53 Odonterpeton 62 Lissamphibia A B Microbrachis 84 Hyloplesion Batropetes Westlothiana 91 Tuditanus Urocordylidae Eucritta Asaphestera Scincosaurus Temnospondyli 98 78 60 Saxonerpeton Diplocaulidae Proterogyrinus A. Brachydectes ? Hapsidopareion Microbrachis 56 Pantylidae modern amphibians 54 L. Aïstopoda 97 Lethiscus Ostodolepididae adelospondyls 91 H. 77 Phlegethontia ? 93 Lethiscus Rhynchonkos 56 N. Urocordylidae 72 Oestocephalus 31 63 Gymnarthridae Aïstopoda Phlegethontia 26 Scincosaurus 97 55 Diplocaulidae Microbrachis E 78 Hyloplesion Tuditanus *Utaherpeton (MJA12) Microsauria Asaphestera Adelogyrinus (ML09) Saxonerpeton A./L./L. Microbrachis (ML09) Pantylidae 68/?/65 Microbrachis (HPSA13) Odonterpeton Asaphestera Batropetes –/?/? –/?/? Tuditanus (MJA12) Hapsidopareion Tuditanus (ML09, HPSA13) –/?/? Ostodolepididae Hapsidopareion Rhynchonkos 47/54/59 Saxonerpeton Gymnarthridae 44/?/? C –/?/? Ostodolepididae (HPSA13) Gymnarthridae (HPSA13) –/?/? –/?/? Colosteidae Pantylus adelospondyls 52/?/? Stegotretus (ML09, HPSA13) –/?/? Stegotretus (MJA12) Westlothiana Ostodolepididae (ML09, MJA12) 29/?/? 77/78/? Pantylidae 12/?/57 Gymnarthridae (MJA12) Brachydectes 52/70/52 L. Brachystelechidae Scincosaurus Batropetes Diplocaulidae 100 *Carrolla (only included in HPSA13) Holospondyli Urocordylidae 7/?/? Gymnarthridae (ML09) Lethiscus 19/?/? Rhynchonkos Oestocephalus –/–/? Eocaecilia (HPSA13) Aïstopoda Phlegethontia Microbrachis (MJA12) Tuditanus Adelogyrinus (MJA12, HPSA13) –/?/? *Utaherpeton (ML09) Asaphestera –/?/? Hapsidopareion Scincosaurus –/?/? Ostodolepididae *Utaherpeton (HPSA13) 19/?/? Urocordylidae Rhynchonkos 93/94/95 Gymnarthridae –/?/? 50/–/? Diplocaulidae (ML09, HPSA13) 83/?/89 Saxonerpeton –/?/? Diplocaulidae (MJA12) Batropetes Aïstopoda Oestocephalus Odonterpeton –/?/? 96/86/96 Phlegethontia Microbrachis 17/?/? Brachydectes Hyloplesion 22/–/– modern amphibians (ML09) D F 32/–/–

114 115 Neldasaurus Westlothiana Dvino- Isodectes Microbrachis Trimerorhachis 67 Hyloplesion adelospondyls Odonterpeton A./L. 12 Urocordylidae Saxonerpeton 26 – Lethiscus Hapsidopareion 15 Oestocephalus Rhynchonkos 26 – Phlegethontia Gymnarthridae 73 – 73 Albanerpetidae 22 Ostodolepididae 75 modern amphibians Eocaecilia Pantylidae Caudata 92 Lissamphibia 12 Tuditanus Batrachia Salientia 24 Asaphestera Scincosaurus Westlothiana 2 56 Diplocaulidae Microbrachis (H.) 57 Batropetes Hyloplesion 19 Brachydectes Lepospondyli Odonterpeton Saxonerpeton Eocaecilia – Lissamphibia Hapsidopareion Albanerpetidae – 65 Rhynchonkos Caudata 53 B. 74 Gymnarthridae 77 Salientia (R1) Ostodolepididae – 90 adelospondyls Pantylidae 47 Urocordylidae Tuditanus – 83 Asaphestera 43 Aïstopoda Lethiscus Oestocephalus Scincosaurus 70 Diplocaulidae 36 Phlegethontia Batropetes A B Brachydectes

Westlothiana *Trihecaton (R4, R5) Microbrachis 66\97 Hyloplesion –\– Brachydectes (R6) –\– Brachydectes (R6) –\– 23\– Amphibia/Lepospondyli/ Batropetes (R6) Lepospondyli 37\– *Carrolla (R6) 35\48 *Quasicaecilia (R6) 13\74 –\– 63\86 Scincosaurus Diplocaulidae –\– 58\100 *Utaherpeton Holospondyli/ adelospondyls Holospondyli 65\100 –\69 Urocordylidae 81\– –\48 Eocaecilia (R6) 30\96 Oestocephalus –\73 –\– –\– Phlegethontia (R4, R5, R6) 63\100 Phlegethontia (R4, R5) Aïstopoda –\– *Pseudophlegethontia (R4, R5) –\61 Phlegethontia (R4, R5) Lethiscus –\– *Pseudophlegethontia (R4, R5, R6) –\– *Coloraderpeton Pantylidae Pantylus 77\93 Stegotretus 1\– 15\– Asaphestera Tuditanus Tuditanidae –\89 *Crinodon –\88 *Goreville microsaur (R4) –\– Saxonerpeton (R5, R6) Rhynchonkos (R5, R6) –\– *Trihecaton (R6) 10\64 Gymnarthridae –\– 65\96 –\– 55\87 Pelodosotis Ostodolepididae *Trihecaton (R6) –\– –\– Micraroter *Trihecaton (R4) Saxonerpeton (R4) –\– Odonterpeton –\– *Sparodus –\– –\– *Goreville microsaur (R5, R6) Hapsidopareion –\– 87\100 *Llistrofus Rhynchonkos (R4) –\– Brachydectes (R4, R5) 23\– Batropetes (R4, R5) –\– 37\– Brachystelechidae *Carrolla (R4, R5) *Quasicaecilia (R4, R5) 15\92 35\48 67\100 Eocaecilia (R4) Albanerpetidae (R4) Lissamphibia –\55 Caudata (R4) 54\81 Salientia (R4) C 115 116

4440 ↑ Figure 29: The relationships of “lepospondyls” in our analyses, and the distribution of 4441 the supratemporal bone. Various named clades are collapsed. Filled rectangles indicate 4442 presence of the supratemporal (state 2 or lower of character 32 – PAR 2/POSFRO 3/INTEMP 4443 1/SUTEMP 1), empty rectangles its absence (state 3 or 4); the absence of a rectangle indicates 4444 missing data. A., Amphibia; B., Batrachia; H., Holospondyli; L., Lepospondyli. A: topology 4445 found in Analyses R1 and R3. Numbers below internodes are BPO; compare unsupported 4446 nodes to Fig. 18. B: topology found in R2. C: topology found in R4–R6. Numbers are 4447 BPE\PP; compare unsupported nodes to Fig. 19, 20. Numbers in red or brown depend on 4448 *Trihecaton or Eocaecilia, respectively, not being members of the clades in question; the 4449 opposite holds for clade names in color. 4450 4451 Analysis R2 (Fig. 29B) groups the adelospondyls with the aïstopods and urocordylids 4452 among the “lepospondyls” that are dragged into Temnospondyli by the constraint on 4453 Lissamphibia. All other phylogenetic analyses place the adelospondyls with the urocordylids 4454 and aïstopods in highly nested positions within a “lepospondyl”/amphibian clade (PP = 76; 4455 Fig. 29A, C). Moving the adelospondyls next to Colosteidae on a tree from Analysis R1 4456 requires only two extra steps; moving them into Colosteidae on a tree from R4 (as the sister- 4457 group to *Aytonerpeton, together forming the sister-group of Colosteus + Greererpeton) 4458 requires no less than six extra steps. The bootstrap analyses do not strongly support any 4459 position; Analysis B1 places the adelospondyls just rootward of Holospondyli (the highest 4460 BPO that keeps them away from Holospondyli is 25, the highest that keeps them away from 4461 Colosteidae is 35), Analysis B2 finds the adelospondyls next to a clade of all other 4462 amphibians (BPE = 13 rootward, 7 crownward). 4463 In spite of our results, including a node with PP = 86 (Caerorhachis and everything 4464 more crownward: Fig. 20), we consider it possible that the adelospondyls do not belong 4465 together with most or all of the other “lepospondyls”, but are rather colosteid-grade animals. 4466 One reason is the fact that their ceratobranchial bones, not considered in the present matrix, 4467 retain longitudinal grooves for arteries (Witzmann, 2013). Such grooves indicate internal 4468 gills (Schoch & Witzmann, 2010) and are not found in the only other possibly aquatic 4469 “lepospondyl” from which hyobranchial bones are known, the lysorophian Brachydectes 4470 (Wellstead, 1991; Witzmann, 2013); there is further no trace of internal gills in extant 4471 amphibians – the gills of , although soon covered by a lid, are homologous to external 4472 gills and thus to the septa between internal gills (Schoch & Witzmann, 2010, and references 4473 therein). In this light, we would like to draw attention to the embolomerous vertebrae of 4474 Acherontiscus, where the intercentra are much larger (state TRU VER 13-14(0)) than in any 4475 other “lepospondyls” that are known to have intercentra. We furthermore wonder if the 4476 single-piece centra of adelogyrinids are pleuro- or intercentra – in the adelogyrinid 4477 **Palaeomolgophis, many centra articulate with two successive neural arches (Andrews & 4478 Carroll, 1991), so perhaps the adelogyrinids were stereospondylous. (We have scored them as 4479 unknown for this question, as we have done with all other OTUs that have single-piece centra 4480 throughout the entire column; for details and discussion, see character 259 – TRU VER 7 – in 4481 Appendix 1.) 4482 In any case, the adelospondyls themselves are relatively well supported as a clade 4483 (BPO = 47; BPE = 40; PP = 100), as is Adelogyrinidae to the exclusion of Acherontiscus 4484 (BPO = 76; BPE = 75; PP = 95). These results agree with those of RC07 (Fig. 1). 4485 Other than Westlothiana and (exclusively in B2) the adelospondyls and *Utaherpeton, 4486 all “lepospondyls” form a clade – with or without some or all modern amphibians, depending 4487 on our constraints – in all of our analyses except R2 (BPO = 22; BPE = 1; PP = 73; Fig. 29B). 4488 The relationships within this clade remain unclear. A basic pattern that emerges from our 4489 results, however (Fig. 29), is a basal (or, in some MPTs from R2, nearly basal) dichotomy

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4490 between a clade that contains most “microsaurs” and another that contains Holospondyli. This 4491 is shared with RC07 (Fig. 28D) and the Anderson-lab matrices (Marjanović & Laurin, 2009; 4492 Maddin, Jenkins & Anderson, 2012; Huttenlocker et al., 2013; Pardo, Small & Huttenlocker, 4493 2017: fig. S6; Fig. 28F); only Analysis EB has Holospondyli deeply nested in a long 4494 “microsaur” grade (PP = 40). Analyses R1, R3 and sometimes R2 (BPO = 23; BPE = 15) find 4495 Microbrachis and Hyloplesion on the “microsaur” side like RC07 (Fig. 28D, 29A, B); the 4496 remaining MPTs from R2 find them outside the dichotomy (Fig. 29B); R4–R6 place them on 4497 the holospondyl side (Fig. 29C). RC07 found the tuditanids on the “microsaur” side but the 4498 pantylids on the holospondyl side; we find both on the holospondyl side (or diplocaulid- 4499 scincosaurid side) in R1–R3 (BPO = 2), but, like the Anderson-lab matrices, both on the 4500 “microsaur” side in R4–R6 (BPE = 1). RC07 and the Anderson-lab matrices recovered 4501 Brachydectes on the holospondyl side but Batropetes on the “microsaur” side; we find both 4502 on the holospondyl side (or diplocaulid-scincosaurid side) in R1–R3 and R6 (BPO = 25; BPE 4503 = 6, PP = 76), but both on the “microsaur” side in R4 and R5. This is reminiscent of the 4504 topology found by Vallin & Laurin (2004), where Aïstopoda, Adelogyrinidae and Nectridea – 4505 each a single composite OTU – clustered at the “lepospondyl” base, from which a long 4506 “microsaurian” stem then separated a Lysorophia-Lissamphibia clade (Fig. 28A). 4507 The alternative to the basal dichotomy, the long “microsaur” grade of Analysis EB, 4508 may be considered suspicious: the “microsaurs” are phenetically similar to the amniotes, and 4509 remain close to them (except for the brachystelechids), while the other “lepospondyl” groups 4510 cluster as many internodes away from Amniota as possible (BPO = 19; against a BPE of 7; PP 4511 = 76). 4512 Even so, the limbless aïstopods and the adelospondyls, for which extremities are 4513 unknown and among which Adelogyrinus is well enough preserved that we have scored it as 4514 limbless (state DIG 1-2-3-4(5); for discussion see character 276 in Appendix 1 as well as 4515 Andrews & Carroll, 1991: 252), never form an exclusive clade in our analyses (Fig. 29) – 4516 even though they did in Germain (2008a: fig. 5.15; simplified in Marjanović & Laurin, 2013a: 4517 fig. 4C). 4518 As in RC07, “nectridean” monophyly is never found; instead (Fig. 29) there is a strong 4519 attraction between the urocordylid “nectrideans” and the aïstopods, which form an exclusive 4520 clade in all analyses (BPO = 43; BPE = 30; PP = 96). Except in Analysis R2 (Fig. 29B), 4521 however, all “nectrideans”, aïstopods, adelospondyls (except in B2) and the “microsaur” 4522 *Utaherpeton (except in B2) consistently form either an exclusive clade (Analyses R1, R4 4523 and R5) or a grade towards lysorophians, brachystelechid “microsaurs” and/or modern 4524 amphibians (Analyses R1, R3, R6 and EB; BPO = 25; BPE = 15; PP = 57; Fig. 29A, C). 4525 Arguably, R2 is an example of the second pattern, because there, too, Diplocaulidae and 4526 Scincosaurus are closer to the lysorophian Brachydectes and the brachystelechid Batropetes 4527 than to Urocordylidae (Fig. 29B). 4528 Consistently, and unlike in RC07, Diplocaulidae and Scincosaurus are sister-groups 4529 (BPO = 56; BPE = 63; PP = 86). This agrees with other recent analyses (e.g. Pawley, 2006; 4530 Milner & Ruta, 2009; Pardo, Small & Huttenlocker, 2017: fig. S6A but not B – Fig. 28B, E). 4531 Unlike in all earlier versions of this matrix (e.g. Marjanović & Laurin, 2015, 2016), 4532 urocordylid phylogeny is resolved, with the original taxon sample making Ptyonius the sister- 4533 group of the other two as in RC07 and Germain (2008a: fig. 5.15), while adding taxa puts 4534 Sauropleura in that position; urocordylid monophyly, unsurprisingly, is well supported (BPO 4535 = 56; BPE = 63; but contradicting a PP of 65). Diplocaulidae (BPO = 57; BPE = 58; PP = 4536 100) contains (Diplocaulus + Diploceraspis) (BPO = BPE = PP = 100) and (Keraterpeton + 4537 Diceratosaurus) (BPO = BPE = 43; PP = 68); Batrachiderpeton is the sister-group of the 4538 former clade (BPO = 46; BPE = 39; PP = 94). Sampling almost no *stereospondyls, our 4539 matrix cannot test the hypothesis by Pardo (2011, 2014) that Diplocaulus and Diploceraspis –

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4540 but not the “keraterpetids” – are **brachyopoid temnospondyls; we await full publication of 4541 that work (see also Marjanović & Laurin, 2013a), which will contain a redescription of 4542 Diploceraspis. 4543 Even though we updated the scores of Lethiscus based on Pardo et al. (2017), who for 4544 the first time found the aïstopods as whatcheeriid-grade animals, and even though we added 4545 *Coloraderpeton mostly from the same source, we recover Aïstopoda nested as deeply among 4546 the “lepospondyls” as in all previous analyses. Attempts to move the aïstopods, the 4547 urocordylids, *Utaherpeton and the adelospondyls next to the colosteids in Mesquite appear 4548 to require ten additional steps on a tree from Analysis R1 and twelve on one from R4, 4549 contradicting a BPO of 35, a BPE of 20 and a PP of 86; placing Aïstopoda + Urocordylidae 4550 next to Ossinodus (crownward of Whatcheeriidae and optionally of Tulerpeton) takes a total 4551 of 15 extra steps in R1 as far as we can determine in Mesquite, against a BPO of 67 and a PP 4552 of 86; moving all these “lepospondyls” next to Ossinodus (one node crownward of 4553 *Densignathus, two of Whatcheeriidae) takes an impressive total of 32 extra steps in R4, 4554 despite contradicting a BPE of only 22. 4555 This could, on the one hand, be due to the fact that our matrix almost completely lacks 4556 braincase characters, which Pardo et al. (2017) sampled more densely than ever before. Most 4557 conspicuously, we were unable to score the remarkable persistence of the buccohypophyseal 4558 canal in (at least) Lethiscus and *Coloraderpeton, a plesiomorphy not otherwise reported 4559 from anywhere crownward of **. We have, however, scored such features as the 4560 exposure of the ventral cranial fissure/suture caudal to the parasphenoid (at least in the 4561 midline) in Lethiscus, *Coloraderpeton and apparently *Pseudophlegethontia (Anderson, 4562 2003b: fig. 2A), the lack of a lingual lamina on the angular in all three, the spiracular notches 4563 and palatal dentition of the first two, or the mostly or fully enclosed mandibular lateral-line 4564 canal and the preopercular bone of *Coloraderpeton (see characters 142, 161, 69, 103, 104, 4565 107, 108, 110, 118, 101, 81 – PASPHE 9, ANG 2-3, SQU 3, VOM 3, VOM 4, VOM 8, VOM 4566 9, PAL 1, ECT 5, SC 2, PREOPE 1 – in Appendix 1). Although we suspect that the supposed 4567 parasymphysial of Lethiscus and *Coloraderpeton – a very large, massive, toothless bone – is 4568 actually a mentomandibular ossification of Meckel’s cartilage, we are currently unable to test 4569 this idea and have scored the bone as the parasymphysial, which has not otherwise been 4570 reported from anywhere crownward of the anthracosaurs (teal in Fig. 24). 4571 Conversely, however, postcranial characters are underrepresented in the matrix by 4572 Pardo et al. (2017) even compared to ours. Being deliberately restricted to taxa with good 4573 braincase data (Pardo et al., 2017: supplementary information part A), their taxon sample 4574 lacks any “lepospondyls” other than Lethiscus, *Coloraderpeton and a few “recumbirostrans” 4575 (on which see below). 4576 On the other hand, the quality of our data for Oestocephalus could have misled our 4577 analyses. Although Carroll (1998a) expressed strong doubts about “lepospondyl” affinities for 4578 aïstopods and a preference for much more rootward placements not unlike the ones eventually 4579 found by Pardo et al. (2017), he described – and illustrated in his specimen drawings – several 4580 apomorphies of Oestocephalus that are unexpected for such a rootward position, for example 4581 a large lingual lamina on the angular. To test these anatomical interpretations, it will be 4582 necessary to restudy the specimens. Pardo et al. (2017) did not include Oestocephalus in their 4583 matrix. 4584 It will be interesting to see in future analyses what the braincase characters used by 4585 Pardo et al. (2017) will do to this area of the tree once they are added to our matrix. In 4586 particular, will the urocordylids follow the aïstopods rootward, in keeping with such 4587 plesiomorphies (not coded in our matrix) as the prearticular denticle row or the huge distal 4588 Meckelian fenestra of Sauropleura (Bossy, 1976; Bossy & Milner, 1998), or will their 4589 vertebral similarities to the other “nectrideans” keep them in a rest-“lepospondyl” clade, or

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4590 will all “nectrideans” come with them in spite of the similarities between the brachystelechid 4591 “microsaurs”, the lysorophians, the modern amphibians and Scincosaurus in particular? 4592 Plesiomorphies unexpected for “lepospondyls” are not limited to the head skeleton. 4593 Wellstead (1982: 204, fig. 8A) reported a cololite in Lethiscus, commenting only that “[i]ts 4594 segmented appearance is likely due to a spiral valve in the intestine”. The spiral valve is 4595 plesiomorphic for gnathostomes, found today in chondrichthyans and lungfish; in extant 4596 tetrapods, however, it is absent, and cololites suggest its absence in temnospondyls as well 4597 (e.g. Godfrey, 2003: fig. 2). Independently of Pardo et al. (2017), this finding – if correct – 4598 implies a phylogenetic position for Aïstopoda rootward of Temnospondyli. 4599 Aïstopoda is perhaps of particular interest because some of its members were 4600 terrestrial beyond reasonable doubt, even though *Coloraderpeton must have been 4601 obligatorily aquatic on account of its mandibular lateral-line canal (Pardo et al., 2017): Rößler 4602 et al. (2012) reported two indeterminate aïstopods from Chemnitz (eastern Germany), where a 4603 was covered by volcanic ash around the - boundary in the 4604 Cisuralian. The forest floor is preserved in situ; no water was involved in the deposition. This 4605 confirms the taphonomic and morphological arguments reviewed by Anderson (2002) and 4606 Germain (2008a: chapters II, III; 2008b), to which we add the absence of lateral and ventral 4607 keels on the centra, which are found (state TRU VER 15(1)) in all other potential anguilliform 4608 swimmers in this matrix. Considering the age of Lethiscus, which lies at the very end of 4609 Romer’s gap, it is conceivable that the “first step on land” was done “without limbs” 4610 (Germain, 2008a: chapter III) – and that Aïstopoda contains a separate origin of a terrestrial 4611 lifestyle. 4612 Following our corrections to Lethiscus after Pardo et al. (2017), aïstopod monophyly is 4613 well supported (BPO = 70; BPE = 63; PP = 100), yet not found in any trees from Analysis R2, 4614 where the aïstopods form a grade towards the modern amphibians. The phylogeny of 4615 Aïstopoda is unchanged from RC07 given the original taxon sample, but the resolution largely 4616 breaks down when taxa are added (Fig. 29). 4617 In addition to finding the aïstopods to be whatcheeriid-grade animals, Pardo et al. 4618 (2017) found all other “lepospondyls” they sampled – Brachydectes and a selection of 4619 “microsaurs” – to form a clade within Sauropsida. Although this was supported (Pardo et al., 4620 2017: extended data figure 7b) by bootstrap percentages of 71 for Sauropsida including the 4621 animals in question (“Recumbirostra”; see below), 95 for Amniota and 96 for Amniota + 4622 Limnoscelis (the only sampled diadectomorph), we wonder if this result is an artefact of the 4623 taxon and character samples. For instance, the hyobranchial apparatus of Brachydectes or 4624 Pantylus would imply several reversals from the ancestral amniote condition or massive 4625 homoplasy among all other amniotes; similarly, many of the sampled “microsaurs” retain 4626 well-developed dorsal scales (e.g. CG78), but not one traditional amniote does. A much larger 4627 matrix will be required to test this question. It is puzzling, too, that Pardo et al. (2017) derived 4628 a large part of their matrix from that of Huttenlocker et al. (2013), which is in turn derived 4629 from that of Anderson et al. (2008a), but did not implement or mention any of the changes to 4630 the latter that were proposed (or repeated from Marjanović & Laurin, 2009) by Sigurdsen & 4631 Green (2011), even though they cited Sigurdsen & Green (2011) as the source of a new 4632 character. 4633 4634 The interrelationships of the “microsaurs” 4635 4636 The Tuditanomorpha appears to be a natural assemblage […]. Among the Microbrachomorpha, 4637 the four genera are so distinct from one another that each has been placed in a monotypic family. 4638 It is possible that this is not a natural assemblage, but these forms share more features in 4639 common with each other than any do with other groups of Paleozoic tetrapods. 4640 – CG78: 11–12

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4641 4642 Although there is considerable question concerning the nature and degree of interrelationship 4643 within the Tuditanomorpha, the included families share a great many features. […] The 4644 remaining microsaurs, in contrast, are a more varied group, and may or may not have a 4645 significant common heritage. […] They are here classified as a natural group, but this may not 4646 prove to be the case. 4647 – CG78: 113 4648 4649 It is not an overstatement to say that “microsaur” phylogeny is a mess. No two analyses, 4650 usually even if based on successive versions of the same matrix, have recovered the same 4651 topology or nearly so (Fig. 28). Ours are no exception (Fig. 29). 4652 Microsaur monophyly does not occur in any of our trees. A clade with a membership 4653 similar to that of Tuditanomorpha Carroll & Gaskill, 1978, is not found in any of our analyses 4654 either, although Analysis R6 comes close by finding a clade composed of all 4655 “tuditanomorphs” and the “microbrachomorph” Odonterpeton. Analyses B1, B2 and EB 4656 feature an (Odonterpeton (Microbrachis, Hyloplesion)) clade reminiscent of 4657 Microbrachomorpha Carroll & Gaskill, 1978 (BPO = 23, BPE = 15 and PP = 35 for the 4658 whole), but even so, this clade (which was also found by RC07) is not close to the sampled 4659 brachystelechids (Batropetes, *Carrolla and *Quasicaecilia, the first two observed by D. M.), 4660 of which Batropetes was cautiously included in Microbrachomorpha by CG78 (the others 4661 were not yet known). 4662 That said, the discrepancies between the reconstructions by CG78, the specimen 4663 drawings by CG78, and D. M.’s personal observations of the holotype of Odonterpeton are 4664 such that Odonterpeton will have to be redescribed. For example, the supposed suture 4665 between the left parietal and the supposed postparietal is a series of unconnected cracks; 4666 Odonterpeton consequently has no identifiable postparietal at all (state POSPAR 1-2(2); see 4667 character 39 in Appendix 1 for details), and symmetry is restored by an additional curve to the 4668 left at the caudal end of the suture between the parietals that is omitted from the drawings by 4669 CG78. 4670 Following the redescription of Microbrachis and Hyloplesion by Olori (2015), these 4671 two OTUs are found as sister-groups throughout all of our analyses, as they were by RC07; 4672 the support for this clade is unusually high (BPO = 67; BPE = 66; PP = 97). 4673 Anderson (2007b: 205–206) coined the name Recumbirostra and carefully defined it 4674 as applying to “the clade descended from the most recent common ancestor of Pantylus, 4675 Cardiocephalus sternbergi, Rhynchonkos, and Micraroter, but not including Tuditanus or 4676 Microbrachis”. This definition, and therefore this name, cannot be applied to the trees from 4677 any of our analyses: while Rhynchonkos, Gymnarthridae (incl. Cardiocephalus) and 4678 Ostodolepididae (incl. Micraroter) form an exclusive clade of elongate “microsaurs” in all 4679 analyses except R4 (variously joined by *Trihecaton in R6 and EB; BPO for clade = 22, BPE 4680 = 26, PP = 64; Fig. 29), the pantylids (Pantylus and Stegotretus; see below for *Sparodus) are 4681 never closer to it than Tuditanus and/or Microbrachis are (BPO = 12; BPE = 1; PP = 40) – 4682 indeed, as described below, Pantylidae and Tuditanidae always fall out as sister-groups (Fig. 4683 29) except in EB. 4684 The original taxon sample contained a single brachystelechid, Batropetes. In Analyses 4685 R1 and R3, it is the sister-group of a clade consisting of Brachydectes (the only included 4686 lysorophian), the adelospondyls, Urocordylidae, Aïstopoda and all available modern 4687 amphibians (Fig. 29A). Analysis B1, however, recovers Batropetes and Brachydectes as 4688 sister-groups (BPO = 37). These two arrangements cannot be distinguished in R2, the entire 4689 clade that forms the sister-group of Brachydectes in R1 lies within the temnospondyls. When 4690 taxa are added, the three brachystelechids (Batropetes, *Carrolla, *Quasicaecilia) form an 4691 exclusive clade (BPE = 37) in Analyses R4, R5 and some MPTs from R6 (Fig. 29C). In the

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4692 remaining MPTs from R6, they form a grade toward Brachydectes; in EB, they form a grade 4693 toward the modern amphibians instead, with Brachydectes on the outside (PP = 88). Only in 4694 R2, R4, R5 and perhaps R6 can the brachystelechids even be considered part of the 4695 “microsaur” grade. 4696 Pawley (2006: 239) reported to have found the “microsaurs” Tuditanus and 4697 Asaphestera (both classified in Tuditanidae by CG78) to score identically except for missing 4698 data. They differ in our matrix. Indeed, the added tuditanid *Crinodon (see below) has more 4699 in common with Tuditanus than Asaphestera does (Fig. 29C), despite being easy to 4700 distinguish from both. Although Asaphestera is found as a tuditanid in all parsimony analyses 4701 (see below), Analysis EB finds it one node crownward of Tuditanidae (PP = 36). 4702 As in RC07, though unlike in the Anderson-lab matrices (Fig. 28F), Hapsidopareion 4703 (together with *Llistrofus, see below) is never the sister-group of the supposed (CG78) 4704 hapsidopareiid Saxonerpeton (kept apart by BPO = 26), except in Analysis B2 (BPE = 10) 4705 and EB (PP = 35), although they are only one internode apart in R1 and R2. In all parsimony 4706 analyses, Tuditanidae (Tuditanus, Asaphestera; in R4–R6 also *Crinodon; in R4 and B2 4707 further the *Goreville microsaur) and Pantylidae (Pantylus, Stegotretus; in B2 also 4708 *Sparodus) consistently form a clade, though it is less well supported (BPO = 12; BPE = 1; 4709 against a PP of 40) than either Tuditanidae (BPO = 24, BPE = 15; PP = 89 excluding 4710 Asaphestera) or Pantylidae (BPO = 92; BPE = 36, BPE = 77 without *Sparodus; PP = 88, PP 4711 = 93 without *Sparodus) on their own. In EB, Tuditanidae forms the sister-group to all other 4712 “lepospondyls” (PP = 36 excluding Asaphestera) except Westlothiana (PP = 73). 4713 4714 Added “microsaurs” 4715 4716 *Carrolla, *Quasicaecilia and *Crinodon have been treated above (see also the next section 4717 for the first two). 4718 *Utaherpeton was described as one of the oldest “microsaurs”; the original description 4719 (Carroll, Bybee & Tidwell, 1991) already noted similarities to the “nectrideans”. Our results 4720 (Fig. 29C), much like those of Marjanović & Laurin (2009; Fig. 28F) but unlike those of 4721 Vallin & Laurin (2004; Fig. 35A) or Pardo, Small & Huttenlocker (2017: fig. S6), place 4722 *Utaherpeton inside the holospondyl clade , next to the clade composed of the adelospondyls, 4723 urocordylids, aïstopods and, in R6, Eocaecilia (PP = 69; against a BPE of 10). We deduce 4724 that, rather than being just another “microbrachomorph” “microsaur”, *Utaherpeton could 4725 occupy a crucial position close to the origin of Holospondyli and deserves future attention. 4726 The corresponding bootstrap tree, however, interestingly makes it the sister-group of 4727 Westlothiana, a position that agrees vaguely with the original description but has negligible 4728 support (BPE = 10; against a PP of 76). 4729 The *“Goreville microsaur” (Lombard & Bolt, 1999) either falls out as a tuditanid 4730 next to *Crinodon (R4; PP = 88; Fig. 29C) or nests with *Sparodus (R5, R6). The bootstrap 4731 trees place it in Tuditanidae, with very low support (BPE = 15), although Bayesian support is 4732 considerable (PP = 89). 4733 *Sparodus was considered a gymnarthrid by CG78 and Carroll (1988). In our analyses 4734 such a relationship is never found. In R4–R6, *Sparodus forms a clade with Odonterpeton 4735 and (in R5 and R6) the *Goreville microsaur; the same cautionary notes about Odonterpeton 4736 as above apply. Pantylus and Stegotretus nest next to *Sparodus in Analyses B2 and EB (BPE 4737 = 36; PP = 88). A pantylid position would not be surprising considering the enormous palatine 4738 and especially coronoid tusks (Carroll, 1988; D. M., pers. obs. of the same specimen – Fig. 3, 4739 4). 4740 *Trihecaton has hitherto been neglected since CG78 because its skull is almost 4741 entirely unknown. The rest of the skeleton including the lower jaw, however, is mostly

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4742 preserved and articulated. Because the postcranium is so close to complete and lower-jaw 4743 characters are well represented in this matrix, D. M. has scored it directly from the specimens 4744 (which probably belong to the same individual). Analyses R4 and R5 resolve its position next 4745 to (Holospondyli (Microbrachis, Hyloplesion)) or, in R4, one node rootward of Saxonerpeton; 4746 R6 places it next to Micraroter within Ostodolepididae or next to Gymnarthridae in different 4747 MPTs (Fig. 29C). Analyses B2 and EB place it next to the Gymnarthridae-Rhynchonkos- 4748 Ostodolepididae clade (BPE = 10; PP = 64). 4749 *Llistrofus is always the sister-group of Hapsidopareion (BPE = 87; PP = 100), as 4750 expected (Bolt & Rieppel, 2009). 4751 4752 Lissamphibian origins 4753 4754 As summarized in Tables 1, 3 and 4, our revision of the matrix of RC07 supports the 4755 lepospondyl hypothesis over the temnospondyl hypothesis, which in turn is more 4756 parsimonious than the polyphyly hypothesis. Adding OTUs, including *Gerobatrachus, to the 4757 matrix increases the difference between the LH and the TH by one step and the difference 4758 between the TH and the PH by two steps, still favoring the LH over its alternatives, contrary 4759 to the results of RC07 (Fig. 1), Sigurdsen & Green (2011), Maddin, Jenkins & Anderson 4760 (2012), Pardo, Small & Huttenlocker (2017: fig. S6) and Pardo et al. (2017); the LH further 4761 has a posterior probability of 92 (Fig. 20). 4762 As discussed above (Materials and methods: Robustness analyses), a reliable statistical 4763 test for whether the differences between these trees are distinguishable from random is not 4764 available. The null hypothesis (that they are not) cannot currently be rejected, except perhaps 4765 for the difference between the LH and the PH, and that only under the original taxon sample 4766 (Table 4). 4767 Monophyly of the modern amphibians is found in all analyses (except of course those 4768 constrained against it, see Table 1: R3, R6) and well supported: BPO = 65; BPE = 67; PP = 4769 100. Note that adding taxa does not decrease the support. 4770 In Analysis R1 (Fig. 10, 11, 29A, 30L), the “lepospondyls” closest to Lissamphibia are 4771 a clade of adelospondyls, urocordylids and aïstopods, a novel and unexpected result. Next 4772 closest is Brachydectes, the only sampled lysorophian. A sister-group relationship between 4773 lissamphibians and lysorophians has long been considered an integral part of the lepospondyl 4774 hypothesis (though see Marjanović & Laurin, 2013a, for discussion) and is consistent with the 4775 results of Vallin & Laurin (2004), Pawley (2006: fig. 91) and Marjanović & Laurin (2008, 4776 2009: supplementary figure), as shown in Fig. 28 and 30A, C, E. On the outside follows 4777 Batropetes, the only brachystelechid “microsaur” in the original taxon sample; this is 4778 congruent with the results of Vallin & Laurin (2004). 4779 However, when taxa are added to the parsimony analysis (R4; Fig. 14, 29C, 30M), 4780 Brachydectes is the sister-group of Brachystelechidae, which includes Batropetes (BPO = 37; 4781 BPE = 23), both together forming the sister-group of Lissamphibia (BPO = 20; BPE = 14). 4782 Analysis EB uniquely finds the modern amphibians nested inside the brachystelechids, closest 4783 to *Quasicaecilia + *Carrolla (PP = 88), followed by Batropetes (PP = 45) and then by 4784 Brachydectes (PP = 92). 4785 The sister-group of the smallest clade formed by all modern amphibians, Brachydectes 4786 and the brachystelechids is Scincosaurus + Diplocaulidae in Analyses R1 and EB (PP = 57). 4787 R4 instead places Rhynchonkos in this position (contradicting a BPE of 26 and a PP of 76); it 4788 has historically played a large role in the PH (Carroll, 2007) and was recovered in the same 4789 position by Vallin & Laurin (2004; Fig. 30A). B1 and B2 place Holospondyli as a whole next 4790 to (Lissamphibia (Batropetes, Brachydectes)) with very weak support (BPO = 25; BPE = 6).

122 Rhynchonkos Brachydectes Brachystelechidae (composite OTU) adelospondyls 31 Nectridea 53 Lysorophia (composite OTU) H. Lethiscus 62 L. Salientia P. 98 Aïstopoda Oestocephalus 84 caudates/urodeles Phlegethontia 40 G. Eocaecilia Albanerpetidae 70 **Gymnophiona A 96 Triadobatrachus modern amphibians caudates Urocordylidae B Eocaecilia Scincosaurus Diplocaulidae H. adelospondyls Amphibamus Lethiscus Doleserpeton < 50 Oestocephalus Albanerpetidae Aïstopoda – Phlegethontia L. < 50 Eocaecilia 67 B. caudates Brachydectes 61 Albanerpetidae 80 Salientia m. 97 L. Eocaecilia D B. caudates C Triadobatrachus Amphibamus 78\92 Doleserpeton Aïstopoda ?\98 L. Eocaecilia 96 B. Caudata (composite OTU) Brachydectes 67\98 17 69\99 Salientia Eocaecilia 100\100 22 L. F 32 Albanerpetidae B. *Urodela (composite OTU) 70 Amphibamus 88 Salientia E 97 Doleserpeton *Gerobatrachus Amphibamus Salientia 76 B. 91 Doleserpeton 86 Albanerpetidae G. **Gymnophiona 99 61 *Urodela (composite OTU) L. 90 Eocaecilia Pantylidae 67 *Gerobatrachus Brachystelechidae Salientia 100 63 B. 81 Rhynchonkos Albanerpetidae Eocaecilia Caudata H G 82

Amphibamus Amphibamus Platyrhinops Platyrhinops ?\– Amphibamus Amphibamus ?\100 Doleserpeton ?\95 Doleserpeton *Gerobatrachus ?\100 *Gerobatrachus G. **Gymnophiona ?\100 Karaurus B. Salientia Eocaecilia 85\100 97\95 **Chinlestegophis *Urodela 51\6274\100 Lissamphibia B. Salientia *Stereo- Karaurus spondyli *Lydekkerina **Rileymillerus Caudata *Urodela ?\100 G. ?\100 **Chinlestegophis *Stereospondyli *Lydekkerina ?\100 Eocaecilia **Rileymillerus 85\100 **Gymnophiona I **Chinlestegophis J 100\100 Amphibamus Amphibamus Doleserpeton 44 Doleserpeton – *Gerobatrachus Salientia (R3) *Lydekkerina Batropetes **Rileymillerus Brachydectes 19 adelospondyls *Stereo- **Chinlestegophis 47 – Urocordylidae spondyli G. **Gymnophiona – 83 43 Aïstopoda Eocaecilia 70 – Eocaecilia Lissamphibia Karaurus 65 Albanerpetidae Salientia L. (R1)/ B. Caudata Batrachia *Urodela Procera (R3) 53 74 K Salientia (R1) L 77 90 Hapsidopareion 87\100 *Llistrofus Aïstopoda Lethiscus Rhynchonkos Oestocephalus –\– Brachydectes Phlegethontia Albanerpetidae –\– 23\– Brachystelechidae m. 37\– Eocaecilia L. Eocaecilia 15\92 L. Albanerpetidae B. Caudata 67\100 other caudates Salientia –\55 B. 25\52 N 54\81 Chelotriton 38\67 Salientia Amphibamus M 87\99 *Gerobatrachus Platyrhinops Doleserpeton Amphibamus other caudates incl. *Micropholis Albanerpetidae Batrachia *Gerobatrachus Chelotriton Doleserpeton Salientia *Gerobatrachus G. adelospondyls L. Caudata = Procera incl. Urocordylidae Eocaecilia + Albanerpetidae Aïstopoda O Salientia P Eocaecilia 124

4791 ↑ Figure 30: The phylogeny of modern amphibians and their closest relatives in recently 4792 published (A–K) and our (L–P) analyses, and the distribution of several character states. 4793 Albanerpetidae is a composite OTU throughout. Numbers in A, D, E, G, H are bootstrap 4794 percentages. B., Batrachia; G., Gymnophionomorpha (not shown when Eocaecilia is the only 4795 included member); L., Lissamphibia; m., modern amphibians (when not synonymous with 4796 L.); P., Procera. A: Vallin & Laurin (2004); the two unnumbered “caudate” nodes have 4797 bootstrap values below 30%. B: Pawley (2006: fig. 88; see Fig. 28B). C: Pawley (2006: fig. 4798 91; see Fig. 28C). D: RC07. We write “< 50” where RC07 (appendix 4) wrote “no bootstrap 4799 support in a 50 % majority-rule consensus” and “–” where they wrote “no boots[t]rap support 4800 compatible with a 50 % majority-rule consensus”. Caudate monophyly is found in some 4801 MPTs and, as shown here, 61% of the bootstrap replicates. E: Marjanović & Laurin (2009). 4802 F: Sigurdsen & Green (2011: fig. 2B, 4). Numbers are bootstrap percentages from 4803 unweighted parsimony (left; not published if below 50) and Bayesian posterior probabilities 4804 (right; in %). G: Maddin, Jenkins & Anderson (2012). Bootstrap percentages below 50 were 4805 not published. The topology of this part is unaffected by our reanalysis (Results: Reanalysis 4806 of the matrix of MJA12). H: Huttenlocker et al. (2013). Bootstrap percentages below 50 were 4807 not published. I–K: MPTs from Pardo, Small & Huttenlocker (2017); see Results: Reanalysis 4808 of the matrix of Pardo, Small & Huttenlocker (2017). Numbers in J are bootstrap percentages 4809 (left; not published if below 50) and Bayesian posterior probabilities (right; in %). The ribs of 4810 **Rileymillerus are scored under the assumption that the tentatively referred postcrania really 4811 belong to a juvenile of the same taxon as the holotype, which is a skull (Bolt & Chatterjee, 4812 2000); this is at least not contradicted by the postcrania of **Chinlestegophis (Pardo, Small & 4813 Huttenlocker, 2017). L: R1 (unconstrained), R3 (constrained for the PH; both original taxon 4814 sample). Numbers are BPO given that Salientia has the position it has in R1. M: R4 4815 (unconstrained, expanded taxon sample). Numbers are BPE\PP. N: R2 (constrained against 4816 the LH, original taxon sample). O: R5 (constrained against the LH, expanded taxon sample); 4817 Micropholis also has two positions outside the clade shown here. P: R6 (constrained for the 4818 PH, expanded taxon sample). 4819 Except where mentioned otherwise below, the rectangles show state 0 (filled) or 1 4820 (empty) of characters 18 (LAC 1 – cyan), 39 (POSPAR 1-2 – teal), 45 (POSFRO 1 – blue), 53 4821 (TAB 1/SQU 4 – violet), 60 (POSORB 1 – reddish purple), 71 (JUG 1 – magenta), 72 (JUG 4822 2-6 – red), 77 (QUAJUG 1 – orange), 102 (VOM 1-13 – bright green and greenish yellow, see 4823 below), 160 (ANG 1 – dark green), 246 (RIB 3 – brown) and 250 (RIB 7 – black). Absence of 4824 a rectangle means missing data, inapplicability or ambiguous optimization at the root of a 4825 collapsed clade, except that *Lydekkerina is polymorphic for character 72. 4826 State 1 of the unordered character 39 does not occur in this figure, so empty rectangles 4827 show state 2. State 2 of the ordered character 72 is limited to Pantylidae in this figure and 4828 therefore shown as state 1. The ordered character 102 has three states: about as wide as 4829 long or wider (0, filled greenish yellow rectangles); intermediate (1, empty bright green 4830 rectangles); at least 2½ times as long as wide (2, filled bright green rectangles). Rectangles 4831 with a bright green rim filled in with greenish yellow indicate ambiguous optimization of state 4832 1 or 2. 4833 Character 18: presence (0) or absence (1) of lacrimal; 39: presence (0) or absence (2) 4834 of postparietals; 45: presence (0) or absence (1) of postfrontal; 53: presence (0) or absence (1) 4835 of tabular; 60: presence (0) or absence (1) of postorbital; 71: presence (0) or absence (1) of 4836 jugal; 72: contact between maxilla and quadratojugal at ventrolateral edge of skull (0), jugal 4837 separates maxilla and quadratojugal and forms part of ventrolateral edge of skull (1 and 2); 4838 77: presence (0) or absence (1) of quadratojugal; 102: see above; 160: presence (0) or absence 4839 (1) of angular; 246: ribs mostly straight (0, empty rectangles) or ventrally curved in at least 4840 part of the trunk (1, filled rectangles); 250: trunk ribs longer (0) or shorter (1) than three

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4841 successive articulated vertebrae in adults. Note that we do not distinguish absence due to loss 4842 of an ossification center from absence as a separate bone due to ontogenetic fusion; in more or 4843 less all cases the ontogeny is insufficiently well known to decide. 4844 For further derivations within Caudata and Salientia, see the text. Adelospondylus has 4845 state 60(1), Notobatrachus is polymorphic for 77. The optimizations for character 72 differ 4846 for Aïstopoda between P and the rest due to the larger taxon sample in P; likewise, the 4847 optimizations for character 160 vary for Caudata/Urodela depending on taxon samples. 4848 4849 When the TH is enforced on the original taxon sample through a constraint (R2; Fig. 4850 12, 29B, 30N), the lissamphibians do not nest with Doleserpeton as expected, or even within 4851 Dissorophoidea at all. Instead, they nest within the dvinosaurs – and take the aïstopods (which 4852 become paraphyletic with respect to Lissamphibia), the urocordylids and the adelospondyls 4853 with them. While it seems remarkable that such a surprising novel topology is more 4854 parsimonious than any conventional version of the TH, the modest magnitude of this 4855 difference – to move all lissamphibians next to Doleserpeton requires three extra steps in 4856 Mesquite, as many as to enforce the PH (Analysis R3; Fig. 30L) – and the lack of statistical 4857 significance for the difference to Analysis R1 suggest that we should ascribe this result to 4858 insufficiencies in the matrix. Indeed, adding taxa (R5; Fig. 15, 30O) “rectifies” the 4859 constrained topology by placing Lissamphibia among the amphibamid dissorophoids, far 4860 from the dvinosaurs and without turning any “lepo-” into temnospondyls; however, both 4861 Doleserpeton and *Gerobatrachus are found as sister-groups of Lissamphibia with equal 4862 parsimony, failing to resolve the disagreement between Sigurdsen & Bolt (2010), who 4863 favored Doleserpeton in this role, and Anderson et al. (2008a), Maddin & Anderson (2012), 4864 Maddin, Jenkins & Anderson (2012 – Fig. 30G), Pardo, Small & Huttenlocker (2017 – Fig. 4865 30I–K) and Pardo et al. (2017), who found *Gerobatrachus to lie closer to (or even within) 4866 Lissamphibia. 4867 Pardo, Small & Huttenlocker (2017: fig. S6) added **Chinlestegophis and 4868 **Rileymillerus to a matrix slightly modified from that of Maddin, Jenkins & Anderson 4869 (2012), which contains almost only dissorophoids and “lepospondyls”, and found them as 4870 temnospondyls – though not as lissamphibians, despite finding the TH. Satisfied that 4871 **Chinlestegophis, **Rileymillerus and the modern amphibians were temnospondyls, Pardo, 4872 Small & Huttenlocker (2017) then added them to a matrix that contained temnospondyls and 4873 modern amphibians but no “lepospondyls”; that matrix is based on Schoch (2013), accepting 4874 (J. Pardo, pers. comm.; D. M., pers. obs.), though not citing, most of the changes proposed by 4875 Dilkes (2015a) but omitting the characters Dilkes added and greatly changing the taxon 4876 sample. Bayesian analysis and some of the MPTs resulting from this second matrix found the 4877 caecilians, **Chinlestegophis and **Rileymillerus as stereospondyls while the batrachians 4878 remained dissorophoids (Pardo, Small & Huttenlocker, 2017: fig. 2C, S7). However, 4879 lissamphibian monophyly – within Stereospondyli or Dissorophoidea – is equally 4880 parsimonious (Results: Reanalysis of the matrix of Pardo, Small & Huttenlocker, 2017; Fig. 4881 30I–K). While **Chinlestegophis and **Rileymillerus are clearly stereospondyls, we 4882 therefore – and for a number of anatomical reasons – remain uncertain for the time being 4883 whether the caecilians are closely related to them. However, it is clear that a very large matrix 4884 – sampling stereospondyls, “lepospondyls” and many characters – will be necessary to 4885 adequately test this question. 4886 Such a matrix will also need to be carefully scrutinized for accuracy before analysis 4887 because accidental misscores are, as we show here, common and because small changes 4888 routinely have disproportionate and unpredictable impacts on the results. In this context, we 4889 note that even though the matrices of Maddin & Anderson (2012), Maddin, Jenkins & 4890 Anderson (2012), Huttenlocker et al. (2013) and Pardo, Small & Huttenlocker (2017: fig. S6)

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4891 are largely derived from that of Anderson et al. (2008a), and that of Pardo et al. (2017) is by 4892 half, none of these publications addressed or even mentioned the changes to that matrix 4893 proposed by Marjanović & Laurin (2009) and Sigurdsen & Green (2011), despite their impact 4894 on the results in the latter publications. Indeed, the matrix and character list of Pardo, Small & 4895 Huttenlocker (2017: fig. S6) remain altogether unpublished. 4896 Other than new braincase characters and one from Maddin & Anderson (2012), the 4897 matrix of Pardo et al. (2017) was composed from those of Clack et al. (2012a) and 4898 Huttenlocker et al. (2013). It is thus not much better equipped to test lissamphibian origins 4899 than the latter. 4900 The albanerpetid **Shirerpeton was published too recently for us to score (Matsumoto 4901 & Evans, 2018). It reinforces our impression that Albanerpetidae should not be omitted from 4902 phylogenetic analyses of lissamphibian origins (as done by Pardo, Small & Huttenlocker, 4903 2017: fig. 2, S7), but instead have potentially crucial new information to offer. For example, a 4904 suproccipital bone had never been documented in a modern amphibian, its presence was 4905 scored as unknown for Albanerpetidae in RC07, and we have kept this score (despite the 4906 suggestive median caudodorsal thickening in the fused braincase of Albanerpeton – Maddin et 4907 al., 2013); **Shirerpeton unambiguously has a suproccipital, which, as Matsumoto & Evans 4908 (2018) noted, strongly resembles that of Brachydectes in its shape and spatial relationships. 4909 The suproccipital, or at least its exposure on the skull surface, is absent in all temnospondyls 4910 that are well enough known, including Doleserpeton; among “microsaurs”, it is absent in 4911 Gymnarthridae and not exposed in Stegotretus, but present and exposed elsewhere, including 4912 in Batropetes. 4913 4914 Lissamphibian phylogeny 4915 4916 All salientians form a clade (BPO = 90; BPE = 87; PP = 99) in all analyses. The salientian 4917 *Liaobatrachus is consistently found as the sister-group of Notobatrachus + Vieraella (BPE = 4918 82; PP = 100). A clade formed by the latter two (BPO = 96) to the exclusion of more 4919 crownward salientians (like *Liaobatrachus: BPE = 68; PP = 58) has not been found 4920 elsewhere (e.g. Dong et al., 2013); this may be due to the character sample, though perhaps 4921 the taxon sample with its many but distant outgroups also plays a role. 4922 Contrary to RC07, or to Pardo, Small & Huttenlocker (2017: fig. 2C, S6A, S7; Fig. 4923 30J, K), the two caudates Karaurus and Valdotriton form a clade in all MPTs derived from 4924 the original taxon sample (BPO = 74). Seemingly bizarre things happen when taxa are added, 4925 including the further caudates *Beiyanerpeton, *Pangerpeton and *Chelotriton, but this is not 4926 surprising: because only two caudates were originally included, the matrix does not contain 4927 any characters that are intended to resolve caudate phylogeny. 4928 The extremely peramorphic salamandrid *Chelotriton (Marjanović & Witzmann, 4929 2015) is the most salientian- and temnospondyl-like caudate, falling out as the sister-group of 4930 Salientia in Analyses R4, R6 and EB (BPE = 38; PP = 67; Fig. 30M, P), and as the sister- 4931 group of a clade that contains all other non-salientian modern amphibians in Analysis R5. 4932 Evidently, its peramorphosis pulls it to the base of, or altogether out of, Caudata given the 4933 present character sample, and indeed toward the base of Lissamphibia or Batrachia in 4934 constrained trees where the closest relatives of Lissamphibia or Batrachia are temnospondyls; 4935 but this is not enough to pull the modern amphibians into the temnospondyls, or to support the 4936 Procera hypothesis (on which see below) unless the TH is enforced (Fig. 30O). We conclude 4937 that ontogeny does not as severely “discombobulate” phylogeny (Wiens, Bonett & 4938 Chippindale, 2005: title) in this case as one could have expected. 4939 The more moderately peramorphic *Pangerpeton is always found within a caudate 4940 clade or grade. In R4–R6 it lies next to a Valdotriton-Karaurus-*Beiyanerpeton clade (which

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4941 has a BPE of 21 and, in R5, is either the sister-group of Albanerpetidae + Eocaecilia or 4942 contains it as the sister-group of Valdotriton); Analysis EB places it next to *Beiyanerpeton + 4943 Karaurus (PP = 57). 4944 *Beiyanerpeton, on the other hand, combines paedomorphosis with unexpected 4945 plesiomorphies. Possibly due to this balance, it is neither attracted to nor repelled from the 4946 caudate root: in R4–R6, it is always found as the sister-group of Karaurus (BPE = 46; PP = 4947 46), which is normally considered a stem-caudate, but found in various nested positions in the 4948 caudate clade or grade in our analyses (a result we ascribe to the character sample). 4949 In trees that support the LH (all unconstrained searches: Analyses R1, R4, B1, B2, EB; 4950 Fig. 30L, M), the Batrachia hypothesis is consistently recovered: Salientia and all caudates 4951 form a clade to the exclusion of Albanerpetidae and Eocaecilia (BPO = 77; BPE = 54; PP = 4952 81). Given the original taxon sample, Salientia nests as the sister-group of Caudata (R1); 4953 otherwise, it forms the sister-group of the unusually peramorphic and therefore -like 4954 caudate *Chelotriton (see above) followed by a clade containing all other caudates. The 4955 sister-group of Batrachia is Albanerpetidae (R1, R4and EB; BPO = 53; PP = 55) or Eocaecilia 4956 (BPE = 44). 4957 In Analysis R5 (Fig. 15, 30O), which is constrained against the LH and supports the 4958 TH, Salientia forms the sister-group to all other modern amphibians (Procera); in other words, 4959 it lies as close as possible to the temnospondyls, while Albanerpetidae and Eocaecilia (both 4960 not constrained) nest within the caudate grade. Procera was likewise found by Pardo, Small & 4961 Huttenlocker (2017: fig. S6A, but not S7) and Pardo et al. (2017: extended data fig. 7). In R2 4962 (Fig. 30N), in which various holospondyls are the closest relatives of lissamphibians and all 4963 of the above are nested among temnospondyls, Eocaecilia always lies outside Batrachia, 4964 while Albanerpetidae is the sister-group to Lissamphibia as a whole; moving Albanerpetidae 4965 back into Lepospondyli (as the sister-group of Brachydectes) cannot be done in Mesquite 4966 without adding at least eight steps. 4967 The constraint for the PH specified only the backbone ((Salientia, Doleserpeton) 4968 (Brachydectes, Eocaecilia)); the positions of the caudates and Albanerpetidae were left open. 4969 Both groups fall out as lepospondyls (next to Eocaecilia) in the original taxon sample (R3; 4970 Fig. 30L), but become temnospondyls when taxa – *Chelotriton? – are added (R6; Fig. 30P). 4971 In summary, Salientia is attracted to Amphibamidae and to Caudata (especially 4972 *Chelotriton), and possibly pushed away by “lepospondyls”; Albanerpetidae is drawn 4973 towards brachystelechids + lysorophians and Eocaecilia as well as towards Caudata, and 4974 repelled by Amphibamidae. 4975 Several of the attractions of Albanerpetidae will likely be reinforced by **Shirerpeton, 4976 which was published too recently for us to score (Matsumoto & Evans, 2018). For example, 4977 **Shirerpeton is the only modern amphibian known to possess a suproccipital, arguing for a 4978 position outside Lissamphibia; the postfrontal is absent as in batrachians but not caecilians; 4979 the supratemporal or tabular, retained in Eocaecilia but no other known lissamphibians so far, 4980 appears to be present; at the same time, the squamosal and the pterygoid of **Shirerpeton 4981 form a tube filled by the rod-like quadrate, a feature shared specifically with Caudata. 4982 4983 Characters 4984 4985 Surprising reversals 4986 4987 It is not surprising that homoplasy is omnipresent (as shown by the tree indices) in a matrix 4988 with 102 or 158 OTUs that span 380 million years. Some reversals, though, are unexpected 4989 even within this context. In this section we present bones that are unambiguously optimized 4990 (by parsimony in Mesquite on the MPTs from Analyses R1–R6; Mesquite presents

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4991 uncertainty as such rather than restricting itself to ACCTRAN or DELTRAN) as having been 4992 lost and then reappeared. Some of these have been discussed before (Sigurdsen & Green, 4993 2011, and references therein), mostly in the context of lissamphibian origins. We do not, at 4994 present, take any position on whether such reversals should be considered particularly 4995 implausible (see Wiens, 2011; Botelho et al., 2014; Diaz & Trainor, 2015; Ossa-Fuentes, 4996 Mpodozis & Vargas, 2015). 4997 RC07 did not specify any state changes as irreversible (or weighted them in other 4998 ways), and their trees (Fig. 1) already require some of the reappearances of lost bones that we 4999 find in our parsimony analyses. We have preferred not to make changes to the matrix or the 5000 analysis procedures that are not clearly necessary; because the development genetics of most 5001 (if not all) of the characters in this matrix are insufficiently well understood, and because 5002 supernumerary skull bones – some of which may or may not be atavistic reappearances – are 5003 known in several taxa with sufficiently large sample sizes (e.g. Greererpeton: Smithson, 5004 1982; Micromelerpeton and other “branchiosaurs”: Boy, 1972; Discosauriscus: Klembara, 5005 Tomášik & Kathe, 2002), we have not coded any state changes as impossible. 5006 One of the apomorphies which support the sister-group relationship of Urocordylidae 5007 and Aïstopoda, and thus “nectridean” paraphyly, in Analyses R1 and R3–R6 is the 5008 reappearance of the supratemporal bone in the skull roof (character 32: transition from state 5009 PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1(3) to state (2), plotted in Fig. 29); this bone is lost 5010 in all other “lepospondyls” except the most rootward one, Westlothiana (and lost again in the 5011 aïstopod Phlegethontia, along with several other skull roof bones). Note that this reversal is 5012 inherited from RC07 (Fig. 1, 28D). Yet more surprising is the fact that the supratemporal is 5013 long and unusually narrow in urocordylids, aïstopods (except Lethiscus), and probably 5014 Westlothiana (character 51: state SUTEMP 3(1), otherwise found only in Orobates and 5015 *Archaeovenator); this character state adds support to the hypothesis that the supratemporal 5016 of urocordylids and aïstopods is indeed a supratemporal rather than a neomorph. 5017 In some trees from R5, the intertemporal, too, reappears up to twice (transitions to 5018 state PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1(0); Fig. 26D). This happens when Capetus, 5019 Balanerpeton and Dendrerpetidae are nested close to Dissorophoidea; in some of those trees, 5020 *Nigerpeton and *Saharastega (and optionally Dvinosauria) are highly nested among the 5021 stereospondylomorphs, necessitating a second reappearance. 5022 The lost parasymphysial bone in the lower jaw, if correctly identified, reappeared once 5023 in the aïstopods Lethiscus and *Coloraderpeton (character 147: state PSYM 1(0); compare 5024 Fig. 24). 5025 The postsplenial bone of the lower jaw reappears (character 157: transitions to state 5026 POSPL 1(0)) up to three times in the original taxon sample, and up to twice in the expanded 5027 sample. The loss in Diadectomorpha + Amniota is reportedly reversed in Petrolacosaurus 5028 (Reisz, 1981; see discussion in Appendix 1), concerning all MPTs from R1–R6. In Analyses 5029 R1–R3 and R6, where the diplocaulids are close enough to Batropetes and Brachydectes 5030 which lack postsplenials, the presence of the postsplenial in Diplocaulus (Douthitt, 1917) – 5031 contrasting with absence in the diplocaulids Diploceraspis and Batrachiderpeton (as correctly 5032 scored by RC07: Beerbower, 1963; Bossy & Milner, 1998) – is unambiguously optimized as a 5033 reversal as well. The third reappearance occurs in the adelogyrinids in R1 and R3. 5034 The anterior tectal is optimized as disappearing early and then reappearing in the 5035 colosteid *Aytonerpeton (see character 6 – TEC 1). This happens not only in Analyses R4– 5036 R6, where Colosteidae and Baphetidae are sister-groups within Temnospondyli, but also 5037 when we move Colosteidae to the more traditional place it has in Analyses R1–R3, because 5038 the anterior tectal is scored as absent in Pederpes and Crassigyrinus. The homology of this 5039 bone is not quite clear, however, and most snout tips in this part of the tree are suboptimally 5040 preserved; see characters 6 and 7 in Appendix 1 for discussion.

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5041 The preopercular bone reappears (character 81: state PREOPE 1(0)) in the aïstopod 5042 *Coloraderpeton after a very long absence. We suspect that this is an artefact of our character 5043 sample and that Aïstopoda belongs far rootward of where we find it (Pardo et al., 2017); 5044 further research on other aïstopods, notably **Ophiderpeton, may be helpful. The same holds 5045 for the return of the mandibular lateral-line canal and its fully or mostly enclosed condition in 5046 *Coloraderpeton; with all other aïstopods currently scored as lacking this canal altogether, 5047 the transition from state 4 to state 1 or 0 of the ordered character 101 (SC 2) counts as (at 5048 least) three autapomorphies. 5049 The suture between the basisphenoid and the basioccipital (“ventral cranial suture”) is 5050 usually covered ventrally by the parasphenoid in limbed vertebrates crownward of 5051 Crassigyrinus. The parasphenoid is, at least in the midline, too short to cover it (character 5052 142: state PASPHE 9(1)) in the aïstopods *Coloraderpeton and probably 5053 *Pseudophlegethontia, and Lethiscus even has an exposed open fissure there if the scan 5054 presented by Pardo et al. (2017) has successfully distinguished spongy bone from rock (which 5055 may not be the case; J. Pardo, pers. comm.). (We have kept state 2, the covered condition, for 5056 Oestocephalus; reinvestigation of the specimens may be warranted. In Phlegethontia, the 5057 braincase is fused up to such an extent that the caudal margin of the parasphenoid cannot be 5058 recognized, so we have kept its score unknown.) While this is an unexpected reversal in our 5059 trees, it also occurs in the diadectomorph Tseajaia and some individuals of Diadectes, 5060 including apparently all of D. absitus (Moss, 1972; Berman, Sumida & Martens, 1998); and in 5061 the dissorophoid temnospondyl Acheloma the lateral parts of the suture are covered very late 5062 in ontogeny (Maddin, Reisz & Anderson, 2010). 5063 Unlike in the earlier version of this matrix discussed by Marjanović & Laurin (2013a), 5064 losses of the posterior (or rather distal) coronoid (character 175: POST COR 1(1)) are no 5065 longer necessarily reversed on any of our MPTs except those of R6, where the bone reappears 5066 in *Coloraderpeton. The precise homology of the bone that bears the lingual toothrow in the 5067 lower jaw and fuses to the dentary in early ontogeny remains, as far as we know, to 5068 be investigated; in the absence of evidence for separate bones, we have scored Eocaecilia as 5069 lacking any coronoids despite the presence of the lingual toothrow on the so-called 5070 pseudodentary (a bone of compound ontogenetic origin in extant caecilians). We have scored 5071 Diplocaulus as unknown; the dentary is unusually broad in dorsal view and bears a short 5072 lingual toothrow around the symphysis (Douthitt, 1917: fig. 2.5), and the area is damaged in 5073 all specimens that Douthitt (1917: 17) had at his disposal, so we cannot exclude that part of 5074 the supposed dentary belongs to a coronoid (or indeed several) and the suture is simply too 5075 eroded to be visible. 5076 Sigurdsen & Green (2011) noted that their reevaluation of the matrix by Vallin & 5077 Laurin (2004) continued to support the LH, but required the return of the lost postparietal 5078 (character 39 in our matrix: POSPAR 1-2(0)), postfrontal (character 45: POSFRO 1(0)) and 5079 tabular (character 53: TAB 1/SQU 4(0); see also below) in Eocaecilia. Our unconstrained 5080 Analyses R1 and R4 do not require any of these reversals, and neither do R3 and R6, which 5081 are constrained for the PH (Fig. 30L, M, P). Conversely, the same three reversals are required 5082 on all MPTs from R2 and R5 (both constrained against the LH, supporting the TH; Fig. 30N, 5083 O). In other words, the losses of these three bones actually favor the LH and the PH over the 5084 TH. 5085 It remains to be seen, however, if the possible tabular of Eocaecilia – here scored as 5086 such (as explained by Marjanović & Laurin, 2008) – really is a tabular or instead a 5087 supratemporal. According to Jenkins, Walsh & Carroll (2007), it is not known if that bone 5088 reaches the caudal margin of the skull table (as expected of a tabular), although it seems to D. 5089 M. (pers. obs. of the holotype, MNA V8066) that it does; see character 53 (TAB 1/SQU 4) in 5090 Appendix 1 for details. Pardo, Small & Huttenlocker (2017) misinterpreted the reconstruction

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5091 in Jenkins, Walsh & Carroll (2007: fig. 1) as indicating that the shape and size of this bone 5092 were known, and argued for considering it a supratemporal based on this erroneous premise. 5093 Whether the similarity of the unusually large squamosal of Eocaecilia to the squamosal and 5094 the unusually large tabular of **Chinlestegophis combined (Pardo, Small & Huttenlocker, 5095 2017: fig. 3; not mentioned in the text) is indicative of homology remains to be tested. 5096 Analysis R5 always nests Eocaecilia and Albanerpetidae within Caudata (Fig. 30O). 5097 Albanerpetidae was not included in the matrix of Vallin & Laurin (2004). The jugal is present 5098 (character 71: JUG 1(0)) in Eocaecilia and Albanerpetidae, but lost in Batrachia; thus, 5099 Analysis R5 requires that an exclusive common ancestor of Eocaecilia and the albanerpetids 5100 has regained the lost jugal (which yields a total of three steps for this character over the entire 5101 tree). This reversal does not occur in any trees from R1 or R4 (Fig. 30L, M); Brachydectes 5102 has lost the jugal, but is never found as the sister-group of the modern amphibians (unlike in 5103 Vallin & Laurin, 2004 – Fig. 30A), so its loss is always optimized as a separate event from 5104 the loss at the root of Batrachia (for a total of two steps). Thus, the presence of the jugal in 5105 Eocaecilia and Albanerpetidae indirectly but unambiguously supports the LH over the TH, 5106 quite contrary to the conclusions of Sigurdsen & Green (2011). (Similarly, R6 nests 5107 Albanerpetidae within Caudata, requiring the same reversal.) 5108 Of the other characters mentioned by Sigurdsen & Green (2011) in this context, the 5109 losses of the lacrimal (character 18: LAC 1(1); Eocaecilia, *Chelotriton + some or all 5110 salientians – unknown in Triadobatrachus –, Diploceraspis, Phlegethontia), the prefrontal 5111 (character 12: PREFRO 1(1); limited to salientians crownward of Triadobatrachus, which 5112 retains the prefrontal: Ascarrunz et al., 2016) and the quadratojugal (character 77: QUAJUG 5113 1(1); Valdotriton, *Beiyanerpeton, part of Notobatrachus, Batropetes, Brachydectes – 5114 unknown in *Carrolla and *Quasicaecilia) do not unambiguously reverse in any of our trees 5115 regardless of constraints (Fig. 30L–P). 5116 The palatine is scored as present (character 114: PAL 8(0)) in only two batrachians in 5117 this matrix: the salientian Triadobatrachus and the caudate *Beiyanerpeton. No reversal is 5118 required in any MPTs from Analyses R1–R3. In R4 and R6, these occurrences of state 0 are 5119 optimized as two separate reversals; in R5, only that of *Beiyanerpeton remains an 5120 unambiguous reversal, to which some MPTs from R5 (supporting the TH) add the occurrence 5121 in Eocaecilia as a further one. Judging from comparisons to the literature, all this appearance 5122 of reversals seems to be clearly due to our small sample of salientians, caudates and caudate- 5123 related characters. 5124 An angular (character 160: ANG 1(0)) has been reported in the caudates Karaurus and 5125 *Chelotriton (see Appendix 1), but in no other lissamphibians in our sample (see, however, 5126 Jia & Gao, 2016a, b, for further occurrences in caudates). The former’s condition is 5127 consistently optimized as a reversal; so is the latter’s in Analysis R4 (Fig. 30M). The same 5128 cautionary notes about our taxon and character sample apply, particularly because 5129 *Chelotriton is a crown-group salamandrid (Marjanović & Witzmann, 2015, and references 5130 therein); moreover, the ventral view of Karaurus has not been adequately described or 5131 illustrated and is not visible on the cast we had access to. 5132 Only three “microsaurs” are scored for the presence (character 167: ANT COR 1(0)) 5133 or absence (state 1) of the “anterior” (actually mesial) coronoid: presence has been described 5134 in Microbrachis, absence in Pantylus and Batropetes. An unambiguous reversal does not 5135 occur among “microsaurs” according to the analyses of the original taxon sample (but does 5136 happen in Lethiscus); the condition of Microbrachis is optimized as a reversal in R4–R6, 5137 where Microbrachis and Hyloplesion are placed next to Holospondyli rather than among other 5138 “microsaurs”. As far as the crushed material allows, the lower jaw of Microbrachis should be 5139 reinvestigated.

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5140 The “nectrideans” Urocordylus (Bossy & Milner, 1998, and references therein) and 5141 Diceratosaurus (Jaekel, 1903; Bossy, 1976; Angela Milner, pers. comm. 2009; D. M., pers. 5142 obs. of MB.Am.776, CM 25468, CM 34617, CM 81504 and CM 81508; contra Bossy & 5143 Milner, 1998: 99) have five fingers per hand (state 2 of character 276 = DIG 1-2-3-4), even 5144 though many other “lepospondyls”, including other “nectrideans” like Sauropleura and 5145 Keraterpeton, are known to have four or three (states 3 and 4). For Diceratosaurus at least, 5146 this is not a case of malformation during limb as sometimes found in the 5147 temnospondyl Micromelerpeton (Fröbisch, Bickelmann & Witzmann, 2014): all five fingers, 5148 and indeed metacarpals, have distinct lengths and widths, with the longest and thickest in the 5149 middle (Jaekel, 1903; D. M., pers. obs. of MB.Am.776, the same specimen). Furthermore, 5150 Urocordylus and Diceratosaurus are not close relatives; Urocordylus is a urocordylid like 5151 Sauropleura (BPO = 83; BPE = 81; PP for Urocordylidae incl. Aïstopoda = 96), while 5152 Diceratosaurus is a diplocaulid like Keraterpeton (BPO = 57; BPE = 63; PP = 100). 5153 Thus, according to our unconstrained results, the supratemporal reappeared once after 5154 having been lost, and pentadactyly even did so twice; the parasymphysial and the anterior 5155 coronoid may have done so once or not at all, the intertemporal (in the expanded taxon 5156 sample) twice, once or never. Perhaps unexpectedly, the shortest trees that are constrained 5157 against the LH (and consequently support the TH: Analysis R2) additionally require the 5158 postparietal, the postfrontal and the tabular of Eocaecilia to be interpreted as reversals; 5159 expanding the taxon sample (Analysis R5) further extends this list to include the jugal found 5160 in Eocaecilia and Albanerpetidae. Conversely, given the expanded taxon sample, the lost 5161 palatine and the lost angular each returned twice according to our unconstrained results (R4), 5162 and once or twice according to constrained analyses (R5), but issues with our taxon and 5163 character samples are evident. 5164 5165 Other recently discussed characters that are included in this matrix 5166 5167 The character that describes whether the maxilla and the quadratojugal touch at the 5168 ventrolateral margin of the skull (character 72: state JUG 2-6(0)) or the jugal intervenes 5169 between them (states 1 and 2) is only applicable when all three of these bones are present, a 5170 fact neglected by Sigurdsen & Green (2011). This character does indeed reverse from state 1 5171 to state 0 in Eocaecilia in the MPTs from Analysis R4 (and R6), while it does not reverse in 5172 those from Analysis R5, which support the TH; however, it also reverses seven additional 5173 times elsewhere in the MPTs from Analyses R4 and R6, compared to seven times in total in 5174 the MPTs from Analysis R5, out of a total of 24 steps in each of the three analyses. We see no 5175 reason to ascribe great subjective significance to this character, which is also known to have 5176 changed states within Amniota several times; indeed, the occurrence of state 0 in 5177 *Caseasauria is unambiguously optimized as a reversal in all of our trees. The holotype of 5178 *Lydekkerina even has state 0 on the left and state 1 on the right side (Hewison, 2007). 5179 Sigurdsen & Green (2011) divided the length/width ratio of the vomer into two states. 5180 In our matrix this character, 102 (VOM 1-13), has three states (because RC07 rendered it as 5181 two characters). The widest vomers (state 0) occur in *Ymeria, Ventastega, Colosteus, 5182 *Spathicephalus, the “core amphibamids” (Eoscopus, Platyrhinops, Amphibamus, 5183 Doleserpeton, *Gerobatrachus; homologous among them), the seymouriamorph 5184 Ariekanerpeton, and all lissamphibians (unknown in Albanerpetidae and Triadobatrachus) 5185 except Eocaecilia and *Pangerpeton. Under the LH (Analysis R4; Fig. 30M), the occurrence 5186 of the intermediate state (1) in Eocaecilia is plesiomorphic, and that in *Pangerpeton is 5187 equally parsimoniously optimized as plesiomorphic or a reversal. Under the TH (Analysis R5; 5188 Fig. 30O), state 0 is homologous among amphibamids and lissamphibians, and state 1 in 5189 Eocaecilia and *Pangerpeton requires either two reversals or (equally parsimoniously) a

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5190 shared reversal followed by a return to state 1. Under the PH (Analysis R6; Fig. 30P), state 1 5191 in *Pangerpeton is unambiguously a reversal from state 0, while state 1 in Eocaecilia is not. 5192 Altogether, this ordered three-state character requires 21 steps in Analysis R4 and 20 in R5 5193 and R6. This character is, in other words, rather inconclusive. 5194 The length and curvature of the ribs was given special attention by Sigurdsen & Green 5195 (2011; and references therein), in that they connected short, straight ribs with buccal pumping 5196 as the mode of ventilation seen in extant amphibians, and long, curved ones with 5197 aspiration by active expansion of the ribcage as seen, plesiomorphically, in amniotes. We find 5198 much to disagree with here. First, long straight ribs exist (e.g. Diplocaulus), as do short 5199 curved ribs (e.g. Acherontiscus); consequently, RC07 treated these features as two characters, 5200 which remain in our matrix as characters 246 (RIB 3) – “Ribs mostly straight (0) or ventrally 5201 curved in at least part of the trunk (1)” – and 250 (RIB 7) – “Trunk ribs longer (0) or shorter 5202 (1) than three successive articulated vertebrae in adults”. Second, short ribs (straight or not) 5203 may require buccal pumping, but long curved ribs do not require aspiration and do 5204 not even automatically make it possible, as the trivial cases of the long but entirely immobile 5205 ribs of ** and such **pterosaurs as **Pteranodon demonstrate; as long as the necessary 5206 research on the mobility of the ribs and their muscle attachment sites has not been done, we 5207 see no reason to think that such animals as anthracosaurs or lysorophians breathed air in a 5208 way much different from **extant caecilians, which use buccal pumping and inhale several 5209 times for each time they exhale, thus compensating for the fact that their heads are much 5210 smaller than their (Carrier & Wake, 1995). Third, such research may be difficult in taxa 5211 without ossified rib heads; that includes even such terrestrial animals as the chroniosuchian 5212 **Bystrowiella (Witzmann & Schoch, 2017). The hypothesis that buccal pumping is not a 5213 lissamphibian or temnospondyl autapomorphy, but rather an ancient plesiomorphy (in 5214 agreement with Lebedev & Coates, 1995, and Witzmann, 2015), is further supported by the 5215 fact that it forms the last stage of air inhalation in the extant actinopterygian **Polypterus 5216 (Graham et al., 2014). – In any case, states RIB 3(0) and RIB 7(1), both found in all 5217 lissamphibians in this matrix except *Chelotriton, support the TH and the PH over the LH by 5218 one step each in the trees with the expanded taxon sample (Fig. 30M, O, P); the PH ranks 5219 with the TH here because these states are optimized as synapomorphies of Eocaecilia and 5220 Aïstopoda under the PH. 5221 It may prove interesting that the ribs of **Chinlestegophis, briefly mentioned but not 5222 illustrated by Pardo, Small & Huttenlocker (2017), are curved (state RIB 3(1); Fig. 30I–K) 5223 and considerably longer than those of any lissamphibians except certain salamandrids like 5224 *Chelotriton, though it is not clear whether state RIB 7(0) was reached (J. Pardo, pers. 5225 comm.). 5226 5227 Preaxial polarity in limb development 5228 5229 Although not included in our matrix, this character has featured prominently in several recent 5230 publications, so we take the opportunity to review the latest developments here. 5231 In frogs and amniotes today, the digits form in a roughly postaxial-to-preaxial 5232 (caudocranial) sequence: IV first, then III and V, then II, then I. In salamanders with free- 5233 living larvae, the opposite is observed: first I and II, then III, then IV, then (in the foot) V. 5234 Fröbisch, Carroll & Schoch (2007) documented the latter (as an ossification sequence) in the 5235 dissorophoid temnospondyl Apateon and proposed that this could be a synapomorphy of (at 5236 least some) temnospondyls and salamanders. Marjanović & Laurin (2013a) discussed this, 5237 finding the optimization ambiguous due to the lack of an outgroup, and pointed out that distal 5238 carpal/tarsal I ossified first in the few temnospondyls, but also anthracosaurs and colosteids, 5239 of which incompletely ossified carpi/tarsi are known; distal carpal/tarsal 4 is known to ossify

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5240 first only in amniotes and diadectomorphs. Recently, Glienke (2015: fig. 6O–S) has 5241 documented that distal tarsal 1 and/or 2 ossified first in the “lepospondyl” Batropetes. This 5242 bolsters the inference that the resemblance of Apateon and salamanders is symplesiomorphic, 5243 and that the amniote/frog pattern of development (see Marjanović & Laurin, 2013a, for 5244 further discussion) is an autapomorphy of Amniota + Diadectomorpha as well as of Salientia 5245 or part thereof. 5246 Olori (2015) found a long delay in the ossification of the fifth toe in the 5247 “lepospondyls” Microbrachis and Hyloplesion; because this is shared with Sauropsida, Olori 5248 (2015) suggested that these “microsaurs” may have shared the frog/amniote pattern (repeated 5249 without further discussion by Fröbisch et al., 2015). We do not find this convincing, 5250 especially in the light of Batropetes. 5251 At this opportunity we would like to report that distal tarsal 2 appears to be the only 5252 ossified tarsal in NHMW 1983/32/11, a large articulated specimen of Sauropleura scalaris 5253 (Fig. 31, 32). At least for the time being, our analyses continue to find Sauropleura as a 5254 “lepospondyl”. Further, we wonder if a poorly mineralized round object proximal to 5255 metacarpal I in *Casineria is distal carpal 1; other carpals are not ossified (Fig. 6; Paton, 5256 Smithson & Clack, 1999: fig. 2, 3). 5257

5258 5259 5260 Figure 31: NHMW 1983/32/11, a natural mold of an articulated skeleton referred to 5261 Sauropleura scalaris. Abbreviations: l.cl, left clavicle; r.cl, right clavicle. Photo taken by D. 5262 M.

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5263 5264 5265 Figure 32: Area around the left hindlimb of a latex cast of the Sauropleura specimen 5266 shown in Fig. 31. Abbreviation: mt, metatarsal. Photo taken by D. M. 5267 5268 Jia & Gao (2016b) pointed out that the ossified parts of radius and tibia are 5269 considerably longer and wider than those of and , respectively, in the smallest 5270 known of the urodele **Nuominerpeton. They considered this fact to 5271 be evidence of a preaxial-to-postaxial sequence in development. If this inference holds, 5272 preaxial polarity is very clearly plesiomorphic: state RAD 2(0), radius longer than ulna (see 5273 character 222 in Appendix 1), is found in our matrix in Eusthenopteron, Panderichthys, 5274 Acanthostega, Crassigyrinus (whose endochondral skeleton is generally poorly ossified) and 5275 the skeletally immature temnospondyl *Tungussogyrinus. 5276 5277 Other characters that are potentially important for the origin of lissamphibians but not 5278 considered in this matrix 5279 5280 Several matrices for the analysis of the phylogeny of the limbed vertebrates have coded 5281 phalangeal formulae as one or more characters. It appears that the first four toes 5282 plesiomorphically have 2-3-4-5- in the pentadactyl clade, as retained by most amniotes and 5283 most “lepospondyls”, while reductions in the number of phalanges (2-2-3-4- or fewer) occur 5284 in temnospondyls and modern amphibians. However, intermediate states are found in 5285 Albanerpetidae, where Celtedens – the only representative for which feet are known – has lost

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5286 only one phalanx (2-3-4-4-; McGowan, 2002), and in Batropetes, which has lost two (2-3-4- 5287 3-; Glienke, 2015: fig. 6O–S). We have not looked into this further, but so far it seems that 5288 phalangeal formulae do not support the TH or the PH over the LH. 5289 Sigurdsen & Bolt (2009) have pointed out that lissamphibians share a particularly 5290 large radial condyle on the humerus with dissorophid and amphibamid temnospondyls, and 5291 Sigurdsen & Green (2011) used this as a character in their supermatrix. Marjanović & Laurin 5292 (2013a) have discussed complications. D. M. has since seen two humeri of Diadectes (AMNH 5293 4380 and AMNH 4709); their radial condyles are proportionally at least as large as those of 5294 Doleserpeton or **Dissorophus (Sigurdsen & Bolt, 2009: fig. 3). 5295 Sigurdsen (2008) drew renewed attention to the fact that the perilymphatic duct in the 5296 inner runs on different sides of the lagena in lissamphibians and amniotes, and presented 5297 evidence that it was positioned in Doleserpeton as in frogs in particular. The conclusion that 5298 this resemblance must be synapomorphic rather than symplesiomorphic rests on the 5299 assumption that the amphibian and the amniote conditions must have evolved independently 5300 from the lack of a perilymphatic duct as seen in **Latimeria. We are not convinced by this 5301 latter inference; it is not clear to us why the duct could not have twisted around the lagena at 5302 some point, or conversely if the condition is homologous among all amniote clades. 5303 Marjanović & Laurin (2013b) discussed the branchial denticles and their occasional 5304 confusion with gill rakers (which most recently occurs in Jia & Gao, 2016a; for an animal that 5305 has branchial denticles and mineralized gill rakers, see **Amia – Grande & Bemis, 1998), but 5306 did not comment on an interesting fact: Plesiomorphically, there is one row of denticle- 5307 bearing dermal bone plates on each of the four ceratobranchials (per side). In branchiosaurids, 5308 the branchial denticles were apparently used for filter-feeding (the way gill rakers often are), 5309 so that each of the three gill slits (per side) was framed by two rows of denticle-bearing plates 5310 – ceratobranchials 1 and 4 bearing one each, ceratobranchials 2 and 3 bearing two each, for a 5311 total of six. Of the four lissamphibians (all of them currently considered crown-group 5312 salamanders) known to retain these plates, *Beiyanerpeton has four rows (Gao & Shubin, 5313 2012), and apparently so does **Qinglongtriton (not quite clear from the illustrations or the 5314 text of Jia & Gao, 2016a) – but **Chunerpeton (Gao & Shubin, 2003) and 5315 **Seminobatrachus (Skutschas & Gubin, 2012) have six. Homoplasy must be assumed under 5316 both the TH and the LH (and even under the PH). 5317 Alone among modern amphibians, most anurans have a tympanic ear, and apparently 5318 so did at least Notobatrachus among stem-salientians (Báez & Nicoli, 2004). Osteological 5319 correlates of this character complex have often been thought to occur in various 5320 temnospondyls, including but not limited to Doleserpeton and **Chinlestegophis. We mostly 5321 disagree with these identifications, which we will discuss at length in a future work; an 5322 incomplete draft is included in the first preprint version of this paper (Marjanović & Laurin, 5323 2015). 5324 5325 Conclusions 5326 5327 Phylogeny 5328 5329 The dataset by RC07 is the largest one that has so far been used in an analysis of the 5330 phylogeny of early limbed vertebrates, a problem field that contains the controversial question 5331 of the origin(s) of the extant amphibian clades. Having studied and revised this dataset for 5332 nine years, we conclude: 5333  After our attempts to improve many thousands of suboptimal scores, deal with effects of 5334 heterochrony, order potentially continuous characters and merge redundant characters, the 5335 matrix supports different results from those found by RC07, most notably the “lepospondyl

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5336 hypothesis” on the origin of Lissamphibia (LH) rather than the “temnospondyl hypothesis” 5337 (TH). This does not change when the taxon sample is expanded or when Bayesian 5338 inference is used instead of parsimony; the expanded taxon sample includes the 5339 lissamphibian-like dissorophoids Gerobatrachus, Micropholis and Tungussogyrinus as 5340 well as the extremely peramorphic and therefore temnospondyl-like salamander 5341 Chelotriton (Marjanović & Witzmann, 2015). 5342  Many parts of the tree are too sparsely sampled in characters to be strongly supported. The 5343 bootstrap values along the “trunk” of the tree are low; while the LH and the “polyphyly 5344 hypothesis” may entail statistically distinguishable topologies unless taxa are added, the 5345 TH is indistinguishable from both (Table 4); and while some Bayesian posterior 5346 probabilities are high (notably 1.00 for lissamphibian monophyly and 0.92 for the LH), 5347 moderately high values are also found for more debatable groupings (in particular, 5348 Aïstopoda, Adelogyrinidae and Acherontiscus are supported as rather close to 5349 Lissamphibia by a posterior probability of 0.76). Future analyses with a taxon sample of 5350 similar or larger size will need to have much larger character samples. 5351 It follows that the “temnospondyl hypothesis” should not be taken for granted as the 5352 default by studies in evolutionary biology. 5353 Similar conclusions hold for less popular questions which nonetheless have sometimes 5354 important implications for evolutionary biology: 5355 The chroniosuchians (represented by Chroniosaurus and Bystrowiella in the expanded 5356 taxon sample) are neither anthracosaurs (Laurin, 2000; Klembara, Clack & Čerňanský, 2010) 5357 nor lepospondyls (Buchwitz et al., 2012) nor seymouriamorphs (Klembara et al., 2014) in our 5358 trees; instead, they lie between the more rootward gephyrostegids, which may be followed 5359 rootward by the temnospondyls, and the more crownward Solenodonsaurus, which is 5360 followed crownward (not rootward as in RC07) by Seymouriamorpha (or may even be a 5361 seymouriamorph, as weakly supported by our Bayesian analysis). Character conflict causes 5362 either the aquatic anthracosaurs or the ecologically diverse temnospondyls to lie more 5363 rootward depending on the taxon sample, the analysis method, and even constraints on the 5364 positions of extant amphibians. Caerorhachis lies in the same region of the tree; it may or 5365 may not be a temnospondyl as found by Pawley (2006). Rather than Casineria being close to 5366 amniote origins, we cannot so far distinguish it from Caerorhachis (as previously noted by 5367 Pawley, 2006); we find it in the gephyrostegid grade, rootward of the chroniosuchians. This is 5368 corroborated by three (possibly four) previously overlooked features of Casineria that would 5369 be unexpected for a close relative of Amniota. Westlothiana retains its position from RC07: it 5370 is the sister-group to all other amphibians. Iberospondylus emerges particularly close to 5371 Dissorophoidea; Nigerpeton and Saharastega are well supported as sister-groups, and 5372 recovered around Eryops or around or even in Stereospondylomorpha in the most 5373 parsimonious trees, but with weak bootstrap support for a position next to Edopoidea and 5374 weak Bayesian support for a position in it; temnospondyl phylogeny otherwise remains 5375 largely mysterious and very strongly depends on the relative positions of temnospondyls and 5376 anthracosaurs, though a sister-group relationship of Eryops (the only sampled eryopid) and 5377 Stereospondylomorpha is likely. “Nectridean” monophyly is never found. “Microsaurian” 5378 monophyly is sometimes approximated, but the brachystelechids usually cannot even be 5379 considered part of a “microsaur” grade; neither can Utaherpeton. Despite the variety of 5380 results, Tuditanomorpha, Microbrachomorpha and Recumbirostra are not found; 5381 Microbrachis and Hyloplesion are sister-groups, however. Perittodus emerges rootward of 5382 Ichthyostega; Densignathus lies just crownward or just rootward of Whatcheeriidae, followed 5383 crownward by Tulerpeton, all of which are rootward of Crassigyrinus and Colosteidae; 5384 Sigournea, Doragnathus and Diploradus are found as baphetoids close to Spathicephalus,

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5385 apparently baphetids; the “St. Louis tetrapod” and Aytonerpeton are unambiguous colosteids; 5386 the “Parrsboro jaw” may be close to temnospondyl origins and/orto Caerorhachis. 5387 Within the LH, the closest relatives of lissamphibians including albanerpetids are not 5388 the lysorophians alone (represented by Brachydectes), but most parsimoniously a clade 5389 composed of the latter and the brachystelechid “microsaurs” (Batropetes, Carrolla and 5390 Quasicaecilia); the Bayesian analysis even nests Lissamphibia within Brachystelechidae with 5391 rather strong support. Within the TH, our constrained analyses find Doleserpeton and 5392 Gerobatrachus to be equally good (or bad) candidates for the lissamphibian sister-group. 5393 5394 Phylogenetics 5395 5396 In spite of generally low support, several poorly known taxa are placed unambiguously in our 5397 trees. Isolated lower jaws and the like, not to mention headless skeletons like Casineria or the 5398 “microsaur” Trihecaton, should not be excluded from phylogenetic analyses a priori; they are 5399 by no means guaranteed to add more noise than signal, let alone noise that conflicts with the 5400 signal. Wildcard behavior is hard to predict and does not, in our dataset, correlate with 5401 amounts or proportions of missing data. 5402 Not all settings for phylogenetic analyses make it likely that all, or any, of the most 5403 parsimonious trees will be found. As we show, Maddin, Jenkins & Anderson (2012) 5404 recovered neither any of the MPTs that are consistent with their matrix, nor the vast majority 5405 of the trees that have the length of the shortest trees they reported; similarly, at least one of 5406 the analyses performed by Skutschas & Gubin (2012) and Schoch (2013) failed to find any 5407 trees of the shortest possible length (reported but not commented on by Skutschas & Gubin, 5408 2012, and Schoch, 2013, respectively), and Baron, Norman & Barrett (2017) found only 93 of 5409 16,632 MPTs (Watanabe, 2017a, b; Langer et al., 2017). Care should be taken to run enough 5410 addition-sequence replicates to find all optimal islands, and to allow sufficient time for the 5411 branch-swapping algorithms to explore these islands thoroughly. However, the “parsimony 5412 ratchet” procedure of RC07 found all MPTs that were compatible with their matrix – even 5413 though it did not find any MPTs, or any trees less than 35 steps longer than the MPTs, when 5414 applied to the much smaller matrix of Skutschas & Gubin (2012, as reported there). 5415 We argue against the majority-rule consensus of the most parsimonious trees. Because 5416 the percentage of MPTs on which a given node occurs is not a support measure, the majority- 5417 rule consensus tree does not provide a better overview over the MPTs than any single MPT 5418 combined with the strict consensus does. (Indeed, a fully resolved majority-rule consensus is 5419 not necessarily identical to any MPT [J. Felsenstein, pers. comm. 2017].) Pardo, Small & 5420 Huttenlocker (2017: fig. S7B) presented only the majority-rule consensus tree of a parsimony 5421 analysis; while that tree shows the same novel hypothesis on lissamphibian origins as the 5422 Bayesian analysis of the same matrix (fig. 2C = S7A), another novel hypothesis and a 5423 traditional one are equally parsimonious. When the strict consensus is not resolved enough to 5424 provide a clear picture, it is necessary to inspect a sample of the MPTs “by hand”; we 5425 recommend 20 to 30 MPTs, evenly spaced among the results, though more are sometimes 5426 needed. 5427 We encourage testing of the behavior of Bayesian inference with large paleontological 5428 matrices (missing data clustered by body part; non-coeval tips), which is currently not well 5429 understood. Homoplasy-free characters are uncommon enough in our matrix that a 5430 prerequisite for parsimony with implied weights is most likely not fulfilled. 5431 Further progress on the questions of phylogeny discussed above – and on many others 5432 – will require the description of new fossils and the redescription of known ones, but also the 5433 mergers of existing matrices to increase the character sample (and to a lesser degree the taxon

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5434 sample) together with a special effort to keep data matrices free from typographic errors and 5435 similar accidental misscores, from the effects of heterochrony and from redundant characters. 5436 In the meantime, we hope to have laid a solid base for future additions of data by 5437 creating a “reasonably clean” dataset that does not contradict current knowledge. We have 5438 documented all of our changes to the matrix of RC07 in Appendices 1 and 2 and invite further 5439 scrutiny. A matrix of morphological data is a matrix of hypotheses and must not be taken for 5440 granted as a set of measured facts; and it must not be assumed that any cell in a matrix could 5441 not influence the resulting trees. 5442 5443 Errata in some of our previous publications 5444 5445 Coding and scoring decisions that differ from our current ones (for similar or identical 5446 characters in different matrices) are explained in Appendix 1 and not repeated here. 5447 Marjanović & Laurin (2008: 197) scored Tuditanus as having “poorly ossified” dorsal 5448 scales; D. M. has since seen the holotype (AMNH 6926) and found that it preserves scales 5449 that are no less well ossified than those of Microbrachis (Olori, 2015; D. M., pers. obs. of 5450 many NHMW specimens), which was scored as having “well ossified” dorsal scales. Such 5451 substantial scales as seen in Fig. 3 are unusual among “microsaurs”. 5452 On p. 154 of the same paper, we spoke of a clade having a definition; we meant the 5453 name Neocaecilia. 5454 In the legend to appendix-table 4 of the same paper, “state K” is state L. 5455 Marjanović & Laurin (2013a: table 1) claimed that the matrix of Maddin, Jenkins & 5456 Anderson (2012) was derived from those of Maddin & Anderson (2012) and Maddin, Olori & 5457 Anderson (2011); the latter was a mistake for Maddin, Russell & Anderson (2012), which we 5458 failed to cite entirely. 5459 In the same paper, we stated on p. 231 that the eryopid temnospondyl Onchiodon 5460 lacked grooves for gill arteries on its ceratobranchials, implying that the animal did not have 5461 internal gills. Florian Witzmann (pers. comm. 2015) has reminded us that the only 5462 mineralized ceratobranchials known for Onchiodon belong to very young individuals that are 5463 expected to have had and to have lacked internal ones correspondingly; adult 5464 Onchiodon may well have had internal gills (and been aquatic, rather than semiaquatic as we 5465 claimed), but their ceratobranchials are unknown and appear to have been unmineralized. This 5466 removes an argument – not coded in the present matrix – for considering Eryopidae and 5467 Dissorophoidea close relatives (as found by Yates & Warren, 2000, but none of our analyses). 5468 Hampson, 1896, is not a beetle as we claimed in the same paper, but a 5469 (Hampson, 1896). We suspect that D. M. confused it with Syntarsus, a beetle that has 5470 preoccupied the name of an dinosaur. 5471 We further noted (Marjanović & Laurin, 2013a: 222–223) a logical link between 5472 characters DIG 1 through DIG 4 in RC07 and Ruta, Coates & Quicke (2003), stating (p. 223, 5473 referring to the character numbers of Ruta, Coates & Quicke, 2003): “If an animal has no 5474 more than three fingers per hand, it also has no more than four and no more than five. This 5475 was not taken into account in the matrices; all OTUs with state 316(1) were also scored as 5476 314(1), 315(1) and 313(1).” This statement is incorrect. In fact, despite having “no more than” 5477 in their names, characters DIG 2 through DIG 4 were scored as if they meant “exactly four 5478 fingers per hand: no (0); yes (1)”, “exactly five” and so on. Each OTU scored as 1 for any of 5479 those three characters was scored as 0, not as 1, for both of the others (Data S2). 5480 Unfortunately, however, the noted redundancy is entirely real: the score of 1 for any of those 5481 three unfailingly predicts a score of 0 for the other two and also a score of 1 for DIG 1 5482 (presence of digits).

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5483 Marjanović & Witzmann (2015: 33) parenthetically called the frontosquamosal arch 5484 an autapomorphy of Pleurodelinae. As implied elsewhere in the paper, this is only accurate 5485 under DELTRAN; under ACCTRAN, this remarkable feature is an autapomorphy of 5486 lost in Salamandrinae. 5487 The same paper called Jason Pardo a doctor. This is not yet accurate (J. Pardo, pers. 5488 comm.); it is, however, only a matter of time. 5489 In the first preprint of this paper (Marjanović & Laurin, 2015), the name Oedaleops 5490 Langston, 1965, was consistently misspelled “Oedalops”, even in the title of Reisz, Godfrey 5491 & Scott (2009) in the references list. (One occurrence remained in the second preprint 5492 [2016].) This was a remarkably persistent oversight on the part of D. M.; Reisz, Godfrey & 5493 Scott (2009) used the correct version throughout, as did Langston (1965). 5494 In the second preprint (Marjanović & Laurin, 2016), we claimed that the taxon names 5495 erected by Pereira Pacheco et al. (2016) were not validly published in the online-early version 5496 because that version lacked evidence of having been registered in ZooBank. In fact, sufficient 5497 evidence (the ZooBank URN) was prominently displayed between the abstract and the 5498 keywords; the names Konzhukovia sangabrielensis and Konzhukoviidae were therefore 5499 validly published on 11 April 2016 (International Commission on Zoological Nomenclature, 5500 1999: article 8.5.3 as amended in 2012), not in 2017 when the paper was paginated and 5501 printed (preserving, incidentally, every typo including all five occurrences of 5502 “Konzhokoviidae”). We apologize for any confusion we may have caused. 5503 5504 Errata caused by the lack of page proofs at PLOS ONE 5505 5506 As they state in their instructions to authors, PLOS journals do not produce page proofs. 5507 Nonetheless, PLOS journals do not publish accepted manuscripts without further changes to 5508 the text; there is a copyediting process – authors are merely not shown its results before their 5509 manuscript is published. This has had detrimental effects on the scientific literature 5510 (Dingemanse, 2016). We have to contribute, unfortunately, a further example: Marjanović & 5511 Witzmann (2015) repeatedly mentioned “the ?I. randeckensis” (e.g. in the abstract), 5512 among other cases of the widespread convention of placing a question mark at the beginning 5513 of a word. The copyediting process consistently turned this into “the Miocene? I. 5514 randeckensis”, and this is the version that was published. F. Witzmann and D. M. would like 5515 to stress that the Miocene age of ? randeckensis (Schoch & Rasser, 2013) is not 5516 at all in doubt; its assignment to Ichthyosaura is what is questionable. 5517 Even though we informed PLOS staff of this issue, the same miscorrection occurs 5518 (with less grave consequences) in Matsumoto & Evans (2018: 50), where “Albanerpeton as 5519 currently defined extends from the? - to the late ”. 5520 5521 Acknowledgments 5522 5523 This work began as chapter V of the doctoral thesis of Damien Germain supervised by M. L. 5524 (Germain, 2008a). D. Germain did not have time to complete this large task, so additional 5525 work came to be done as chapter 5 of the doctoral thesis of D. M., again supervised by M. L. 5526 (Marjanović, 2010; parts were presented in Marjanović & Laurin, 2013a). This, too, remained 5527 incomplete for lack of time. Further work was later done by D. M.; this is presented here for 5528 the first time. We thank Damien Germain for sharing his data and expertise with us; he did 5529 not feel that he had contributed enough to this study to coauthor it. 5530 We warmly thank José Grau (Museum für Naturkunde, Berlin) for coming up with, 5531 and implementing, ways to run the bootstrap and Bayesian analyses in parallel on a computer 5532 he has access to. Previously, they took a week each, even though we had restricted the

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5533 bootstrap analyses to very few heuristic replicates per bootstrap replicate and extremely few 5534 rearrangements per heuristic replicate, restrictions that were no longer necessary this time. 5535 We are indebted to Ronan Allain and Bernard Battail for prolonged access to casts of 5536 Triadobatrachus and Karaurus at the MNHN (as well as to the original of Triadobatrachus, a 5537 natural mold, for shorter periods). D. M. further thanks Jasons Anderson and Pardo, Andrew 5538 and Angela Milner, Marcello Ruta, Rainer Schoch, Trond Sigurdsen, Florian Witzmann and 5539 David Černý for discussions, Andrew Milner in particular for discussion of the postcranium 5540 of Isodectes and David Černý for discussion of the current state of Bayesian inference in 5541 phylogenetics (in comments to Mortimer, 2017); Florian Witzmann, Oliver Hampe and the 5542 librarian Annegret Henkel (now retired) for access to dead-tree literature; Ursula Göhlich, 5543 Mathias Harzhauser and Alexander Lukeneder for access to specimens of Microbrachis, 5544 Hyloplesion, Sauropleura (Fig. 31, 32), Sparodus (Fig. 3, 4) and others at the NHMW, Ursula 5545 Göhlich for permission to publish photos (Fig. 3, 4, 38, 39), Amy Henrici and Matt Lamanna 5546 for access to many specimens of Chenoprosopus, Isodectes, Diceratosaurus, Ptyonius, 5547 Tseajaia and others at the CM (twice), Michael Brett-Surman and Hans-Dieter Sues for 5548 access to specimens of Chenoprosopus, Isodectes, Eryops, Tuditanus, Odonterpeton and 5549 others at the USNM, J. Chris Sagebiel and Timothy Rowe for access to specimens of 5550 Acanthostega, Ichthyostega, Greererpeton, Gephyrostegus, Eryops, Seymouria, Diadectes, 5551 Paleothyris, Carrolla and others at the BEG/TMM, Carl Mehling for access to specimens of 5552 Ichthyostega, Colosteus, Trimerorhachis, Eryops, Phonerpeton, Doleserpeton, Platyrhinops, 5553 Diadectes, Tuditanus, Diceratosaurus and others at the AMNH, Mark Norell for access to a 5554 microscope in his office at the AMNH (that’s the office with the amazing view), Jessica 5555 Cundiff for access to specimens of Ichthyostega, Edops (including the large, heavy skull on 5556 exhibit and its separately kept right stapes), Eryops, Acheloma, Phonerpeton, Eocaecilia, 5557 Archeria, Paleothyris, Ptyonius, Lethiscus, Eothyris, Oedaleops and others at the MCZ, Stig 5558 Walsh for access to Casineria (Fig. 5–7) and a microscope with a digital camera at the NMS 5559 (and for explaining that the almost Я-shaped glyph in the specimen number on the part and 5560 counterpart of Casineria is a G), Florian Witzmann, Oliver Hampe, Thomas Schossleitner and 5561 Rodrigo Soler-Gijón for access to specimens of Gephyrostegus, Batropetes, Scincosaurus, 5562 Diceratosaurus, Iberospondylus, Sclerocephalus and Chelotriton at the Museum für 5563 Naturkunde, Berlin; Chris Sidor, Meredith Rivin and Ron Eng for access to the collection of 5564 the Burke Museum at the University of Washington (Seattle) where all known material of 5565 Nigerpeton and Saharastega is currently kept; Jason Anderson for access and transportation 5566 to a specimen of Asaphestera (currently on loan in his lab at the University of Calgary), not to 5567 mention others that will feature in future publications; Frederik Spindler, Ralf Werneburg, 5568 Ronny Rößler and Jörg Schneider for access to and discussion of the only known skull of 5569 Madygenerpeton during a conference-associated excursion in 2014, during which the 5570 abovementioned two aïstopod specimens from Chemnitz (Rößler et al., 2012) were also 5571 shown; and Antonia Bookbinder and family, Keating Holland, Maryann Haggerty and Erin 5572 Machniak for hospitality during collection visits. Adam Bodzioch and Jakub Kowalski kindly 5573 enabled D. M. to participate in the excavations in Krasiejów (Poland) of 2015 and to partially 5574 prepare a Metoposaurus clavicle discovered there by Weronika Kulikowska. Andrew Milner, 5575 Laura Nicoli, Jasons Anderson and Pardo, Florian Witzmann, Jorge Bar, Guilhem Carbasse, 5576 José R. Guzmán Gutiérrez, Graeme Lloyd, Krzysztof Rogoż, Thiago Carlisbino and Eduardo 5577 Ascarrunz sent electronic reprints, some of which would have been impossible to acquire 5578 otherwise; Eduardo Ascarrunz and John Nyakatura shared their digital models of 5579 Triadobatrachus (Ascarrunz et al., 2016) and Orobates (Nyakatura et al., 2015); Trond 5580 Sigurdsen sent a version of the NEXUS file of RC07 to clear up our confusion. Finally, D. M. 5581 would like to thank the security staff at the AMNH for successfully wrestling with the new

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5582 badge system in 2013. We apologize for any omissions from these lists; their order is meant 5583 to be chronological. 5584 The authors of Ascarrunz et al. (2016) and Pardo & Anderson (2016) kindly allowed 5585 us to use their manuscripts before publication. 5586 D. M. thanks David Peters for making a claim about Eocaecilia and Microbrachis that 5587 turned out to be incorrect but led D. M. to consulting the literature and correcting two scores 5588 for Acherontiscus and Adelospondylus. 5589 The reviewers Alexander Pyron, Michael Buchwitz and Jason Pardo took the time to 5590 read the huge manuscript twice (J. Pardo four times), for which we are very grateful; their 5591 comments helped clarify our explanations. 5592 5593 References 5594 5595 Ahlberg PE. 1995. Elginerpeton pancheni and the earliest tetrapod clade. Nature 373:420– 5596 425. 5597 Ahlberg PE. 1998. Postcranial stem tetrapod remains from the Devonian of Scat Craig, 5598 Morayshire, Scotland. Zoological Journal of the Linnean Society 122:99–141. 5599 Ahlberg PE. 2011. Humeral homology and the origin of the tetrapod : a 5600 reinterpretation of the enigmatic specimens ANSP 21350 and GSM 104536. Special 5601 Papers in Palaeontology 86:17–29. 5602 Ahlberg PE, Clack JA. 1998. Lower jaws, lower tetrapods – a review based on the Devonian 5603 genus Acanthostega. Transactions of the Royal Society of Edinburgh: Earth Sciences 5604 89:11–46. 5605 Ahlberg PE, Clack JA, Blom H. 2005. The axial skeleton of the Devonian tetrapod 5606 Ichthyostega. Nature 437:137–140. 5607 Ahlberg PE, Clack JA, Lukševičs R. 1996. Rapid braincase evolution between 5608 Panderichthys and the earliest tetrapods. Nature 381:61–64. 5609 Ahlberg PE, Friedman M, Blom H. 2005. New light on the earliest known tetrapod jaw. 5610 Journal of Vertebrate Paleontology 25:720–724. 5611 Ahlberg PE, Lukševičs E, Lebedev O. 1994. The first tetrapod finds from the Devonian 5612 (Upper ) of . Philosophical Transactions of the Royal Society B 5613 343:303-328. 5614 Ahlberg PE, Clack JA, Lukševičs E, Blom H, Zupiņš I. 2008. Ventastega curonica and the 5615 origin of tetrapod morphology. Nature 453:1199–1204. 5616 Anderson JS. 2001. The phylogenetic trunk: maximal inclusion of taxa with missing data in 5617 an analysis of the Lepospondyli (Vertebrata, Tetrapoda). Systematic Biology 50:170– 5618 193. 5619 Anderson JS. 2002. Revision of the aïstopod genus Phlegethontia (Tetrapoda– 5620 Lepospondyli). Journal of Paleontology 76:1029–1046. 5621 Anderson JS. 2003a. Cranial anatomy of Coloraderpeton brilli, postcranial anatomy of 5622 Oestocephalus amphiuminus, and reconsideration of Ophiderpetontidae (Tetrapoda: 5623 Lepospondyli: Aistopoda). Journal of Vertebrate Paleontology 23:532–543. 5624 Anderson JS. 2003b. A new aïstopod (Tetrapoda: Lepospondyli) from Mazon Creek, . 5625 Journal of Vertebrate Paleontology 23:79–88. 5626 Anderson JS. 2007a. Direct evidence of the rostral anatomy of the aïstropod Phlegethontia, 5627 with a new cranial reconstruction. Journal of Paleontology 81:408–410. 5628 Anderson JS. 2007b. Incorporating ontogeny into the matrix: a phylogenetic evaluation of 5629 developmental evidence for the origin of modern amphibians. In: Anderson JS, Sues 5630 H-D, ed. Major transitions in vertebrate evolution. Bloomington: Indiana University 5631 Press, 182–227.

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6914 Smithson TR, Browne MAE, Davies SJ, Marshall JEA, Millward D, Walsh SA, Clack 6915 JA. 2017. A new Mississippian tetrapod from Fife, Scotland, and its environmental 6916 context. Papers in Palaeontology 3:547–557. DOI 10.1002/spp2.1086 6917 Sookias RB, Böhmer C, Clack JA. 2014. Redescription and phylogenetic analysis of the 6918 mandible of an enigmatic Pennsylvanian (Late Carboniferous) tetrapod from Nova 6919 Scotia, and the lability of Meckelian jaw ossification. PLOS ONE 9:e109717. DOI 6920 10.1371/journal.pone.0109717 6921 Spindler F, Falconnet J, Fröbisch J. 2015 (printed 2016). Callibrachion and Datheosaurus, 6922 two historical and previously mistaken basal caseasaurian synapsids from Europe. 6923 Acta Palaeontologica Polonica 61:597–616. DOI 10.4202/app.00221.2015 6924 Steen MC. 1934. The amphibian fauna from the South Joggins, Nova Scotia. Proceedings of 6925 the Zoological Society of London 104:465–504. 6926 Steyer JS, Damiani R, Sidor CA, O’Keefe FR, Larsson HCE, Maga A, Ide Ou. 2006. The 6927 vertebrate fauna of the Upper Permian of Niger. IV. Nigerpeton ricqlesi 6928 (Temnospondyli: Cochleosauridae), and the edopoid colonization of Gondwana. 6929 Journal of Vertebrate Paleontology 26:18–28. 6930 Strong EE, Lipscomb D. 1999. Character coding and inapplicable data. Cladistics 15:363– 6931 371. 6932 Sumida SS, Modesto S. 2001. A phylogenetic perspective on locomotory strategies in early 6933 amniotes. American Zoologist 41:586–597. 6934 Sumida SS, Pelletier V, Berman DS. 2014. New information on the basal pelycosaurian- 6935 grade synapsid Oedaleops. In: Kammerer CF, Angielczyk KD, Fröbisch J, eds. Early 6936 evolutionary history of the Synapsida. Dordrecht, Heidelberg, New York, London: 6937 Springer, 7–23. 6938 Swofford DL. 2003. PAUP*: Phylogenetic Analysis Using Parsimony (*and other methods). 6939 Version 4.0b10. Sunderland, Massachusetts: Sinauer Associates. 6940 Swofford DL. 2017. PAUP*: Phylogenetic Analysis Using Parsimony (*and other methods). 6941 Version 4.0a158. http://phylosolutions.com/paup-test/ 6942 Szostakiwskyj M, Pardo JD, Anderson JS. 2015. Micro-CT study of Rhynchonkos stovalli 6943 (Lepospondyli, Recumbirostra), with description of two new genera. PLOS ONE 6944 10:e0127307. DOI 10.1371/journal.pone.0127307 6945 Tschopp E, Mateus O, Benson RBJ. 2015. A specimen-level phylogenetic analysis and 6946 taxonomic revision of Diplodocidae (Dinosauria, Sauropoda). PeerJ 3:e857. DOI 6947 10.7717/peerj.857 6948 Tykoski RL. 2005. Anatomy, ontogeny, and phylogeny of coelophysoid theropods. Doctoral 6949 dissertation, The University of Texas at Austin. http://hdl.handle.net/2152/3992 6950 Vallin G, Laurin M. 2004. Cranial morphology and affinities of Microbrachis, and a 6951 reappraisal of the phylogeny and lifestyle of the first amphibians. Journal of 6952 Vertebrate Paleontology 24:56–72. DOI 10.1671/5.1 6953 Venczel M, Gardner JD. 2005. The geologically youngest albanerpetontid amphibian, from 6954 the Lower Pliocene of Hungary. Palaeontology 48:1273–1300. 6955 Vorobyeva E, Schultze H-P. 1991. Description and systematics of panderichthyid fishes 6956 with comments on their relationship to tetrapods. In: Schultze H-P, Trueb L, ed. 6957 Origins of the Higher Groups of Tetrapods—Controversy and Consensus. Ithaca: 6958 Cornell University Press, 68–109. 6959 Wake DB. 2009. What salamanders have taught us about evolution. Annual Review of 6960 Ecology, Evolution, and Systematics 40:333–352. 6961 Wang Y, Dong L, Evans SE. 2015 (printed 2016). Polydactyly and other limb abnormalities 6962 in the Jurassic salamander Chunerpeton from China. Palaeobiology and 6963 Palaeoenvironments 96:49–59.

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6964 Wang Y, Evans SE. 2006. A new short-bodied salamander from the Upper Jurassic/Lower 6965 Cretaceous of China. Acta Palaeontologica Polonica 51:127–130. 6966 Warren A. 1999. tupilakosaurid: a relict from Gondwana. Transactions of the Royal 6967 Society of Edinburgh: Earth Sciences 89:145–160. DOI 10.1017/S0263593300007094 6968 Warren A. 2007. New data on Ossinodus pueri, a stem tetrapod from the Early 6969 Carboniferous of Australia. Journal of Vertebrate Paleontology 27:850–862. 6970 Warren A, Rozefelds AC, Bull S. 2011. Tupilakosaur-like vertebrae in Bothriceps australis, 6971 an Australian brachyopid stereospondyl. Journal of Vertebrate Paleontology 31:738– 6972 753. DOI 10.1080/02724634.2011.590563 6973 Warren A, Schroeder N. 1995. Changes in the capitosaur skull with growth: an extension of 6974 the growth series of aliciae (Amphibia, Temnospondyli) with comments 6975 on the otic area of capitosaurs. Alcheringa 19:41–46. 6976 Warren A, Turner S. 2004. The first stem tetrapod from the Lower Carboniferous of 6977 Gondwana. Palaeontology 47:151–184. 6978 Watanabe A. 2015 (printed 2016). The impact of poor sampling of polymorphism on 6979 cladistic analysis. Cladistics 32:317–334. DOI 10.1111/cla.12130 6980 Watanabe A. 2017a. [tweet]. https://twitter.com/akiopteryx/status/844954395431391232 6981 Watanabe A. 2017b. [tweet]. https://twitter.com/akiopteryx/status/845284614319063040 6982 Watson DMS. 1940. The origin of frogs. Transactions of the Royal Society of Edinburgh 6983 60:195–231. 6984 Wellstead CF. 1982. A Lower Carboniferous aïstopod amphibian from Scotland. 6985 Palaeontology 25:193–208. 6986 Wellstead CF. 1991. Taxonomic revision of the Lysorophia, Permo-Carboniferous 6987 lepospondyl amphibians. Bulletin of the American Museum of Natural History 209:1– 6988 90. 6989 Werneburg R. 1991. Die Branchiosaurier aus dem Unterrotliegend des Döhlener Beckens 6990 bei Dresden. Veröffentlichungen des Naturhistorischen Museums Schleusingen 6:75– 6991 99. 6992 Werneburg R. 2007a. Der „Manebacher Saurier“ – ein neuer großer Eryopide (Onchiodon) 6993 aus dem Rotliegend (Unter-Perm) des Thüringer Waldes. Veröffentlichungen des 6994 Naturhistorischen Museums Schleusingen 22:3–40. 6995 Werneburg R. 2007b. Timeless design: colored pattern of skin in Early Permian 6996 branchiosaurids (Temnospondyli: Dissorophoidea). Journal of Vertebrate 6997 Paleontology 27:1047–1050. DOI 10.1671/0272- 6998 4364(2007)27[1047:TDCPOS]2.0.CO;2 6999 Werneburg R. 2009. The Permotriassic branchiosaurid Tungussogyrinus Efremov, 1939 7000 (Temnospondyli, Dissorophoidea) from Siberia restudied. Fossil Record 12:105–120. 7001 Werneburg R. 2012a. Eryopid temnospondyls from different ecosystems of Pennsylvanian 7002 up to Upper Permian Laurasia [abstract]. Terra Nostra 2012(3):196. 7003 Werneburg R. 2012b. Dissorophoide Amphibien aus dem Westphalian [sic] D (Ober- 7004 Karbon) von Nýřany in Böhmen (Tschechische Republik) – der Schlüssel zum 7005 Verständnis der frühen ‚Branchiosaurier‘. Semana – Naturwissenschaftliche 7006 Veröffentlichungen des Naturhistorischen Museums Schleusingen 27:3–50. 7007 Werneburg R, Berman DS. 2012. Revision of the aquatic eryopid temnospondyl 7008 Glaukerpeton avinoffi Romer, 1952, from the Upper Pennsylvanian of North America. 7009 Annals of Carnegie Museum 81:33–60. 7010 Werneburg R, Steyer JS. 2002. Revision of Cheliderpeton vranyi FRITSCH, 1877 7011 (Amphibia, Temnospondyli) from the Lower Permian of Bohemia (Czech Republic). 7012 Paläontologische Zeitschrift 76:149–162.

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7013 Werneburg R, Steyer JS, Sommer G, Gand G, Schneider JW, Vianey-Liaud M. 2007. 7014 The earliest tupilakosaurid amphibian with diplospondylous vertebrae from the Late 7015 Permian of southern France. Journal of Vertebrate Paleontology 27:26–30. DOI 7016 10.1671/0272-4634(2007)27[26:TETAWD]2.0.CO;2 7017 White TE. 1939. Osteology of Seymouria baylorensis Broili. [Lack of italics in the original.] 7018 Bulletin of the Museum of Comparative Zoölogy 85:325–409. 7019 Wiens JJ. 2001. Character analysis in morphological phylogenetics: problems and solutions. 7020 Systematic Biology 50:689–699. 7021 Wiens JJ. 2011. Re-evolution of lost mandibular teeth in frogs after more than 200 million 7022 years, and re-evaluating Dollo’s law. Evolution 65:1283–1296. DOI 10.1111/j.1558- 7023 5646.2011.01221.x 7024 Wiens JJ, Bonett RM, Chippindale PT. 2005. Ontogeny discombobulates phylogeny: 7025 paedomorphosis and higher-level salamander relationships. Systematic Biology 54:91– 7026 110. DOI 10.1080/10635150590906037 7027 Williston SW. 1909. The skull and extremities of Diplocaulus. Transactions of the Kansas 7028 Academy of Science 22:122–131. 7029 Williston SW. 1912. Restoration of Limnoscelis, a cotylosaur reptile from New Mexico. 7030 American Journal of Science 34:457–468. 7031 Williston SW. 1916. Synopsis of the American Permocarboniferous Tetrapoda. Contributions 7032 from Walker Museum 1:193–236. 7033 Witzmann F. 2006. Cranial morphology and ontogeny of the Permo-Carboniferous 7034 temnospondyl Archegosaurus decheni Goldfuss, 1847 from the Saar–Nahe Basin, 7035 Germany. Transactions of the Royal Society of Edinburgh: Earth Sciences 96:131– 7036 162. 7037 Witzmann F. 2007. The evolution of the scalation pattern in temnospondyl amphibians. 7038 Zoological Journal of the Linnean Society 150:815–834. 7039 Witzmann F. 2010 (printed 2011). Morphological and histological changes of dermal scales 7040 during the fish-to-tetrapod transition. Acta Zoologica (Stockholm) 92:281–302. DOI 7041 10.1111/j.1463-6395.2010.00460.x 7042 Witzmann F. 2013. Phylogenetic patterns of character evolution in the hyobranchial 7043 apparatus of early tetrapods. Earth and Environmental Science Transactions of the 7044 Royal Society of Edinburgh 104:145–167. 7045 Witzmann F. 2015 (printed 2016). CO2-metabolism in early tetrapods revisited: inferences 7046 from osteological correlates of gills, skin and lung ventilation in the fossil record. 7047 Lethaia 49:492–506. DOI 10.1111/let.12161 7048 Witzmann F, Schoch RR. 2006a. Skeletal development of the temnospondyl 7049 Acanthostomatops vorax from the Lower Permian Döhlen Basin of Saxony. 7050 Transactions of the Royal Society of Edinburgh: Earth Sciences 96:365–385. 7051 Witzmann F, Schoch RR. 2006b. The postcranium of Archegosaurus decheni, and a 7052 phylogenetic analysis of temnospondyl postcrania. Palaeontology 49:1211–1235. 7053 Witzmann F, Schoch RR. 2017. Skull and postcranium of the bystrowianid Bystrowiella 7054 schumanni from the Middle Triassic of Germany, and the position of chroniosuchians 7055 within Tetrapoda. Journal of Systematic Palaeontology online early: 29 pp. DOI 7056 10.1080/14772019.2017.1336579 7057 Witzmann F, Schoch RR, Maisch MW. 2008. A relict basal tetrapod from Germany: first 7058 evidence of a Triassic chroniosuchian outside Russia. Naturwissenschaften 95:67–72. 7059 DOI 10.1007/s00114-007-0291-6 7060 Worobjewa [Vorobyeva] EJ. 1975. Formenvielfalt und Verwandtschaftsbeziehungen der 7061 Osteolepidida (Crossopterygii, Pisces). Paläontologische Zeitschrift 49:44–55.

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7062 Wright AM, Hillis DM. 2014. Bayesian analysis using a simple likelihood model 7063 outperforms parsimony for estimation of phylogeny from discrete morphological data. 7064 PLOS ONE 9:e109210. DOI 10.1371/journal.pone.0109210 7065 Yates A (as “Adam” only, but known to be Yates). 2007. [Comment to Naish D. 2007. 7066 Temnospondyls the early years (part II)]. In: Naish D. Tetrapod Zoology. 7067 http://scienceblogs.com/tetrapodzoology/2007/07/09/temnospondyls-the-early-years- 7068 1/#comment-1935 7069 Yates A, Warren AA. 2000. The phylogeny of the ‘higher’ temnospondyls (Vertebrata: 7070 Choanata) and its implications for the monophyly and origins of the Stereospondyli. 7071 Zoological Journal of the Linnean Society 128: 77–121. DOI 10.1006/zjls1998.0184 7072 Zupiņš I. 2008. A new tristichopterid (Pisces, Sarcopterygii) from the Devonian of Latvia. 7073 Proceedings of the Latvian Academy of Sciences B 62:40–46. 7074

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7075 Supplementary Information 7076 7077 Data S1: Revised data matrix for parsimony analyses. NEXUS file (plain text) containing 7078 our revised data matrix (the machine-readable version of Appendix 2), one MPT from each of 7079 Analyses R1–R6, the bootstrap trees from B1 and B2, and the settings used for these analyses. 7080 Executing the file in PAUP* repeats Analyses R1–R6 in this order and then performs the 7081 statistical comparisons (Kishino-Hasegawa test, Templeton test, winning-sites test) of the 7082 trees that are already stored in the file. 7083 7084 Data S2: Excel file containing our measurements and their ratios relevant to characters 7085 PREMAX 7 and SKU TAB 1. 7086 On the sheet “Data”, the OTUs are listed such that the line numbers are the same as 7087 the numbers the OTUs have in the matrix; OTUs that cannot be measured for any of the 7088 parameters are represented by blank lines. Calculations are underlain in yellow or blue. The 7089 raw measurements, in cm, will mostly be difficult to reproduce: they were taken from 7090 illustrations (we preferred reconstruction drawings to avoid the effects of diagenetic 7091 distortion) on paper or on a screen, in the latter cases usually but not always at a 7092 magnification such as 150%, 200% or 300%. The ratios, however, should be fairly well 7093 reproducible. Column B is the distance (at a right angle to the sagittal plane) between the 7094 lateral extremities of the premaxillae, measured in ventral view when the premaxillae are 7095 insufficiently exposed in dorsal view. Column C is the maximum width of the 7096 dermatocranium in dorsal view. Column D is the maximum width of the skull table; when 7097 sharp edges between the table and the temporal regions are absent or unknown, this can be 7098 measured across the “tabular horns”, across the supratemporals across the rostral ends of the 7099 temporal notches, or across the intertemporals, whichever is widest. When possible, we have 7100 consulted lateral views to determine where the dorsal and the lateral surfaces of the skull roof 7101 meet. Column E cites our sources (all of them are also cited in the main text and/or Appendix 7102 1 and therefore listed in the References section). Column G is the ratio of premaxillary width 7103 to skull roof width (B divided by C), which we decided to use as the raw data for PREMAX 7 7104 (Appendix-Table 1). Column H is the ratio of premaxillary width to skull table width (B/D). 7105 Column I is the postorbital skull table length, in other words the rostrocaudal distance 7106 between the caudal margins of the orbits or orbitotemporal fenestrae (averaged if necessary) 7107 and the caudal end of the skull table in the midline. In salientians, the rostral margin of the 7108 otic capsule was assumed to lie at the caudal margin of the orbitotemporal fenestra, not at that 7109 of the lateral process of the parietal which covers only the caudal or caudomedial part of the 7110 otic capsule. Column J is the postorbital skull roof length, in other words the rostrocaudal 7111 distance between the caudal margins of the orbits (averaged if necessary) and the caudalmost 7112 extent of the dermatocranium, which may be the caudal end of the skull table in the midline, 7113 the tips of “tabular horns” (averaged if necessary), or the caudal ends of the suspensoria 7114 excluding the quadrates (averaged if necessary). Column K is the ratio of skull roof width to 7115 postorbital skull roof length (C/J). Column L is the ratio of skull table width to postorbital 7116 skull table length (D/I), which we decided to use as the raw data for SKU TAB 1 (Appendix- 7117 Table 3). Column M is the ratio of skull roof width to postorbital skull table length (C/I), and 7118 column N is the ratio of skull table width to postorbital skull roof length (D/J). OTUs are 7119 represented by their most complete and skeletally most mature known members, except that 7120 Sauropleura is represented by S. scalaris rather than the morphological outlier S. pectinata 7121 (which is measured in line 153); Dendrerpetidae is represented by Dendrysekos, 7122 Albanerpetidae by Celtedens, *Caseasauria by Eothyris. 7123 On all other sheets, OTUs scored 0 by RC07 are underlain in blue (for PREMAX 7 on 7124 the sheets “pmx-roof” and “pmx-table”, for SKU TAB 1 on the others), OTUs scored 1 by

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7125 RC07 are underlain in yellow, and OTUs scored as unknown by RC07 as well as those that 7126 we have added retain a white background. On each sheet, the values from one of the 7127 calculated columns on “Data” are ordered by size in column B (from highest to lowest for 7128 PREMAX 7, from lowest to highest for SKU TAB 1, in agreement with the original state 7129 definitions) and plotted; the line between the data points is of course meaningless, but we 7130 included it in order to see more easily where morphological gaps would lie. Column C on the 7131 sheets “pmx-roof” (for PREMAX 7) and “po table” (for SKU TAB 1) shows the state we 7132 have assigned to each OTU. Sheet “pmx-roof” is column G of the sheet “Data”, “pmx-table” 7133 is H, “po roof” is K, “po table” is L, “roof width, table length” is M, “table width, roof 7134 length” is N. 7135 7136 Data S3: Revised data matrix for Bayesian analysis. NEXUS file (plain text) containing 7137 our revised data matrix, a tree from Analysis EB in two formats (one with the posterior 7138 probabilities as node labels), and the settings used for this analysis. The stepmatrix characters 7139 (32 and 134 in both Appendices and Data S1) are split into two or three characters each, as 7140 explained in the text and Appendix 1. Executing the file in MrBayes repeats Analysis EB. 7141 7142 Data S4: Original data matrix of RC07. NEXUS file (plain text) containing the original 7143 data matrix of RC07, a tree from Analyses O1 and O2 each, as well as the settings for these 7144 analyses. Executing the file in PAUP* repeats these analyses in this order and then performs 7145 the statistical comparisons of the trees that are already stored in the file. 7146 7147 Data S5: Homoplasy per character in our revised matrix given an MPT from Analysis 7148 R1 (unconstrained, original taxon sample) and one from R4 (unconstrained, expanded 7149 taxon sample). The line numbers are the numbers of the characters (1–277). Column A 7150 shows the minimum of necessary steps per character (its number of states minus one); column 7151 B shows the steps actually found in R1 or R4 on the trees included in Data S1; column C is 7152 the difference between A and B, sorted from lowest to highest in column E, counted in 7153 columns G and H and plotted in the file as well as in Fig. 22. The line between the data points 7154 in the plots is meaningless, but makes it easier to compare the distributions to an exponential 7155 curve. Compare Goloboff, Torres & Arias (2017: fig. 1(a)). 7156

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7157 Appendix 1: Complete list of characters and modifications to the data matrix of RC07, 7158 with reports of new observations of specimens. 7159 The names, the abbreviations and the order of all characters and their states are 7160 unchanged from RC07 unless a change is explained. We renumbered the characters we did 7161 not delete from 1 to 277, so the character numbers do not match those of RC07. However, 7162 merged characters retain the abbreviations of all their components: PREMAX 1-2-3 (our 7163 character 1) consists of the characters PREMAX 1, PREMAX 2 and PREMAX 3 of RC07, 7164 while MAX 5/PAL 5 (our character 22) is assembled from MAX 5 and PAL 5 of RC07. We 7165 did not add any characters, except for splitting state 1 of INT FEN 1 into the new state 1 of 7166 INT FEN 1 (character 84) and states 1 and 2 of the new character MED ROS 1 (character 85), 7167 undoing the merger of PIN FOR 1 and PIN FOR 2 (characters 91 and 92) and splitting state 0 7168 of TEETH 3 into the new state 0 of TEETH 3 (character 183) and the entire new character 7169 TEETH 10 (character 190). A few characters have additional states or are recoded in other 7170 ways. Deleted characters are retained here, together with the reasons why we deleted them 7171 and the changes we made to their scores. 7172 All multistate characters mention in their names whether they are ordered, unordered, 7173 or treated according to a stepmatrix. 7174 Taxa are by default mentioned in the same order as in the matrix, at least within the 7175 same paragraph. 7176 In the interest of making our scoring decisions transparent, the taxa we have added as 7177 separate OTUs are mentioned in cases where their scores could be controversial. Their names 7178 are preceded by an asterisk; the names of taxa that are not included (but mentioned for 7179 comparison) are marked with two asterisks. 7180 Similarly, scores we have decided not to change are mentioned in cases where they 7181 could be controversial. Lack of mention equals lack of change from RC07. 7182 “Broiliellus” is B. brevis throughout; other species, including the type species B. 7183 texensis, were not considered (as explained in Material and methods: Treatment of OTUs: 7184 Taxa added as parts of existing OTUs). 7185 7186 1. PREMAX 1-2-3: Caudodorsal process of premaxilla: broad, low, indistinct (0); alary 7187 process (vaguely triangular, not occupying entire available mediolateral width at its 7188 base) (1); moderately tall, vaguely rectangular, or acutely triangular but occupying the 7189 entire mediolateral width between the nares and the median suture at its base (2); 7190 narrow and long, along the sagittal plane or parasagittal (3) (unordered). Within state 3, 7191 the mediolateral position of the process is not considered, because it probably depends on the 7192 width of the premaxilla. 7193 This character changes states from 0 to 1 in the ontogeny of Apateon gracilis (Schoch 7194 & Fröbisch, 2006); we have tried to take this into account when scoring OTUs known only 7195 from immature or paedomorphic individuals (Wiens, Bonett & Chippindale, 2005; 7196 Marjanović & Laurin, 2008, 2013a). 7197 RC07 treated this character complex as three separate characters: PREMAX 1, 7198 “Premaxillary alary process: absent (0); present (1)”; PREMAX 2, “Premaxilla alary process 7199 shorter than wide (0) or as long as/ longer than wide (1)”; and PREMAX 3, “Premaxilla alary 7200 process less than (0) or at least one-third as wide as premaxilla (1)”. Not only are PREMAX 2 7201 and PREMAX 3 inapplicable when PREMAX 1 has state 0; they do not (even together) cover 7202 the diversity of shapes of the contact between premaxilla and nasal seen in the taxon sample. 7203 Accordingly, we have replaced all three characters by character 26 of Marjanović & Laurin 7204 (2009), itself based on character 2 of Marjanović & Laurin (2008) and the work of Good & 7205 Wake (1992).

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7206 Crassigyrinus and Microbrachis were scored for PREMAX 2 and PREMAX 3 by 7207 RC07 in spite of being also scored PREMAX 1(0), which, as mentioned, made PREMAX 2 7208 and PREMAX 3 inapplicable. Some OTUs were scored for the latter two characters in spite of 7209 being also scored PREMAX 1(?), which had the same effect. 7210 State 0 occurs in Eusthenopteron (Jarvik, 1967; Brazeau & Ahlberg, 2006), 7211 Panderichthys (Vorobyeva & Schultze, 1991), Ventastega (Ahlberg et al., 2008), 7212 Acanthostega (Clack, 2007), Ichthyostega (Clack & Milner, 2015: fig. 8), Whatcheeria 7213 (Lombard & Bolt, 1995), Baphetes and Megalocephalus (Beaumont, 1977), Eucritta (Clack, 7214 2001 – it looks like 2 in the reconstruction, but the photo strongly suggests the pieces of bone 7215 in question are median rostrals rather than processes of the premaxilla), Chenoprosopus 7216 (Langston, 1953), Cochleosaurus (Sequeira, 2004), Neldasaurus (Chase, 1965), Caerorhachis 7217 (Ruta, Milner & Coates, 2002 – though 1 and 2 would also be more or less defensible scores), 7218 Eoherpeton (Smithson, 1985, though this is somewhat arguable), Proterogyrinus (Holmes, 7219 1984), Archeria (Holmes, 1989), Discosauriscus (Klembara & Ruta, 2005a), Keraterpeton, 7220 Batrachiderpeton, Ptyonius and Sauropleura (Bossy & Milner, 1998), Ariekanerpeton 7221 (Laurin, 1996a; Klembara & Ruta, 2005a) and Utegenia (Laurin, 1996b; Klembara & Ruta, 7222 2004a). We have further assigned state 0 to the frogs Notobatrachus (Báez & Nicoli, 2004), 7223 Vieraella (Báez & Basso, 1996) and *Liaobatrachus (Dong et al., 2013): their so-called alary 7224 processes are entirely ventral to the nares and are laterally bordered by a neomorphic fenestra 7225 that is more or less confluent with the naris on the same side. 7226 Colosteus and Greererpeton are here tentatively scored 1 (Smithson, 1982; Hook, 7227 1983; see Bolt & Lombard, 2010, for grounds for caution). State 1 further occurs in Isodectes 7228 (Sequeira, 1998), Trimerorhachis (Schoch & Milner, 2013), Balanerpeton (Milner & 7229 Sequeira, 1994), Dendrerpetidae (Holmes, Carroll & Reisz, 1998), Eryops, Acheloma (Polley 7230 & Reisz, 2011 – although it is arguably a special case), Ecolsonia (Berman, Reisz & Eberth, 7231 1985), Amphibamus (Schoch, 2001), Doleserpeton (Bolt, 1969; Sigurdsen & Bolt, 2010), 7232 Platyrhinops (Clack & Milner, 2010), Micromelerpeton (arguably borderline to state 3: 7233 Schoch, 2009), Apateon (Schoch & Fröbisch, 2006), Karaurus (Ivachnenko, 1978: fig. 1; D. 7234 M. and M. L., pers. obs. of unnumbered MNHN cast of PIN 2585/2), Dolichopareias 7235 (Andrews & Carroll, 1991), Capetus (Sequeira & Milner, 1993) and, perhaps surprisingly, 7236 *Utaherpeton (Carroll, Bybee & Tidwell, 1991: fig. 6.1, 7). 7237 State 2 occurs in Tulerpeton (as far as can be told from the isolated premaxilla + 7238 vomer; Lebedev & Clack, 1993), Crassigyrinus (Clack, 1998), Albanerpetidae, Eocaecilia 7239 (Jenkins, Walsh & Carroll, 2007), Pholiderpeton attheyi (Panchen, 1972), Anthracosaurus 7240 (Clack, 1987a), Pholiderpeton scutigerum (Clack, 1987b), Bruktererpeton (Boy & Bandel, 7241 1973), Gephyrostegus (Carroll, 1970; Klembara et al., 2014), Seymouria (Laurin, 1996c; see 7242 Marjanović & Laurin [2009: Electronic Supplementary Material 1] for discussion), 7243 Captorhinus (Fox & Bowman, 1966; Heaton, 1979), Petrolacosaurus (Reisz, 1981), 7244 Westlothiana (Smithson et al., 1994), Batropetes (Carroll, 1991; Glienke, 2013), Tuditanus, 7245 Pantylus, Asaphestera, Saxonerpeton, Hapsidopareion, Micraroter, Pelodosotis, 7246 Cardiocephalus, Hyloplesion and Odonterpeton (CG78), Rhynchonkos (CG78; 7247 Szostakiwskyj, Pardo & Anderson, 2015), Microbrachis (Vallin & Laurin, 2004), Stegotretus 7248 (Berman, Eberth & Brinkman, 1988), Diceratosaurus, Diplocaulus, Diploceraspis, 7249 Scincosaurus, Adelogyrinus, Silvanerpeton (Ruta & Clack, 2006) and Tseajaia (Moss, 1972). 7250 State 3 occurs in Phonerpeton (Dilkes 1990: fig. 3), Eoscopus (Daly, 1994), 7251 Valdotriton (Evans & Milner, 1996), Diadectes (Berman, Sumida & Martens, 1998), 7252 Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 2010), Lethiscus (Pardo et al., 2017) and 7253 Orobates (Berman et al., 2004). 7254 Unknown (but not scored as such by RC07) in Edops (Romer & Witter, 1942 – the 7255 area is reconstructed in MCZ 1378: D. M., pers. obs.), Leptorophus and Schoenfelderpeton

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7256 (Boy, 1986, 1987), Triadobatrachus (Roček & Rage, 2000), Solenodonsaurus (Laurin & 7257 Reisz, 1999), Kotlassia (Bulanov, 2003), Paleothyris (Carroll, 1969a), Adelospondylus 7258 (Andrews & Carroll, 1991), Urocordylus (Bossy & Milner, 1998), Leptoropha & Microphon 7259 (Bulanov, 2003 – known to be 0 in juvenile skulls, but this could be ontogenetic), Ossinodus 7260 (Warren, 2007), Pederpes (Clack & Finney, 2005); also unknown in *Gerobatrachus 7261 (Marjanović & Laurin, 2009: Electronic Supplementary Material 1). 7262 Euryodus is polymorphic, possessing states 0 and 2 (CG78). 7263 Brachydectes has state 1 or 2 (Wellstead, 1991; Pardo & Anderson, 2016). 7264 Oestocephalus (specimen drawings in Carroll, 1998a) and Phlegethontia (Anderson, 7265 2007a) have state 2 or 3. 7266 *Acanthostomatops is polymorphic, in at least one case (Witzmann & Schoch, 2006a: 7267 fig. 3D) showing states 1 and 2 on different sides of the same individual. 7268 States 1 and 3 occur in “large adults” of *Glanochthon (Schoch & Witzmann, 2009b: 7269 fig. 2). 7270 The premaxillae of *Quasicaecilia are unknown, but the nasals make state 3 7271 impossible (Pardo, Szostakiwskyj & Anderson, 2015); we have thus scored state 0, 1 or 2. 7272 7273 2. PREMAX 4: Premaxilla with flat, expanded anteromedial dorsal surface and 7274 elongated along its lateral margin but not along its medial margin, when observed in 7275 dorsal aspect: absent (0); present (1). This character is a case of non-additive binary coding; 7276 it is likely that dividing state 0 (which is defined only as everything that is not state 1) into 7277 several states would reveal further phylogenetic signal. 7278 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994). We have kept 7279 it for Acanthostega, Ichthyostega and the colosteids because the anteromedial surface is 7280 probably not “expanded”, although the lateral margin is much longer than the medial one 7281 (Clack, 2007; Bolt & Lombard, 2010; Porro, Rayfield & Clack, 2015; Clack & Milner, 2015); 7282 the same holds for *Elginerpeton (Ahlberg, 1995). 7283 State 1 is, however, present in Phlegethontia (Anderson, 2007a). 7284 This character is invisible in *Saharastega; there are so many fractures that each of 7285 them could be a suture (D. M., pers. obs. of MNN MOR 73). 7286 7287 3. PREMAX 7: Ratio of maximum width of both premaxillae together to maximum 7288 width of skull roof: ≥ 0.5 (0); ]0.5-0.4] (1); ]0.4-0.3] (2); ]0.3-0.2] (3); < 0.2 (4) (ordered). 7289 The wording of this character, but not its scores, changed substantially between Ruta, Coates 7290 & Quicke (2003) and RC07. Ruta, Coates & Quicke (2003) put it as follows: 7291 “PREMAX 7. Premaxillae more (0) or less than (1) two-thirds as wide as skull. This 7292 is a modified version of one of Gauthier et al.’s (1988b) characters, found ubiquitously among 7293 ‘reptiliomorphs’, and which characterizes also several lepospondyls and some primitive 7294 lissamphibians (e.g. Eocaecilia; Carroll, 2000). Narrow premaxillae, even in stem-amniotes 7295 showing broad and spade-shaped snouts (e.g. Discosauriscus; Klembara, 1997), contrast with 7296 the broad premaxillae of temnospondyls and several stem-tetrapods.” 7297 Compare RC07: 7298 “PREMAX 7. Premaxillae more (0) or less than (1) two-thirds as wide as skull table. 7299 The total width of the conjoined premaxillae is measured as the distance between their 7300 lateralmost extremities; the total skull table width is between the lateral extremities of the 7301 suspensoria.” 7302 Thus, the 2007 version described the width of the skull, but called it “skull table 7303 width”. This appears to be yet another instance of the constant confusion of the terms “skull 7304 roof” and “skull table” by RC07 (see main text). However, we have measured the total width 7305 of the premaxillae (“between their lateralmost extremities”) and the maximum width of the

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7306 skull roof (“between the lateral extremities of the suspensoria”) in all taxa in this matrix (Data 7307 S2); it turns out that a ratio of 0.67 or more does not occur in the original or the expanded 7308 taxon sample – except in Caerorhachis (Ruta, Milner & Coates, 2002), which was scored as 7309 unknown in RC07. Only 11 OTUs even reach a ratio of 0.5. Moreover, the correlation 7310 between the scores by RC07 and the ratios we have calculated is quite low (Appendix-Table 7311 1), and it does not improve if we boldly interpret “two-thirds” as “one-third” (which would 7312 give state 0 to 65 of the 127 measurable OTUs). 7313 Because Ruta, Coates & Quicke (2003) claimed that this character carried 7314 phylogenetic signal, we did not want to simply delete it as parsimony-uninformative. We 7315 therefore speculated that the change from “skull” to “skull table” may in this case really have 7316 been a correction and measured the width of the skull table (see main text and legend to Data 7317 S2; including “tabular horns”) in all taxa in this matrix as well. Indeed, 50 of 129 measurable 7318 OTUs have a ratio of two-thirds or more, but the correlation between the ratios we have found 7319 and the scores by RC07 remains extremely low (Data S2). 7320 Except for a few cases of missing data, RC07 assigned state 1 to all amniotes, 7321 diadectomorphs, “microsaurs”, seymouriamorphs, anthracosaurs, Silvanerpeton, 7322 Gephyrostegus, Diplocaulus, Diploceraspis and finally Eocaecilia (mentioned in the quote 7323 above), and state 0 to all the rest. It appears to us that they did not measure most OTUs at all, 7324 but instead scored them after presumed close relatives – which would be an example of 7325 circular logic, because those presumptions of relationship are the very hypotheses that their 7326 phylogenetic analyses aimed to test. We have therefore entirely discarded the original scores 7327 and state definitions. 7328 Regardless of whether the skull table or the entire skull roof is measured, this 7329 character is continuous; the question thus arises of how best to divide it into states, and 7330 whether to choose the table or the whole roof. Concerning the second question, we have 7331 arbitarily chosen the whole roof in order to conform to the definition by RC07 and the name 7332 of the 2003 version of the character. The ideal solution to the first question would be 7333 stepmatrix gap-weighting (Wiens, 2001) as used by Marjanović & Laurin (2008), but PAUP* 7334 only allows 32 states, while our matrix has 128 measurable OTUs with 122 different values 7335 (so that arbitrary binning and averaging would have to be performed), and even with “only” 7336 32 states the calculation time would skyrocket. The character lacks large morphological gaps 7337 except toward the extremes, and it seems clear that the existing small gaps are artefacts of 7338 taxon sampling because the taxa we have added have filled many (Appendix-Table 1; Data 7339 S2). We have arbitrarily created a state for each interval of 0.1, with the two OTUs above 0.6 7340 (Caerorhachis, Crassigyrinus) and the two below 0.1 (Diplocaulus, Diploceraspis) merged 7341 into the neighboring bins to avoid making a near-uninformative state in Caerorhachis and 7342 Crassigyrinus, and a near-uninformative state correlated with the famous boomerang shape of 7343 the skull in Diplocaulus and Diploceraspis. 7344 The ratios, sources, and state changes are presented in Appendix-Table 1; they and our 7345 measurements are contained in Data S2. 7346 Baphetes is polymorphic: B. kirkbyi has state 1 (Beaumont, 1977: fig. 21), B. 7347 orientalis changes from state 1 to state 0 in ontogeny (Beaumont, 1977: fig. 25; Milner, 7348 Milner & Walsh, 2009). 7349 *Saharastega is too poorly preserved to measure, but states 0 and 4 can still be 7350 excluded (D. M., pers. obs. of MNN MOR 73): the squished skull roof was something like 28 7351 cm wide, the minimum width across both premaxillae is about 7 cm, the maximum about 12 7352 cm, corresponding to ratios of 0.25 to 0.43 – adding further margins of error, we have scored 7353 state 1, 2 or 3. 7354 The skull roof width of *Archaeovenator has not been reconstructed, but the ratio of 7355 premaxillary width to skull table width is 0.225 (Data S2; Reisz & Dilkes, 2003); it follows

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7356 that the ratio of premaxillary width to skull roof width must have been 0.225 or lower, 7357 meaning states 3 or 4. 7358 7359 Appendix-Table 1: Ratios of premaxillary width to skull roof width, and changes to the 7360 scores of character 3 (PREMAX 7). Taxa underlain in blue were scored 0 by RC07, taxa 7361 underlain in yellow were scored 1, and the remainder were scored as unknown or have been 7362 added by us; the latter are marked with an asterisk. Abbreviation: Ph., Pholiderpeton. See 7363 Data S2 and its legend for more information. 7364 OTU Ratio New Measured in: (rounded) score Brachydectes 0.780 0 Pardo & Anderson, 2016: fig. 4B Caerorhachis 0.689 0 Ruta, Milner & Coates, 2002 Crassigyrinus 0.620 0 Clack, 1998 Phlegethontia 0.569 0 Anderson, 2007a Ventastega 0.568 0 Ahlberg et al., 2008 Cochleosaurus 0.556 0 Schoch & Milner, 2014: fig. 13D *Spathicephalus 0.544 0 Beaumont & Smithson, 1998: fig. 5 *Erpetosaurus 0.541 0 Milner & Sequeira, 2011 Eryops 0.535 0 Schoch & Milner, 2014: fig. 3C Dendrerpetidae 0.533 0 Dendrysekos: Schoch & Milner, 2014: fig. 17C Karaurus 0.508 0 Ivachnenko, 1978 Edops 0.491 1 Schoch & Milner, 2014: fig. 13A Chenoprosopus 0.484 1 Schoch & Milner, 2014: fig. 13E Capetus 0.479 1 Sequeira & Milner, 1993 *Konzhukovia 0.479 1 Gubin, 1991: drawing 6a Albanerpetidae 0.477 1 Celtedens: McGowan, 2002 Orobates 0.469 1 Kissel, 2010: fig. 32B Balanerpeton 0.462 1 Schoch & Milner, 2014: fig. 17A Amphibamus 0.462 1 Schoch & Milner, 2014: fig. 30 *Llistrofus 0.456 1 Bolt & Rieppel, 2009 *Pholidogaster 0.452 1 Panchen, 1975 Eucritta 0.446 1 Clack, 2001: fig. 8 Ptyonius 0.446 1 Bossy & Milner, 1998 *Sclerocephalus 0.445 1 Schoch & Witzmann, 2009a *Mordex 0.445 1 Schoch & Milner, 2014: fig. 32A *Micropholis 0.443 1 Schoch & Rubidge, 2005: fig. 3B Vieraella 0.440 1 Báez & Basso, 1996: fig. 6, 7 Eoscopus 0.432 1 Daly, 1994: fig. 3 Doleserpeton 0.430 1 Sigurdsen & Bolt, 2010 Trimerorhachis 0.427 1 Schoch & Milner, 2014: fig. 20A *Acanthostomatops 0.426 1 Witzmann & Schoch, 2006a *Nigerpeton 0.419 1 Steyer et al., 2006 Apateon 0.417 1 Schoch & Fröbisch, 2006: fig. 1D *Iberospondylus 0.411 1 Laurin & Soler-Gijón, 2006: fig. 1A; left side approximately doubled Platyrhinops 0.408 1 Clack & Milner, 2010: fig. 9 Panderichthys 0.407 1 Vorobyeva & Schultze, 1991

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Greererpeton 0.402 1 Smithson, 1982 Lethiscus 0.402 1 J. Pardo, pers. comm. 2017 Ichthyostega 0.404 1 Clack & Milner, 2015: fig. 8 *Palatinerpeton 0.399 2 Boy, 1996: fig. 3 Saxonerpeton 0.395 2 CG78: fig. 22 *Glanochthon 0.392 2 Schoch & Witzmann, 2009b: fig. 2A approximately doubled Eocaecilia 0.386 2 Jenkins, Walsh & Carroll, 2007 Diadectes 0.385 2 Kissel, 2010: fig. 36B Valdotriton 0.377 2 Evans & Milner, 1996 Phonerpeton 0.375 2 Dilkes, 1990: fig. 1 *Deltaherpeton 0.370 2 Bolt & Lombard, 2010: fig. 2; left premaxilla doubled, otherwise right side approximately doubled *Gerobatrachus 0.370 2 estimated based on Anderson et al., 2008a: fig. 2b Acanthostega 0.368 2 Porro, Rayfield & Clack, 2015 *Cheliderpeton 0.366 2 Werneburg & Steyer, 2002 Westlothiana 0.365 2 Smithson et al., 1994 Isodectes 0.365 2 Schoch & Milner, 2014: fig. 20E Megalocephalus 0.362 2 Beaumont, 1997: fig. 8 *Liaobatrachus 0.360 2 Dong et al., 2013 Gephyrostegus 0.360 2 Klembara et al., 2014 Asaphestera 0.358 2 CG78: fig. 7 *Carrolla 0.355 2 Maddin, Olori & Anderson, 2011 Acheloma 0.348 2 Polley & Reisz, 2011 *Pangerpeton 0.346 2 estimated based on Wang & Evans, 2006 Ecolsonia 0.344 2 Berman, Reisz & Eberth, 1985: fig. 5A Micromelerpeton 0.341 2 Boy, 1995: fig. 8A Solenodonsaurus 0.339 2 Danto, Witzmann & Müller, 2012; maximum possible width of premaxilla estimated *Saharastega 0.339 2 Damiani et al., 2006 *Chroniosaurus 0.335 2 Clack & Klembara, 2009 Silvanerpeton 0.333 2 Ruta & Clack, 2006 Rhynchonkos 0.330 2 CG78: fig. 63 Microphon 0.328 2 Bulanov, 2003: fig. 22 Broiliellus 0.327 2 Carroll, 1964 Eoherpeton 0.326 2 Panchen, 1975 Schoenfelderpeton 0.325 2 Boy, 1986: fig. 13 Colosteus 0.322 2 Hook, 1983 Anthracosaurus 0.321 2 Clack, 1987a *Lydekkerina 0.320 2 Hewison, 2007: fig. 30 Seymouria 0.317 2 Laurin, 1996c Keraterpeton 0.314 2 Bossy & Milner, 1998 Paleothyris 0.313 2 Carroll, 1969a: fig. 4B Micraroter 0.313 2 CG78: fig. 56 Ossinodus 0.309 2 Warren, 2007 *Palaeoherpeton 0.306 2 Panchen, 1964

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Sauropleura 0.306 2 Bossy & Milner, 1998 Oestocephalus 0.306 2 Anderson, 2003b Pelodosotis 0.304 2 CG78: fig. 48 Euryodus 0.304 2 CG78: fig. 37 *Tungussogyrinus 0.304 2 Werneburg, 2009 Ph. attheyi 0.299 3 Panchen, 1972 Discosauriscus 0.299 3 Klembara et al., 2006 Leptorophus 0.298 3 Boy, 1986: fig. 4 Pederpes 0.298 3 Clack & Finney, 2005 Limnoscelis 0.298 3 Kissel, 2010: fig. 13A1 Eusthenopteron 0.293 3 Clack, 2007 Microbrachis 0.292 3 Vallin & Laurin, 2004 Batropetes 0.291 3 Glienke, 2013: fig. 2 *Caseasauria 0.290 3 Eothyris: Reisz, Godfrey & Scott, 2009 *Archegosaurus 0.289 3 Witzmann, 2006: fig. 5 Scincosaurus 0.289 3 Milner & Ruta, 2009 Proterogyrinus 0.277 3 Holmes, 1984 *Utaherpeton 0.272 3 Carroll, Bybee & Tidwell, 1991 Stegotretus 0.271 3 Berman, Eberth & Brinkman, 1988: fig. 10B Hyloplesion 0.271 3 CG78: fig. 89B Ph. scutigerum 0.271 3 Clack, 1987b Ariekanerpeton 0.271 3 Klembara & Ruta, 2005a *Crinodon 0.268 3 CG78: fig. 11 Captorhinus 0.266 3 Fox & Bowman, 1966: fig. 3 Urocordylus 0.262 3 Bossy & Milner, 1998 Neldasaurus 0.254 3 Schoch & Milner, 2014: fig. 20C Notobatrachus 0.252 3 Báez & Nicoli, 2004 Diceratosaurus 0.250 3 Bossy & Milner, 1998 Utegenia 0.250 3 Klembara & Ruta, 2004a Bruktererpeton 0.246 3 estimated based on Boy & Bandel, 1973: fig. 7 Tseajaia 0.245 3 Berman, Sumida & Lombard, 1992: fig. 11 Tuditanus 0.240 3 Carroll & Baird, 1968: fig. 9 *Karpinskiosaurus 0.240 3 Klembara, 2011 Petrolacosaurus 0.238 3 Berman, Sumida & Lombard, 1992: fig. 11 Cardiocephalus 0.235 3 CG78: fig. 69 *Pseudophlegethontia 0.233 3 Anderson, 2003b: fig. 3 *Australerpeton 0.228 3 Eltink et al., 2016: fig. 5 Archeria 0.227 3 Holmes, 1989 *Chelotriton 0.226 3 Marjanović & Witzmann, 2015: fig. 7 *Neopteroplax 0.222 3 Romer, 1963: fig. 3 Kotlassia 0.216 3 Bulanov, 2003: fig. 30 *Bystrowiella 0.203 3 Witzmann & Schoch, 2017: fig. 15C *Sparodus 0.193 4 Carroll, 1988 *Platyoposaurus 0.193 4 Gubin, 1991: drawing 3a Odonterpeton 0.188 4 CG78: fig. 99B

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Batrachiderpeton 0.153 4 Bossy & Milner, 1998 Pantylus 0.149 4 Romer, 1969: fig. 1 Diplocaulus 0.091 4 Olson, 1951: pl. 5B left side doubled Diploceraspis 0.077 4 Beerbower, 1963: fig. 2 7365 7366 1 A line drawing identical to Berman, Reisz & Scott (2010: fig. 3A), but slightly more 7367 convenient to measure. 7368 7369 4. PREMAX 8: Anteriormost surface of premaxilla oriented obliquely, so that mouth 7370 opens subterminally: absent (0); present (1). 7371 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Lethiscus (Anderson, Carroll 7372 & Rowe, 2003; Pardo et al., 2017) have state 0. 7373 Panderichthys is famous for having a subterminal mouth (state 1; e.g. Brazeau & 7374 Ahlberg, 2006). This condition has also been reconstructed for Ichthyostega (Clack & Milner, 7375 2015: fig. 8). 7376 Unknown in Edops (Romer & Witter, 1942; D. M., pers. obs. of MCZ 1378). 7377 Although we have kept the score of 1 for Batropetes, this seems to be a very weak 7378 case (Glienke, 2013, 2015). 7379 Conversely, while the premaxillae of *Quasicaecilia are unknown, the nasals 7380 themselves are recurved so that the nostrils opened on the ventral side of the snout (Pardo, 7381 Szostakiwskyj & Anderson, 2015); the mouth was inevitably subterminal, so we have scored 7382 state 1. 7383 7384 5. PREMAX 9: Maxilla in ventral view more or less limited to toothrow (0); contributes 7385 to the palate labial to the for at least twice the width of the toothrow (1). The 7386 original wording was: “Shelf-like contact between premaxilla and maxilla occurring mesial to 7387 marginal tooth row on palate and extending medially for at least twice the width of such a 7388 row: absent (0); present (1)”, but it took us a long time to understand this wording. – From 7389 here on, RC07 consistently wrote “mesial” (toward the jaw symphysis, along the curvature of 7390 the jaw) when they were clearly aiming at “medial” (toward the sagittal plane) and actually 7391 meant “lingual” (toward the tongue, at 90° to the curvature of the jaw – caudal at the 7392 symphysis, medial around the jaw joints). 7393 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), most likely Amphibamus (Schoch 7394 & Milner, 2014: fig. 30B; implicitly Daly, 1994), Albanerpetidae (McGowan, 2002, Venczel 7395 & Gardner, 2005) and Lethiscus (Anderson, Carroll & Rowe, 2003) have state 0. We also 7396 continue to consider the tiny teeth of frogs, which create a wide palatal contribution not only 7397 labial to the choana, but along the entire length of the maxilla, as state 0, and have therefore 7398 kept the scores of Notobatrachus and Vieraella. 7399 Orobates has state 0 (Nyakatura et al., 2015: digital reconstruction). 7400 In Ossinodus (Warren, 2007), the contribution of the maxilla to the palate lateral of the 7401 choana is easily twice as wide as the toothrow (not counting the very large caniniforms) at the 7402 caudal end of the choana (at the mediolateral suture to the palatine), but only about once as 7403 wide at the rostral end (at the suture to the premaxilla). We count this as state 1. 7404 We have scored state 0 for *Perittodus and *Aytonerpeton after Clack et al. (2016: 7405 matrix). 7406 7407 6. TEC 1: Anterior tectal: present (0); absent (1). We follow Panchen (1967), Beaumont 7408 (1977), Clack (1998) and RC07 in considering the septomaxilla homologous to the lateral 7409 rostral rather than the anterior tectal, because the septomaxilla lies caudal and/or ventral to the 7410 naris, like the lateral rostral and unlike the dorsally positioned anterior tectal (contra

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7411 Sigurdsen & Green, 2011: supp. inf.), though we would like to point out that this question has 7412 received disquietingly little attention in the literature. Clack et al. (2012a) presented a 7413 phylogenetic, arguably scenario-based argument for the reduction and complete loss of the 7414 lateral rostral and for the homology of anterior tectal and septomaxilla. We fear that this 7415 question cannot be decided without new material, because at the moment the seeming 7416 disappearance of the anterior tectal, the seeming disappearance of the lateral rostral, and the 7417 seeming appearance of the septomaxilla are optimized as happening in indistinguishable 7418 places in the tree – we need more fossil noses from the Late Devonian and the Mississippian. 7419 A good candidate for possessing both an anterior tectal and a septomaxilla is *Aytonerpeton, 7420 but this is currently unclear and requires further study, if not further specimens (see below). 7421 State 0 is almost certainly present in Ventastega (Ahlberg, Lukševičs & Lebedev, 7422 1994). 7423 The condition is unknown in Colosteus and Greererpeton (Bolt & Lombard, 2010), in 7424 Whatcheeria (Lombard & Bolt, 1995) and in Batropetes (Glienke, 2013, 2015). 7425 Phonerpeton was scored as unknown in RC07. Although many sutures are difficult or 7426 impossible to find in AMNH 7150 or MCZ 2313, there is no evidence for an anterior tectal in 7427 either of them; in particular, the margins of both nares are undamaged in both skulls (D. M., 7428 pers. obs.). We have therefore scored state 1 for Phonerpeton. 7429 State 1 is likewise present in Lethiscus (Pardo et al., 2017). 7430 Due to the argument above, we have scored the mystery bone of *Ymeria as the 7431 septomaxilla, so that the presence of the anterior tectal is unknown. 7432 In *Pholidogaster, Panchen (1975) reconstructed state 1 with confidence. However, of 7433 the two specimens, the type (which exposes the dorsal surface) has undergone compression 7434 and shearing (Panchen, 1975: 614; Bolt & Lombard, 2010), including but not limited to 7435 disruption by the tusks on the dentary and the palatine (Panchen, 1975: fig. 11; Bolt & 7436 Lombard, 2010) which could have obscured the distinction between a break and a suture 7437 between the nasal, the anterior tectal and/or the prefrontal (the nasal-prefrontal suture is 7438 shown in fig. 11 as having an unusual shape and running in part in a lateral-line groove on the 7439 strongly ornamented snout). The referred specimen is only exposed in ventral view and 7440 heavily damaged medial to the septomaxilla (Panchen, 1975: fig. 13). Given that the only 7441 illustrations (other than fig. 12, a not very large photograph of the type skull) are thick-lined 7442 line drawings, restudy of both specimens will be necessary – and perhaps insufficient – to 7443 resolve this and related issues. In short, we have joined the skepticism of Bolt & Lombard 7444 (2010) and scored this character as unknown. 7445 Panchen (1964) thought that anterior tectals were present in *Palaeoherpeton; we 7446 follow his later assessment (Panchen, 1972: 287) that these areas were in fact part of the 7447 lacrimals and have therefore scored state 1. 7448 We accept the inference of Ahlberg (1995) that a slot on the premaxilla of 7449 *Elginerpeton is the sutural surface for the anterior tectal, and have therefore scored state 0. 7450 The septomaxilla identified in *Aytonerpeton by Clack et al. (2016) is clearly an 7451 anterior tectal; we have scored state 0. 7452 7453 7. SPTMAX 1-2: Septomaxilla with exposure on skull surface (0), wholly inside nostril 7454 (1), absent (2) (unordered). RC07 had deleted the character SPTMX 1 of Ruta, Coates & 7455 Quicke (2003), which concerned the presence of the septomaxilla; SPTMX 2 was 7456 “Septomaxilla a detached ossification inside nostril: no (0); yes (1)”. We have assigned state 2 7457 only to taxa of which many articulated skulls are known; otherwise we have interpreted 7458 absence as possible post-mortem loss or incomplete preparation (as cautioned by RC07) and 7459 scored it as partial uncertainty (state 1 or 2). Nonetheless, state 2 is present in Acanthostega 7460 (Ahlberg, Lukševičs & Lebedev, 1994; Clack, 1994b, 2002, 2003a; Clack et al., 2012a; by

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7461 implication Porro, Rayfield & Clack, 2015), Microbrachis (no evidence of a septomaxilla in 7462 100 inspected specimens: Olori, 2015), apparently Lethiscus (Pardo et al., 2017) and 7463 Phlegethontia (Anderson, 2002, 2007a) as well as in Notobatrachus, from which no 7464 septomaxilla has been reported despite the enormous number of known and superbly 7465 preserved individuals (Báez & Basso, 1996; Báez & Nicoli, 2004, 2008); Acanthostega was 7466 scored SPTMAX 2(0) by RC07, the others as unknown. – We have also assigned state 2 to 7467 the added OTU *Sclerocephalus (Schoch & Witzmann, 2009a). 7468 Panderichthys (Vorobyeva & Schultze, 1991), Baphetes (judging from the presence of 7469 dermal ornament on the septomaxilla: Milner, Milner & Walsh, 2009), Trimerorhachis 7470 (Milner & Schoch, 2013), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Gephyrostegus 7471 (apparently: Klembara, 2014: fig. 5B) and Seymouria (Laurin, 1996c; Klembara et al., 2005) 7472 show state 0. While the septomaxilla is not preserved in Batropetes, Glienke (2013: 79) 7473 confidently reconstructed state 0 for this taxon as well, “owing to the premaxilla and the 7474 naris” (and presumably the prefrontal). 7475 We have tentatively kept state 0 for Ichthyostega under the assumption that the lateral 7476 rostral identified by Jarvik (1996) was correctly identified as such and is homologous to the 7477 septomaxilla (see above); but we caution that it has not been found again (Clack & Milner, 7478 2015). 7479 Romer & Witter (1942) stated very explicitly that Edops has state 0. However, 7480 assuming that both they and D. M. (pers. obs.) have traced the sutures in MCZ 1378 correctly, 7481 the sculpture on the septomaxilla is much lower and finer than that on the rest of the skull 7482 roof, and the surface lies on a more ventral level, bounded by a sharp vertical step formed by 7483 the maxilla and the lacrimal (the margin of the nasal, which most likely participated, is not 7484 preserved). This constitutes state 1. – The same condition occurs in *Pholidogaster (Panchen, 7485 1975: 617). 7486 Acheloma shows state 1 (Dilkes & Reisz, 1987). Phonerpeton, on the other hand, has 7487 state 0 (D. M., pers. obs. of the type specimen, MCZ 1419). 7488 State 1 is present in Doleserpeton (Sigurdsen & Bolt, 2010) as well as 7489 Hapsidopareion, Micraroter and Rhynchonkos (CG78). 7490 Following Clack & Milner (2010), we assign state 1 or 2 to Eoscopus and 7491 Platyrhinops. 7492 While Colosteus and Greererpeton have been reconstructed as possessing state 2 7493 (Smithson, 1982; Hook, 1983), they should rather be scored as unknown (Bolt & Lombard, 7494 2010). 7495 *Acanthostomatops is apparently polymorphic, showing states 0 and 1 (illustrations in 7496 Witzmann & Schoch, 2006a). It is possible that this is ontogenetic, as state 0 is seemingly 7497 only found in the largest specimens, but the sample size is probably not large enough to tell. 7498 We have tentatively scored state 0 for *Ymeria as explained for TEC 1. 7499 The septomaxilla identified in *Aytonerpeton by Clack et al. (2016) is clearly an 7500 anterior tectal (see TEC 1 immediately above). Whether a septomaxilla is or was present is 7501 unclear: the caudoventral rim of the naris is damaged, and a fragment bounded by the naris, 7502 the anterior tectal, the lacrimal and the maxilla may or may not be the septomaxilla, as may be 7503 the continuation of the maxilla in the naris (no sutures are visible anywhere in the 7504 supplementary video). 7505 7506 8. NAS 1: Paired nasals: absent (0); present (1). We interpret this character as referring to 7507 identifiable nasals as separate bones; Eusthenopteron and Panderichthys have a “postrostral 7508 mosaic” (now state 84(0)) which contains several candidates for nasal homologues, so we 7509 have scored them as unknown, unlike Diplocaulus and Diploceraspis, in which nasals are 7510 definitely absent according to published descriptions.

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7511 Ventastega has state 1 (Lukševičs, Ahlberg & Clack, 2003, Ahlberg et al., 2008). 7512 Bulanov (2003: fig. 30) reconstructed state 1 for Kotlassia; judging from the text (p. S53), this 7513 appears to be correct. 7514 Although there is evidence of nasals in *Palatinerpeton, the sagittal suture of the 7515 dorsal side of the skull is entirely unknown (Boy, 1996), so we cannot tell if the presumed 7516 nasals were fused and have scored *Palatinerpeton as unknown. 7517 7518 9. NAS 2: Nasals more (0) or less than (1) one-third as long as frontals. 7519 State 0 is present in Panderichthys (whichever bones actually are the nasals: 7520 Vorobyeva & Schultze, 1991), Ventastega (Ahlberg et al., 2008), Microbrachis (Vallin & 7521 Laurin, 2004), Hyloplesion (CG78), Lethiscus (Pardo et al., 2017), Oestocephalus (Carroll, 7522 1998a; Anderson, 2003a) and Phlegethontia (Anderson, 2007a). Bulanov (2003: fig. 30) 7523 reconstructed state 0 for Kotlassia; judging from the text (p. S53), this appears to be correct. 7524 State 0 is furthermore plesiomorphic for Albanerpetidae, as far as can be reconstructed 7525 from the fact that it occurs in both species of Celtedens (McGowan, 2002) as well as in 7526 Albanerpeton pannonicum (Venczel & Gardner, 2005). Only A. inexpectatum shows state 1 7527 (Estes & Hoffstetter, 1976), if that reconstruction is even correct (Venczel & Gardner, 2005); 7528 1 is the state RC07 ascribed to Albanerpetidae as a whole. Unfortunately, no other 7529 albanerpetids preserve nasals. 7530 The state of this character is unknown in Adelospondylus, Adelogyrinus and 7531 Dolichopareias (Andrews & Carroll, 1991) and Leptoropha (Bulanov, 2003). 7532 7533 10. NAS 5: Narial margins of nasals parallel to each other and to the sagittal plane (0), at 7534 an angle (so that, if extended as straight lines, they would meet rostral to the snout) (1). 7535 The original wording, “Nasals broad plates delimiting most of the posterodorsal and me[d]ial 7536 margins of nostrils and with lateral margins diverging abruptly in their anterior portions: 7537 absent (0), present (1)”, describes a combination of three characters: the length/width ratio of 7538 the nasals (possibly correlated to the length-width ratio of the snout and thus probably to the 7539 nasal/frontal length ratio, NAS 2, as well as the nasal/parietal length ratio, NAS 6), the 7540 relative position of nasals and external nares (plausibly correlated to the position and shape of 7541 the nasal-premaxilla suture, PREMAX 1-2-3), and the character described here. 7542 This character is inapplicable when the nasal does not participate in the narial margin. 7543 This is the case in Acanthostega, Ichthyostega and *Aytonerpeton, where the anterior tectal 7544 intervenes, in Proterogyrinus (Holmes, 1984), which has a premaxilla-lacrimal suture instead, 7545 and possibly in Colosteus, Greererpeton and *Pholidogaster (Smithson, 1982; Hook, 1983; 7546 Bolt & Lombard, 2010; see above under TEC 1 – character 6), in which the narial region is 7547 poorly preserved and the premaxilla and the prefrontal or the anterior tectal may meet instead 7548 of the nasal and the naris. The state of this character is furthermore unknown in Westlothiana 7549 (Smithson et al., 1994), Tuditanus (CG78) and Lethiscus (Wellstead, 1982; Anderson, Carroll 7550 & Rowe, 2003). 7551 State 0 is found contrary to RC07 in Phonerpeton (D. M., pers. obs. of AMNH 7150 7552 and MCZ 2313), and Ptyonius (Bossy & Milner, 1998). We also assign state 0 to 7553 Phlegethontia (Anderson, 2007a), where the margins form an extremely small angle, to 7554 *Nigerpeton, where in the best-preserved snout (Sidor, 2013) the left nasal only contributes to 7555 the rostral margin of the naris, while the right naris forms a symmetric mediolateral notch in 7556 the right nasal. 7557 State 1 is almost ubiquitous, being found in Crassigyrinus (Clack, 1998), Whatcheeria 7558 (Bolt & Lombard, 2000), Baphetes (adult) and Megalocephalus (Beaumont, 1977), Eucritta 7559 (Clack, 2001), Chenoprosopus (Langston, 1953), Isodectes (Sequeira, 1998), Trimerorhachis 7560 (Milner & Schoch, 2013), Dendrerpetidae (Holmes, Carroll & Reisz, 1998), Eryops (Sawin,

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7561 1941), Broiliellus (Carroll, 1964; Schoch, 2012), Eoscopus (Daly, 1994), Micromelerpeton 7562 (though the least paedomorphic morphotype is somewhat borderline: Boy, 1995), 7563 Albanerpetidae (Venczel & Gardner, 2005), Eocaecilia (Jenkins, Walsh & Carroll, 2007), 7564 Caerorhachis (Ruta, Milner & Coates, 2002), Eoherpeton (though this is not entirely clear: 7565 Panchen, 1975; Smithson, 1985), Archeria (Holmes, 1989), Pholiderpeton attheyi (Panchen, 7566 1972), Anthracosaurus (Clack, 1987a), Pholiderpeton scutigerum (Clack, 1987b), 7567 Bruktererpeton (Boy & Bandel, 1973: pl. 8), Gephyrostegus (Carroll, 1970; Klembara et al., 7568 2014), Solenodonsaurus (Danto, Witzmann & Müller, 2012: fig. 8A), Kotlassia (Bulanov, 7569 2003: S53, S54), Discosauriscus, Ariekanerpeton, Microphon and Utegenia (Bulanov, 2003, 7570 2014; Klembara & Ruta, 2004a, 2005a), Diadectes (Berman, Sumida & Lombard, 1992; 7571 Berman, Sumida & Martens, 1998), Limnoscelis (Fracasso, 1983; Berman, Reisz & Scott, 7572 2010), Captorhinus (Fox & Bowman, 1966; Heaton, 1979), Paleothyris (perhaps a bit 7573 borderline; Carroll, 1969a), Petrolacosaurus (Reisz, 1981), Batropetes (Carroll, 1991; 7574 Glienke, 2013), Pantylus, Asaphestera, Saxonerpeton, Hapsidopareion, Micraroter, 7575 Pelodosotis, Rhynchonkos, Cardiocephalus, Euryodus, Microbrachis, Hyloplesion and 7576 Odonterpeton (CG78; Vallin & Laurin, 2004; Szostakiwskyj, Pardo & Anderson, 2015), 7577 Stegotretus (Berman, Eberth & Brinkman, 1988), Brachydectes (Wellstead, 1991; Pardo & 7578 Anderson, 2016), Acherontiscus (Carroll, 1969b), Adelogyrinus and Dolichopareias 7579 (Andrews & Carroll, 1991), Batrachiderpeton (Bossy & Milner, 1998), Diceratosaurus 7580 (Jaekel, 1903; A. C. Milner, 1980; Bossy & Milner, 1998), Oestocephalus (Carroll, 1998a), 7581 Capetus (Sequeira & Milner, 1993), apparently Orobates (Berman et al., 2004), Pederpes 7582 (Clack & Finney, 2005), Silvanerpeton (Ruta & Clack, 2006), and Tseajaia (Moss, 1972; 7583 Berman, Sumida & Lombard, 1992). 7584 7585 11. NAS 6: Parietal/nasal length ratio less than (0) or greater than 1.45 (1). 7586 State 1 is known to occur in Panderichthys (no matter which of the candidates are in 7587 fact the nasals: Clack, 2007), Trimerorhachis (Milner & Schoch, 2013), Amphibamus (Milner, 7588 1982; Schoch & Milner, 2014), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Karaurus 7589 (Ivachnenko, 1978), Batropetes (Glienke, 2013), Asaphestera, Saxonerpeton, Cardiocephalus 7590 and Euryodus (CG78), and Brachydectes (Wellstead, 1991; Pardo & Anderson, 2016). 7591 Bulanov (2003: fig. 30) further reconstructed state 1 for Kotlassia; judging from the text (p. 7592 S53), this appears to be correct. 7593 Westlothiana is polymorphic: it shows state 1 on the left and (as scored by RC07) state 7594 0 on the right side of the type specimen (Smithson et al., 1994). Discosauriscus pulcherrimus 7595 has state 0 as scored by RC07 (Klembara, 1997: fig. 33), while D. austriacus has state 1 7596 (Klembara, 1997: fig. 27; Klembara et al., 2006: fig. 4C); we have accordingly scored 7597 polymorphism for Discosauriscus. 7598 Unknown in Stegotretus (Berman, Eberth & Brinkman, 1988), Acherontiscus (Carroll, 7599 1969b), Adelospondylus, Adelogyrinus and Dolichopareias (Andrews & Carroll, 1991); 7600 inapplicable to Phlegethontia, where the parietals are absent (Anderson, 2002, 2007a). 7601 Unknown and likely borderline in *Pholidogaster (Panchen, 1975). 7602 7603 12. PREFRO 1: Separately ossified prefrontal: present (0); absent (1). 7604 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994); we follow 7605 Ascarrunz et al. (2016) in also scoring it for Triadobatrachus. 7606 In *Palaeoherpeton the sutures between the prefrontal, lacrimal and jugal have not 7607 been traced (Panchen, 1964); given the sutures to the postfrontal and the quadratojugal, we 7608 presume that if any of these bones was absent, that was the lacrimal (LAC 1(?)), so we have 7609 scored state 0 of the present character and also of PREFRO 7 while leaving the other 7610 PREFRO characters as unknown.

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7611 Similarly, the region where the suture between prefrontal and lacrimal would be 7612 expected is not preserved in *Neopteroplax (Romer, 1963: fig. 1); we have again concluded 7613 that the presence of the lacrimal is unknown. Even so, however, *Neopteroplax has PREFRO 7614 2(0). 7615 We have scored *Aytonerpeton as unknown because the supplementary video of Clack 7616 et al. (2016) hints that the supposed nasal may be composed of the nasal and the prefrontal. 7617 7618 13. PREFRO 2: Prefrontal less than (0) or more than (1) three times longer than wide 7619 […] in dorsal aspect. 7620 State 0 is present in Ventastega (Ahlberg et al., 2008). 7621 Colosteus has state 0 regardless of how the prefrontal is reconstructed (Hook, 1983; 7622 Bolt & Lombard, 2010). Greererpeton, however, does just reach state 1 even if a large 7623 anterior tectal is assumed, so that it was scored correctly in RC07 in any case (Bolt & 7624 Lombard, 2010). 7625 If the prefrontal is correctly identified as such, Triadobatrachus must share state 0 7626 (Ascarrunz et al., 2016: fig. 12). 7627 State 1 is found in Acanthostega (Porro, Rayfield & Clack, 2015), Eocaecilia (Jenkins, 7628 Walsh & Carroll, 2007), Gephyrostegus (Klembara et al., 2014) and Solenodonsaurus (Danto, 7629 Witzmann & Müller, 2012) as well as in Glienke’s (2013, possibly also 2015) reconstructions 7630 of Batropetes. 7631 The adult specimen of Baphetes orientalis has state 0 on the left but state 1 on the 7632 right side (Beaumont, 1977: fig. 25), making Baphetes polymorphic. 7633 Albanerpeton pannonicum, the only albanerpetid that can be scored with confidence, 7634 just barely reaches state 1 (Venczel & Gardner, 2005), so we ascribe this state to 7635 Albanerpetidae as a whole. 7636 Unknown in Lethiscus due to insufficient preservation (Pardo et al., 2017). 7637 *Beiyanerpeton is always close to the cutoff point, but at least one specimen has state 7638 0 on the left and state 1 on the right side (Gao & Shubin, 2012: fig. 2); we have scored it as 7639 polymorphic. 7640 *Australerpeton is polymorphic, sometimes within an individual (Eltink et al., 2016: 7641 fig. 2–5). 7642 We have assigned state 1 to *Quasicaecilia by measuring along the curve formed by 7643 the orbit (Pardo, Szostakiwskyj & Anderson, 2015: fig. 3A). In strict rostrocaudal terms, the 7644 prefrontal is about as long as it could be without extending dorsal to the nostril, and it is not as 7645 short as it could be. 7646 The stippled lines in Anderson (2003a: fig. 3A) are justified by Pardo et al. (2017: ext. 7647 data fig. 4, video) to the extent of making state 1 very probable for *Coloraderpeton. 7648 7649 14. PREFRO 3: Antorbital portion of prefrontal forming near-equilateral triangular 7650 lamina: absent (0); present (1). State 0, which unites a wide range of different states, may 7651 have to be split to reveal more phylogenetic signal. 7652 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and 7653 Solenodonsaurus (Danto, Witzmann & Müller, 2012) as well as in the most mature specimens 7654 of Micromelerpeton (Schoch, 2009b: fig. 2b). 7655 State 1 is documented in Ichthyostega (a larger version perhaps: Clack & Milner, 7656 2015: fig. 8), Balanerpeton (arguably: Milner & Sequeira, 1994), Phonerpeton (Dilkes, 1990; 7657 D. M., pers. obs. of AMNH 7150 and MCZ 2313), Kotlassia (Bulanov, 2003: fig. 30), 7658 Discosauriscus (both species, though sometimes borderline: Klembara, 1997), and 7659 Ariekanerpeton (Klembara & Ruta, 2005a), and makes a surprise appearance in Lethiscus 7660 (Pardo et al., 2017: extended data fig. 1a, b, 3b).

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7661 Baphetes is best scored as unknown because of its antorbital fenestrae. Even so, 7662 however, the shape of the rostral end of the prefrontal only allows state 0 in Megalocephalus 7663 (Beaumont, 1977) and *Spathicephalus (Smithson et al., 2017: fig. 3C). 7664 Eucritta is polymorphic, sometimes within the same individual (Clack, 2001: fig. 6). 7665 The condition is unknown in Valdotriton (Evans & Milner, 1996), Westlothiana 7666 (Smithson et al., 1994) and Tseajaia (Moss, 1972; Berman, Sumida & Lombard, 1992). 7667 *Acanthostomatops is polymorphic, sometimes within the same individual (Witzmann 7668 & Schoch, 2006a). This may be at least partly ontogenetic, in that state 0 is only found in 7669 large individuals, but these same individuals are sometimes polymorphic. 7670 7671 deleted PREFRO 6: Prefrontal/premaxilla suture: absent (0); present (1). 7672 State 0 is present in Ventastega (Ahlberg et al., 2008). 7673 Unknown in Colosteus and Greererpeton (Bolt & Lombard, 2010; see above under 7674 TEC 1 – character 6) as well as Adelospondylus (Andrews & Carroll, 1991). We have also 7675 scored Diplocaulus as unknown, because it lacks nasals (see NAS 1 above) that would 7676 separate the prefrontals from the premaxillae – just like Diploceraspis, which was already 7677 scored as unknown. 7678 State 1 is possibly present in Albanerpeton inexpectatum, but absent in A. pannonicum 7679 and in Celtedens (Venczel & Gardner, 2005). According to Gardner, Evans & Sigogneau- 7680 Russell (2003), Albanerpeton and Celtedens are sister-groups; the condition in the sister- 7681 group to the clade formed by both, Anoualerpeton, is unknown. We consequently infer that 7682 state 0 is the plesiomorphy for Albanerpetidae and have scored Albanerpetidae as possessing 7683 state 0. 7684 This reduces the distribution of state 1 to Acherontiscus, which is very fragmentarily 7685 preserved (Carroll, 1969b); even accepting that Acherontiscus has state 1, the character is 7686 parsimony-uninformative in the original taxon sample, so we have deleted it. This also 7687 relieves us from worrying about correlation with PREFRO 8 (see below) – PREFRO 6(1) is 7688 probably impossible without PREFRO 8(2) (which is unknown but likely in Acherontiscus). 7689 State 1 is unambiguously present in *Utaherpeton (Carroll, Bybee & Tidwell, 1991), 7690 but, given the uncertainty in Acherontiscus, we have not reintroduced this character for the 7691 analysis with added taxa, either as a character or as an additional state of PREFRO 8 (which 7692 would then need a stepmatrix). 7693 7694 15. PREFRO 7: Prefrontal without (0) or with (1) stout, lateral outgrowth. 7695 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), 7696 Triadobatrachus (Ascarrunz et al., 2016: fig. 4, 12) and Diploceraspis (Beerbower, 1963). 7697 State 1 is not limited to baphetids – Karaurus possesses a very clear case of it 7698 (Ivachnenko, 1978; D. M. and M. L., pers. obs. of unnumbered MNHN cast of PIN 2585/2), 7699 and Acanthostega has a small version (Porro, Rayfield & Clack, 2015). 7700 We have scored *Spathicephalus as polymorphic, although it is conceivable that the 7701 observed distribution (S. mirus: 0; S. marsdeni: 1) is ontogenetic because the only known 7702 specimen of S. marsdeni is half the size of that of S. mirus (Smithson et al., 2017). 7703 7704 16. PREFRO 8: Caudal margin of external naris, including anterior tectal and 7705 septomaxilla, formed by lacrimal/nasal contact (0) or maxilla/nasal contact (excluding 7706 the lacrimal from the margin) (1); prefrontal entering nostril margin (2) (unordered). 7707 The original wording was: “Prefrontal entering nostril margin: no (0); yes (1).” Now that we 7708 have split state 0 to make explicit which conditions it represents, this character makes use of 7709 the phylogenetic signal in the difference between the new states 0 and 1. We count the 7710 anterior tectal and the septomaxilla as part of the naris even if the latter lies entirely on the

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7711 skull surface (as the former always does); this way, correlation with TEC 1 and SPTMAX 2 7712 can be avoided. 7713 State 0 is present in Ventastega (Ahlberg et al., 2008) and Micraroter (CG78). 7714 State 1 is rare outside of stereospondylomorphs (*Sclerocephalus, *Cheliderpeton, 7715 *Archegosaurus, *Konzhukovia, *Lydekkerina [polymorphic, see below], *Glanochthon, 7716 *Platyoposaurus, *Australerpeton), but occurs in other particularly long-snouted animals, 7717 namely Megalocephalus (Beaumont, 1977), Chenoprosopus (Hook, 1993; Reisz, Berman & 7718 Henrici, 2005), Neldasaurus (Chase, 1965; Boy, 1993; Milner & Schoch, 2013), 7719 Pholiderpeton attheyi (Panchen, 1972), *Nigerpeton (Steyer et al., 2006) and probably 7720 *Saharastega (unless the lacrimal had a quite unusual shape: Damiani et al., 2006; D. M., 7721 pers. obs. of MNN MOR 73). However, state 1 is also found in the distinctly short-snouted 7722 Microphon gracilis (even though M. exiguus and M. arcanus retain state 0, so that we have 7723 scored Microphon as polymorphic; Bulanov, 2003); outside the present taxon sample, it is 7724 shared by many short-snouted amniotes, and the snout of *Sclerocephalus is not all that long 7725 either. 7726 We have kept state 2 for Acheloma, Phonerpeton and Ecolsonia (and also scored it for 7727 *Mordex); however, an indeterminate juvenile trematopid (Dilkes, 1993: fig. 4) shows state 0 7728 instead. This implies that the naris only reached the prefrontal later during its allometric 7729 growth (NOS 3(2)), which in turn suggests that the OTUs with NOS 3(2) should be scored as 7730 unknown for the present character; in *Mordex, however, state 2 is already seen in an aquatic 7731 larva (Werneburg, 2012b: fig. 14d). 7732 Unknown in Colosteus; Greererpeton (like *Pholidogaster) has state 0 or 2 (Bolt & 7733 Lombard, 2010; see above under TEC 1 – character 6). Pholiderpeton scutigerum has state 0 7734 or 1. 7735 In Eocaecilia (Jenkins, Walsh & Carroll, 2007), Diploceraspis (Beerbower, 1963), and 7736 Phlegethontia (Anderson, 2002), the lacrimal is absent, but the prefrontal is present. We have 7737 scored them as possessing the observed state 2 or the impossible state 0 – state 1 would be 7738 possible but is not observed. The presence of a lacrimal is unknown in Valdotriton, but we 7739 have scored it the same way because the prefrontal does appear to have reached the naris, and 7740 the maxilla would have needed an extremely tall process to reach the nasal (Evans & Milner, 7741 1996: compare p. 632 to fig. 6b). 7742 The lacrimal is likewise absent and the prefrontal present in *Chelotriton; we have 7743 scored it as possessing the observed state 1 or the impossible state 0. 7744 Glienke (2013) stated that Batropetes fritschi and B. niederkirchensis have state 2, and 7745 reconstructed both of them accordingly (if only in stippled lines for B. fritschi). Glienke 7746 (2015: character 5) scored all four species as having state 2 – but stated (p. 7) and illustrated 7747 (fig. 1D) that B. palatinus just barely has state 0, and made clear (p. 15) that neither the 7748 prefrontal nor the lacrimal of B. appelensis are well enough known to rule out any of the three 7749 states. Glienke (2015) found B. appelensis to be the sister-group of the other three species 7750 together, and B. palatinus as the closest relative of B. fritschi; consequently, the 7751 plesiomorphic state of Batropetes cannot be determined without an outgroup, and we have 7752 scored Batropetes as possessing both state 0 and state 2. 7753 A rather clear case of state 2 occurs in Lethiscus (Pardo et al., 2017: especially 7754 extended data figure 3b). 7755 *Lydekkerina has states 0 and 1 (Jeannot, Damiani & Rubidge, 2006). 7756 We have scored state 0 or 2 for *Aytonerpeton. 7757 Incidentally, as for a few other characters (see below), RC07: 94 claimed that this 7758 character “shows no clear phylogenetic pattern”. Yet, the distribution of its states is far from 7759 chaotic. According to Analysis R4, state 2 is an autapomorphy of Holospondyli (reversed in 7760 Lethiscus, Batropetes palatinus, *Quasicaecilia and the Batrachiderpeton-Diplocaulus-

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7761 Diploceraspis clade, as well as Lissamphibia in those trees where it lies within Holospondyli); 7762 a synapomorphy of *Mordex, Acheloma, Phonerpeton, and Ecolsonia, reversed in the clade of 7763 all other dissorophoids; and a synapomorphy of Isodectes and *Erpetosaurus (reversed in 7764 Trimerorhachis). Clearly isolated occurrences of state 2 are limited to Crassigyrinus and 7765 Karaurus. In total, there are only 11–12 transitions to or from state 2 for 150 OTUs. 7766 7767 deleted PREFRO 9: Prefrontal/maxilla suture rostral to lacrimal: absent (0); present (1). 7768 The original wording did not distinguish a suture rostral to the lacrimal from a suture caudal 7769 to it; the latter condition is covered by LAC 2, see below. 7770 State 0 is present in Ventastega (Ahlberg et al., 2008). 7771 Unknown in Colosteus and Greererpeton (Bolt & Lombard, 2010) as well as 7772 Adelospondylus and Dolichopareias (Andrews & Carroll, 1991). 7773 This character is inapplicable when the lacrimal is absent (LAC 1(1) below) or 7774 unknown; this is the case in Eocaecilia (Jenkins, Walsh & Carroll, 2007) and Valdotriton 7775 (Evans & Milner, 1996). 7776 The redefinition further confers state 0 on Karaurus (Ivachnenko, 1978) and 7777 Diplocaulus (Bossy & Milner, 1998). 7778 This leaves state 1 solely to, probably, Adelogyrinus (Andrews & Carroll, 1991). The 7779 character is therefore parsimony-uninformative; we have accordingly deleted it. 7780 7781 17. PREFRO 10: Prefrontal contributes to more (0) or less than (1) half of orbit 7782 anterome[d]ial margin. We interpret “anteromesial margin” as the rostromedial/rostrodorsal 7783 quarter of the orbit margin; state 1 means that less than half of this quarter is contributed by 7784 the prefrontal. This character has to be scored as unknown for all baphetoids except Eucritta 7785 because the antorbital fenestra occupies at least the other half of this quarter. 7786 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Ecolsonia 7787 (Berman, Reisz & Eberth, 1985), Amphibamus (Milner, 1982: fig. 3a; Daly, 1994: fig. 18), 7788 Platyrhinops (Clack & Milner, 2010), Schoenfelderpeton (Boy, 1987), Eocaecilia (Jenkins, 7789 Walsh & Carroll, 2007), Karaurus (Ivakhnenko, 1978) and Urocordylus (Bossy & Milner, 7790 1998). 7791 State 1 is found in Ichthyostega (Clack & Milner, 2015), Greererpeton (Smithson, 7792 1982), Proterogyrinus (Holmes, 1984), Westlothiana (Smithson et al., 1994), Micraroter and 7793 Hyloplesion (CG78) and Diploceraspis (Beerbower, 1963). It also appears to be reached in 7794 *Spathicephalus (Smithson et al., 2017: fig. 3C). 7795 Apateon is polymorphic, sometimes within the same individual (Schoch & Milner, 7796 2008; Fröbisch & Schoch, 2009b). So is Diplocaulus (Bossy & Milner, 1998). 7797 Unknown or borderline in Eoscopus (appears to be exactly borderline: Daly, 1994: fig. 7798 3), Micromelerpeton (Schoch, 2009b: fig. 2b), Leptorophus (Boy, 1987), Valdotriton (Evans 7799 & Milner, 1996), Pholiderpeton scutigerum (Clack, 1987b), Bruktererpeton (Boy & Bandel, 7800 1973), Lethiscus (reconstructed as borderline: J. Pardo, pers. comm.; Pardo et al., 2017: ext. 7801 data fig. 3b, c, suggest state 0, but may not be in strict lateral view) and *Nigerpeton (state 1 7802 cannot be excluded: D. M., pers. obs. of MNN MOR 70). 7803 7804 18. LAC 1: Separately ossified lacrimal: present (0); absent (1). 7805 Eocaecilia has state 1 (Jenkins, Walsh & Carroll, 2007), as does Diploceraspis 7806 (Beerbower, 1963). 7807 The condition in Valdotriton (Evans & Milner, 1996) and Westlothiana (Smithson et 7808 al., 1994) is unknown. 7809

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7810 19. LAC 2: Contact between lacrimal and orbit (0); prefrontal contacts jugal or maxilla 7811 at its orbital margin (1). We have added a mention of the maxilla to state 1 so that Karaurus, 7812 which lacks jugals, can be scored (as having state 1). 7813 This character is inapplicable when the lacrimal is missing, e.g. in Eocaecilia (see 7814 LAC 1 above). It is further inapplicable when the orbit has a large rostroventral extension that 7815 separates the jugal from the prefrontal, in other words, in OTUs with state ORB 3/LAC 5(2) – 7816 the baphetoids. Similarly, we have scored Isodectes and Micromelerpeton as unknown, where 7817 the lateral exposure of the palatine (state MAX 5/PAL 5(2)) is so long as to reach the 7818 prefrontal, excluding the lacrimal from the orbit margin entirely (Sequeira, 1998; Schoch, 7819 2009b: fig. 2b). 7820 State 0 is now known in Ossinodus (Warren, 2007) and appears to be preserved in 7821 Kotlassia (Bulanov, 2003: fig. 30). 7822 The condition is unknown in Proterogyrinus (Holmes, 1984) as well as in 7823 Adelospondylus, Adelogyrinus and Dolichopareias (Andrews & Carroll, 1991). 7824 Crassigyrinus has both states, sometimes within the same individual (Clack, 1998). 7825 7826 20. LAC 4: Lacrimal without (0) or with (1) dorsome[d]ial digitiform process. Because 7827 this process lies at the orbit margin, state 1 is impossible when the lacrimal does not 7828 participate in the orbit margin; we have accordingly scored this character as unknown in all 7829 taxa that have or may have state LAC 2(1), as well as in all baphetoids due to their antorbital 7830 emargination. 7831 We have further scored Tseajaia as unknown (Moss, 1972; Berman, Sumida & 7832 Lombard, 1992; D. M., pers. obs. of CM 38033). 7833 State 0 is now known in Brachydectes (Pardo & Anderson, 2016) and Ossinodus 7834 (Warren, 2007) and appears to be preserved in Kotlassia (Bulanov, 2003: fig. 30). 7835 State 1 is documented in Albanerpetidae (Venczel & Gardner, 2005), Pelodosotis 7836 (CG78) and probably borderline in Microbrachis (Vallin & Laurin, 2004). 7837 Colosteus (Hook, 1983) is polymorphic. So is Trimerorhachis, where T. insignis has 7838 state 1 but the other species all have state 0 (Milner & Schoch, 2013); this potentially 7839 contradicts the finding by Milner & Schoch (2013) that T. insignis lacks autapomorphies. 7840 7841 LAC 5 is merged with ORB 3, see below. 7842 7843 deleted LAC 6: Portion of lacrimal lying anteroventral to orbit abbreviated: absent (0); 7844 present (1). RC07 explained this character as follows: “In several lepospondyls (as well as in 7845 some temnospondyls), the antorbital part of the lacrimal is considerably foreshortened, 7846 regardless of relative snout proportions[,] and barely extends for one fourth of its total length 7847 anteroventral to the orbit.” 7848 Despite this statement, and a similar one by Ruta, Coates & Quicke (2003: 307) which 7849 names several lepospondyls as having state 1, state 0 is instead present in all “lepospondyls”, 7850 including Acherontiscus and the adelogyrinids, according to all sources. Usually the entire 7851 lacrimal lies rostral to the orbit; even in small, large-eyed animals like Doleserpeton 7852 (Sigurdsen & Bolt, 2010), Batropetes (Carroll, 1991; Glienke, 2013, 2015), Microbrachis 7853 (Vallin & Laurin, 2004) and the urocordylids (Bossy, 1976), more than half of it does. With 7854 state 0 occurring even in Acheloma (Bolt, 1974; Dilkes & Reisz, 1987; arguably Olson, 1941) 7855 and Phonerpeton (Dilkes, 1990, 1993; D. M., pers. obs. of USNM 437796 and MCZ 2313), 7856 state 1 does not occur in this matrix at all; this makes the character parsimony- 7857 uninformative, so we have deleted it. 7858 In the future, this character could be made informative by redefining it to describe how 7859 much of the ventral margin of the orbit the lacrimal forms, that is, how far the lacrimal

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7860 extends caudally rather than rostrally to the rostral margin of the orbit. If redefined in such a 7861 way, however, this character would have to be merged with MAX 5/PAL 5 (see below). 7862 7863 21. MAX 3-9: Caudal end of maxilla lying caudal to caudal margin of orbit (0), between 7864 caudal margin of orbit and caudal margin of vomer (1), at the same level as the caudal 7865 end of the vomer or rostral to it (2) (ordered). This character is ordered because potentially 7866 continuous characters should be ordered (Wiens, 2001; Grand et al., 2013). 7867 RC07 used two separate characters, MAX 3 having the caudal margin of the orbit and 7868 MAX 9 the caudal margin of the vomer as the threshold. We have merged them because half 7869 of the states of these characters predicted each other – except in Brachydectes (see below), the 7870 vomer never extends caudal to the orbit, which means that MAX 3(0) predicted MAX 9(0), 7871 while MAX 9(1) required MAX 3(1). 7872 State 0 occurs in Cochleosaurus (Sequeira, 2004), Eocaecilia (Jenkins, Walsh & 7873 Carroll, 2007), Bruktererpeton (Boy & Bandel, 1973), Gephyrostegus (most likely: Klembara 7874 et al., 2014) and Lethiscus (Pardo et al., 2017). We have also scored it for Triadobatrachus: 7875 although the caudal ends of the preserved fragments of the maxillae lie rostral of the caudal 7876 ends of the orbitotemporal fenestrae, they lie well caudal of the caudal margins of the largest 7877 possible eyes that would fit into the fenestrae (Ascarrunz et al., 2016: fig. 4, 12, 3D model 1). 7878 State 1 is seen in Batropetes (Glienke, 2013, 2015) and most likely Solenodonsaurus 7879 (Danto, Witzmann & Müller, 2012). We have also scored it for Brachydectes where the 7880 caudal ends of orbit and maxilla variably coincide or nearly so (apparently independently of 7881 ontogeny – J. Pardo, pers. comm. – so that fig. 4A and 4C of Pardo & Anderson, 2016, 7882 represent different individuals), while the vomer has unusual caudal processes that extend 7883 farther caudal than both the orbit and the maxilla (Pardo & Anderson, 2016: fig. 4C). 7884 Westlothiana has states 0 or 1 (Smithson et al., 1994). The same is the best score for 7885 Albanerpetidae (Venczel & Gardner, 2005: fig. 4, 8) and *Saharastega (D. M., pers. obs. of 7886 MNN MOR 73). In several specimens of *Liaobatrachus, however, the eyes themselves are 7887 preserved (Dong et al., 2013), so that its orbitotemporal fenestra does not prevent us from 7888 scoring state 0. 7889 The maxillae of *Quasicaecilia are unknown. State 0 is nonetheless ruled out by the 7890 fact that the jaw articulation lay well rostral of the caudal margin of the orbit; we have scored 7891 state 1 or 2. 7892 7893 22. MAX 5/PAL 5: Ventral margin of the orbit formed by: lacrimal-jugal, prefrontal- 7894 jugal or lacrimal-postorbital suture (0); maxilla (1); lateral exposure of the palatine (2) 7895 (unordered). This is another merger of two characters that partly predicted each other. State 0 7896 includes cases where the mentioned suture is rostroventral to the orbit, so that the entire 7897 ventral margin is formed by the jugal alone. It also includes the unique condition of 7898 Trimerorhachis (excluding ?T. sandovalensis), where the jugal (let alone the maxilla and the 7899 palatine) is excluded from the orbit margin by a long lacrimal-postorbital suture (Milner & 7900 Schoch, 2013); making this condition a state of its own would be pointless, because it is 7901 unique, and would necessitate a stepmatrix for this character, so we have kept the score of 0 7902 for Trimerorhachis. 7903 When the jugal is absent (see JUG 1 below: Triadobatrachus, Brachydectes, 7904 *Beiyanerpeton), state 0 and 1 cannot be distinguished; when the palatine is absent (see VOM 7905 5-10/PAL 8/PTE 10-12-18/INT VAC 1 below: Oestocephalus; Phlegethontia as already 7906 scored by RC07), states 1 and 2 cannot be distinguished; when both are absent (Karaurus, 7907 Valdotriton, Notobatrachus, ?Vieraella, *Liaobatrachus, *Pangerpeton, *Chelotriton), this 7908 character is entirely inapplicable.

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7909 Apateon was scored as showing state 1 in RC07, but acquired state 2 after 7910 metamorphosis, judging from the one known adult specimen of A. gracilis (Schoch & 7911 Fröbisch, 2006); we have scored state 2. Schoenfelderpeton was given state 1 or 2 by RC07; 7912 we have scored it (and also *Tungussogyrinus) as unknown because the jugal does not (yet) 7913 extend to the region ventral to the orbit in the first place in the known specimens. 7914 Among albanerpetids, only Albanerpeton pannonicum can be scored with confidence; 7915 it shows state 0. The dorsal margin of the maxilla is similar enough in all albanerpetids that 7916 Venczel & Gardner (2005) consider it likely that the same state prevailed throughout 7917 Albanerpetidae. 7918 State 0 further occurs in Ossinodus (Warren, 2007). 7919 Rhynchonkos has state 1 (Szostakiwskyj, Pardo & Anderson, 2015). 7920 Sigurdsen & Green (2011: appendix 2) stated that this character was unknown in 7921 Amphibamus; Schoch & Milner (2014: fig. 30A), however, showed state 2 in a new 7922 reconstruction based in part on Schoch’s personal observations. We have therefore tentatively 7923 scored state 2. 7924 Acheloma dunni is a special case, in that (Polley & Reisz, 2011) the palatine and the 7925 ectopterygoid are exposed laterally (like in state 2) but do not participate in the orbit margin, 7926 being separated from the latter by a very long lacrimal-jugal suture (state 0). We have kept its 7927 score of 0, not least because A. cumminsi lacks a lateral exposure of the palatine altogether 7928 (Polley & Reisz, 2011), but caution that this may be ontogeny- or size-related: perhaps, as the 7929 orbit shrinks in relation to the rest of the skull, state 2 would generally turn into state 0 and 7930 leave such a lateral exposure of the palatine that does not participate in the orbit margin. This 7931 idea may be supported by the fact that in Phonerpeton (already scored as polymorphic), 7932 AMNH 7150 shows state 2 on the left side but possibly reaches state 0 on the right (Dilkes, 7933 1990: fig. 3; D. M., pers. obs.). 7934 *Caseasauria has states 0 and 1 (Eothyris has state 1, Oedaleops has state 0, and the 7935 condition in Eocasea is unknown: Reisz, Godfrey & Scott, 2009; Reisz & Fröbisch, 2014). 7936 7937 23. MAX 6: Maxillary arcade closed (0) or open (1) posteriorly. In state 1, the orbit is open 7938 (caudo)ventrally; (caudo)ventrally open temporal fenestrae as in Oestocephalus and most 7939 likely *Coloraderpeton do not prevent state 0. 7940 State 0 appears to be preserved in Kotlassia (Bulanov, 2003: fig. 30). 7941 Schoenfelderpeton is now scored as unknown (like *Tungussogyrinus), because the 7942 observed condition (state 1) is likely due to paedomorphosis, if not indeed larval age of the 7943 known individuals. This is based on the ontogeny of its close relative Apateon. 7944 Brachydectes, in contrast, is now scored as possessing state 1; from what is known of 7945 the ontogeny of this “lepospondyl”, there is no evidence it would ever have reached state 0 7946 (Pardo & Anderson, 2016). The jugal and the quadratojugal bones are lacking entirely (see 7947 JUG 1 and QUAJUG 1 below). 7948 Notobatrachus reigi has state 0 (Báez & Nicoli, 2008). As the jugal and the 7949 quadratojugal are absent in N. degiustoi (Báez & Nicoli, 2008), and the caudal end of the 7950 maxilla is not received by the palatine as it is in Brachydectes, we interpret the open maxillary 7951 arcade of N. degiustoi as inapplicable and have scored Notobatrachus as possessing state 0. 7952 Unknown in Triadobatrachus (all sources). 7953 7954 24. MAX 7: Dorsal margin of maxilla forming distinct dorsal ‘step’: no (0); yes (1). 7955 State 1 is not confined to pantylids – it occurs in Broiliellus (Carroll, 1964: fig. 9B) 7956 and Doleserpeton (Sigurdsen & Bolt, 2010) as well as some but not all specimens of 7957 *Glanochthon (Schoch & Witzmann, 2009b). Surprisingly, it is also found in *Pholidogaster 7958 (Panchen, 1975: fig. 15) and *Neopteroplax (Romer, 1963: fig. 4 – less well visible in fig. 1),

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7959 even though both have state MAX 8(0) and in the former the entire maxilla lies ventral to the 7960 nostril; these cases show that this character is independent from MAX 8. 7961 *Platyoposaurus shows a borderline condition (Gubin, 1991: drawing 3) that we have 7962 also counted as state 1. We have further counted the condition in *Erpetosaurus, where the 7963 nares lie so far dorsomedial that the maxillae, which have state MAX 8(0), have a long 7964 dorsomedial process to reach their ventrolateral margin (Milner & Sequeira, 2011). 7965 7966 25. MAX 8: Dorsal margin of maxilla: low compared to naris and/or septomaxilla (0); 7967 tall and rounded (1); distinct process (2) (unordered). The original wording mentions an 7968 “approximately rectangular flange”, which is called “subrectangular” in the next sentence; 7969 such a condition does not occur in the taxon sample (except arguably *Iberospondylus) – the 7970 dorsal process (if present) is always rounded and/or triangular to varying degrees. 7971 Furthermore, there were unambiguous mistakes in the scoring – Triadobatrachus was scored 7972 as possessing the (sub)rectangular process even though the whole region is unknown. Rather 7973 than jettisoning this character, we have coded the states that we see in the sampled taxa. The 7974 character is unordered because intermediates between 1 and 2 as well as directly between 0 7975 and 2 exist, see below. 7976 State 0: Eusthenopteron, Panderichthys and Acanthostega (Long & Gordon, 2004; 7977 Porro, Rayfield & Clack, 2015), Ventastega (Ahlberg, Lukševičs & Lebedev, 1994; Ahlberg 7978 et al., 2008), Ichthyostega (Ahlberg, Clack & Blom, 2005), Colosteus (Hook, 1983), 7979 Greererpeton (Smithson, 1982), Crassigyrinus (Clack, 1998), Whatcheeria (Lombard & Bolt, 7980 1995), Baphetes and Megalocephalus (Beaumont, 1977), Edops (Romer & Witter, 1942; D. 7981 M., pers. obs. of MCZ 1378), Chenoprosopus (Hook, 1993), Isodectes (Sequeira, 1998), 7982 Trimerorhachis (Case, 1935; Milner & Schoch, 2013), Balanerpeton (Milner & Sequeira, 7983 1994), Dendrerpetidae (A. R. Milner, 1980, 1996; Godfrey, Fiorillo & Carroll, 1987; Holmes, 7984 Carroll & Reisz, 1998), Eryops (Sawin, 1941), Acheloma (Bolt, 1974), Ecolsonia (Berman, 7985 Reisz & Eberth, 1985), Broiliellus (Carroll, 1964; Schoch, 2012), Eoscopus (Daly, 1994; 7986 Huttenlocker, Small & Pardo, 2007), Platyrhinops (Schoch, 2002: fig. 4), Micromelerpeton 7987 (Boy, 1995), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Caerorhachis (Ruta, Milner & 7988 Coates, 2002), Eoherpeton (Panchen, 1975; Smithson, 1985), Proterogyrinus (Holmes, 1984), 7989 Archeria (Holmes, 1989), Pholiderpeton attheyi (Panchen, 1972), Anthracosaurus (Panchen, 7990 1977), Pholiderpeton scutigerum (Clack, 1987b), Bruktererpeton (Boy & Bandel, 1973), 7991 Gephyrostegus (Brough & Brough, 1967), Solenodonsaurus (Laurin & Reisz, 1999), 7992 Kotlassia (Bulanov, 2003), Discosauriscus (Klembara, 1993, 1997; Klembara et al., 2006, 7993 2007), Seymouria (Laurin, 2000; Klembara et al., 2005), Diadectes (Berman, Sumida & 7994 Lombard, 1992; Berman, Sumida & Martens, 1998), Limnoscelis (Romer, 1946; Berman, 7995 Reisz & Scott, 2010), Captorhinus (Heaton, 1979), Paleothyris (Carroll, 1969a), 7996 Petrolacosaurus (Reisz, 1981), Westlothiana (Smithson et al., 1994), all “microsaurs” (CG78; 7997 Berman, Eberth & Brinkman, 1988; Caroll, 1991; Glienke, 2013, 2015; Szostakiwskyj, Pardo 7998 & Anderson, 2015) except Pantylus (which has state 2: Romer, 1969; CG78), Brachydectes 7999 (Wellstead, 1991; Pardo & Anderson, 2016), Acherontiscus (Carroll, 1969b), Dolichopareias 8000 (Andrews & Carroll, 1991), all “nectrideans” (Jaekel, 1903: pl. II; Moodie, 1912; Bossy & 8001 Milner, 1998; Milner & Ruta, 2009) except Diploceraspis (unknown because the skull is so 8002 flattened and it is not clear if maxilla and lacrimal are separate: Beerbower, 1963), Lethiscus 8003 (Pardo et al., 2017), Oestocephalus (Carroll, 1998a), Phlegethontia (Anderson, 2002), 8004 Ariekanerpeton (Laurin, 1996a; Klembara & Ruta, 2005a), Capetus (Sequeira & Milner, 8005 1993), Orobates (Berman et al., 2004), Pederpes (Clack & Finney, 2005), Silvanerpeton 8006 (Ruta & Clack, 2006), Tseajaia (Moss, 1972; D. M., pers. obs. of CM 38033) and Utegenia 8007 (Laurin, 1996b; Klembara & Ruta, 2004a).

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8008 State 1: Cochleosaurus (Sequeira, 2004: fig. 8A), Phonerpeton (Dilkes, 1990; D. M., 8009 pers. obs. of AMNH 7150 – counting the orbit and the lateral exposure of the palatine rather 8010 than the caudodorsal expansion of the naris), Karaurus (Ivachnenko, 1978), Leptoropha and 8011 Microphon (Bulanov, 2003), Ossinodus (Warren, 2007), arguably *Iberospondylus (Laurin & 8012 Soler-Gijón, 2006) and apparently *Mordex (Werneburg, 2012b: fig. 17b); a surprise 8013 appearance occurs in *Aytonerpeton (Clack et al., 2016: fig. 4 and especially supplementary 8014 video 2). 8015 State 2: Doleserpeton (Sigurdsen & Bolt, 2010), Apateon (Werneburg, 1991: fig. 2, 5), 8016 Leptorophus (somewhat uncertain: Boy, 1986), Schoenfelderpeton (Boy, 1986), 8017 Albanerpetidae where codable, though close to state 0 (unknown in Celtedens: McGowan, 8018 2002; unique condition in Anoualerpeton priscum: Gardner, Evans & Sigogneau-Russell, 8019 2003: fig. 3D1), Pantylus (Romer, 1969; CG78), Notobatrachus (like Albanerpetidae: Estes & 8020 Reig, 1973; Báez & Nicoli, 2004). 8021 Unknown: Eucritta (Clack, 2001 – the fossils are so crushed and split through the 8022 bone that the photo, the specimen drawing, the reconstruction, and the text do not really 8023 cooperate), Adelospondylus and Adelogyrinus (Andrews & Carroll, 1991). 8024 We have scored Neldasaurus as possessing state 0 or 1 because of its intermediate 8025 condition (Chase, 1965). Amphibamus is scored the same way based on Schoch (2001: fig. 4), 8026 because illustrations of its skull in lateral view do not seem to exist. Vieraella is likewise 8027 partially uncertain (Estes & Reig, 1973; Báez & Basso, 1996). 8028 Valdotriton has state 1 or 2 (“The maxillae bear facial processes of uncertain size”: 8029 Evans & Milner, 1996: 632). 8030 Because Eothyris has state 1 on the right and state 2 on the left side (Reisz, Godfrey & 8031 Scott, 2009; D. M., pers. obs. of MCZ 1161), we have scored polymorphism for *Caseasauria. 8032 All three states occur in *Glanochthon (Schoch & Witzmann, 2009b: fig. 2). 8033 8034 26. FRO 1: Frontal unpaired (0) or paired (1). 8035 State 0 is a very rare condition in this matrix. It is called 0 instead of 1 because RC07 8036 assigned it to the outgroup (Eusthenopteron), but the large unpaired bone in the “snout 8037 mosaic” is just one of several possibilities for homologues of the frontals. (It is reminiscent of 8038 the “pineal plate” of stem-gnathostomes.) Judging from the fontanelle of Ventastega (Ahlberg 8039 et al., 2008) and Acanthostega (Clack, 2003a; Porro, Rayfield & Clack, 2015), it is at least as 8040 probable that the large median bone disappeared and lacks a homologue in limbed vertebrates 8041 (except possibly the sporadic interfrontal/interfrontonasal, see IFN 1 below), while one of the 8042 bone pairs lateral to it is homologous to the frontals. We have accordingly scored 8043 Eusthenopteron as unknown. 8044 State 1 is present in Ventastega (Lukševičs, Ahlberg & Clack, 2003; Ahlberg et al., 8045 2008). 8046 8047 27. FRO 2: Frontals shorter than parietals (0), approximately equal in length (1), or 8048 longer than parietals (2) (ordered). We have exchanged states 1 and 2 to make it possible to 8049 order this continuous character. In part, it appears, RC07 had already done that in the matrix 8050 but not in the character list. 8051 State 1 or 2 is present in Ventastega (Ahlberg et al., 2008). We have also scored state 1 8052 or 2 for Crassigyrinus: state 1 is present in the reconstruction by Clack (1998), which has the 8053 postfrontals meeting each other between the frontals and the parietals – given the stippled 8054 lines and poor preservation of the skull surface, we do not feel confident about this. 8055 The frontals become longer in the ontogeny of Apateon; adults have state 2 as already 8056 scored (Schoch & Fröbisch, 2006). For this reason, we have scored Leptorophus as having 8057 state 1 or 2, and Schoenfelderpeton as unknown.

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8058 Neldasaurus (Chase, 1965, though arguably borderline), Broiliellus (Carroll, 1964; 8059 Schoch, 2012), Pantylus (Romer, 1969; CG78), Adelogyrinus (Andrews & Carroll, 1991), 8060 Diceratosaurus, Diplocaulus and Ptyonius (Bossy & Milner, 1998) and Diploceraspis 8061 (Beerbower, 1963) show state 0. 8062 State 1 is found in Trimerorhachis (Milner & Schoch, 2013), Micromelerpeton 8063 (Schoch, 2009b: fig. 2b) and Eocaecilia (Jenkins, Walsh & Carroll, 2007). 8064 Acanthostega (Clack, 2007; Porro, Rayfield & Clack, 2015), Ichthyostega (Clack & 8065 Milner, 2015: fig. 8), Saxonerpeton, Pelodosotis and Rhynchonkos (CG78; Szostakiwskyj, 8066 Pardo & Anderson, 2015: fig. 1), Sauropleura (Bossy, 1976, Bossy & Milner, 1998) and 8067 Lethiscus (Wellstead, 1982) show state 2. 8068 The condition of Pholiderpeton scutigerum (Clack, 1987b), Dolichopareias (Andrews 8069 & Carroll, 1991) and Ossinodus (Warren, 2007) is unknown. 8070 States 0 and 1 are reconstructed for different albanerpetids (Venczel & Gardner, 8071 2005); we have scored both states. Both also seem to occur in different species of Batropetes 8072 (Glienke, 2013, 2015), where neither is clearly plesiomorphic. 8073 States 1 and 2 are both found in Balanerpeton (left vs. right side: Milner & Sequeira, 8074 1994) and Platyrhinops (Clack & Milner, 2010) as well as *Mordex (usually left vs. right 8075 side: Werneburg, 2012b); in all of these cases we have scored polymorphism. 8076 Complete frontals and parietals are apparently seldom found in the same specimen of 8077 *Branchiosaurus; the largest ones where both seem to be preserved in full have state 1 8078 (Werneburg, 2012b). 8079 8080 28. FRO 4: Prefrontal/postfrontal suture (0); frontal contributes to orbit margin (1). 8081 State 0 was originally called “Frontal excluded from […] orbit margin”; we have defined it 8082 more precisely and scored the character as inapplicable when the pre- and/or the postfrontal is 8083 absent, which is the case in Albanerpetidae, Karaurus, Triadobatrachus, Valdotriton, 8084 Brachydectes, Notobatrachus and Vieraella in the original taxon sample. However, because 8085 the aïstopod “postorbital” may be an ontogenetic fusion product of postorbital and postfrontal 8086 (Anderson, Carroll & Rowe, 2003: fig. 9B), we have scored the aïstopods: Lethiscus has state 8087 1 (J. Pardo, pers. comm.; although the lateral process on the frontal mentioned by Pardo et al., 8088 2017, but absent from their figures, appears not to exist, the frontal has a long contribution to 8089 the orbit margin), Oestocephalus has state 0 as already scored (Anderson, 2003a), and 8090 Phlegethontia has state 1 (Anderson, 2002, 2007a). 8091 The condition is furthermore unknown in Pholiderpeton scutigerum (Clack, 1987b). 8092 Ventastega (Ahlberg et al., 2008) shows state 0, as does Asaphestera (CG78). 8093 Trimerorhachis is polymorphic (Milner & Schoch, 2013). 8094 Apateon dracyi has state 0; but because Schoch & Milner (2008) and Fröbisch & 8095 Schoch (2009b) found this to be an unambiguous reversal within Apateon, we have kept the 8096 score of 1 for Apateon. Among branchiosaurids, state 0 does occur in *Tungussogyrinus 8097 (Werneburg, 2009) and *Branchiosaurus (Schoch & Milner, 2008; Werneburg, 2012b). 8098 Klembara et al. (2014) have documented state 0 in Gephyrostegus. 8099 CG78 reconstructed state 1 in Saxonerpeton. It is not evident why they did so, 8100 however; the drawings of the specimens do not indicate either state, and the skull table is not 8101 mentioned in the text at all. We have kept its score as unknown. Similarly, we have changed 8102 the score of Odonterpeton to unknown because CG78 reconstructed state 0 on the left but 8103 state 1 on the right side, mentioned in the text that the right postfrontal is not preserved, and 8104 included a specimen drawing that does not clarify the situation. 8105 It is possible (Sumida, Pelletier & Berman, 2014) that Oedaleops is polymorphic, 8106 specifically that some specimens show state 0 rather than the state 1 preserved in others 8107 (Reisz, Godfrey & Scott, 2009; Sumida, Pelletier & Berman, 2014). For the time being, we

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8108 have ignored this and scored only state 1 for *Caseasauria; state 1 is seen in Eothyris (Reisz, 8109 Godfrey & Scott, 2009), and the condition in Eocasea is unknown. 8110 The smallest specimen of *Acanthostomatops probably has state 1, but all others 8111 clearly show state 0 (Witzmann & Schoch, 2006a), so we have scored Acanthostomatops as 8112 possessing state 0, even though this character does not show ontogenetic variation elsewhere. 8113 The holotype of *Konzhukovia vetusta is polymorphic, with the left side showing state 8114 0 and the right side state 1 (Gubin, 1991: drawing 6a). 8115 Like Brachydectes (see above), *Beiyanerpeton possesses prefrontals but lacks 8116 postfrontals; yet, the frontal does not contribute to the orbit margin, because the prefrontals 8117 contact processes of the parietals that look as if the postfrontals had fused to the parietals. 8118 This intriguing condition is common in extant salamanders, yet absent in Karaurus and, as far 8119 as known, all other Mesozoic salamanders except *Beiyanerpeton (character 61 of Gao & 8120 Shubin, 2012) – Valdotriton has the processes, but they may not have reached the prefrontals 8121 (Evans & Milner, 1996: fig. 6b); for this reason, and because it is restricted to a single OTU in 8122 the original taxon sample, we have refrained from coding this condition as a third state of the 8123 present character. *Beiyanerpeton is scored as unknown. 8124 One specimen of *Platyoposaurus has state 1 on the right side (Gubin, 1991: 34). We 8125 have counted this as polymorphism. 8126 8127 29. FRO 5: Coossified frontal and parietal (frontoparietal bone): absent (0); present (1). 8128 Ventastega has state 0 (Ahlberg et al., 2008). 8129 There is no evidence of a preserved frontal or a preserved rostral edge of a parietal in 8130 *Sparodus (D. M., pers. obs. of NHMW 1899/0003/0006); the “frontal” in the mirrored fig. 8131 1A of Carroll (1988) is the right prefrontal, as is already clear by comparison to the left side 8132 of the same figure. The most defensible score is therefore “?”, contra Carroll (1988). 8133 8134 30. FRO 6: Frontal anterior margin deeply wedged between nasal posterolateral margins 8135 for at least 1/3 of the length of the nasals: absent (0); present (1). We interpret state 1 as 8136 meaning that both frontals together form such a wedge. 8137 Ventastega has state 0 (Ahlberg et al., 2008), as do Adelospondylus, Adelogyrinus and 8138 Dolichopareias (Andrews & Carroll, 1991) and Lethiscus (Pardo et al., 2017). Although 8139 Limnoscelis has a conspicuous wedge, it has state 0 as well (Berman, Reisz & Scott, 2010: 8140 fig. 3); Gephyrostegus, too, does not reach state 1 (Klembara et al., 2014). 8141 State 1 is found in Acanthostega (Porro, Rayfield & Clack, 2015), Albanerpetidae 8142 (Venczel & Gardner, 2005) and Phlegethontia (Anderson, 2007a). 8143 Danto, Witzmann & Müller (2012) followed RC07 in scoring Solenodonsaurus as 8144 possessing state 1, but, according to their figures, the wedge is shallow or absent (as far as it 8145 is not obscured by the strong interdigitation). We have assigned state 0 to it. 8146 The only known skull of Westlothiana is polymorphic, showing state 0 on the left and 8147 1 on the right side (Smithson et al., 1994). 8148 In Sauropleura pectinata, state 1 (which was scored in RC07) was not quite reached: 8149 although a long wedge is present, the nasals participate in the extreme elongation of the tip of 8150 the snout. Because this elongation is autapomorphic, we have kept state 1 for Sauropleura, as 8151 found in S. scalaris (both known ontogenetic stages) and S. bairdi (Bossy & Milner, 1998: 8152 fig. 53A–D, 58A, 72A, 73A). 8153 *Glanochthon is polymorphic (Schoch & Witzmann, 2009b: fig. 2). 8154 In *Palaeoherpeton (Panchen, 1964: fig. 11), state 1 is reached on the right side but 8155 not on the left, even though the suture on the left side runs rostromedial to caudolateral as 8156 well; we have scored polymorphism. 8157

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8158 31. PAR 1: Supratemporal/postparietal suture (0); parietal/tabular suture (1). This 8159 character is inapplicable when any of these bones are missing. RC07 did not specify state 0 8160 (calling the character “Parietal/tabular suture: absent (0); present (1)”), leading them to score 8161 many cells in ways predictable from other cells. 8162 Megalocephalus is polymorphic: state 1 is found on the right side of the holotype, 8163 state 0 everywhere else (Beaumont, 1977: 52). 8164 The supratemporal is missing in all albanerpetids (as far as known), as well all 8165 “lepospondyls” except the following, which all have state 1 (as already scored for all except 8166 the last two): Westlothiana (Smithson et al., 1994), Ptyonius and Sauropleura (Bossy & 8167 Milner, 1998), Lethiscus (Pardo et al., 2017) and Oestocephalus (Anderson, 2003a: fig. 3C). 8168 By comparison with Oestocephalus, *Coloraderpeton and to a lesser degree Lethiscus 8169 (Anderson, 2003a; Pardo et al., 2017) it seems evident that the supposed right supratemporal 8170 of *Pseudophlegethontia (Anderson, 2003b) is the process of the parietal that contacts the 8171 tabular. (On the left side, however, the bone dorsomedial of the squamosal probably is a 8172 supratemporal; we have scored it as such in the next and other characters below.) The 8173 supposed postfrontal may well belong to the parietal, too, for the same reasons. We have 8174 scored state 1 of the present character. 8175 8176 32. PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1: Intertemporal present (0); 8177 supratemporal/postfrontal contact (1); parietal/postorbital contact, supratemporal 8178 present (2); parietal/postorbital or parietal/squamosal contact, supratemporal absent 8179 (3); tabular/postfrontal contact, supratemporal absent (4) (stepmatrix). Four redundant 8180 characters have been merged: no known limbed vertebrate that has an intertemporal 8181 (INTEMP 1(1) in the original) lacks a supratemporal (SUTEMP 1(0)); states 1 through 3 track 8182 gradual shrinking of the supratemporal (its rostral end reaches the postfrontal in state 1, but 8183 not in state 2, and in states 3 and 4 the bone is entirely absent); all states other than 0 are 8184 impossible when the intertemporal is present; and a parietal-postorbital contact (states 2 and 8185 3, originally PAR 2(1)) is impossible when the supratemporal is too large (states 0 and 1) as 8186 well as when the tabular contacts the postfrontal (state 4, originally POSFRO 3(1)). The 8187 stepmatrix for this character is Appendix-Table 2. 8188 Whenever there is an intertemporal, it contacts the postfrontal and the supratemporal, 8189 separating the parietal and the postorbital. The only possible exception is the right side of one 8190 specimen of Greererpeton (Smithson, 1982): it has a tiny extra bone that could be an atavistic 8191 reappearance of the intertemporal (even though a long parietal-postorbital contact is present) 8192 or a pathological neomorph; see various “branchiosaurs” for supposed occurrences of such 8193 phenomena (Boy, 1972). We have therefore scored Greererpeton as possessing state 2 of this 8194 character (and as unknown for the INTEMP characters, see below). 8195 Mentioning the squamosal in state 3 accounts for Eocaecilia, which is unique in this 8196 matrix in combining absence of the postorbital with presence of the tabular and the 8197 postfrontal. Taxa that lack not only the supratemporal but also the tabular and/or postfrontal 8198 (Acherontiscus, Adelogyrinidae, Odonterpeton, Brachydectes, modern amphibians other than 8199 Eocaecilia, Phlegethontia and *Quasicaecilia) are scored as having state 3 or 4. 8200 State 0 is present in Panderichthys (Vorobyeva & Schultze, 1991) and in Ventastega 8201 (Lukševičs, Ahlberg & Clack, 2003; Ahlberg et al., 2008). 8202 Solenodonsaurus has state 1 according to Danto, Witzmann & Müller (2012). 8203 The condition of Dolichopareias is wholly unknown (Andrews & Carroll, 1991). 8204 Although the description of this character does not quite fit Lethiscus or 8205 Oestocephalus, where the parietal laterally participates in the margin of the temporal fenestra 8206 and a single bone occupies the places where the postfrontal and the postorbital would be 8207 expected, we have kept state 2 for both: in Oestocephalus, the supratemporal and/or the

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8208 “postfrontal” would have to be extremely long and narrow to meet each other along the 8209 unusually elongate parietal (Anderson, 2003b: fig. 2, 3C); in Lethiscus, the parietal even has a 8210 wide lateral flange between the caudal margin of the “postorbital” and the rostral margin of 8211 the supratemporal (Wellstead, 1982; Pardo et al., 2017), so that the latter two bones would 8212 again need to have highly unusual shapes to meet each other if the temporal fenestra were 8213 absent. – Much the same holds for *Coloraderpeton (Anderson, 2003a; Pardo et al., 2017), 8214 which we have also scored 2. 8215 To account for its possible intertemporal, we have scored Ossinodus as showing state 8216 0 or 2. 8217 *Spathicephalus is polymorphic, with state 1 in S. marsdeni and state 2 in S. mirus 8218 (Smithson et al., 2017). 8219 *Pseudophlegethontia has state 0, 1 or 2 following the argument under the preceding 8220 character. 8221 8222 For Analysis EB, this character is split as follows: 8223 PAR 2/POSFRO 3: Postfrontal contacts supratemporal or tabular (0); parietal contacts 8224 postorbital or squamosal (1). Inapplicable when the intertemporal is present, and also when 8225 the tabular or the postfrontal is absent. 8226 INTEMP 1/SUTEMP 1: Intertemporal and supratemporal present (0); intertemporal 8227 absent, supratemporal present (1); both absent (2) (ordered). 8228 8229 Appendix-Table 2: Stepmatrix for character 32 (PAR 2/POSFRO 3/INTEMP 8230 1/SUTEMP 1). 8231 from ↓ to → 0 1 2 3 4 0 0 1 1 2 3 1 1 0 1 1 2 2 1 1 0 1 2 3 2 1 1 0 1 4 3 2 2 1 0 8232 8233 33. PAR 4: Anterior margin of parietal lying in front of (0), level with (1), or behind (2) 8234 orbit midlength (ordered). We have ordered this continuous character. 8235 Because of the orbitotemporal fenestra, batrachians (already done for Karaurus by 8236 RC07) are scored as having their observed state (corresponding to the clearly wrong 8237 assumption that the entire orbitotemporal fenestra is homologous to the orbit) or higher. In the 8238 case of Valdotriton, this means a score as unknown. 8239 State 1 is present in Ventastega (Ahlberg et al., 2008) and arguably Eryops (D. M., 8240 pers. obs. of MCZ 1129). 8241 State 2 is recorded in Albanerpetidae (Venczel & Gardner, 2005), Kotlassia (Bulanov, 8242 2003), Brachydectes (Pardo & Anderson, 2016) and Ossinodus (Warren, 2007). 8243 *Sparodus is best scored as unknown, see FRO 5 above. 8244 *Archegosaurus has state 1 on the left and state 2 on the right side in at least two 8245 individuals (Witzmann, 2006). 8246 Even if the caudal angle of the left orbit (indenting the postorbital) is ignored as a 8247 taphonomic artefact, *Neopteroplax reaches state 1 on the left side – quite likely not on the 8248 right, but most of the margin of the right orbit is not preserved – according to the specimen 8249 drawing (Romer, 1963: fig. 1) but not the reconstruction (fig. 3). While the text mentions 8250 dorsoventral compression, we cannot imagine what kind of rostrocaudal shear could be 8251 compatible with the specimen drawing; given the precedent of *Archegosaurus, we have

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8252 scored states 1 and 2 in order to avoid scoring just state 1 as a certainty. (There is currently no 8253 way of scoring “state 1 and possibly state 2”.) 8254 8255 34. PAR 5: Anteriormost third of parietals not wider (0) or at least marginally wider (1) 8256 than frontals. 8257 State 0 is present in Ventastega (Ahlberg et al., 2008), Ichthyostega (Jarvik, 1996; 8258 Clack & Milner, 2015: fig. 8), Cochleosaurus (Sequeira, 2004), Ecolsonia (Berman, Reisz & 8259 Eberth, 1985), Broiliellus (Carroll, 1964; Schoch, 2012), Amphibamus (Schoch, 2001), 8260 Micromelerpeton (Boy, 1995: fig. 8), Apateon (throughout its ontogeny: Schoch & Fröbisch, 8261 2006), Karaurus (Ivachnenko, 1978), Gephyrostegus (Klembara et al., 2014), Tuditanus, 8262 Saxonerpeton and Hapsidopareion (CG78), Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 8263 2015) and Lethiscus (Pardo et al., 2017). 8264 State 1 is found in Acanthostega (Porro, Rayfield & Clack, 2015). 8265 Dendrerpetidae is polymorphic: while Dendrysekos has state 1 as scored in RC07 8266 (Holmes, Carroll & Reisz, 1998), most or all specimens of Dendrerpeton (all species: A. R. 8267 Milner, 1980, 1996) have state 0. *Acanthostomatops (Witzmann & Schoch, 2006a) and 8268 *Glanochthon (Schoch & Witzmann, 2009b) are polymorphic as well. While only state 1 is 8269 known in the single individual of Batropetes niederkirchensis (Glienke, 2013: fig. 2), B. 8270 fritschi is polymorphic (Glienke, 2013: fig. 6), as is the reconstructed individual of B. 8271 palatinus because its two parietals have such different lengths (Glienke, 2015: fig. 1E). 8272 Unclear and probably about equal in Edops (D. M., pers. obs. of MCZ 1378; the 8273 reconstruction by Romer & Witter [1942] just barely indicates state 1, but seems not to 8274 acknowledge a patch of reconstructed surface that probably covers at least part of the 8275 parietal/postfrontal suture). 8276 A (separate) parietal is absent in Triadobatrachus (see FRO 5 above), Phlegethontia, 8277 Notobatrachus and Vieraella; we have accordingly scored them as unknown. 8278 The state of *Pseudophlegethontia depends on whether the supposed postfrontal 8279 belongs to the parietal (see character 31, PAR 1, above); we have scored it as unknown. 8280 8281 35. PAR 6: Parietals more (0) or less (1) than two and a half times as long as wide each. 8282 “Each” is added; we have interpreted it from the coding, which makes clear that this character 8283 does not concern the combined widths of both parietals. 8284 Brachydectes is apparently polymorphic, with Permian specimens having state 1 and 8285 Carboniferous specimens reaching state 0 (Wellstead, 1991). 8286 *Sparodus is probably borderline, but unknown, see FRO 5 above. 8287 *Lydekkerina is polymorphic (Jeannot, Damiani & Rubidge, 2006). 8288 8289 36. PAR 7: Squamosal participates in dorsal surface of skull roof: no (0); yes (1). The 8290 original wording, “Parietal/squamosal suture extending in part onto the dorsal surface of the 8291 skull table: no (0); yes (1)”, is not applicable to the vast majority of the taxon sample, because 8292 the parietal and the squamosal are separated by other bones; yet, all those OTUs were scored 8293 as possessing state 0. We therefore speculate that our wording, which can be applied to all 8294 taxa in this matrix, was intended. 8295 Skutschas & Martin (2011) suggested that state 1 results from fusion of the 8296 supratemporal to the squamosal. While it is not testable (except by phylogenetic bracketing) if 8297 this has happened in the extinct salamanders they had in mind (ontogenetic series are not 8298 known), state 1 occurs in several taxa in this matrix that retain a separate supratemporal. One 8299 example is Ichthyostega (Clack & Milner, 2015: fig. 8). Another is the one dendrerpetid skull 8300 that is not squished flat (Holmes, Carroll & Reisz, 1998) – which leaves us to suspect that

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8301 most small temnospondyls should actually be scored 1 as well, although we have remained 8302 conservative and kept state 0 for all except Dendrerpetidae. 8303 Triadobatrachus is somewhat disarticulated and crushed flat, making it difficult to 8304 judge whether the parietal/squamosal contact was on the dorsal or the lateral side of the skull 8305 roof; we have scored it as unknown. 8306 Captorhinus is borderline in that the parietal-squamosal suture forms the boundary 8307 between the skull table and the cheek (Heaton, 1979); unlike RC07, we have chosen to count 8308 this as state 0. State 0 is further present in Ventastega (Ahlberg et al., 2008), Paleothyris 8309 (Carroll, 1969a), Batropetes (Carroll, 1991; Glienke, 2013), Microbrachis (Olori, 2015) and 8310 Tseajaia (Moss, 1972). Under our reinterpretation of this character, state 0 is also found in 8311 Albanerpetidae (McGowan, 2002; Venczel & Gardner, 2005) and Notobatrachus (Estes & 8312 Reig, 1973; Báez & Nicoli, 2004). 8313 We retain the score of Petrolacosaurus (Reisz, 1981) as possessing state 1 because we 8314 consider the dorsally-facing supratemporal fenestrae to form part of the dorsal surface of the 8315 skull. 8316 We assign state 1 to *Acanthostomatops because the squamosal extends medially 8317 beyond the lateral margin of the supratemporal (Witzmann & Schoch, 2006a); the skull is 8318 apparently very flat, and illustrations (let alone reconstructions) in lateral view seem not to 8319 exist, but the supratemporal generally does not participate in the lateral skull surface. 8320 8321 37. PAR 8: Parietal/frontal suture strongly interdigitating: no (0); yes (1). 8322 State 0 is present in Ventastega (Ahlberg et al., 2008). 8323 Although “strongly” is not defined, we have scored Kotlassia as possessing state 0 8324 (Bulanov, 2003: fig. 30). 8325 Apateon has state 1 based on the largest metamorphic individual (Werneburg, 1991: 8326 fig. 5b). State 1 is further found in Baphetes (Milner, Milner & Walsh, 2009), Edops (Romer 8327 & Witter, 1942; D. M., pers. obs. of MCZ 1378), Trimerorhachis (Milner & Schoch, 2013), 8328 Balanerpeton (Milner & Sequeira, 1994) and Diadectes (Berman, Sumida & Lombard, 1992; 8329 Berman, Sumida & Martens, 1998). We have further assigned state 1 to Gephyrostegus based 8330 on Klembara et al. (2014: especially fig. 1A, 5B). 8331 Batropetes is polymorphic (Glienke, 2013, 2015). 8332 Hapsidopareion probably qualifies for state 1 (CG78: fig. 13A), which we have 8333 therefore scored. 8334 Unknown in Acanthostega (Porro, Rayfield & Clack, 2015). 8335 Phlegethontia lacks parietals (Anderson, 2002), so we have scored it as unknown. 8336 Assuming that the existing reconstructions of S. mirus are too schematic or thick-lined 8337 to score this character, we have scored state 1 for *Spathicephalus based on S. marsdeni 8338 (Smithson et al., 2017: fig. 3C). 8339 8340 38. PAR 9: Parietal/postparietal suture strongly interdigitating: no (0); yes (1). RC07 8341 stated that “[t]here appears to be no clear phylogenetic signal associated with this character”. 8342 It has at most 28 steps on the shortest trees from Analysis R4 (158 OTUs); state 1 is an 8343 autapomorphy of Temnospondyli except Eucritta (reversed in part of Colosteus, in 8344 Megalocephalus, Cochleosauridae, Eryops, Neldasaurus and in most dissorophoids, with a 8345 reappearance in *Gerobatrachus), of Archeria, of *Palaeoherpeton + *NSM 994 GF 1.1 + 8346 *Neopteroplax, of Solenodonsaurus, Diadectes, *Caseasauria, Pantylus, Hyloplesion and 8347 Keraterpeton, and holds the aïstopod-urocordylid-adelospondyl clade together; it may also be 8348 homologous between *Sparodus, *Llistrofus and Brachydectes. 8349 Kotlassia has state 0 (Bulanov, 2003: fig. 30); Eoscopus is somewhat borderline 8350 (Daly, 1994), but we prefer scoring it as sharing state 0.

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8351 State 1 occurs in Acanthostega (Clack, 2007; Porro, Rayfield & Clack, 2015), 8352 Baphetes (Beaumont, 1977: fig. 25; Milner, Milner & Walsh, 2009), Edops (Romer & Witter, 8353 1942; D. M., pers. obs. of MCZ 1378), Trimerorhachis (Milner & Schoch, 2013), 8354 Balanerpeton (Milner & Sequeira, 1994), Diadectes (Berman, Sumida & Lombard, 1992; 8355 Berman, Sumida & Martens, 1998) and Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 8356 2010), probably also *Saharastega (D. M., pers. obs. of MNN MOR 73). 8357 Unclear in Hapsidopareion (CG78: fig. 13A). 8358 This character is inapplicable to Odonterpeton because Odonterpeton lacks 8359 postparietals, as explained in the next character. 8360 Assuming that the existing reconstructions of S. mirus are too schematic or thick-lined 8361 to score this character, we have scored state 1 for *Spathicephalus based on S. marsdeni 8362 (Smithson et al., 2017: fig. 3C). 8363 *Bystrowiella has state 1 on the ventral side, but state 0, which we have scored, on the 8364 dorsal side (Witzmann & Schoch, 2017: 6th page, fig. 2). 8365 8366 39. POSPAR 1-2: Postparietal(s) paired (0), single (1), or absent (2) (unordered). The two 8367 original characters, presence/absence of postparietals and absence/presence of median fusion 8368 of the postparietals, make each other inapplicable, so we have fused them. 8369 State 0 is present in Ventastega (Ahlberg et al., 2008). 8370 States 0 and 1 are known in Ichthyostega (Clack & Milner, 2015); in the absence of 8371 evidence on whether this could be ontogenetic, we have scored polymorphism. 8372 There is no evidence for postparietals in any albanerpetid, so we have scored 8373 Albanerpetidae as having state 2. 8374 Bruktererpeton has state 0 or 1 (Boy & Bandel, 1973). We have scored 8375 *Gerobatrachus the same way because it is not evident whether the sutured fragment close to 8376 the caudal end of the skull table belongs to the parietals or the postparietals. 8377 Odonterpeton was interpreted as possessing state 1 by CG78. However, the supposed 8378 suture between the left parietal and the postparietal consists of a discontinuous series of 8379 cracks (D. M., pers. obs. of USNM 4465+4467, the holotype). We have accordingly assigned 8380 state 2 to Odonterpeton and would like to use this opportunity to mention that fig. 98A and 8381 99A of CG78 differ from the specimen in other ways as well; they are idealized and 8382 simplified to the point of being unreliable. In particular, the suture between the right parietal 8383 and the “postparietal” has an additional curve to the left at its caudal end, so that the 8384 asymmetry between the parietals is considerably smaller than one would think. 8385 The condition is unknown in Adelogyrinus and Dolichopareias (Andrews & Carroll, 8386 1991). 8387 Although a stippled line indicates a suture in the reconstruction drawings of Lethiscus 8388 by Pardo et al. (2017), it is not apparent in the scan images or in Wellstead (1982); we have 8389 kept state 0 or 1 for the moment. 8390 As we have not seen the type specimen, we have trouble understanding the condition 8391 of Tseajaia: Moss (1972: 10) reported state 1, and his photos (pl. 1, 3) are compatible with 8392 this – if they show a suture, then that suture is much thinner than the others in that skull. 8393 Berman, Sumida & Lombard (1992: 490) said explicitly that Moss was wrong (reiterated by 8394 Berman, Reisz & Scott, 2010: 192) and presented another photo of the same skull (the 8395 holotype, UCMP 59012) which is much brighter, shows drastically narrower sutures, and 8396 lacks a strong contrast between the suture between the postparietals and the other sutures. It 8397 looks like all sutures in that photo are enhanced in black ink, though. In the photo of UCMP 8398 59012 shown by Reisz (2007: pl. 26), the postparietals look very clearly separate. D. M. has 8399 seen CM 38033, a largely complete skeleton containing a complete skull illustrated by 8400 Berman, Sumida & Lombard (1992: fig. 9-2, 10-2), but this does not help for this character,

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8401 because the occipital region is preserved as tiny fragments and there is generally no safe way 8402 of distinguishing sutures from cracks in this specimen; indeed, Berman, Sumida & Lombard 8403 (1992: fig. 10-2) did not reconstruct the postparietal(s) of the skull of CM 38033, and while 8404 Reisz (2007) briefly described that skull, he did not mention this feature and did not illustrate 8405 it. Supported by Reisz (2007: pl. 26), we accept the more recent interpretation (Berman, 8406 Sumida & Lombard, 1992; Berman, Reisz & Scott, 2010) and have kept the score of Tseajaia 8407 as 0, unusual though this is for a diadectomorph (Reisz, 2007: 243, listed “single median 8408 postparietal” as an autapomorphy of Diadectomorpha; Berman, Reisz & Scott, 2010, repeated 8409 that the postparietal is single in Limnoscelis, Orobates and Diadectes as scored by RC07). 8410 *Caseasauria is polymorphic: state 0 is found in Eothyris and Eocasea, state 1 in 8411 Oedaleops (Reisz, Godfrey & Scott, 2009; Reisz & Fröbisch, 2014). 8412 Reisz & Dilkes (2003) were cautious, but we accept their argument for state 0 in 8413 *Archaeovenator. 8414 8415 40. POSPAR 3-6: Dorsally exposed part of postparietals together less (0) or more than 8416 four times as wide (mediolaterally) as long (1) or absent, postparietals entirely on 8417 occipital surface of skull (2) (ordered). We have fused two characters (POSPAR 3: size of 8418 dorsal exposure; POSPAR 6: presence of dorsal exposure) that we consider parts of a single 8419 continuous character. The original wording had “postparietal” instead of “postparietals 8420 together”, but that does not remotely fit the original scores, so it was probably not intended. 8421 State 0 is present in Ventastega (Ahlberg et al., 2008), Ichthyostega (Clack, 2007), 8422 Eucritta (Clack, 2001), Isodectes (Sequeira, 1998), Dendrerpetidae (Holmes, Carroll & Reisz, 8423 1998), Eryops (D. M., pers. obs. of MCZ 1129), Acheloma (Polley & Reisz, 2011), 8424 Phonerpeton (Dilkes, 1990), Ecolsonia (Berman, Reisz & Eberth, 1985), Platyrhinops (Clack 8425 & Milner, 2010), Micromelerpeton (Schoch, 2009b: fig. 2b), Apateon, Leptorophus and 8426 Schoenfelderpeton (Schoch & Milner, 2008), Bruktererpeton (Boy & Bandel, 1973), probably 8427 Solenodonsaurus (Danto, Witzmann & Müller, 2012), Discosauriscus (Klembara, 1997; 8428 Klembara et al., 2006), Seymouria (Laurin, 1996c; Klembara et al., 2005), Microbrachis 8429 (Vallin & Laurin, 2004; Olori, 2015), Lethiscus (Wellstead, 1982; Pardo et al., 2017), and 8430 Ariekanerpeton, Leptoropha and Microphon (Bulanov, 2003). 8431 State 1 is found in Amphibamus (Schoch & Milner, 2014: fig. 30B; possibly Daly, 8432 1994: fig. 18) and Limnoscelis (Reisz, 2007), and in Diploceraspis because of its “horns” 8433 (Beerbower, 1963). 8434 Diadectes possesses both state 0 (North American species: Berman, Sumida & 8435 Lombard, 1992) and state 1 (D. absitus: Berman, Sumida & Martens, 1998). 8436 Saxonerpeton has state 1 (CG78: fig. 17). 8437 Hyloplesion has state 2 (CG78; D. M., pers. obs. of NHMW 1983/82/54 and other 8438 NHMW specimens). 8439 Pelodosotis was scored POSPAR 3(0) and POSPAR 6(?) in RC07. Of these 8440 contradictory scores, the former is correct (CG78); Pelodosotis thus possesses state 0 of the 8441 present character. 8442 Adelogyrinus and Dolichopareias have state 0 or 1 (Andrews & Carroll, 1991). 8443 Because the skull roof of *Gerobatrachus is exposed in ventral view only, we have 8444 scored it as having state 0 or 1. 8445 *Caseasauria shows both state 1 (in Eothyris and possibly Eocasea; Reisz, Godfrey & 8446 Scott, 2009; Reisz & Fröbisch, 2014) and state 2 (Oedaleops; Reisz, Godfrey & Scott, 2009). 8447 8448 41. POSPAR 4-8: Edge between the dorsal and the caudal surfaces of the skull lacking 8449 (0) or possessing (1) a caudal process in the midline. This is a fusion of two characters we 8450 deem not merely correlated but identical, with POSPAR 4 (“Postparietals without (0) or with

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8451 (1) median lappets”) meaning the combination of a caudal process with a vertical occipital 8452 surface and POSPAR 8 (“Postparietals without (0) or with (1) sinuous posterior ridge”) the 8453 combination of a caudal process with an inclined occipital surface. (The difference between a 8454 vertical and an inclined surface is character POSPAR 7, see below.) Fitting this interpretation, 8455 POSPAR 8(1) was only scored for Micraroter and Pelodosotis, while POSPAR 4(1) was 8456 limited to Crassigyrinus, Whatcheeria, embolomeres other than Eoherpeton, and Ptyonius. – 8457 Our wording makes the character applicable to taxa that lack postparietals; in particular, 8458 Triadobatrachus (all sources and pers. obs.) has state 0, and Batropetes has state 1 (Glienke, 8459 2013, 2015). 8460 Crassigyrinus in fact has a very clear case of state 0 (Panchen, 1985; Clack, 1998). We 8461 have also kept state 0 for Micromelerpeton and Apateon because this condition is seen in the 8462 most mature known specimens (Schoch, 2009b: fig. 2b; Schoch & Fröbisch, 2006). 8463 State 1 is present in Ventastega (Ahlberg et al., 2008), Balanerpeton (weakly: Milner 8464 & Sequeira, 1994), Dendrerpetidae (weakly: A. R. Milner, 1980, 1996; Holmes, Carroll & 8465 Reisz, 1998), Platyrhinops (Clack & Milner, 2010), Eocaecilia (Jenkins, Walsh & Carroll, 8466 2007), Diadectes (Berman, Sumida & Lombard, 1992; very weakly expressed in D. absitus, 8467 but present throughout [Berman, Sumida & Lombard, 1998]; see also Case, 1910), 8468 Asaphestera (where the caudal process comprises the entire caudal edge of the postparietal; 8469 CG78), Brachydectes (Pardo & Anderson, 2016: fig. 3D, 4B), Oestocephalus (Carroll, 1998a; 8470 Anderson, 2003a), Capetus (Sequeira & Milner, 1993), Orobates (Berman et al., 2004), and 8471 Tseajaia (Moss, 1972; Berman, Sumida & Lombard, 1992; Reisz, 2007: pl. 26; D. M., pers. 8472 obs. of CM 38033). 8473 Solenodonsaurus was scored POSPAR 4(?) but POSPAR 8(0) in RC07. The latter is 8474 correct according to Danto, Witzmann & Müller (2012). 8475 Ossinodus was scored in the same ways in RC07. Here, we have kept the question 8476 mark, because precisely that part of the postparietals is not preserved (Warren, 2007). 8477 State 1 is seen in a skull fragment referred to Baphetes kirkbyi (Beaumont, 1977: fig. 8478 20(a)); this area is damaged in the holotype of that species (Beaumont, 1977: fig. 18), but B. 8479 orientalis has state 0 (Beaumont, 1977: fig. 25), so we have scored polymorphism for 8480 Baphetes. 8481 Likewise, Sauropleura is polymorphic: S. scalaris and S. pectinata have state 1, but S. 8482 bairdi shows state 0 (Bossy & Milner, 1998: fig. 53). *Micropholis has both states as well 8483 (Schoch & Rubidge, 2005: fig. 3). 8484 Probably unknown in Kotlassia (Bulanov, 2003: fig. 28–30); we have changed the 8485 score. 8486 Unclear in Lethiscus (Pardo et al., 2017). 8487 Because of possible damage (D. M., pers. obs. of MNN MOR 70), we have scored 8488 *Nigerpeton as unknown. 8489 Though damage makes MNN MOR 73 difficult to interpret (D. M., pers. obs.), 8490 *Saharastega most likely has state 0. 8491 Gently rounded but present (state 1) in *Beiyanerpeton (Gao & Shubin, 2012: fig. 3). 8492 8493 POSPAR 5 is merged with OPI 2, see below. 8494 8495 42. POSPAR 7: Postparietals without (0) or with (1) posteroventrally sloping occipital 8496 exposure. Only unusually low angles count as state 1; the occipital surface is almost never 8497 perfectly vertical. 8498 State 0 is present in Ventastega (Ahlberg et al., 2008). 8499 State 1 occurs in Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 2010), 8500 Oestocephalus (Carroll, 1998a; Anderson, 2003a) and Orobates (Berman et al., 2004).

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8501 Diadectes is polymorphic (Berman, Sumida & Martens, 1998: 57). 8502 The condition is unknown in Westlothiana (Smithson et al., 1994). 8503 Adults of *Acanthostomatops have state 0 (Witzmann & Schoch, 2006a). 8504 8505 43. POSPAR 9: Edge between the dorsal and the caudal surfaces of the skull without (0) 8506 or with (1) broad, concave posterior emargination in the central bones. Our wording 8507 makes the character applicable to taxa whose postparietals lie entirely on the occipital surface 8508 (POSPAR 3-6(2)) or are absent (POSPAR 1-2(2)); in particular, Triadobatrachus (all sources) 8509 has state 0, while Captorhinus (Heaton, 1979) and Batropetes (Glienke, 2013, 2015) have 8510 state 1, though B. fritschi may be considered borderline (Glienke, 2013). 8511 State 0 is present in Ventastega (Ahlberg et al., 2008). We have also assigned it to 8512 *Saharastega, though damage makes MNN MOR 73 difficult to interpret (D. M., pers. obs.). 8513 According to RC07, state 1 is limited to “some” diplocaulids (i.e. all except 8514 Keraterpeton); however, other than in Captorhinus and Batropetes as mentioned above, it is 8515 also found in Ichthyostega (Clack & Milner, 2015: fig. 8), Edops (arguably borderline: D. M., 8516 pers. obs. of MCZ 1378), Trimerorhachis (Milner & Schoch, 2013), Dendrerpetidae (weakly: 8517 A. R. Milner, 1980, 1996; Holmes, Carroll & Reisz, 1998), Acheloma (borderline: Polley & 8518 Reisz, 2011), Eoscopus (Daly, 1994), Discosauriscus (Klembara, 1997; Klembara et al., 8519 2006), Seymouria (Laurin, 1996c: fig. 3A; Klembara et al., 2006), Diadectes (Berman, 8520 Sumida & Lombard, 1992: fig. 1, 3), Limnoscelis (Romer, 1946; Fracasso, 1983; Reisz, 2007; 8521 Berman, Reisz & Scott, 2010), Brachydectes (Pardo & Anderson, 2016: fig. 4B), 8522 Oestocephalus (Carroll, 1998a; Anderson, 2003a), Ariekanerpeton (Klembara & Ruta, 8523 2005a), Capetus (Sequeira & Milner, 1993), Orobates (marginally: Berman et al., 2004) and 8524 Ossinodus (Warren, 2007), as well as in *Micropholis (Schoch & Rubidge, 2005), 8525 *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Sclerocephalus (only the type species, 8526 the only one considered here, and only in late ontogenetic stages: Schoch & Witzmann, 8527 2009a). 8528 Although the reconstruction of Baphetes kirkbyi by Beaumont (1977: fig. 21) shows 8529 an almost straight margin as previously scored, the specimen drawings in the same work (fig. 8530 18, 20) clearly show state 1, which is also shown in both the specimen drawing and the 8531 reconstruction of B. orientalis (Beaumont, 1977: fig. 25). 8532 Acanthostega appears to be polymorphic (Porro, Rayfield & Clack, 2015: fig. 3E, 4B). 8533 So is Megalocephalus (Beaumont, 1977: fig. 10(b), 11(a)). 8534 Eryops is polymorphic, the broad-skulled morph having state 0 and the narrow-skulled 8535 morph, to which the holotype of the type species (E. megacephalus) belongs, having state 1 8536 (Werneburg, 2007a: figs. 6, 7). So is *Acanthostomatops (Witzmann & Schoch, 2006a). 8537 Microphon exiguus changes from state 0 to state 1 in ontogeny (Bulanov, 2003: fig. 8538 16, 19; 2014); only the “juvenile” stage of M. gracilis is known, so we cannot take its state 0 8539 at face value. We have therefore assigned state 1 to Microphon. Similarly, only the “juvenile” 8540 stage of Leptoropha is known, so we have scored it as unknown as well even though it shows 8541 the originally scored state 0. 8542 We have scored Tseajaia as unknown, because the state depends on the unclear 8543 position of the suture between postparietal and tabular. Moss (1972) located this suture lateral 8544 enough for state 1 to result, Berman, Sumida & Lombard (1992) preferred a more medial 8545 position that would cause state 0, and Reisz (2007: 245) simply said “the size of the tabular is 8546 uncertain in Tseajaia”. 8547 It seems fair to assign state 1 to *Karpinskiosaurus, although it is arguably borderline 8548 (Klembara, 2011).

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8549 Of the *Cheliderpeton specimens figured by Werneburg & Steyer (2002), the smallest 8550 and the largest have arguably borderline cases of state 1, while at least two others (fig. 1b, 6) 8551 clearly have state 0; we have scored *Cheliderpeton as polymorphic. 8552 We have scored *Konzhukovia as having state 1, but it is arguably borderline (Gubin, 8553 1991). 8554 *Australerpeton is polymorphic (Eltink et al., 2016: fig. 2). 8555 8556 44. POSPAR 10: Nasals not smaller (0) or smaller (1) than postparietals. 8557 State 0 is present in Ventastega (Ahlberg et al., 2008). 8558 Judging from their own figures, Danto, Witzmann & Müller (2012) miscoded this 8559 character in Solenodonsaurus, which clearly has state 0 (as scored by RC07), not 1: the nasals 8560 have several times the area of the postparietals. 8561 State 1 occurs in Brachydectes (Pardo & Anderson, 2016: fig. 2E, 4B). 8562 8563 45. POSFRO 1: Separately ossified postfrontal: present (0); absent (1). 8564 In the aïstopods, a single bone occupies the area where the postorbital and the 8565 postfrontal would be expected. (The separation in Lethiscus identified by Wellstead, 1982, is 8566 a break: Pardo et al., 2017; J. Pardo, pers. comm.) This bone has been variously identified as 8567 one or the other in the literature; there seems to be no evidence on which to base a decision, 8568 and the ontogeny of Phlegethontia suggests that the bone is a fusion product of postorbital 8569 and postfrontal (Anderson, Carroll & Rowe, 2003: fig. 9b). We have arbitrarily followed the 8570 latest publication (Pardo et al., 2017) and, by analogy, the tradition for **dinosaurs in scoring 8571 the postfrontal as absent and the postorbital (POSORB 1, character 61 below) as present; 8572 however, we have also scored several POSORB characters as unknown for all aïstopods under 8573 the assumption that the dorsal ossification center of Phlegethontia may be the postfrontal. 8574 Reexamination of **Ophiderpeton could help to test this approach. – We have scored 8575 *Pseudophlegethontia as unknown for all POSFRO and POSORB characters; see character 8576 31 (PAR 1) above. 8577 State 0 is present in Ventastega (Ahlberg et al., 2008) and Bruktererpeton (Boy & 8578 Bandel, 1973). 8579 8580 46. POSFRO 4: Postfrontal posterior margin lying flush with jugal posterior margin: no 8581 (0); yes (1). Most or all cases of state 1 are only approximate, making it difficult to decide 8582 where exactly state 0 should begin. We have changed as few scores as possible, except for 8583 scoring all aïstopods as unknown (see immediately above). 8584 Ventastega (Ahlberg et al., 2008) and Westlothiana (Smithson et al., 1994) have state 8585 0. 8586 Orobates shows state 1 (Berman et al., 2004), as does Microphon (Bulanov, 2003). 8587 *Cheliderpeton passes from state 0 to state 1 in ontogeny (Werneburg & Steyer, 2002: 8588 fig. 1), so we have scored the latter. 8589 Nonetheless, *Glanochthon is polymorphic (Schoch & Witzmann, 2009b: fig. 2), and 8590 so is *Australerpeton (Eltink et al., 2016: fig. 2). 8591 8592 47. INTEMP 2: Intertemporal not interdigitating (0) or interdigitating (1) with cheek. 8593 “There appears to be no signal associated with the derived state of this character” according to 8594 RC07. Yet, even for the full taxon sample (Analysis R4), this character has only six steps. 8595 State 1 is an autapomorphy of Whatcheeriidae, Temnospondyli and/or Caerorhachis, possibly 8596 homologous among these groups (unambiguously so in MPTs where Ossinodus is not a 8597 whatcheeriid); of (Pholiderpeton attheyi + Anthracosaurus + *NSM 994 GF 1.1 + 8598 *Palaeoherpeton + *Neopteroplax); and of (Seymouria (Kotlassia, *Karpinskiosaurus)) – the

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8599 only unambiguous reversal in all MPTs occurs in Capetus. Thus, even though the present 8600 character is unknown or inapplicable in most OTUs, it clearly displays phylogenetic signal. 8601 State 0 is present in Ventastega (Ahlberg et al., 2008). 8602 Trimerorhachis has state 1 (Milner & Schoch, 2013); so does *Saharastega (D. M., 8603 pers. obs. of MNN MOR 73). 8604 We have scored Ossinodus as having state 1 because the suture between skull table 8605 and cheek is not smooth and because a separate intertemporal is fairly likely present (Warren, 8606 2007). Of character 32 of this matrix (PAR 2/POSFRO 3/INTEMP 1/SUTEMP 1), we have 8607 assigned state 0 (intertemporal present) or 2 (parietal-postorbital contact, supratemporal 8608 present) to it. 8609 Although the expression is very weak, we have kept state 1 for Cochleosaurus 8610 (Sequeira, 2004) and assigned it to *Karpinskiosaurus (Klembara, 2011). 8611 8612 48. INTEMP 3: Intertemporal/squamosal contact: absent (0); present (1). RC07 called it a 8613 suture, but explained it as a contact in the next sentence; we have therefore scored any contact 8614 between these two bones as state 1, without considering whether it counts as a suture. 8615 State 1 is thus present in Ventastega (Ahlberg et al., 2008), Crassigyrinus (Clack, 8616 1998: fig. 4), apparently Eoherpeton (Smithson, 1985: fig. 7; tentatively accepted in the 8617 reconstruction, fig. 8) and Gephyrostegus (Klembara et al., 2014). 8618 State 0 is found in Panderichthys (Vorobyeva & Schultze, 1991). 8619 As for the preceding character, we have scored Ossinodus as showing state 1 in case 8620 there is a suture separating the possible intertemporal from the postorbital (Warren, 2007). 8621 8622 49. INTEMP 4: Intertemporal not (0) much smaller than supratemporal in area and 8623 about as wide as long (1). The original name was: “Intertemporal shaped like a small, 8624 subquadrangular bone, less than half as broad as the supratemporal: absent (0); present (1)”; 8625 but under this definition, state 1 is limited to the right side of the largest Eucritta specimen 8626 (Clack, 2001: fig. 6), making the character parsimony-uninformative. RC07 had scored state 1 8627 also for Baphetes, Isodectes, Trimerorhachis and Balanerpeton, but both B. kirkbyi 8628 (Beaumont, 1977: fig. 21) and B. orientalis (Milner, Milner & Walsh, 2009: fig. 5) have state 8629 0 by the width criterion, as do Isodectes (by width – the shape is somewhat arguable: 8630 Sequeira, 1998), Trimerorhachis (both by shape and by width: Milner & Schoch, 2013) and 8631 Balanerpeton (by width: Milner & Sequeira, 1994). State 0 is further present in Ventastega 8632 (by shape and almost certainly width: Ahlberg et al., 2008); as for the preceding two 8633 characters, we have scored Ossinodus as showing state 0 in case there is a suture separating 8634 the possible intertemporal from the postorbital (Warren, 2007). 8635 Rather than deleting this character, however, we turned to the explanation of this 8636 character by RC07 (p. 96), which speaks of “a diminutive intertemporal” and ends in: “The 8637 ornamented surface of the intertemporal is approximately square and can be ‘contained’ 8638 within the supratemporal in the derived condition [ = state 1] of this character.” Indeed, 8639 intertemporals seem to occur in two size classes. If we replaced “broad” by “long” in the 8640 original name, state 1 would occur in some individuals of Isodectes and nowhere else; 8641 specifying a square shape would restrict state 1 to Baphetes orientalis (not B. kirkbyi, where 8642 the intertemporal is pentagonal) and again the right side of the largest Eucritta specimen; the 8643 present formulation, however, justifies the original scores (Trimerorhachis may be a 8644 borderline case, but we have kept it), except for making Dendrerpetidae polymorphic (A. R. 8645 Milner, 1980; Godfrey, Fiorillo & Carroll, 1987; Holmes, Carroll & Reisz, 1998). 8646 Utegenia seems to change from state 1 to state 0 in ontogeny (Klembara & Ruta, 8647 2004a); we have kept state 0. 8648

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8649 50. SUTEMP 2: Rostral border of temporal embayment formed only by squamosal (0) or 8650 at least in part by supratemporal (1). Except for the clarifying addition of “at least in part”, 8651 this wording is equivalent to the description of this character by Ruta, Coates & Quicke 8652 (2003). RC07 changed that to: “Supratemporal forming entire edge of dorsalmost part (in 8653 lateral aspect) of temporal notch: no (0); yes (1).” When we use this wording, however, we 8654 cannot replicate the coding of this character, because we do not know where to draw the line 8655 between the “notch” and the rest of the “embayment” that RC07 mention in the explanation of 8656 this character. (No explanation was given in the 2003 version.) – We here use 8657 “tympanic/otic/temporal/spiracular notch/embayment” as synonyms regardless of inferred 8658 functions. 8659 Contrary to the coding by RC07, this character is inapplicable when there is no 8660 embayment (SQU 3(0), see below). It is furthermore not applicable to Acanthostega, because 8661 the entire edge of its temporal embayment is formed by the tabular, or to taxa with a 8662 squamosal/tabular suture (the ones to which TAB 5 is applicable). 8663 State 1 is present in Ventastega (Ahlberg et al., 2008), Crassigyrinus (Clack, 1998), 8664 Whatcheeria (Lombard & Bolt, 1995) and Silvanerpeton (Ruta & Clack, 2006: fig. 3A). 8665 Diadectes is polymorphic (North American species: 0 [Berman, Sumida & Lombard, 8666 1992]; D. absitus: 1 [Berman, Sumida & Martens, 1998]). 8667 This character is difficult to apply to *Saharastega (D. M., pers. obs. of MNN MOR 8668 73); we have scored it as unknown. 8669 Romer (1963) quite unambiguously showed state 1 on the preserved left side in the 8670 drawing of the specimen of *Neopteroplax (fig. 1). The reconstruction (fig. 3, 4), however, 8671 the left side has a tabular/squamosal suture, and the right side – which is not preserved – has 8672 state 1. The text does not mention this question, except for stating (p. 423): “Laterally, 8673 intertemporal and supratemporal curve smoothly downward from the plane of the skull table.” 8674 Encouraged by this sentence, which implies state 1 assuming that there is no 8675 squamosal/tabular suture, we have accepted the specimen drawing at face value and scored 8676 state 1. 8677 *Australerpeton is polymorphic, with both states apparently occurring in the two 8678 largest specimens (Eltink et al, 2016: fig. 2). 8679 8680 51. SUTEMP 3: Supratemporal narrow and strap-like, at least three times as long as 8681 wide: absent (0); present (1). 8682 The text and the skull reconstruction by Smithson et al. (1994) ascribe state 0 to 8683 Westlothiana (making it similar to diadectomorphs and basal amniotes), and RC07 accepted 8684 this. However, based on the specimen drawing (Smithson et al., 1994: fig. 5B), we strongly 8685 suspect that the occipital bone plate in question belongs to the squamosal rather than to the 8686 supratemporal. If this is correct, the supratemporal is within the range of state 1 (which is 8687 otherwise limited to urocordylids, aïstopods, and the diadectomorph Orobates). We have 8688 therefore changed the score of Westlothiana to 1, and hope that the ongoing redescription of 8689 Westlothiana (M. Ruta, pers. comm. 2015; Clack & Milner, 2015) will clarify the issue. It is 8690 highly unfortunate that the published specimens were split through the bone, so that one slab 8691 contains the dorsal side of the skull roof in ventral view and the other side holds the ventral 8692 side of the skull roof in dorsal view. 8693 Lethiscus has state 0, which we have scored, unless (and then only borderline) if 8694 measured along the curve of its long axis (Pardo et al., 2017). 8695 8696 52. SUTEMP 4: Supratemporal/squamosal suture: smooth (0); interdigitating (1). 8697 According to RC07, “no clear signal is associated with the distribution of the derived state”. 8698 At 20 steps for 158 OTUs (Analysis R4), the state distribution of this character is indeed not

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8699 very tidy; nonetheless, state 1 is synapomorphic of Whatcheeria and Pederpes, of 8700 Temnospondyli (reversed in *Deltaherpeton and at least six times among traditional 8701 temnospondyls), of Seymouria, Kotlassia and *Karpinskiosaurus and also of 8702 *Coloraderpeton and *Pseudophlegethontia (unknown in other aïstopods except 8703 Oestocephalus). Clearly, this character is not useless. 8704 State 0 is present in Ventastega (Ahlberg et al., 2008) and Acanthostega (Porro, 8705 Rayfield & Clack, 2015). We have also assigned it to Dendrerpetidae, where the suture is not 8706 straight (especially in lateral view) but still smooth (A. R. Milner, 1980, 1996; Holmes, 8707 Carroll & Reisz, 1998). 8708 State 1 is known in Acheloma (Polley & Reisz, 2011) and in one middle-sized 8709 specimen of *Acanthostomatops (Witzmann & Schoch, 2006a: fig. 2C), while the others have 8710 state 0. We have also scored state 1 in *Nigerpeton; the suture is difficult to find and to 8711 confirm, but it is clearly not a straight line (D. M., pers. obs. of MNN MOR 70). 8712 Unknown in Lethiscus (Pardo et al., 2017: ext. data fig. 2, 3). 8713 *Spathicephalus has state 1 (Smithson et al., 2017: fig. 3C). So does 8714 *Pseudophlegethontia (on the left side; see character 31, PAR 1). 8715 *Glanochthon is polymorphic (Schoch & Witzmann, 2009b: fig. 2). 8716 We have assigned state 1 to *Platyoposaurus, though it is a somewhat borderline case 8717 (Gubin, 1991: drawing 3). Similarly, although weak, interdigitation is present in 8718 *Pholidogaster (Panchen, 1975: fig. 14) and *Australerpeton (Barberena, 1998: fig. 3). 8719 8720 53. TAB 1/SQU 4: Separately ossified tabular: present (0); absent (1). RC07 distinguished 8721 TAB 1, which had the present name, from SQU 4, which described the absence (0) or 8722 presence (1) of a single bone in the places normally occupied by the squamosal, the tabular, 8723 and the supratemporal. SQU 4(1) was limited to the adelogyrinids. Based on which bones are 8724 lost in other taxa in this matrix (and elsewhere among limbed vertebrates), we interpret the 8725 “squamosotabular bone” (Andrews & Carroll, 1991) as simply the squamosal, so that the 8726 adelogyrinids lack tabulars and SQU 4 turns out to be a duplicate of TAB 1. We do, however, 8727 identify potential homologues of the “tabular horns” in Adelospondylus, which we have 8728 scored TAB 2(1) and TAB 6(1), and Adelogyrinus, which we have scored TAB 6(1) (TAB 2 8729 being unknown), both after the drawings by Andrews & Carroll (1991). 8730 Ventastega shows state 0 (Ahlberg et al., 2008). 8731 State 1 is present in Albanerpetidae (McGowan, 2002). 8732 State 0, tentatively reconstructed by Jenkins, Walsh & Carroll (2007), appears likely 8733 for Eocaecilia: what appears to be the tabular or supratemporal is caudally broken on the left 8734 side of the crushed type specimen (MNA V8066, formerly MCZ 9010), but appears to have 8735 reached the caudal edge of the skull table on the right side (D. M., pers. obs.). 8736 8737 54. TAB 2-3-9: “Ventral tabular horn” (caudal process of tabular lying ventral to 8738 tabular ornamented surface): absent (0); pointed (1); button-like (2); rectangular (3) 8739 (unordered). No sequence for ordering is apparent: the longest rectangles are as long as the 8740 longest buttons, while the shortest rectangles are extremely short; the widest buttons are no 8741 wider than the widest horns, and the widest horns are at least as wide as the widest rectangles, 8742 while the narrowest horns are extremely narrow. 8743 RC07 distinguished three characters: TAB 2, the presence or absence of a “[b]lade- 8744 like […] horn”; TAB 3, the presence or absence of a “[r]ounded, button-like posterior 8745 process”; and TAB 9, the presence or absence of a “[d]orsoventrally flattened, posteriorly 8746 directed, subhorizontal outgrowth” from the ventral rather than the caudal surface of the 8747 tabular. Tellingly, these characters had almost completely mutually exclusive distributions: 8748 TAB 2(1) was assigned to Acanthostega, Crassigyrinus, Whatcheeria, Caerorhachis, all

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8749 anthracosaurs, Gephyrostegus, Silvanerpeton and Utegenia; TAB 3(1) was scored for 8750 Greererpeton, Baphetes, Megalocephalus, Edops, “Dendrerpeton” and Pederpes; TAB 9(1) 8751 was ascribed to Discosauriscus, Ariekanerpeton, Microphon and Utegenia. Most of these 8752 OTUs were scored 0, rather than “unknown”, for the other two characters, which means that 8753 RC07 treated these three characters as describing three different processes that were not 8754 homologous to each other. 8755 From comparison across the taxon sample, it is obvious that all three processes are 8756 primary homologues of each other; indeed, state TAB 3(1) becomes state TAB 2(1) in the 8757 ontogeny of Apateon pedestris (compare fig. 7 of Boy & Sues, 2000, to fig. 3D of Schoch & 8758 Milner, 2008). “Horns” are apparently always at or close to the lateral margin of the tabular, 8759 while “buttons” are usually near the medial margin; but buttons can be approximately in the 8760 middle as in various baphetids (Beaumont, 1977), quite close to the lateral margin (immature 8761 Apateon pedestris: Boy & Sues, 2000: fig. 7; Pederpes: Clack & Finney, 2005; *Bystrowiella: 8762 Witzmann & Schoch, 2017: fig. 2A), and even at the lateral margin, projecting lateral to it 8763 (*Spathicephalus: Beaumont & Smithson, 1998). “Flattened processes” stand out from the 8764 ventral side of the tabular to which they are attached (all the way to the caudal edge of the 8765 skull table); but so, in many or perhaps all cases, do “horns” (Platyrhinops: Clack & Milner, 8766 2010; Anthracosaurus: Clack, 1987a: fig. 2; *Branchiosaurus: Werneburg, 2012b: fig. 7) and 8767 even “buttons” (baphetoids: Beaumont, 1977, Beaumont & Smithson, 1998; Greererpeton: 8768 Smithson, 1982: fig. 13B). 8769 All four states are mutually exclusive; this fact lets us merge all three of the original 8770 characters. 8771 To their description of TAB 2, RC07 (p. 97) added: “Under the definition of a tabular 8772 ‘horn’, we include processes of the subdermal part of the bone, which in anthracosaurs has 8773 also a separate dermal component.” This dermal component, the “dorsal tabular horn”, is not 8774 limited to anthracosaurs, however; what is unique to anthracosaurs is that the dorsal and the 8775 ventral horn point in different directions (most prominently in Proterogyrinus, but also in 8776 Anthracosaurus and to a lesser degree Pholiderpeton attheyi: Clack, 1987a). More commonly, 8777 it lies directly on top of the ventral horn, and that this is the condition seen in the other 8778 anthracosaurs which have a single, dorsoventrally thick “horn” per side (e.g. *Neopteroplax: 8779 Romer, 1963). Gephyrostegus even has a dorsal horn without a ventral horn: the horn is a 8780 dorsoventrally very thin process of the ornamented surface alone (Klembara et al., 2014). We 8781 have redefined TAB 6 to code for the presence or absence of the “dorsal tabular horn”. 8782 State 0 is present in Solenodonsaurus (Danto, Witzmann & Müller, 2012). 8783 State 1 occurs in Ventastega (Ahlberg et al., 2008), Ichthyostega (Clack & Milner, 8784 2015: fig. 8), Eryops (Sawin, 1941), Acheloma (Polley & Reisz, 2011), most likely Broiliellus 8785 (Carroll, 1964: fig. 9), Eoscopus (Daly, 1994), Platyrhinops (Clack & Milner, 2010; 8786 Werneburg, 2012b), Apateon (Schoch & Milner, 2008) and Leptorophus (Boy, 1986, 1987; 8787 Schoch, 2014a) as well as apparently Chenoprosopus (Hook, 1993), Westlothiana (Smithson 8788 et al., 1994: fig. 5A) and Adelospondylus (Andrews & Carroll, 1991; see TAB 1/SQU 4). 8789 Further, *Nigerpeton has state 1 (D. M., pers. obs. of MNN MOR 69 and MNN MOR 70); the 8790 “horn” is merely curved ventrally and therefore only shown as a stippled line in Steyer et al. 8791 (2006: fig. 2A). 8792 State 2 is found in Trimerorhachis (“only a very rudimentary horn well set off from 8793 the sculptured part of the bone”: Milner & Schoch, 2013: 99), likely Phonerpeton (Dilkes, 8794 1990), and Limnoscelis (“a distinct, low, dome-like swelling of unknown function”: Berman, 8795 Reisz & Scott, 2010: 196, fig. 3, 4). 8796 Kotlassia (Bulanov, 2003: fig. 30) and Seymouria (Laurin, 1996c, 2000; Klembara et 8797 al., 2007) have state 3, even though the rectangle becomes extremely short in (adult) S. 8798 baylorensis and Kotlassia.

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8799 Unknown in Balanerpeton (Milner & Sequeira, 1994), Dendrerpetidae (A. R. Milner, 8800 1980, 1996; Holmes, Carroll & Reisz, 1998) and Capetus (Sequeira & Milner, 1993). 8801 The tabulars of Brachydectes are so modified that this character is hard to apply 8802 (Pardo & Anderson, 2016); we have scored it as unknown. 8803 Best scored as unknown in *Saharastega due to damage and problems of applicability 8804 (D. M., pers. obs. of MNN MOR 73). 8805 The condition of *Karpinskiosaurus is intermediate between state 1 and 2 (Klembara, 8806 2011: fig. 3C); we have scored partial uncertainty. 8807 In *Sclerocephalus, the ornamented surface possibly grows over the ventral horn in 8808 large specimens, but this is not the case in the specimen illustrated by Schoch & Witzmann 8809 (2009a: fig. 5A) which clearly shows state 1. Schoch (2009a), however, stated that state 0 8810 occurs in the “terrestrial” morph and state 1 is restricted to the aquatic morph; we have 8811 accepted this and have scored *Sclerocephalus as polymorphic, but caution that preservation 8812 may cause false appearances of state 0 when skulls are only exposed in dorsal view. 8813 8814 deleted TAB 4: Tabular/squamosal suture extending onto skull table dorsal surface: 8815 present (0); absent (1). This character was scored for almost all taxa in RC07, yet almost 8816 none possess a tabular/squamosal suture. It could be reinterpreted as the presence or absence 8817 of participation of the squamosal in the dorsal surface of the skull roof, but that is already 8818 PAR 7. Because it is further influenced by presence and position of the supratemporal and the 8819 temporal embayment, it would be inapplicable to most of the taxon sample if taken literally. 8820 We have therefore deleted this character. As it was scored by RC07, it required the same 8821 number of steps under the TH and the LH. 8822 8823 55. TAB 5: Tabular/squamosal suture: smooth (0); interdigitating (1). This character is 8824 inapplicable in the absence of contact between the tabular and the squamosal, notably in 8825 Eusthenopteron and Panderichthys, which were originally scored 0. 8826 Broiliellus has state 0 (Carroll, 1964: fig. 9). 8827 Batropetes is polymorphic (Glienke, 2013, 2015). 8828 State 1 occurs in Brachydectes (Pardo & Anderson, 2016: fig. 3A, C). 8829 *Micropholis shows state 1 when the suture is present and long enough to tell (Schoch 8830 & Rubidge, 2005: fig. 1C, 3; not the oversimplified fig. 2C, which shows the same specimen 8831 as fig. 1C). 8832 In Ecolsonia (Berman, Reisz & Eberth, 1985), *Acanthostomatops (Witzmann & 8833 Schoch, 2006a) and *Erpetosaurus (Milner & Sequeira, 2011), the suture is probably too 8834 short to tell. 8835 8836 56. TAB 6: “Dorsal tabular horn”: absent (0); present (1). 8837 The original wording was: “Tabular (including its ornamented surface) elongate 8838 posterolaterally or posteriorly in the form of a massive, horn-like process, conferring a 8839 boomerang-like shape to skull outline in plan view: absent (0); present (1)”. (Evidently “plan” 8840 means dorsal and ventral.) State 1 was exclusively limited to Diplocaulus and Diploceraspis. 8841 To make this character more useful, we have excluded the size of the tabulars in this character 8842 (very large ones are necessary to give a boomerang shape to the entire skull instead of just the 8843 skull table) and compromised on “massive”, interpreting this character as the presence or 8844 absence of tabular “horns” composed of the ornamented surface (different from TAB 2-3-9) 8845 that extend markedly caudal to the postparietals. Thus, Baphetes (Beaumont, 1977: fig. 18, 8846 20), Megalocephalus (Beaumont, 1977: fig. 10(b), 11(a)), Platyrhinops (Clack & Milner, 8847 2010), Micromelerpeton (Schoch, 2009), *Micropholis (Schoch & Rubidge, 2005: fig. 3) and 8848 *Cheliderpeton (Werneburg & Steyer, 2002) are polymorphic, while state 1 alone is

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8849 documented in Ventastega (Ahlberg et al., 2008), Acanthostega (Clack, 2003), 8850 Chenoprosopus (Hook, 1993; Reisz, Berman & Henrici, 2005), Cochleosaurus (Sequeira, 8851 2004), Trimerorhachis (Milner & Schoch, 2013), Balanerpeton (at least sometimes: Milner & 8852 Sequeira, 1994: fig. 2, 4, 5), Dendrerpetidae (A. R. Milner, 1980, 1996; Holmes, Carroll & 8853 Reisz, 1998), Eryops (both morphotypes: Werneburg, 2007a), Acheloma (Maddin, Reisz & 8854 Anderson, 2010; Polley & Reisz, 2011), Broiliellus (Carroll, 1964), tentatively Amphibamus 8855 (Schoch & Milner, 2014: fig. 30A; possibly Daly, 1994: fig. 18), Eoscopus (Daly, 1994), 8856 Apateon and Leptorophus (Schoch & Milner, 2008), Eoherpeton (Panchen, 1975; Smithson, 8857 1985), Proterogyrinus (Holmes, 1984), Archeria (Holmes, 1989), both species of 8858 Pholiderpeton (Panchen, 1972; Clack, 1987b), Anthracosaurus (Clack, 1987a), 8859 Bruktererpeton (Boy & Bandel, 1973), Gephyrostegus (Klembara et al., 2014), 8860 Discosauriscus and Seymouria (Laurin, 1996c, 2000; Klembara, 1997), apparently 8861 Westlothiana (Smithson et al., 1994: fig. 5B), Adelospondylus and Adelogyrinus (Andrews & 8862 Carroll, 1991; see TAB 1/SQU 4), Sauropleura (all three species illustrated in Bossy & 8863 Milner, 1998: fig. 53), Lethiscus (Pardo et al., 2017), Capetus (Sequeira & Milner, 1993), 8864 Silvanerpeton (Ruta & Clack, 2006: especially fig. 5), *Chroniosaurus (Clack & Klembara, 8865 2009), *Iberospondylus (Laurin & Soler-Gijón, 2006), *Karpinskiosaurus (Klembara, 2011), 8866 *NSM 994 GF 1.1 (Holmes & Carroll, 2010), *Spathicephalus (Beaumont & Smithson, 8867 1998), *Sclerocephalus (Schoch & Witzmann, 2009a), *Glanochthon (Schoch & Witzmann, 8868 2009b), *Archegosaurus (Witzmann, 2006), *Platyoposaurus (Gubin, 1991), *Konzhukovia 8869 (Gubin, 1991), *Lydekkerina (Shishkin, Rubidge & Kitching, 1996; Jeannot, Damiani & 8870 Rubidge, 2006; Hewison, 2007), *Acanthostomatops (Witzmann & Schoch, 2006a), 8871 *Erpetosaurus (Milner & Sequeira, 2011), *Mordex and *Branchiosaurus (Werneburg, 8872 2012b), *Palaeoherpeton (Panchen, 1964), *Neopteroplax (Romer, 1963) and 8873 *Australerpeton (Barberena, 1998; Eltink et al., 2016). 8874 Unknown in Urocordylus (Bossy & Milner, 1998: fig. 53); not preserved in 8875 *Nigerpeton (D. M., pers. obs. of MNN MOR 69 and MNN MOR 70); damaged in MNN 8876 MOR 73 (D. M., pers. obs.), therefore unknown in *Saharastega. 8877 The tabulars of Brachydectes are so modified that this character is hard to apply 8878 (Pardo & Anderson, 2016); we have scored it as unknown. 8879 8880 57. TAB 7: Parietal-parietal width smaller than (0) or greater than (1) distance between 8881 skull table posterior margin and orbit posterior margin, measured along skull midline. 8882 We interpreted the width to mean the maximum width between the lateral margins of the 8883 parietals. 8884 State 0 is found in Ventastega (Ahlberg et al., 2008), Kotlassia (just barely; Bulanov, 8885 2003: fig. 30) and Brachydectes (barely: Pardo & Anderson, 2016: fig. 4B). 8886 State 1 occurs in Broiliellus (Carroll, 1964), Gephyrostegus (Klembara et al., 2014) 8887 and Scincosaurus (Milner & Ruta, 2009). 8888 *Saharastega is scored 1 because it has state 1 for the left orbit and exact equality 8889 between the distances for the right orbit. 8890 Probably subequal in *NSM 994 GF 1.1, therefore scored as unknown. 8891 Unclear in Hapsidopareion due to disarticulation (CG78: fig. 13A); unclear and likely 8892 borderline in *Neopteroplax (Romer, 1963: fig. 1, 3). 8893 8894 58. TAB 8: Tabular without (0) or with (1) posteroventrally sloping occipital exposure. 8895 See POSPAR 7 for the meaning of “sloping”. 8896 State 0 is present in Ventastega (Ahlberg et al., 2008), Rhynchonkos (Szostakiwskyj, 8897 Pardo & Anderson, 2015) and Lethiscus (Pardo et al., 2017).

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8898 State 1 occurs in Oestocephalus (Carroll, 1998a; Anderson, 2003a), Orobates (Berman 8899 et al., 2004) and Tseajaia (Moss, 1972; Berman, Sumida & Lombard, 1992), and probably in 8900 Hapsidopareion (CG78: fig. 13A). 8901 Diadectes is polymorphic (Berman, Sumida & Lombard, 1992; Berman, Sumida & 8902 Martens, 1998). 8903 Unknown for Eocaecilia (where it is not clear if the tabular had any occipital 8904 exposure; Jenkins, Walsh & Carroll, 2007) and Westlothiana (Smithson et al., 1994). The 8905 tabulars of Brachydectes are so modified that this character is hard to apply (Pardo & 8906 Anderson, 2016); we have scored it as unknown as well. 8907 8908 59. TAB 10: Tabulars entirely on occipital surface: no (0); yes (1). 8909 State 0 is present in Ventastega (Ahlberg et al., 2008) and Limnoscelis (Berman et al., 8910 2010). 8911 8912 60. POSORB 1: Separately ossified postorbital: present (0); absent (1). 8913 State 0 is present in Ventastega (Ahlberg et al., 2008). 8914 State 1 is documented in Albanerpetidae (McGowan, 2002, Venczel & Gardner, 8915 2005). 8916 Adelospondylus was scored 1 in RC07. Ruta, Coates & Quicke (2003: 311) cited 8917 Andrews & Carroll (1991) as their only source for this score. However, Andrews & Carroll 8918 (1991: 364, fig. 13A, B) stated that whether a small postorbital was present or absent is 8919 unknown. Carroll & Andrews (1998: 151) considered the postorbital “small or absent in 8920 Adelospondylus”, and also noted that the adelogyrinid postorbital is in the position where the 8921 intertemporal would be expected, complicating this issue further. Not having seen the 8922 specimen, we have changed the score to unknown for the time being. 8923 8924 61. POSORB 2: Postorbital without (0) or with (1) ventrolateral digitiform process fitting 8925 into deep, vertical groove along jugal lateral surface. 8926 State 0 is present in Ventastega (Ahlberg et al., 2008) and, given the assumption 8927 explained under character 45 (POSFRO 1), Oestocephalus (Anderson, 2003: fig. 2) and 8928 Phlegethontia (Anderson, 2002). 8929 State 1 is found in Eryops (Sawin, 1941) and more weakly in Rhynchonkos 8930 (Szostakiwskyj, Pardo & Anderson, 2015). 8931 Cochleosaurus (Sequeira, 2004) and Platyrhinops (Clack & Milner, 2010) are 8932 polymorphic; so is *Acanthostomatops (Witzmann & Schoch, 2006a). 8933 Unknown in Westlothiana (Smithson et al., 1994). 8934 State 1 is documented in one specimen of *Glanochthon (Schoch & Witzmann, 8935 2009b: fig. 2J); but because this specimen is juvenile and all other illustrated specimens show 8936 state 0, we have decided to ignore it and score state 0 for *Glanochthon. 8937 8938 62. POSORB 3: Postorbital contributing to (0) or excluded from (1) orbit margin. 8939 State 0 is present in Ventastega (Ahlberg et al., 2008) and, given the assumption 8940 explained under character 45 (POSFRO 1), Oestocephalus (Anderson, 2003: fig. 2) and 8941 Phlegethontia (Anderson, 2002). 8942 Acherontiscus was scored 1 in RC07. Ruta, Coates & Quicke (2003: 311) cited Carroll 8943 (1969b) as their only source for this score; however, Carroll (1969b) did not mention this 8944 question in the text, presented a reconstruction drawing where the postorbital does contribute 8945 substantially to the orbit margin, and included a specimen drawing that can be interpreted 8946 either way, depending on which faint lines are sutures and which are breaks. Carroll (1998c) 8947 did not show drawings of the skull, but stated: “In contrast with adelogyrinids, the postorbital

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8948 appears to enter the margin of the orbit.” Not having seen the specimen, we have changed the 8949 score to unknown for the time being. 8950 8951 63. POSORB 4: Postorbital irregularly polygonal (0) or broadly crescentic and 8952 narrowing to a posterior point (1). We have adopted a very broad interpretation of “broadly 8953 crescentic” and concentrated on absence and presence of the pointed caudal end; RC07 8954 emphasized that the postorbital “terminates in an acute posterior extremity” in state 1. Very 8955 likely, however, many more states – or characters – should be distinguished to represent the 8956 diversity of postorbital shapes that occur in the OTUs of this matrix. 8957 Taking the drawings by Clack & Milner (2015: fig. 8A, C) at face value, we have 8958 scored polymorphism for Ichthyostega. 8959 Ventastega (Ahlberg et al., 2008) and Platyrhinops (Clack & Milner, 2010) display 8960 state 0. We have kept state 0 for Baphetes: although the juvenile B. orientalis described by 8961 Milner, Milner & Walsh has a very clear case of state 1, the adult (Beaumont, 1977: fig. 25) is 8962 borderline, and in B. kirkbyi the caudal suture with the supratemporal is almost perfectly 8963 transverse (Beaumont, 1977: fig. 18, 21). 8964 Megalocephalus has rather polygonal postorbitals as well, but a clear caudal point is 8965 there, the suture with the supratemporal being oblique; we have therefore scored state 1 8966 (Beaumont, 1977). Trimerorhachis has very long postorbitals with a very clear caudal point 8967 (Milner & Schoch, 2013). State 1 is also found in Chenoprosopus (Reisz, Berman & Henrici, 8968 2005), in *Saharastega (D. M., pers. obs. of MNN MOR 73), and, borderline, in 8969 Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015: fig. 1); note that fig. 63 of CG78 is 8970 mirrored. 8971 Kotlassia was scored 1 in RC07, but its caudal point is far ventral (Bulanov, 2003: fig. 8972 30), instead of dorsal as usual; we prefer to treat this unique condition as state 0. 8973 Seymouria was scored 1 in RC07, but the caudal end of its postorbital is a straight 8974 vertical suture (Laurin, 2000: fig. 1). 8975 State 1 is present in Paleothyris (Carroll, 1969a), Petrolacosaurus (though this may be 8976 due to the temporal fenestrae; Reisz, 1981), and Westlothiana (at least on the right side, and at 8977 least in the specimen drawings as opposed to the reconstruction; Smithson et al., 1994). 8978 Batropetes fritschi and its sister-group B. niederkirchensis have state 0 (Glienke, 8979 2013), but B. palatinus has state 1 (Glienke, 2015), making Batropetes polymorphic. 8980 *Micropholis is polymorphic as well (Schoch & Rubidge, 2005: fig. 3). 8981 Unknown in Hapsidopareion, where the temporal embayment is so large that it 8982 constrains the shape of the postorbital, and Lethiscus (see character 45 – POSFRO 1 – and 8983 Anderson, Carroll & Rowe, 2003: fig. 9B). 8984 We have assigned state 0 to *Spathicephalus because the postorbital is only crescentic 8985 insofar as it parallels the orbit margin and because it lacks a caudal point. 8986 *Platyoposaurus seems to be polymorphic, judging from the drawings by Efremov 8987 (1932), Konzhukova (1955) and Gubin (1991). So is *Lydekkerina (Jeannot, Damiani & 8988 Rubidge, 2006). 8989 *Erpetosaurus has a clear caudal point, but the extremely long postorbitals are 8990 lozenge-shaped, being much wider in the middle than at the orbit margin; we have assigned 8991 state 0, even though this polygon is not irregular. 8992 8993 64. POSORB 5: Postorbital/tabular suture: absent (0); present (1). Unlike RC07, we have 8994 scored this character as unknown (inapplicable) when the supratemporal is present. This 8995 affects all OTUs scored 0 in RC07 except Hyloplesion, the diplocaulids and Hapsidopareion; 8996 we have scored the latter as unknown as well, however, because its temporal embayment is 8997 unusually large and acts like a supratemporal for the purpose of this character.

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8998 Microbrachis has state 1 (Olori, 2015). 8999 9000 65. POSORB 6: Postorbital not wider (0) or wider (1) than orbit. Judging from the original 9001 scores, this is meant to be measured in strict dorsal view. 9002 State 0 occurs in Ventastega (Ahlberg et al., 2008). We have kept state 0 for 9003 Limnoscelis, which is borderline (Berman, Reisz & Scott, 2010: fig. 3A). 9004 State 1 occurs in Ichthyostega (Clack & Milner, 2015: fig. 8) and Cochleosaurus 9005 (Sequeira, 2004). 9006 Unknown in Lethiscus (see character 45 – POSFRO 1 – and Anderson, Carroll & 9007 Rowe, 2003: fig. 9B); Phlegethontia, however, has state 0 regardless of how much of the 9008 apparently compound bone consists of the postorbital (Anderson, 2002). 9009 The condition is so borderline in the reconstruction of *Nigerpeton (Steyer et al., 9010 2006) and the specimen drawings of *Lydekkerina (Jeannot, Damiani & Rubidge, 2006) that 9011 we have scored both as unknown. Pers. obs. of *Nigerpeton (by D. M.) failed to clarify its 9012 condition: the orbit margin is only preserved on two separate pieces of MNN MOR 70. 9013 9014 66. POSORB 7: Postorbital at least one-fourth of the width of the skull table at the same 9015 transverse level: absent (0); present (1). RC07 used “skull roof” instead of “skull table”. 9016 Again, this character is evidently meant to be measured in strict dorsal view. 9017 State 0 occurs in Ventastega (Ahlberg et al., 2008), Colosteus (Hook, 1983) and 9018 Silvanerpeton (Ruta & Clack, 2006) as well as *Nigerpeton (D. M., pers. obs. of MNN MOR 9019 70). 9020 State 1 occurs in Ichthyostega (Clack & Milner, 2015: fig. 8), Baphetes and 9021 Megalocephalus (Beaumont, 1977), Eucritta (Clack 2001), Edops (Romer & Witter, 1942; D. 9022 M., pers. obs. of MCZ 1378), Cochleosaurus (Sequeira, 2004), Neldasaurus (Chase, 1965), 9023 Trimerorhachis (Milner & Schoch, 2013), Eryops (Sawin, 1941), Amphibamus (Schoch, 9024 2001), Doleserpeton (Sigurdsen & Bolt, 2010), Eoscopus (Daly, 1994), Kotlassia (Bulanov, 9025 2003: fig. 30), Scincosaurus (Milner & Ruta, 2009), all diplocaulids (A. C. Milner, 1980), and 9026 *Chroniosaurus (Clack & Klembara, 2009). 9027 Apateon passes from state 0 to state 1 during ontogeny (Schoch & Fröbisch, 2006). 9028 Still, Leptorophus retains state 0 as scored by RC07 (Boy, 1986), so we have kept the score of 9029 0 for Schoenfelderpeton. 9030 Unknown in Adelogyrinus (Andrews & Carroll, 1991) and Lethiscus (see character 45 9031 – POSFRO 1 – and Pardo et al., 2017). 9032 Microphon is polymorphic (Bulanov, 2003: fig. 16, 22), though we caution that this 9033 difference between M. exiguus (state 1) and M. gracilis (state 0) could be ontogenetic, with 9034 the known skull of M. gracilis being closer to maturity than that of M. exiguus (literally “the 9035 tiny one”). 9036 *Acanthostomatops is polymorphic, often within the same specimen, and all cases are 9037 close to the boundary between the states (Witzmann & Schoch, 2006a). 9038 *Glanochthon is likewise polymorphic, sometimes between the left and the right side 9039 of the same individual (Schoch & Witzmann, 2009b: fig. 2). 9040 9041 67. POSORB 8: Anteriormost part of postorbital [dorso]me[d]ial margin with sigmoid 9042 profile in dorsal or lateral aspect: absent (0); present (1). A clearer wording could be 9043 “ventrolateral digitiform process on the postfrontal: absent (0); present (1)”. 9044 State 0 is seen in Ventastega (Ahlberg et al., 2008) and Batropetes (Glienke, 2013). 9045 Some specimens of Trimerorhachis show state 1 on one side (Milner & Schoch, 9046 2013); we have scored this as polymorphism.

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9047 Unknown in Lethiscus (see character 45 – POSFRO 1 – and Pardo et al., 2017); not 9048 preserved in *Nigerpeton (D. M., pers. obs. of MNN MOR 70). 9049 State 1 is documented in one specimen of *Glanochthon (Schoch & Witzmann, 2009a: 9050 fig. 2I); but because this specimen is juvenile and all other illustrated specimens show state 0, 9051 we have decided to ignore it and score state 0 for *Glanochthon. 9052 On the right side of *Palaeoherpeton, the process could be considered just another 9053 part of the interdigitation of the suture, but on the left side, state 1 is clearly present (Panchen, 9054 1964: fig. 11, 12). 9055 *Australerpeton is polymorphic (Eltink et al., 2016: fig. 2–5). 9056 9057 68. SQU 1: Rostral end of squamosal lying posterior to (0) or anterior to (1) parietal 9058 midlength (measured along the midline). RC07 phrased “rostral end” as “anterior part” 9059 without defining where the caudal end of this part might lie. 9060 Ventastega (Ahlberg et al., 2008), Westlothiana (Smithson et al., 1994) and 9061 Micraroter and Euryodus (CG78) show state 0, which is also borderline present in 9062 Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015). 9063 State 1 occurs in Eucritta (Clack, 2001), Valdotriton (Evans & Milner, 1996), 9064 Batropetes (Glienke, 2013) and Cardiocephalus (CG78) as well as Adelospondylus and 9065 Adelogyrinus (Andrews & Carroll, 1991). 9066 Trimerorhachis is usually borderline; there are a few clear cases (at least on one side 9067 of certain skulls) of state 1 and a few less clear ones of state 0 (Milner & Schoch, 2013). We 9068 have scored polymorphism. 9069 The specimen of *Archegosaurus illustrated by Witzmann (2006: fig. 5) has state 1 9070 when the right parietal is used for measurement and is borderline when the left one is chosen; 9071 we have scored state 1. 9072 In *Konzhukovia the rostral ends of the squamosals are at parietal midlength (Gubin, 9073 1991); we have scored it as unknown. 9074 *Erpetosaurus is polymorphic and often borderline (Milner & Sequeira, 2011), much 9075 like Trimerorhachis. 9076 *Branchiosaurus starts out with state 1, but apparently reaches state 0 in ontogeny 9077 (Werneburg, 2012b); we have scored state 0. 9078 9079 SQU 2 is merged with JAW ART 1 and DEN 8, see below. 9080 9081 69. SQU 3: Caudolateral edge of skull: straight or convex (0); dorsoventrally tall 9082 embayment (1); dorsally restricted notch (2) (unordered). The original name and 9083 description of this character contradict each other: “Squamosal without (0) or with (1) broad, 9084 concave embayment. An embayment is widespread among early tetrapods, a deeply incised 9085 squamosal notch is seen only in some stem amniotes and, conspicuously, in temnospondyls 9086 and salientians.” [italics in the original] Judging from its name, the “deeply incised squamosal 9087 notch” (found, incidentally, in few temnospondyls and no salientians!) was lumped with the 9088 complete absence of an embayment into the same state – and indeed this was reflected in the 9089 matrix. We have not ordered this character because the temporal embayment could disappear 9090 by rostrocaudal shortening (which might pass from state 2 over 1 to 0 or directly from 2 to 0) 9091 or by dorsoventral narrowing (from 1 over 2 to 0). As the criterion for distinguishing between 9092 states 1 and 2, we have primarily used whether the embayment encroaches on the 9093 quadratojugal (state 1) or has its ventral end within the squamosal (state 2). 9094 Within state 2, a difference between a short triangular notch (e.g. Eoherpeton: 9095 Smithson, 1985; *Llistrofus: Bolt & Rieppel, 2009: fig. 4) and a narrow, deep one which has 9096 almost parallel edges for much of its length (e.g. Seymouria: Laurin, 1996c, 2000;

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9097 Phonerpeton: Dilkes, 1990; D. M., pers. obs. of MCZ 2313) could be recognized, but this is 9098 already included in other characters (TAB 7, ORB 5). 9099 The temnospondyls Capetus (Sequeira & Milner, 1993) and Phonerpeton (Dilkes, 9100 1990: state 2: D. M., pers. obs. of AMNH 7150 [7 cm skull length]: borderline state 1; MCZ 9101 2313 [10 cm skull length]: extreme case of state 2) appear to pass from state 1 to state 2 in its 9102 ontogeny; so does, more clearly, the seymouriamorph *Karpinskiosaurus (Klembara, 2011). 9103 The difference between these states is not, however, size-dependent, as demonstrated by the 9104 fact that Phonerpeton has state 2 while Dendrysekos (Dendrerpetidae), at the same skull size 9105 as Phonerpeton, has state 1 (Holmes, Carroll & Reisz, 1998). 9106 State 1 further occurs in Gephyrostegus; although not rounded, the embayment is 9107 extremely tall (Klembara et al., 2014), quite unlike what is seen in anthracosaurs. State 1 is 9108 unambiguously present in Ecolsonia (Berman, Reisz & Eberth, 1985; that the tabular and the 9109 quadratojugal meet caudal to the embayment does not matter), Solenodonsaurus (Laurin & 9110 Reisz, 1999), Diadectes (Berman, Sumida & Lombard, 1992; Berman, Sumida & Martens, 9111 1998), arguably Batropetes (Glienke, 2015: fig. 9D, E), Adelogyrinus (Andrews & Carroll, 9112 1991), Ariekanerpeton and Utegenia (Klembara & Ruta, 2004a, 2005a), Leptoropha 9113 (Bulanov, 2003), Orobates (Berman et al., 2004), Silvanerpeton (Ruta & Clack, 2006), and 9114 Tseajaia (Moss, 1972; Berman, Sumida & Lombard, 1992; Reisz, 2007; D. M., pers. obs. of 9115 CM 38033). It is also seen in *Iberospondylus and *Acanthostomatops, even though the 9116 greatly enlarged quadratojugal creates the appearance of state 2 in dorsal view (Laurin & 9117 Soler-Gijón, 2006; Witzmann & Schoch, 2006a). 9118 State 2, the plesiomorphy, is seen in Ventastega (Ahlberg, Lukševičs & Lebedev, 9119 1994; Ahlberg et al., 2008), Ichthyostega (Clack & Milner, 2015: fig. 8), Edops (D. M., pers. 9120 obs. of MCZ 1378), adult Chenoprosopus (Langston, 1953: fig. 8), Cochleosaurus (Sequeira, 9121 2004), Trimerorhachis (Milner & Schoch, 2013), Balanerpeton (somewhat arguably; Milner 9122 & Sequeira, 1994), Eryops (D. M., pers. obs. of casts on exhibit in various museums as well 9123 as TMM, CM, USNM and MCZ specimens; very difficult to tell from publications like 9124 Sawin, 1941), Acheloma (Polley & Reisz, 2011), the most mature specimens of 9125 Micromelerpeton (Schoch, 2009b: fig. 2b), Apateon (throughout ontogeny: Boy, 1987; 9126 Schoch & Fröbisch, 2006), Leptorophus (though borderline: Boy, 1986), Caerorhachis (Ruta, 9127 Milner & Coates, 2002), all anthracosaurs, Lethiscus (Pardo et al., 2017) and Microphon 9128 (Bulanov, 2003). 9129 From the available illustrations, we cannot tell if Kotlassia (Bulanov, 2003: fig. 30) 9130 has state 1 or 2. We have assigned the same partial uncertainty to *Pholidogaster (Panchen, 9131 1975: fig. 15). 9132 Dendrerpetidae is polymorphic, with Dendrysekos having state 1 (see above) but 9133 Dendrerpeton acadianum showing state 2 instead (Milner, 1996: fig. 6A; Schoch & Milner, 9134 2014: fig. 16B). Unfortunately the state of Dendrerpeton confusum is unknown (Milner, 9135 1996: fig. 8), and D. rugosum probably but not certainly has state 2 (A. R. Milner, 1980: fig. 9136 6a, c), so we cannot reconstruct the ancestral state for Dendrerpetidae. 9137 We have scored state 0 or 2 for Oestocephalus: a very small notch as seen in Lethiscus 9138 cannot be excluded judging from Carroll (1998a: fig. 2A, 3C). 9139 This character is not applicable to Phlegethontia because so much of the dermal skull 9140 roof is lost; the caudal edge of the putative squamosal (Anderson, 2002) could be called state 9141 1 or even 2, but is most likely unrelated, lacking e.g. a caudomedial lamina. 9142 Despite diagenetic squishing, an unusual version of state 0 is recognizable in 9143 *Saharastega (D. M., pers. obs. of MNN MOR 73). 9144 We have assigned state 1 to *Liaobatrachus, although L. zhaoi might be said to have 9145 state 2 instead (Dong et al., 2013: fig. 6C, 7D).

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9146 In *caseasaurs the supratemporals project caudally beyond the rest of the skull table, 9147 producing the impression of state 2 (Oedaleops, Eocasea) or possibly 1 (Eothyris) in lateral 9148 view. We consider this an unrelated feature and have scored state 0 for *Caseasauria. 9149 Although the reconstruction of *Bystrowiella (Witzmann & Schoch, 2017: fig. 15) 9150 suggests state 2, the photo and specimen drawing (fig. 3A, C) strongly suggest state 1, which 9151 we have scored. 9152 State 2 is visible in *Coloraderpeton (Pardo et al., 2017: video). 9153 9154 70. SQU 5: Squamosal without (0) or with (1) internal shelf bracing quadrate from 9155 behind. RC07 scored state 1 for the distinctive condition found in diplocaulids and 9156 Scincosaurus. Therefore, we have not considered the smaller caudal exposure of the 9157 squamosal found in amniotes, diadectomorphs and possibly Batropetes niederkirchensis and 9158 *Crinodon as state 1. However, state 1 is unambiguously found in *Australerpeton, where a 9159 medial process of the squamosal meets the pterygoid dorsal to the occipital exposure of the 9160 quadrate (Barberena, 1998; Eltink et al., 2016). 9161 Lethiscus has state 0 (Pardo et al., 2017). 9162 Unknown in Bruktererpeton (Boy & Bandel, 1973); best scored as unknown in 9163 *Saharastega (D. M., pers. obs. of MNN MOR 73). 9164 9165 71. JUG 1: Separately ossified jugal: present (0); absent (1). 9166 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Lethiscus 9167 (Pardo et al., 2017). 9168 Given the seemingly bad preservation of this area in Triadobatrachus (all sources), we 9169 have scored it as unknown, as RC07 had already done for the quadratojugal (QUAJUG 1). 9170 9171 72. JUG 2-6: Maxilla-quadratojugal contact excluding jugal from ventral edge of skull 9172 (0); jugal contributes to ventral edge of skull between maxilla and quadratojugal, but 9173 does not project laterally beyond toothrow (1); jugal laterally overlaps toothrow (2) 9174 (ordered). We have merged two correlated characters that we interpret as parts of a 9175 continuous character. This character is not applicable to taxa with state JUG 1(1); a maxilla- 9176 quadratojugal contact can be present when there is no jugal (if the quadratojugal is present: 9177 QUAJUG 1(0)), but this is then the only possible manifestation of MAX 6(0) and thus already 9178 covered in this matrix. 9179 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Eocaecilia 9180 (Jenkins, Walsh & Carroll, 2007). We have kept it for Oestocephalus, where the lower 9181 temporal bar is interrupted but the maxilla extends much farther caudally than the jugal does 9182 (Carroll, 1998a; Anderson, 2003a); the same condition appears to be present in 9183 *Coloraderpeton (Anderson, 2003a; Pardo et al., 2017). 9184 Gephyrostegus has state 1 (Klembara et al., 2014), as does Lethiscus (Pardo et al., 9185 2017). 9186 State 2 is not confined to pantylids; it is shared by Broiliellus (Carroll, 1964: figs. 9, 9187 10). 9188 Schoenfelderpeton is scored as unknown due to its paedomorphosis. 9189 Unknown in Leptoropha (Bulanov, 2003: fig. 12). Inapplicable to Batropetes due to 9190 QUAJUG 1(1), to Hapsidopareion, Pelodosotis and *Llistrofus due to CHE EMA 1(1), and to 9191 Rhynchonkos due to QUAJUG 1(?) (which was already scored by RC07); see below for those 9192 characters. 9193 Unknown in *Nigerpeton (D. M., pers. obs. of MNN MOR 69 and MNN MOR 70). 9194 *Lydekkerina is polymorphic, having state 0 on the left and state 1 on the right side of 9195 the holotype (Hewison, 2007).

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9196 We have scored state 0 for *Diploradus and *Aytonerpeton after Clack et al. (2016: 9197 matrix). 9198 9199 73. JUG 3: Jugal/pterygoid contact: absent (0); present (1). 9200 Eocaecilia (Jenkins, Walsh & Carroll, 2007), Limnoscelis (Reisz, 2007; Berman, 9201 Reisz & Scott, 2010) and Lethiscus (Pardo et al., 2017) have state 0. So does Ossinodus, in 9202 spite of the palatal exposure of the jugal (Warren, 2007) that gives state 1 to Cochleosaurus 9203 (as already scored; Sequeira, 2004), *Saharastega (Damiani et al., 2006) and *Konzhukovia 9204 (Gubin, 1991) but not *Palatinerpeton (Boy, 1996), *Platyoposaurus (Gubin, 1991: drawing 9205 3б) or *Australerpeton (Eltink et al., 2016). 9206 Unknown in Edops (Romer & Witter, 1942: fig. 3B; D. M., pers. obs. of MCZ 1378) 9207 and Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015). 9208 *Nigerpeton has state 0 as illustrated by Steyer et al. (2006: fig. 2B), although that 9209 drawing is downright idealized (D. M., pers. obs. of MNN MOR 70, where these bones are 9210 very hard to identify; they are not preserved in the other two skulls). 9211 Milner & Sequeira (2011) considered state 1 probably present in *Erpetosaurus. 9212 Although this is not clear from their figures 2 and 5, we have accepted it. (Milner & Sequeira, 9213 2011: 65, referred to a specimen number and fig. 2, but the specimen with that number is 9214 shown in fig. 5 instead, at least judging from the captions.) 9215 Clack et al. (2012b: 22) implied state 0 for the *St. Louis tetrapod by stating: “The 9216 ectopterygoid appears to contribute to the margin of the adductor fossa.” The caudal (distal) 9217 end of the preserved right ectopterygoid, however, is broken off; fig. 2B of Clack et al. 9218 (2012b) is misleading in representing the break at the caudal end of the specimen as a line, 9219 implying a vertical surface – it is an inclined surface (D. M., pers. obs. of MB.Am.1441.1 and 9220 MB.Am.1441.2). The lingual margin does not appear to be broken, but is too irregular to 9221 represent the edge of the subtemporal fenestra; most likely, then, it is part of the sutural 9222 surface for the pterygoid. By comparison to other animals, the caudal end of the ectopterygoid 9223 would be expected far distal to the ectopterygoid fang rather than such a short distance distal 9224 to it. On the left side, most of the large Meckelian fenestra is preserved; if the mesiodistal 9225 overlap between the adductor fossa and the Meckelian fenestra was not substantially larger 9226 than in Greererpeton (Bolt & Lombard, 2001: fig. 5), the entire adductor fossa of the lower 9227 jaw and thus the entire subtemporal fenestra must have lain well distal (caudal) of the entire 9228 preserved fragment of the ectopterygoid. We have therefore scored the *St. Louis tetrapod as 9229 unknown. 9230 9231 74. JUG 4: Maximum depth of jugal ventral to orbit greater (0) or smaller (1) than half 9232 of anteroposterior eye diameter. One might think that this character is size-related, with 9233 larger animals having relatively smaller eyes at comparable ontogenetic stages and therefore 9234 deeper jugals ventral to them, but that is clearly not the case in our taxon samples. 9235 Ventastega has state 1 (Ahlberg, Lukševičs & Lebedev, 1994). So do Albanerpetidae 9236 (McGowan, 2002; Venczel & Gardner, 2005) and Lethiscus (Pardo et al., 2017). 9237 For Trimerorhachis (not including ?T. sandovalensis), where the jugal is excluded 9238 from the orbit margin by a strikingly long lacrimal/postorbital suture, we have combined the 9239 width of the jugal with that of the lacrimal and/or postorbital. Doing so marginally results in 9240 state 0 (Milner & Schoch, 2013). 9241 We have scored Eucritta as unknown because only juvenile specimens are known and 9242 relative eye size decreases in the ontogeny of most animals. 9243 Batropetes is polymorphic, with B. fritschi having state 1 while B. niederkirchensis 9244 and B. palatinus have state 0 (in lateral view) (Glienke, 2013, 2015).

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9245 Even the largest adults of *Glanochthon angusta show both states (Schoch & 9246 Witzmann, 2009b: fig. 2A, B). 9247 9248 75. JUG 7: Jugal without (0) or with (1) V-shaped indentation of its orbital margin. 9249 State 1 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and, though 9250 weakly expressed, in Eucritta (Clack, 2001: fig. 4, 6) and Edops (D. M., pers. obs. of MCZ 9251 1378; not very well visible in Romer & Witter, 1942: fig. 1). 9252 For Trimerorhachis (not including ?T. sandovalensis), where the jugal does not 9253 contact the orbit, we have applied this character to the lacrimal and the postorbital instead; 9254 this confirms the score of 0 (Milner & Schoch, 2013). 9255 Unknown in Westlothiana (Smithson et al., 1994). Also unknown in Baphetes and 9256 Megalocephalus due to the antorbital fenestra and/or incomplete preservation (Beaumont, 9257 1977; Milner, Milner & Walsh, 2009), as well as in *Spathicephalus, where the jugal may not 9258 even reach the orbit proper (Beaumont & Smithson, 1998; Smithson et al., 2017). 9259 *Sclerocephalus is polymorphic, sometimes between the left and right sides of the 9260 same individual (Schoch & Witzmann, 2009a). 9261 9262 76. JUG 8: Jugal not extending (0) or extending (1) anterior to orbit anterior margin. 9263 This character is only applicable to OTUs with MAX 5/PAL 5(0) and applies to the 9264 (dorso)lateral surface of the skull, not to underlapping processes. 9265 We do not count the baphetoid antorbital fenestra as part of the orbit. Although 9266 Eucritta nonetheless seems to have state 0 as already scored (Clack, 2001: fig. 4, 6, 8), 9267 Baphetes and Megalocephalus have state 1 (Beaumont, 1977). 9268 Lethiscus has state 0 (Pardo et al., 2017). 9269 State 1 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and 9270 Limnoscelis (Berman, Reisz & Scott, 2010: fig 3B). 9271 Unknown in Westlothiana (Smithson et al., 1994). 9272 9273 77. QUAJUG 1: Separately ossified quadratojugal: present (0); absent (1). 9274 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994). 9275 Batropetes appears to have state 1 (Glienke, 2015). 9276 Notobatrachus is polymorphic (Báez & Nicoli, 2008). 9277 The quadratojugal is unknown in Hapsidopareion; CG78 interpreted this as genuine 9278 absence. However, for unknown reasons, Hapsidopareion has been assigned state 0 of this 9279 character ever since Ruta, Coates & Quicke (2003); neither Ruta, Coates & Quicke (2003) nor 9280 RC07 commented on this. Bolt & Rieppel (2009) pointed out that *Llistrofus has state 0 and 9281 that the absence in Hapsidopareion is likely taphonomic; we have scored Hapsidopareion as 9282 unknown. 9283 Most or all of the supposed squamosal of Phlegethontia (Anderson, 2002) is better 9284 considered the quadratojugal by comparison to other aïstopods, particularly Lethiscus (Pardo 9285 et al., 2017); we have scored state 0 of the present character. 9286 The quadratojugal of *Nigerpeton identified in Steyer et al. (2006: fig. 1B) is not 9287 reproducible; the area where this bone would be expected is ossified, but the suture between 9288 the jugal and the quadratojugal is not preserved in MNN MOR 70 and wholly covered by hard 9289 sandstone in MNN MOR 69 (D. M., pers. obs.). We have consequently scored *Nigerpeton as 9290 unknown for all three QUAJUG characters. 9291 All four species of *Liaobatrachus are said to have state 0, but in three of the four 9292 species the quadratojugal is said to be fused to the quadrate, and no statement has been made 9293 about the fourth (L. beipiaoensis; Dong et al., 2013). The published figures do not resolve the 9294 situation. Given the shape of the supposedly compound bone and the lack of an explicit

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9295 statement about fusion or lack thereof in L. beipiaoensis, we have scored state 0 for the time 9296 being, but this should be investigated further. 9297 Without further comment, Schoch, Poschmann & Kupfer (2015) described their 9298 specimens of *Chelotriton as having quadratojugals separate from their quadrates. As 9299 discussed by Marjanović & Witzmann (2015), this would be the first documented case in all 9300 of Urodela; while separate bones are clearly shown in the line drawings (Schoch, Poschmann 9301 & Kupfer, 2015: fig. 4b–d), the photograph (fig. 4a) is unclear. However, the putative 9302 quadratojugals would immediately be considered quadratojugals if *Chelotriton were 9303 compared only to other taxa in this matrix rather than to other salamandrids, having as they do 9304 a large ornamented surface that is sutured to those of the maxillae and the squamosals. We 9305 have here accepted them as such and scored state 0. 9306 In *Bystrowiella, the preserved margins of the jugal and the squamosal make it hard to 9307 imagine that a separate quadratojugal, or perhaps a separate-looking one as in *Chelotriton, 9308 was absent; we have scored state 0 for this character (but not the next four, which remain 9309 unknown). 9310 We interpret the unlabeled purple slivers in Pardo et al. (2017: ext. data fig. 4) as the 9311 articulated, though probably incomplete, quadratojugal of *Coloraderpeton. 9312 9313 78. QUAJUG 2: Quadratojugal depth less than one-fourth of squamosal depth: absent 9314 (0); present (1). 9315 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), apparently 9316 Asaphestera (CG78) and Lethiscus (Pardo et al., 2017). 9317 Unknown in Scincosaurus (Milner & Ruta, 2009). 9318 Notobatrachus reigi has state 1 (Báez & Nicoli, 2008). 9319 9320 79. QUAJUG 3: Quadratojugal anteroposteriorly elongate and bar-like: no (0); yes (1). 9321 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Lethiscus 9322 (rather elongate, but a plate, not a bar, barely reaching the temporal fenestra: Pardo et al., 9323 2017). 9324 State 1 is reconstructed for Eocaecilia (Jenkins, Walsh & Carroll, 2007) and, though 9325 borderline so, for *Spathicephalus (Beaumont & Smithson, 1998). 9326 9327 80. QUA 1: Quadrate without (0) or with (1) dorsal process caudal to temporal 9328 embayment. RC07 did not specify which dorsal process they meant; the one they scored as 9329 present in Seymouria, Diadectes and Limnoscelis is simply the ossification of the dorsal part 9330 of the shaft, rostromedial to where the embayment is or would be and clearly not homologous 9331 to the process found in dissorophoid temnospondyls. 9332 That process is not limited to dissorophoids, however (among which it is also found in 9333 Ecolsonia [Berman, Reisz & Eberth, 1985: 16] and *Micropholis [Schoch & Rubidge, 2005]): 9334 as Hook (1993) pointed out, Chenoprosopus has state 1, even though the process of USNM 9335 437646 seems to have been accentuated by damage and it is at best very difficult to trace the 9336 sutures around the quadrate in that specimen (D. M., pers. obs.). State 1 further occurs in 9337 *Iberospondylus (Laurin & Soler-Gijón, 2006) and in the stereospondyls *Lydekkerina 9338 (Jeannot, Damiani & Rubidge, 2006: “hyoid tubercle”; Hewison, 2007: “quadrate tubercle”, 9339 “quadrate boss”) and *Australerpeton (Barberena, 1998; Eltink et al., 2016: fig. 8: 9340 caudolateral to the “tympanic crest”). 9341 Clearly, this character is inapplicable in the absence of a temporal embayment (SQU 9342 3(0)) or if the quadrate is inclined caudodorsally to rostroventrally (JAW ART 1/SQU 2/DEN 9343 8(3/4)).

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9344 State 0 is found in Solenodonsaurus (Danto, Witzmann & Müller, 2012), 9345 Discosauriscus (Klembara, 2009), Microphon (Bulanov, 2014: fig. 2) and Orobates 9346 (Nyakatura et al., 2015: digital reconstruction). 9347 Unknown in *Nigerpeton (D. M., pers. obs. of MNN MOR 69 and MNN MOR 70). 9348 9349 81. PREOPE 1: Preopercular: present (0); absent (1). RC07 had exchanged the states in the 9350 text but not in the matrix. 9351 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Ossinodus (Warren, 2007) 9352 have state 0. 9353 So does Whatcheeria (Lombard & Bolt, 1995; Bolt & Lombard, 2000). Ruta, Coates 9354 & Quicke (2003), the preceding version of RC07, cited Clack (1998, 2001) for the absence of 9355 the preopercular (state 1) in all post-Devonian tetrapods, but Clack (1998) confirmed the 9356 presence of the preopercular in Whatcheeria (as part of the argument for the absence of this 9357 bone in Crassigyrinus), and Clack (2001) mentioned neither the preopercular nor 9358 Whatcheeria. 9359 Unknown in Batropetes (Glienke, 2013, 2015), Lethiscus (area not preserved: Pardo et 9360 al., 2017) and *Nigerpeton (D. M., pers. obs. of MNN MOR 69 and MNN MOR 70). 9361 The position of the putative preopercular in *Coloraderpeton (Pardo et al., 2017: ext. 9362 data fig. 4, video; scored as present in their matrix) excludes all alternatives rather clearly; we 9363 have scored state 0. 9364 9365 deleted NOS 1: Nostrils posterolaterally expanded: absent (0); present (1). RC07 stated: 9366 “This is a feature of branchiosaurid dissorophoids, in which the external nostril outline widens 9367 in its posterolateral portion (Boy & Sues, 2000).” They proceeded to score state 1 for their 9368 three branchiosaurids (and no other OTUs). Yet, while state 1 is clearly present in Apateon 9369 dracyi (Schoch & Milner, 2008: fig. 1H) and arguably in A. pedestris (fig. 1G), it is clearly 9370 not in Schoenfelderpeton, where the nostril has a narrow caudal extension instead (fig. 4A). 9371 Leptorophus has a wider caudal extension, but it does not seem wider than the rostral half of 9372 the nostril, at least not in dorsal view (fig. 4B). State 0 is clearly found in Apateon gracilis 9373 (Schoch & Fröbisch, 2006), the sister-group to most or all of the rest of Apateon (Schoch & 9374 Milner, 2008). Scoring Schoenfelderpeton as having state 0 and Apateon as polymorphic 9375 makes this character parsimony-uninformative regardless of the condition in Leptorophus, so 9376 we have deleted it. This incidentally obviates the question of correlation with NOS 3, which 9377 describes a lengthening and widening of the nostril in its caudolateral part. 9378 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994). 9379 Unknown in Westlothiana (Smithson et al., 1994). 9380 9381 82. NOS 3: Nostrils: margins concave throughout (0); intermediate (1); keyhole-shaped 9382 (2) (ordered). The intermediate state is new; it accounts for Broiliellus (Schoch, 2012: fig. 9383 1F) and some, though not all, **other dissorophids (Schoch, 2012) as well as the amphibamid 9384 **Georgenthalia (Anderson et al., 2008b), where the dorsal and ventral margins are convex, 9385 approaching each other somewhat, but the extreme elongation of the nostril seen in state 2 is 9386 not reached. We have also assigned it to the very long nostrils of *Archaeovenator (Reisz & 9387 Dilkes, 2003). 9388 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and 9389 Solenodonsaurus (Danto, Witzmann & Müller, 2012). 9390 Brachydectes appears to have state 0 or 1 (Pardo & Anderson, 2016: fig. 3A, B). 9391 Phlegethontia seems to have state 2 (Anderson, 2007a: fig. 2). 9392 *Saharastega has state 0 or 1 regardless of which candidate holes actually are the 9393 nostrils (D. M., pers. obs. of MNN MOR 73).

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9394 83. NOS 4: Nostrils elliptical, with greater axis orientated obliquely in anteromedial to 9395 posterolateral direction: absent (0); present (1). RC07 added a further restriction on the 9396 length of the external nares in relation to the suture between the nasals, but this would make 9397 the character correlated to the length of the snout (for instance, it would require *Saharastega 9398 to have 10-cm-long nares to qualify for state 1, which it otherwise does whether or not 9399 Damiani et al. [2006] correctly identified the nares) and inapplicable in taxa without a suture 9400 between the nasals or without nasals. 9401 Inapplicable to greatly expanded nostrils (NOS 3(2) – Acheloma, Phonerpeton, 9402 Ecolsonia, *Mordex). 9403 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994). 9404 State 1 is present in Isodectes (Sequeira, 1998), Trimerorhachis (Milner & Schoch, 9405 2013), Balanerpeton (Milner & Sequeira, 1994), Eryops (though the nostrils are not very 9406 elliptical: Sawin, 1941), Broiliellus (Carroll, 1964; Schoch, 2012), Eoscopus (borderline: 9407 Daly, 1994), apparently Platyrhinops (Werneburg, 2012b), Micromelerpeton (Schoch, 9408 2009b), albanerpetids where known (McGowan, 2002; Venczel & Gardner, 2005), Eocaecilia 9409 (Jenkins, Walsh & Carroll, 2007), Caerorhachis (other shapes would be difficult to 9410 accommodate: Ruta, Milner & Coates, 2002), Gephyrostegus (Klembara et al., 2014: fig. 5– 9411 7), Diadectes (Kissel, 2010: fig. 34–36), Limnoscelis (Berman, Reisz & Scott, 2010), 9412 Petrolacosaurus (Reisz, 1981), apparently Asaphestera, Hapsidopareion, Micraroter, 9413 Pelodosotis, Rhynchonkos, Cardiocephalus (at least C. peabodyi), Euryodus and Hyloplesion 9414 (CG78; Szostakiwskyj, Pardo & Anderson, 2015), Microbrachis (Vallin & Laurin, 2004), 9415 Brachydectes (an extreme case: Wellstead, 1991; Pardo & Anderson, 2016), Lethiscus (Pardo 9416 et al., 2017), Capetus (even though its nostrils are quite small: Sequeira & Milner, 1993), 9417 Orobates (Berman et al., 2004) and Tseajaia (Moss, 1972). It is also present in Batropetes, 9418 though the reconstructions in dorsal and lateral view by Glienke (2013: fig. 2E, F) contradict 9419 each other on the exact angle. 9420 Unknown in Paleothyris (Carroll, 1969a) and Westlothiana (Smithson et al., 1994); 9421 unclear and likely unknown in Saxonerpeton and Odonterpeton (CG78). 9422 Dendrerpetidae is polymorphic, with state 0 appearing in Dendrysekos (Holmes, 9423 Carroll & Reisz, 1998) and state 1 in at least some Dendrerpeton specimens (A. R. Milner, 9424 1980, 1996); *Acanthostomatops is likewise polymorphic, sometimes within the same 9425 individual (Witzmann & Schoch, 2006a). 9426 We assign state 1 to *Sclerocephalus even though its nostrils have an additional 9427 triangular extension that points dorsomedially and even though the caudal margin is pointed 9428 in some cases (Schoch & Witzmann, 2009a). 9429 9430 84. INT FEN 1: Internarial fenestra or fontanelle: absent, mosaic of “postrostral” bones 9431 (0); present (1); absent, no “postrostral bones” (2) (ordered). State 2 is new (and 9432 corresponds to all instances of the original state 0 except Eusthenopteron and Panderichthys); 9433 the order follows the scenario suggested by Ahlberg et al. (2008). 9434 RC07 counted the presence of “median rostrals/internasals” as state 1, regardless of 9435 whether there is a fenestra (fontanelles are not mentioned) present additional to them or not. 9436 We cannot replicate this decision and find the characters independent: Ventastega (Ahlberg et 9437 al., 2008) and Acanthostega (Clack, 2003a, 2007; Porro, Rayfield & Clack, 2015) possess 9438 both a fontanelle (state 1 of the present character) and a pair of “median rostrals”; baphetids 9439 have a pair of “median rostrals” and a fully closed snout roof (state 2); Ichthyostega shows a 9440 single “median rostral” and a fully closed snout (state 2); *Deltaherpeton preserves a single 9441 “median rostral/internasal” and probably had a round fontanelle or at least a deep pit (state 1; 9442 Bolt & Lombard, 2010: figs. 1, 2, 3). We have therefore split this character and coded the 9443 number of “median rostrals/internasals” as a new one, MED ROS 1 (see below).

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9444 Lethiscus has state 1 (Pardo et al., 2017; J. Pardo, pers. comm.). 9445 Silvanerpeton has state 2 (Ruta & Clack, 2006). 9446 Unknown in Eucritta (Clack, 2001) and Edops (Romer & Witter, 1942; D. M., pers. 9447 obs. of MCZ 1378). Also unknown in Platyrhinops lyelli (Clack & Milner, 2010), but P. 9448 fritschi almost certainly shows state 2 (Werneburg, 2012b). 9449 States 1 and 2 occur in Trimerorhachis, even in T. insignis alone (Milner & Schoch, 9450 2013). The same appears to hold for Dendrerpetidae, with state 1 appearing in Dendrysekos 9451 (Holmes, Carroll & Reisz, 1998) while state 2 is probably present in Dendrerpeton confusum 9452 (Milner, 1996: fig. 7B); whether D. acadianum and D. rugosum have state 1 or 2 appears to 9453 be unknown (A. R. Milner, 1980, 1996). 9454 Balanerpeton has state 1 or 2 (specimen drawings in Milner & Sequeira, 1994). 9455 Apateon has states 1 and 2, with A. gracilis having state 2 throughout its ontogeny 9456 (Schoch & Fröbisch, 2006). 9457 State 2 seems pretty clear in *Aytonerpeton (Clack et al., 2016: supplementary video 9458 2). 9459 9460 85. MED ROS 1: “Median rostrals”/“medial rostrals”/“internasals”: paired (0); single 9461 (1); absent (2) (unordered). This character is split off from INT FEN 1 (see above). Pawley 9462 (2006: appendix 14) introduced a character with the same abbreviation, but only distinguished 9463 presence from absence – our state 1 would have been parsimony-uninformative in her matrix. 9464 All three names for these bones are unsatisfying. Strictly speaking, two bones in a 9465 transversely arranged pair cannot both be median, only a single bone can be; more 9466 importantly, the homology of these bones to any part of the “postrostral” mosaic of finned 9467 sarcopterygians is an underresearched and difficult problem – several pairs of “rostrals” can 9468 be “medial”. The “internasals” never lie only between the nasals, and in Ventastega they do 9469 not lie between them at all – they do not even contact the nasals, instead the premaxillae 9470 border the internarial fenestra, and the “internasals” lie far rostral of the “nasals” in their 9471 entirety (Ahlberg et al., 2008: fig. 3c, 4a). – The name “medial rostral” occurs only, to the 9472 best of our knowledge, in fig. 6 of Clack (2002), while the text of Clack (2002, 2003a) used 9473 “median”. 9474 We have scored Eusthenopteron and Panderichthys as unknown because homology is 9475 unclear, and Crassigyrinus likewise because its snout roof is very difficult to interpret. In 9476 Eucritta, this area of the skull is not preserved in any specimen (Clack, 2001), and the same 9477 holds for Edops (Romer & Witter, 1942; D. M., pers. obs. of MCZ 1378). 9478 One specimen of Megalocephalus has state 1, unlike the others, which have state 0 9479 (Beaumont, 1977: 51, 79); we have scored polymorphism. 9480 Otherwise, state 0 occurs in Ventastega (Ahlberg et al., 2008), Acanthostega (Clack, 9481 2002, 2003a, 2007; Porro, Rayfield & Clack, 2015) and Baphetes (Beaumont, 1977); 1 is 9482 restricted to Ichthyostega, *Deltaherpeton and *Elginerpeton; state 2 accounts for all other 9483 OTUs with a known snout roof. 9484 Part of the supposed premaxilla of *Aytonerpeton could be a “medial rostral” (Clack et 9485 al., 2016: supplementary video 2); we have scored state 0 or 2. 9486 9487 86. ORB 1: Interorbital distance greater than (0), subequal to (1), or smaller than half of 9488 skull […] width at the same level (2) (ordered). We have exchanged states 1 and 2 to make 9489 ordering of this continuous character possible and added the specification on where to 9490 measure skull width. 9491 Ventastega has state 2 (Ahlberg et al., 2008), as do Cochleosaurus (Sequeira, 2004), 9492 Bruktererpeton (Boy & Bandel, 1973), Notobatrachus (Báez & Nicoli, 2004), Vieraella (Báez

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9493 & Basso, 1996) and Tseajaia (Moss, 1972; Berman, Sumida & Lombard, 1992 – CM 38033, 9494 seen by D. M., is too distorted for comparison). 9495 Dendrerpetidae is polymorphic, with Dendrysekos reaching state 1 as already scored 9496 (Holmes, Carroll & Reisz, 1998) but Dendrerpeton having state 2 (A. R. Milner, 1980, 1996). 9497 The situation is unclear in Hapsidopareion due to disarticulation (CG78: fig. 13A). 9498 Diadectes is polymorphic, having states 0 and 1 (Berman, Sumida & Lombard, 1992; 9499 Berman, Sumida & Martens, 1998). So is Batropetes, with state 0 documented in B. 9500 niederkirchensis and B. palatinus and state 1 likely present in B. fritschi (Glienke, 2013, 9501 2015). 9502 Brachydectes has state 0 (Wellstead, 1991; Pardo & Anderson, 2016). 9503 Danto, Witzmann & Müller (2012) claimed state 0 for Solenodonsaurus. This is 9504 incorrect according to their fig. 3, which shows the already scored state 2. 9505 9506 87. ORB 2: Interorbital distance greater than (0), subequal to (1), or smaller than 9507 maximum orbit diameter (2) (ordered). We have exchanged states 1 and 2 to allow 9508 ordering of this continuous character. 9509 State 0 is found in Acanthostega (Porro, Rayfield & Clack, 2015) and Brachydectes 9510 (Pardo & Anderson, 2016). We further keep state 0 for Dendrerpetidae because it is found in 9511 Dendrysekos (Holmes, Carroll & Reisz, 1998), Dendrerpeton rugosum (A. R. Milner, 1980) 9512 and D. confusum (A. R. Milner, 1980, 1996); only D. acadianum, which is only known from 9513 considerably smaller specimens than the other two species, reaches state 1 (A. R. Milner, 9514 1980, 1996; Schoch & Milner, 2014). 9515 State 1 is found in Ichthyostega (Clack & Milner, 2015: fig. 8) and Trimerorhachis 9516 (Milner & Schoch, 2013). 9517 State 2 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994; Ahlberg et al., 9518 2008). 9519 Tseajaia shows state 1 or arguably 2 (Moss, 1972, Berman, Sumida & Lombard, 9520 1992); we have decided on state 1. (CM 38033, seen by D. M., is too distorted for 9521 comparison.) 9522 Eucritta is scored as unknown for having juvenile eye size. 9523 We have scored Albanerpetidae, Karaurus, Valdotriton, Notobatrachus, Vieraella, 9524 *Beiyanerpeton and *Pangerpeton as unknown, because it is unknown how much of the 9525 orbitotemporal fenestra is homologous to the orbit. (RC07 had scored Brachydectes as 9526 unknown, presumably for the same reason; though see above.) Only the interorbital width of 9527 Triadobatrachus is so small that even the smallest realistic estimates for eyeball size result in 9528 state 2, which was already scored. In several specimens of *Liaobatrachus, the eyes are 9529 preserved as circular stains, which are about as wide as the interorbital distance; allowing for 9530 some space around the eye in the orbit proper, we have therefore scored state 2 for 9531 *Liaobatrachus. 9532 As for most lissamphibians, we have assigned state 1 or 2 to *Spathicephalus. 9533 *Cheliderpeton passes from state 2 to state 0 in ontogeny (Werneburg & Steyer, 2002: 9534 fig. 1). 9535 States 1 and 2 are found in the largest illustrated adults of *Glanochthon (Schoch & 9536 Witzmann, 2009b: fig. 2). 9537 9538 88. ORB 3/LAC 5: Rostroventral margin of orbit: round (0); angled (1); “antorbital 9539 vacuity” present (2) (ordered). State 2, which corresponds to the original LAC 5(1), occurs 9540 in Baphetes, Megalocephalus and *Spathicephalus; we count it as a state of this character 9541 because it makes state 1 inapplicable and because it may be an exaggerated version of it.

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9542 Because its ontogenetic development is unknown, we have scored Eucritta as having state 1 9543 (as observed) or 2. 9544 State 1 is also observed in Acanthostega (Clack, 2007; Porro, Rayfield & Clack, 9545 2015), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Seymouria (both species: Laurin, 1996c, 9546 2000; Klembara et al., 2005, 2006, 2007) and Batropetes (Glienke, 2013, 2015) as well as 9547 *Caseasauria (especially Eothyris) and *Neopteroplax (Romer, 1963). 9548 Dendrerpetidae is polymorphic: the previously scored state 0 is found in Dendrerpeton 9549 rugosum and D. acadianum (A. R. Milner, 1980, 1996: fig. 4A), while Dendrysekos reaches 9550 state 1 (Holmes, Carroll & Reisz, 1998: fig. 4C). 9551 The condition in Westlothiana is unknown (Smithson et al., 1994). 9552 *Palaeoherpeton (like Ventastega and Ichthyostega) appears to have a rostral and a 9553 ventral angle, but a negative rostroventral one, thus state 0 (Panchen, 1964). 9554 9555 89. ORB 4: Orbit deeper than long: no (0); yes (1). 9556 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and 9557 Brachydectes (Pardo & Anderson, 2016) and seems highly likely in *Aytonerpeton (Clack et 9558 al., 2016: especially supplementary video 2). 9559 Eocaecilia has state 0 as already scored (Jenkins, Walsh & Carroll, 2007). However, 9560 we have scored all other modern amphibians as unknown because it is unknown how much of 9561 the orbitotemporal fenestra is homologous to the orbit. 9562 9563 90. ORB 5: Orbit anteroposterior diameter shorter than (0), subequal to (1), or longer 9564 than (2) distance between orbit posterior margin and suspensorium anterodorsal margin 9565 (ordered). We have exchanged states 1 and 2 to make ordering of this continuous character 9566 possible, and interpret the rostral end of the temporal embayment (if present) as 9567 “suspensorium anterodorsal margin”. Note that the wording implies a rostrodorsally-to- 9568 caudoventrally-inclined suspensorium; when the suspensorium is inclined the other way 9569 around (state JAW ART1/SQU 2/DEN 8(3,4), see below), we have used its caudodorsal end 9570 as the “anterodorsal margin”. 9571 “The distribution of the different states of this character is extremely irregular and 9572 shows several instances of parallel developments and reversals”, wrote RC07. On the shortest 9573 of our trees from Analysis R4, it waxes and wanes gently for a total of 39 steps; there are only 9574 five direct transitions between states 0 and 2. State 2 holds Dissorophoidea and 9575 *Iberospondylus together (ambiguously also Balanerpeton, depending on the position of 9576 *Palatinerpeton); there is only a single reversal in this clade (within *Micropholis, an OTU 9577 which shows all three states). State 2 is further synapomorphic between Ventastega and 9578 Acanthostega, and between Whatcheeria and Pederpes; state 1 ties at least the latter together 9579 with everything as far crownward as Amniota, with a total of 11 reversals to state 0 (four of 9580 them in Anthracosauria). Clearly, this character carries phylogenetic signal. 9581 Euryodus has state 0 (CG78); so does Brachydectes (Pardo & Anderson, 2016). 9582 Not counting the antorbital fenestra (see ORB 3/LAC 5) rostral to the lateral 9583 outgrowth of the prefrontal (PREFRO 7), Baphetes and Megalocephalus have state 0 as well 9584 (Beaumont, 1977). 9585 Ventastega (Ahlberg et al., 2008) has state 2, as do Acanthostega (Clack, 2003a, 2007; 9586 Porro, Rayfield & Clack, 2015), Balanerpeton (Milner & Sequeira, 1994, with the exception 9587 of the rather small specimen in fig. 4 that may have state 1), Phonerpeton (an extreme case of 9588 state 2: Dilkes, 1990; D. M., pers. obs. of AMNH 7150 and MCZ 2313), Doleserpeton 9589 (Sigurdsen & Bolt, 2010) and Gephyrostegus (Klembara et al., 2014).

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9590 We have scored all modern amphibians other than Eocaecilia and *Chelotriton as 9591 unknown because it is unknown how much of the orbitotemporal fenestra is homologous to 9592 the orbit. 9593 All three states occur in *Micropholis (Schoch & Rubidge, 2005). 9594 While Oedaleops has state 2, the larger Eothyris has state 1; we have scored only the 9595 latter state for *Caseasauria. 9596 *Cheliderpeton passes from at least state 1 to state 0 in ontogeny (Werneburg & 9597 Steyer, 2002: fig. 1). 9598 9599 91. PIN FOR 1: Pineal foramen present in adults (0); absent in adults (1). Ruta, Coates & 9600 Quicke (2003) had coded the presence and the position of the pineal foramen as PIN FOR 1 9601 and PIN FOR 2, respectively. Ruta & Coates (2007) merged them into a character they called 9602 PIN FOR 2. We kept this in the first two preprints of this paper (Marjanović & Laurin, 2015, 9603 2016) except for Analysis EB. Here we separate them again because the pineal foramen has a 9604 known position – PIN FOR 2(1) – in immature Cochleosaurus even though it is lost in adults 9605 (Milner & Sequeira, 2003; Sequeira, 2004, and references therein), showing that absence does 9606 not in fact make position inapplicable. Further, PIN FOR 2 can now simply be ordered instead 9607 of requiring a stepmatrix. 9608 The situation in Hapsidopareion is unclear because of disarticulated parietals and 9609 frontals (CG78: figs. 13, 14). 9610 State 1 is now known in Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015). 9611 Both species of Cardiocephalus are polymorphic, and so is Micraroter (CG78). 9612 Euryodus is polymorphic, with E. primus having state 1 and E. dalyae having state 0 9613 (CG78). 9614 9615 92. PIN FOR 2: Pineal foramen caudal to (0), at the level of (1), or rostral to (2) 9616 interparietal suture midlength (ordered). 9617 Unknown in Ventastega (Ahlberg et al., 2008). 9618 Acanthostega has state 2 (Porro, Rayfield & Clack, 2015). 9619 Ichthyostega appears to have states 0 and 1 (Clack & Milner, 2015: 21, fig. 8). 9620 Chenoprosopus has state 0 (Reisz, Berman & Henrici, 2005). 9621 State 1 is found in Cochleosaurus (Milner & Sequeira, 2003). 9622 Limnoscelis shows state 1 (Berman, Reisz & Scott, 2010: fig. 3A). 9623 The situation in Hapsidopareion is unclear because of disarticulated parietals and 9624 frontals (CG78: figs. 13, 14). 9625 Micraroter has state 2 (Carroll & Gaskill, 1978). 9626 Although Phlegethontia lacks parietals, we have kept state 2 because the frontals reach 9627 the pineal foramen (Anderson, 2002). 9628 *Caseasauria has states 0 and 1 (state 1 in Eothyris, state 0 in Oedaleops: Reisz, 9629 Godfrey & Scott, 2009). 9630 States 0, 1 and 2 are documented in *Glanochthon, apparently independent of 9631 ontogenetic age (Schoch & Witzmann, 2009b: fig. 2). 9632 Milner & Sequeira (2011: 63) stated that state 1 is “almost” reached in *Erpetosaurus, 9633 and reconstructed state 1 (fig. 11); their photos and drawings of specimens, however, show 9634 varying extents of state 2. Because Milner & Sequeira (2011) documented the existence of 9635 many more specimens than they figured, we have scored polymorphism. 9636 In *Neopteroplax, only state 2 can be excluded; the presence of the foramen (PIN 9637 FOR 1) remains unknown (Romer, 1963: fig. 1). 9638

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9639 93. L SC SKU 1: Lightly sculptured area (subdued ornament) adjacent to skull roof 9640 midline: absent (0); present (1). 9641 State 0 is present in Ventastega (Ahlberg et al., 2008). 9642 State 1 makes a surprise appearance in Ossinodus (Warren & Turner, 2004). 9643 Steyer et al. (2006: appendix 2: character 39) scored state 1 of this character for 9644 *Nigerpeton, but did not mention it anywhere in the text and illustrated it only ambiguously 9645 (fig. 2A). Consequently, we scored state 0 in the first two preprints of this paper (Marjanović 9646 & Laurin, 2015, 2016). State 1 is in fact correct, so we have now scored it: although 9647 somewhat difficult to find or to photograph, it is found on the frontals and a third of the 9648 parietals of MNN MOR 70 (D. M., pers. obs.). 9649 Although conditions that may count as state 1 are widespread in *Chelotriton (Schoch, 9650 Poschmann & Kupfer, 2015), MB.Am.45 has state 0, which we have scored. 9651 9652 94. PTF 1: Posttemporal fossa occurring at occiput dorsolateral corner, delimited 9653 dorsally by skull table, not bordered laterally and floored by dorsolateral extension of 9654 opisthotic (0); fossa present near occiput dorsolateral corner, delimited dorsally by 9655 occipital flanges of tabular and postparietal and bordered laterally as well as ventrally 9656 by dorsolateral extension of opisthotic meeting tabular ventromedial flange (1); small 9657 fossa present near occiput ventrolateral corner, bordered laterally by tabular 9658 ventromedial flange, delimited dorsally by dorsal portion of the lateral margin of the 9659 suproccipital–opisthotic complex and floored by lateral extension of opisthotic (2); 9660 absence of fossa (3) (unordered). It is possible that this character should be ordered or be 9661 treated according to a more complex stepmatrix, but we are not sure about this and cannot 9662 find a suggestive pattern in the data. 9663 State 0 is present in Panderichthys (Brazeau & Ahlberg, 2006) and Ventastega 9664 (Ahlberg et al., 2008) and makes a surprise appearance in Edops (D. M., pers. obs. of MCZ 9665 1378 – the short paroccipital process has an unfinished end in this huge skull). 9666 The potentially informative specimen of Chenoprosopus, USNM 437646, is crushed, 9667 but state 1 is the best fit (D. M., pers. obs.). 9668 Doleserpeton shows state 1, even though the lateral border is formed by the tabular 9669 rather than the opisthotic (Sigurdsen, 2008). This is common in stereospondyls as well, 9670 including *Australerpeton (Barberena, 1998; Eltink et al., 2016). 9671 State 2 fits the condition reconstructed for Batropetes best, though there may not have 9672 been any floor (Glienke, 2013). 9673 Rhynchonkos shows state 2 or 3 (Szostakiwskyj, Pardo & Anderson, 2015); Lethiscus 9674 has state 1 or 3 (Pardo et al., 2017). 9675 Eocaecilia (Jenkins, Walsh & Carroll, 2007), Brachydectes (Pardo & Anderson, 2016) 9676 and Orobates (Berman et al., 2004) have state 3. 9677 Triadobatrachus has state 1 (ignoring the fact that the frontoparietal plays the roles of 9678 the absent postparietals and tabulars) or 3; despite the crushing and the preservation as a 9679 natural mold, the other states can most likely be excluded (Ascarrunz et al., 2016: 3D model 9680 1). 9681 *Saharastega has state 1 or 3 (D. M., pers. obs. of MNN MOR 73). 9682 State 1 makes a somewhat unexpected appearance in *Caseasauria (Eothyris; Reisz, 9683 Godfrey & Scott, 2009). While the fenestra is too small to reach the postparietal, state 1 is 9684 otherwise a perfect match; state 2, expected for very early amniotes, is not. 9685 *Quasicaecilia has state 0 or 3 (Pardo, Szostakiwskyj & Anderson, 2015: fig. 2). 9686 9687

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9688 95. SKU TAB 1: Ratio of width to postorbital midline length of skull table: ≤ 1 (0); 9689 ]1;1.5] (1); ]1.5;2] (2); ]2;2.5] (3); > 2.5 (4) (ordered). We have recoded this character much 9690 like we did with PREMAX 7. Ruta, Coates & Quicke (2003) worded it as follows, under the 9691 section headline “Proportions of skull table” (italics in the original): 9692 “SKU TAB 1. Absence (0) or presence (1) of condition: postorbital region of skull 9693 roof abbreviated. Although shortening of the postorbital skull roof region occurs in various 9694 degrees, several crown-group taxa are distinctly different from the outgroup and from stem- 9695 tetrapods in that their skull roof is usually wider than long, regardless of the morphology and 9696 proportions of its various constituent bones. Several temnospondyls more crownward than 9697 trimerorhachoids […] and crown-lissamphibians […] have acquired the derived state of this 9698 character independent of several basal and crown-amniotes, Westlothiana, microsaurs, 9699 Scincosaurus and derived diplocaulids […].” 9700 Compare RC07 (italics in the original): 9701 “SKU TAB 1. Postorbital region of skull table abbreviated and at least one-third 9702 wider than long: absent (0); present (1). The derived state is acquired in parallel by total 9703 group amniotes and amphibians (except the most basal taxa of both groups).” 9704 The 2003 version was irreproducible. The 2007 version is close to unambiguous (fully 9705 so for many OTUs) if taken at face value, but the question remains whether the skull table or 9706 the skull roof was meant (see main text). As with PREMAX 7, the original scores fail to 9707 provide evidence: the width/length ratio of the skull table, the width/length ratio of the skull 9708 roof, the ratio of the width of the skull table to the length of the skull roof and the ratio of the 9709 width of the skull roof to the length of the skull table are all about equally bad matches for the 9710 scores by RC07 (Appendix-Table 3, Data S2). We have decided in favor of the skull table for 9711 both measurements (the postorbital length of the skull table is, as in TAB 7, the distance 9712 between the caudal extremities of the orbits/orbitotemporal fenestrae – averaged where 9713 necessary – and the transverse level of the caudal end of the skull table in the sagittal plane); 9714 one reason is the fact that the postorbital length of the skull roof depends on the position of 9715 the caudal extremities of the suspensoria, which is already a character in this matrix (JAW 9716 ART 1/SQU 3/DEN 8). 9717 Like PREMAX 7, this is a continuous character which we have arbitrarily divided into 9718 states by creating a state for each interval of 0.5 (lumping the few extreme outliers above 3 9719 into the same state as the other OTUs above 2.5). 9720 The ratios, sources, and state changes are presented in Appendix-Table 3; they and our 9721 measurements are contained in Data S2. In salientians, the caudal margin of the 9722 orbitotemporal fenestra was taken to be the rostral margin of the otic capsule, not of the 9723 lateral process of the parietal that covers only the caudal or caudomedial part of the otic 9724 capsule. 9725 *Llistrofus has state 0 (Appendix-Table 3). Hapsidopareion appears to differ starkly in 9726 having state 2, but this could be ontogenetic: the skull the reconstruction (CG78: fig. 13B) is 9727 based on is much smaller than the *Llistrofus skull, and indeed only about half as long as 9728 another skull which CG78 referred to Hapsidopareion but only illustrated in ventral view (fig. 9729 14E); the latter skull appears to have a proportionally longer postorbital region. We therefore 9730 scored Hapsidopareion as having state 0, 1 or 2. 9731 Unknown in Acherontiscus (Carroll, 1969b) and Dolichopareias (Andrews & Carroll, 9732 1991). 9733 9734 9735 9736

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9737 Appendix-Table 3: Ratios of skull table width to postorbital (postorbitotemporal) skull 9738 table length, and changes to the scores of character 95 (SKU TAB 1). Taxa underlain in 9739 blue were scored 0 by RC07, taxa underlain in yellow were scored 1, and the remainder were 9740 scored as unknown or have been added by us; the latter are marked with an asterisk. 9741 Abbreviation: Ph., Pholiderpeton. See Data S2 and its legend for more information. 9742 OTU Ratio New Measured in: (rounded) score *Coloraderpeton 0.231 0 Anderson, 2003a: fig. 3A; not measurable in Pardo et al., 2017, but looks the same and clearly does not leave state 0 *Llistrofus 0.515 0 Bolt & Rieppel, 2009 *Pseudophlegethontia 0.600 0 Anderson, 2003b: fig. 3 Phlegethontia 0.652 0 Anderson, 2007a Odonterpeton 0.698 0 CG78: fig. 99B Sauropleura 0.706 0 Bossy & Milner, 1998 Eocaecilia 0.716 0 Jenkins, Walsh & Carroll, 2007 *Erpetosaurus 0.724 0 Milner & Sequeira, 2011 Oestocephalus 0.732 0 Anderson, 2003b Adelogyrinus 0.745 0 Andrews & Carroll, 1991 Notobatrachus 0.813 0 Báez & Nicoli, 2004 *Sparodus 0.826 0 Carroll, 1988 Lethiscus 0.836 0 J. Pardo, pers. comm. 2017 Adelospondylus 0.852 0 Andrews & Carroll, 1991 Captorhinus 0.906 0 Fox & Bowman, 1966: fig. 3 Neldasaurus 0.912 0 Schoch & Milner, 2014: fig. 20C Colosteus 0.983 0 Hook, 1983 Ventastega 1.000 0 Ahlberg et al., 2008 Urocordylus 1.000 0 Bossy & Milner, 1998 Greererpeton 1.074 1 Smithson, 1982 Crassigyrinus 1.078 1 Clack, 1998 *Pholidogaster 1.087 1 Panchen, 1975 Isodectes 1.090 1 Schoch & Milner, 2014: fig. 20E Paleothyris 1.091 1 Carroll, 1969a: fig. 4B Panderichthys 1.103 1 Vorobyeva & Schultze, 1991 *Deltaherpeton 1.106 1 Bolt & Lombard, 2010: fig. 2; right side approximately doubled *Utaherpeton 1.111 1 Carroll, Bybee & Tidwell, 1991 Euryodus 1.119 1 CG78: fig. 37 Eusthenopteron 1.130 1 Clack, 2007 *Chroniosaurus 1.132 1 Clack & Klembara, 2009 *Cheliderpeton 1.155 1 Werneburg & Steyer, 2002 *Archegosaurus 1.159 1 Witzmann, 2006: fig. 5 Baphetes 1.159 1 Beaumont, 1977: fig. 21 Chenoprosopus 1.170 1 Schoch & Milner, 2014: fig. 13E Trimerorhachis 1.191 1 Schoch & Milner, 2014: fig. 20A Eucritta 1.200 1 Clack, 2001: fig. 8 Ptyonius 1.200 1 Bossy & Milner, 1998 *Australerpeton 1.206 1 Eltink et al., 2016: fig. 5

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*Glanochthon 1.214 1 Schoch & Witzmann, 2009b: fig. 2A approximately doubled Ph. attheyi 1.228 1 Panchen, 1972 Cardiocephalus 1.228 1 CG78: fig. 69 Pantylus 1.281 1 Romer, 1969: fig. 1 Proterogyrinus 1.304 1 Holmes, 1984 Caerorhachis 1.306 1 Ruta, Milner & Coates, 2002 Silvanerpeton 1.344 1 Ruta & Clack, 2006 Ph. scutigerum 1.346 1 Clack, 1987b *Konzhukovia 1.348 1 Gubin, 1991: drawing 6a *Sclerocephalus 1.358 1 Schoch & Witzmann, 2009a *Neopteroplax 1.366 1 Romer, 1963: fig. 3 Cochleosaurus 1.388 1 Schoch & Milner, 2014: fig. 13D *Palatinerpeton 1.404 1 Boy, 1996: fig. 3 Albanerpetidae 1.414 1 Celtedens: McGowan, 2002 *Platyoposaurus 1.419 1 Gubin, 1991: drawing 3a Balanerpeton 1.458 1 Schoch & Milner, 2014: fig. 17A Bruktererpeton 1.458 1 estimated based on Boy & Bandel, 1973: fig. 7 Edops 1.459 1 Schoch & Milner, 2014: fig. 13A Acanthostega 1.465 1 Porro, Rayfield & Clack, 2015 Dendrerpetidae 1.466 1 Dendrysekos: Schoch & Milner, 2014: fig. 17C Megalocephalus 1.468 1 Beaumont, 1997: fig. 8 Capetus 1.500 1 Sequeira & Milner, 1993 Micromelerpeton 1.500 1 Beaumont, 1997: fig. 8 Westlothiana 1.500 1 Smithson et al., 1994 *Palaeoherpeton 1.500 1 Panchen, 1964 Kotlassia 1.542 2 Bulanov, 2003: fig. 30 Keraterpeton 1.545 2 Bossy & Milner, 1998 Whatcheeria 1.586 2 Lombard & Bolt, 1995: fig. 1A Vieraella 1.594 2 Báez & Basso, 1996: fig. 6, 7 *Mordex 1.605 2 Schoch & Milner, 2014: fig. 32A Gephyrostegus 1.614 2 Klembara et al., 2014 *Lydekkerina 1.634 2 Hewison, 2007: fig. 30 Stegotretus 1.667 2 Berman, Eberth & Brinkman, 1988: fig. 10B Hyloplesion 1.667 2 CG78: fig. 89B Ichthyostega 1.667 2 Clack & Milner, 2015: fig. 8 Pederpes 1.674 2 Clack & Finney, 2005 *Iberospondylus 1.685 2 Laurin & Soler-Gijón, 2006: fig. 1A left side approximately doubled Microbrachis 1.689 2 Vallin & Laurin, 2004 Ossinodus 1.705 2 Warren, 2007 Valdotriton 1.711 2 Evans & Milner, 1996 *Micropholis 1.750 2 Schoch & Rubidge, 2005: fig. 3B Phonerpeton 1.778 2 Dilkes, 1990: fig. 1 Discosauriscus 1.780 2 Klembara et al., 2006 Rhynchonkos 1.825 2 CG78: fig. 63

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Pelodosotis 1.829 2 CG78: fig. 48 Ariekanerpeton 1.854 2 Klembara & Ruta, 2005a Seymouria 1.877 2 Laurin, 1996c Archeria 1.900 2 Holmes, 1989 *NSM 994 GF 1.1 1.920 2 Holmes & Carroll, 2010 Amphibamus 1.938 2 Schoch & Milner, 2014: fig. 30 Eoherpeton 1.943 2 Panchen, 1975 Brachydectes 1.965 2 Pardo & Anderson, 2016: fig. 4b Solenodonsaurus 1.972 2 Danto, Witzmann & Müller, 2012 *Karpinskiosaurus 2.020 3 Klembara, 2011 Scincosaurus 2.027 3 Milner & Ruta, 2009 Doleserpeton 2.044 3 Sigurdsen & Bolt, 2010 Schoenfelderpeton 2.048 3 Boy, 1986: fig. 13 Broiliellus 2.050 3 Carroll, 1964 *Bystrowiella 2.051 3 Witzmann & Schoch, 2017: fig. 15C Diceratosaurus 2.061 3 Bossy & Milner, 1998 Orobates 2.092 3 Kissel, 2010: fig. 32B *Saharastega 2.105 3 D. M., pers. obs. of MNN MOR 73 *Nigerpeton 2.113 3 Steyer et al., 2006 Eoscopus 2.130 3 Daly, 1994: fig. 3 Leptorophus 2.156 3 Boy, 1986: fig. 4 Eryops 2.167 3 Schoch & Milner, 2014: fig. 3C Petrolacosaurus 2.186 3 Berman, Sumida & Lombard, 1992: fig. 11 Micraroter 2.189 3 CG78: fig. 56 Microphon 2.195 3 Bulanov, 2003: fig. 22 Asaphestera 2.326 3 CG78: fig. 7 Karaurus 2.333 3 Ivachnenko, 1978 *Acanthostomatops 2.333 3 Witzmann & Schoch, 2006a Limnoscelis 2.364 3 Kissel, 2010: fig. 13A1 Ecolsonia 2.371 3 Berman, Reisz & Eberth, 1985: fig. 5A Anthracosaurus 2.388 3 Clack, 1987a Acheloma 2.395 3 Polley & Reisz, 2011 Batrachiderpeton 2.397 3 Bossy & Milner, 1998 *Caseasauria 2.398 3 Eothyris: Reisz, Godfrey & Scott, 2009 Batropetes 2.445 3 Glienke, 2013: fig. 2 Platyrhinops 2.471 3 Clack & Milner, 2010: fig. 9 Saxonerpeton 2.471 3 CG78: fig. 22 *Carrolla 2.563 4 Maddin, Olori & Anderson, 2011 Utegenia 2.627 4 Klembara & Ruta, 2004a *Gerobatrachus 2.657 4 estimated based on Anderson et al., 2008a: fig. 2b *Tungussogyrinus 2.795 4 Werneburg, 2009 Apateon 2.860 4 Schoch & Fröbisch, 2006: fig. 1D *Spathicephalus 2.867 4 Beaumont & Smithson, 1998: fig. 5 Tuditanus 2.889 4 Carroll & Baird, 1968: fig. 9 *Archaeovenator 2.963 4 Reisz & Dilkes, 2003 Tseajaia 2.976 4 Berman, Sumida & Lombard, 1992: fig. 11

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*Liaobatrachus 3.100 4 Dong et al., 2013 *Crinodon 3.500 4 CG78: fig. 11 *Chelotriton 3.571 4 Marjanović & Witzmann, 2015: fig. 7 Triadobatrachus 3.724 4 Roček & Rage, 2000; roof estimated *Quasicaecilia 3.809 4 Pardo, Szostakiwskyj & Anderson, 2015: fig. 3 Diplocaulus 5.238 4 Olson, 1951: pl. 5B left side doubled Diploceraspis 5.849 4 Beerbower, 1963: fig. 2 Diadectes 6.280 4 Kissel, 2010: fig. 36B 9743 9744 1 A line drawing identical to Berman, Reisz & Scott (2010: fig. 3A), but slightly more 9745 convenient to measure. 9746 9747 96. FONT 1: Dorsal exposure of frontoparietal fontanelle: absent (0); present (1). 9748 State 0 is present in Ventastega (Ahlberg et al., 2008). This was already correctly 9749 scored by RC07, who had not known of that material. Probably they intended to score 9750 Ventastega for TEM FEN 1, but slipped one column to the left; Ventastega indeed has state 0 9751 of that character (Ahlberg, Lukševičs & Lebedev, 1994). 9752 9753 97. TEM FEN 1: Broad opening in skull postorbital region: absent (0); present (1). RC07 9754 had added “(aïstopod pattern)”, but potential primary homologues of the aïstopod temporal 9755 fenestra can be found elsewhere. 9756 Most obviously, the diapsid Petrolacosaurus has two temporal fenestrae. In principle, 9757 they could have arisen from a single fenestra that was subdivided by a contact between 9758 processes of the postorbital and the squamosal. There is no evidence that this actually 9759 happened, but, firstly, to take this into account would mean to insert assumptions about 9760 secondary homology into the determination of primary homology; secondly, the lateral 9761 temporal fenestra has subdivided itself in just such a fashion (by a contact between 9762 neomorphic processes of the jugal and the squamosal) in several **dinosaurs, e.g. 9763 **Cryolophosaurus (Hammer & Hickerson, 1994), giving these animals a total of three 9764 temporal fenestrae per side. We have therefore scored Petrolacosaurus as possessing state 1. 9765 On the other hand, fenestrae can become confluent with other openings. Both temporal 9766 fenestrae (per side) and the orbit of Cenozoic and many Mesozoic **birds have indeed 9767 merged in such a way; at least in principle, the orbitotemporal fenestra found in Brachydectes 9768 and all modern amphibians in this matrix other than Eocaecilia might be the result of a similar 9769 merger. We have therefore scored all these OTUs as sharing state 1. This does not, however, 9770 apply to the very elongate orbit of Batropetes, which retains the postfrontal and postorbital 9771 bones at its caudal margin (Glienke, 2013, 2015). 9772 Finally, states 1 of this character and the next are not mutually exclusive. In particular, 9773 the temporal fenestra of most diapsids is open ventrally, as the contact between jugal and 9774 quadratojugal has been lost. Because of the orientation of the quadratojugal in *Llistrofus 9775 (Bolt & Rieppel, 1999: fig. 4), we have scored state 1 of the present character for that OTU. 9776 State 0 is in any case present in Ventastega (see FONT 1 above). 9777 9778 98. CHE EMA 1: Ventral emargination of cheek (pattern of certain tuditanomorph 9779 microsaurs): absent (0); present (1). This pattern is not limited to Hapsidopareion, 9780 Micraroter and Pelodosotis (and *Llistrofus): a very mild version occurs in Batropetes 9781 (Glienke, 2015), a less mild one in Lethiscus (Pardo et al., 2017; also scored in their matrix) 9782 and Phlegethontia (Anderson, 2002). We have scored Oestocephalus and *Coloraderpeton as 9783 unknown because there is no non-phylogenetic way to tell if their ventrally open temporal

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9784 fenestra is continuous with an emargination (Carroll, 1998a; Anderson, 2003a; Pardo et al., 9785 2017, excluding their matrix, where state 1 was scored for *Coloraderpeton). 9786 State 0 is present in Ventastega (Ahlberg et al., 2008). 9787 Unknown in *Nigerpeton (D. M., pers. obs. of MNN MOR 69 and MNN MOR 70). 9788 The cheek (jugal, quadratojugal) is absent in Brachydectes, possibly Triadobatrachus, 9789 and all salamanders except (see QUAJUG 1 above) *Chelotriton; we have accordingly scored 9790 them as unknown. 9791 9792 deleted IFN 1: Interfrontonasal: absent (0); present (1). As RC07 explicitly mentioned, 9793 this character is parsimony-uninformative because state 1 is limited to Eryops. We have 9794 therefore deleted it. Our addition of *Crinodon has made it parsimony-informative again, but 9795 there would be little point in reintroducing this character, given the fact that *Crinodon and 9796 Eryops are among the least similar taxa in the entire matrix except where symplesiomorphies 9797 are concerned. 9798 Recently an interfrontal has been discovered in most specimens of Batropetes, though 9799 it is absent in some of both B. fritschi and B. palatinus (Glienke, 2013, 2015; tentatively 9800 confirmed for B. palatinus by D. M., pers. obs. of MB.Am.1232.1). Because PAUP* cannot 9801 reconstruct ancestors as polymorphic, state 1 could not hold Batropetes and *Crinodon 9802 together. 9803 The evidence for paired interfrontonasals in any colosteids (Bolt & Lombard, 2010) is 9804 not convincing. If Greererpeton has a single bone between the frontals, nasals and 9805 premaxillae, it should probably be considered a “median rostral” (see MED ROS 1 above) 9806 rather than an interfrontonasal. 9807 One specimen of *Sclerocephalus has an interfrontonasal (Boy, 1988: 116), as does 9808 one of *Lydekkerina (Jeannot, Damiani & Rubidge, 2006). Given the fact that so many more 9809 specimens of both (Jeannot, Damiani & Rubidge, 2006; Schoch & Witzmann, 2009a) lack it, 9810 and the fact that the *Lydekkerina individual with an interfrontal also has an interparietal 9811 (Jeannot, Damiani & Rubidge, 2006), we have decided to ignore these cases as aberrations of 9812 development. In Eryops, every one of the many known skulls shows the interfrontonasal, 9813 while even its **closest relatives always lack it (Werneburg, 2007a, 2012a; Werneburg & 9814 Berman, 2012). 9815 9816 99. SUS 1: Anteroposteriorly narrow, bar-like squamosal: absent (0); present (1). 9817 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and most 9818 likely Batropetes (Glienke, 2013: fig. 6H; contra Carroll, 1991). It is also known in Lethiscus 9819 (Pardo et al., 2017) and *Saharastega (D. M., pers. obs. of MNN MOR 73). 9820 State 1 is found in all modern amphibians in this matrix except Eocaecilia (0 as 9821 already scored) and Vieraella (unknown). We note, however, that **Gobiates, possibly 9822 closely related to *Liaobatrachus, has state 0 (Roček, 2008). 9823 Cardiocephalus was scored as sharing state 1 in RC07. The squamosal shown on both 9824 sides of the skull in CG78: fig. 30A is dorsoventrally narrow, not rostrocaudally. We have 9825 scored state 0. 9826 Most of the squamosal of *Carrolla is unknown, but state 1 is likely enough (Maddin, 9827 Olori & Anderson, 2011) that we have scored it as present. 9828 9829 100. SC 1: Lateral-line system on skull roof totally enclosed (0), mostly enclosed with 9830 short sections in grooves (1), mostly in grooves with short sections enclosed (2), entirely 9831 in grooves (3), absent (4) (ordered). RC07 had “skull table” instead of “skull roof”. We have 9832 ordered this and the following character because the present sequence of states represents a

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9833 gradual movement of the lateral-line organ from inside the bones to their surface and beyond 9834 (the organ is present in extant aquatic lissamphibians, but never leaves traces on bones). 9835 States 0 and 4 can be difficult to distinguish from the outside. Indeed, Warren (2007) 9836 reported that Edops, Chenoprosopus and Eryops, previously thought to have state 4 (but see 9837 below for Chenoprosopus), have state 0. We have scored both as possibilities in Edops and 9838 Eryops, because it is not clear if this canal in the quadratojugal which had no connection to 9839 the outside – at least in that bone – is homologous to a lateral-line canal or rather carried 9840 nerves and/or blood vessels; Čerňanský et al. (2016) did not commit to any interpretation and 9841 called for more research. Because the quadratojugal of Cochleosaurus is only known in 9842 external (dorsolateral and edge-on ventral) view, we have scored it the same way. 9843 Pawley (2006: 188) claimed that Dendrerpeton (Dendrerpetidae) has “pits and 9844 perforations” for the postcranial in the ventralmost row of dorsal scales, and 9845 Schoch (2013: 21; not citing Pawley, 2006) even spoke of “possible lateral line sulci”, both 9846 implying that the absence of traces of cranial lateral lines in this taxon (e.g. A. R. Milner, 9847 1980, 1996) is unexpected and may turn out to be erroneous. However, Pawley (2006) and 9848 Schoch (2013) both cited only Dawson (1882) for these observations. Although Dawson 9849 (1882: 647) mentioned “minute round pores, probably mucous or perspiratory pores” in 9850 dorsal scales (“horny scales”, as opposed to the more strongly mineralized “bony” ventral 9851 ones) and mentioned that the ventralmost row of dorsal scales is “in some specimens” 9852 composed of unusually large scales “forming a sort of Vandyke edging”, he gave no 9853 indication that the pores are restricted to that row. The closest Dawson (1882: 647) came to 9854 such a statement is the following somewhat enigmatic sentence: “In front the skin projects 9855 into long pendant lappets, terminated by similar angular points, and covered with oval scales, 9856 not imbricated, and each having a pore in its centre.” No pores or pits or sulci are illustrated in 9857 plate 40; fig. 5 (p. 648) shows a pore on one scale without indicating where on the body it lay. 9858 Earlier, Dawson (1863: pl. IV: fig. 25 – not cited by Pawley, 2006, or Schoch, 2013) had 9859 drawn pores on each one of six or seven rows of scales of “Dendrerpeton oweni” (junior 9860 synonym of D. acadianum: Milner, 1996; Schoch & Milner, 2014), and the accompanying 9861 description gives no indication that the supposed pores were – one might guess – only visible 9862 on one row and extrapolated to the others; rather, “[a] limited portion of the upper, and I 9863 suppose, anterior part [of an isolated patch of scales preserved in contact with “many 9864 fragments of the skull” of D. acadianum] is covered with imbricated scales, which […] 9865 generally have a small spot or pore near the outer margin” (Dawson, 1863: 34). – There is 9866 another patch of scales (Dawson, 1863: pl. V: fig. 22–24) where very large scales, each with a 9867 supposed pore, form a row between much smaller dorsal scales (drawn too small to determine 9868 if pores were present) and ventral scales (drawn too small in fig. 22, not shown in fig. 23–24). 9869 It was described as follows (Dawson, 1863: 36–37): “The best preserved specimen (Fig. 22 9870 [of pl. V]), which is about one inch in length and half an inch in breadth, is covered with very 9871 small imbricated scales. It is crossed by six or seven obscure ridges, which both at the bottom 9872 and along a mesial line, projected into points covered with larger scales. A row of large scales 9873 with round pores, connects these along the lower side (Figs. 23 and 24.) [sic] If, as seems 9874 probable, this fragment belonged to the side of the trunk or tail, it would perhaps indicate a 9875 division of the sub-cutaneous muscles into an upper and lower band, as in the .” This 9876 patch, which Dawson (1863) tentatively referred (not in the text, only in the legend to plate V 9877 on page 48) to the nomen dubium (Steen, 1934) **“” wymani, is similar to the 9878 patch drawn in p. VI, fig. 62, where a row of very large scales separates two areas of much 9879 smaller ones, but no pores are shown (only parallel striations); that patch was referred to 9880 “Hylonomus aciedentatus”, which is a junior synonym of D. acadianum (Milner, 1996; 9881 Schoch & Milner, 2014). – Given that the supposed pores are not restricted to a single row in 9882 at least one specimen, we suspect that the “pores” may be growth centers – denser than the

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9883 rest of the scale, not a hole in it. In any case, Dawson (1882) cannot be cited as evidence that 9884 any dendrerpetid had a postcranial lateral line, and while one specimen described and 9885 illustrated by Dawson (1863) may in principle provide such evidence, such a conclusion 9886 requires numerous assumptions about correct anatomical identification and the referral of that 9887 specimen. At present, thus, no dendrerpetid should be thought to have had a postcranial lateral 9888 line; if Pawley (2006) and Schoch (2013) did not merely miscite Dawson (1863 or 1882), they 9889 must have relied on unpublished personal observations which they did not mention. In any 9890 case, however, it is painfully obvious that dendrerpetid scales have never been adequately 9891 described or illustrated. Dawson’s descriptions of his light-microscopic observations are 9892 superficial and confused by modern standards, and his line drawings – in stark contrast to 9893 contemporary illustrations of dinosaur or crocodyliform bones, which have been called 9894 “almost better than the bone” – are of extremely limited usefulness. 9895 Ventastega shows state 1 (Ahlberg, Lukševičs & Lebedev, 1994). RC07 scored it as 0, 9896 but probably they intended to score Ventastega for SC 2, the only mandible character they did 9897 not score, and slipped one column to the left; Ventastega indeed has state 0 of SC 2 (Ahlberg, 9898 Lukševičs & Lebedev, 1994). 9899 “Lateral line sulci intermittently present, but state of preservation and coarse sculpture 9900 tend to obscure their courses except anterolateral to nares and partly across quadratojugal” in 9901 Chenoprosopus (Langston, 1953: 365). The smaller specimen USNM 437646 lacks lateral- 9902 line sulci (Hook, 1993; D. M., pers. obs.), but this may be ontogenetic: perhaps sulci only 9903 appeared with progressing metaplastic ossification of the dermis. We have scored state 3, 9904 which may be visible in CM 34909 (D. M., pers. obs.) as a sulcus (wide, shallow sculpture) 9905 rostral to the right naris (this area is not preserved on the left side) and possibly along the left 9906 jaw margin (this area is not preserved on the right side); the most convincing candidate for a 9907 lateral-line sulcus lies on the left jugal ventral to the orbit (this area is not preserved on the 9908 right side). Mehl’s (1913) “mucus canal” must be the nasolacrimal canal and has not been 9909 mentioned in more recent literature as far as we know. 9910 Isodectes was scored in RC07 as possessing state 1. There is, however, no clear 9911 evidence for enclosed canals anywhere on the animal; we have been cautious and scored the 9912 interrupted grooves (Sequeira, 1998) as state 2 or 3. 9913 Trimerorhachis was scored as having state 2 or 3, yet there is no evidence for state 2 9914 (Milner & Schoch, 2013); we have scored 3 alone. 9915 Acheloma shows state 4 (Polley & Reisz, 2011). 9916 Traces of the lateral lines have never been mentioned or reconstructed for Broiliellus 9917 (Carroll, 1964; Schoch, 2012; Schoch & Milner, 2014). Because they would be preserved and 9918 visible, we have scored state 4. 9919 Traces of the lateral lines have never been mentioned for Amphibamus and are absent 9920 from all reconstructions (most recently Schoch & Milner, 2014: fig. 30A). Because the 9921 implied state 4 may be visible in Daly (1994: fig. 18), we have scored it. 9922 Micromelerpeton has state 4 when adult (Schoch, 2009b). 9923 Apateon was scored as unknown; the only species known from metamorphosed 9924 individuals shows state 4 – apparently throughout ontogeny (Werneburg, 1991: 85). 9925 Albanerpetidae has state 4 according to all literature about this taxon. 9926 Proterogyrinus was scored as possessing state 1 or 2. It has state 3; the grooves, where 9927 present at all, are shallow and not bridged, but evidently interrupted (Holmes, 1984) like in 9928 *Archegosaurus (Witzmann, 2006) – the lateral-line organ was not deeper in the bone, but 9929 deeper in the thicker skin than in more obvious cases of state 3. 9930 Similarly, Archeria was given state 2 or 3, while it has state 3 (Holmes, 1989); 9931 Pholiderpeton attheyi was scored 2, but shares 3 (Panchen, 1972: 288–291, fig. 4); and

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9932 Anthracosaurus, usually claimed to have state 4 but scored 1 by RC07, shows state 3 as well 9933 (Clack, 1987a). 9934 Discosauriscus reached state 4 when adult (Klembara, 2009). This is interpreted as 9935 part of a transition to terrestrial life. Accordingly, we have added state 4 as an option (partial 9936 uncertainty) to all seymouriamorphs for this and the following character, except of course 9937 Seymouria (which already had state 4 for both) and Kotlassia (which is unknown for both). 9938 Batropetes was scored 1; it has state 4 – the large pits on the frontals are unrelated to 9939 lateral-line canals (Glienke, 2015). 9940 Saxonerpeton was scored as completely unknown, but CG78: 33 probably allow only 9941 states 3 and 4; we have scored it as possessing state 3 or 4. 9942 Microbrachis has state 3 (Olori, 2015). 9943 Of the traces identified in Hyloplesion by Olori (2015), not all are convincing – 9944 notably those on the maxilla (Olori, 2015: fig. 28C) are very narrow, sharp and irregular –, 9945 but the remainder (in particular Olori, 2015: fig. 28A, B dorsal of the arrow, D) are good 9946 enough to score state 3, which is not unexpected in this apparently fully aquatic animal. 9947 Acherontiscus was scored as having state 1 or 2. It rather clearly has state 3, with 9948 wide, long, likely interrupted rather than bridged grooves (Carroll, 1969b). 9949 Adelospondylus, too, was scored as having state 1 or 2. Judging from Andrews & 9950 Carroll (1991: 254, fig. 13A, B, 14A, B), it is better scored as having state 3 or 4, because the 9951 possible grooves are wide and may well be interrupted rather than bridged. 9952 Dolichopareias was scored as having state 1. In the absence of evidence that the wide 9953 grooves (Andrews & Carroll, 1991) continued inside the bone, we have changed the score to 9954 3. 9955 Scincosaurus is polymorphic, with most specimens having state 4 but some showing a 9956 very weak version of state 3 instead (Milner & Ruta, 2009). 9957 Bossy & Milner (1998: 83–84, 122) stated that diplocaulids, without further 9958 qualifications, have lateral-line canals; to our surprise, all diplocaulids were originally 9959 assigned state 4. Keraterpeton (Bossy & Milner, 1998: 83–84, 122) and Batrachiderpeton 9960 (Bossy & Milner, 1998: fig. 58B) have state 3, and so do Diceratosaurus (D. M., pers. obs. of 9961 MB.Am.778 – very deep sculpture lies mostly, but not only around the orbits) and 9962 Diploceraspis (Beerbower, 1963); in the absence of evidence that Diplocaulus had state 4, we 9963 have scored it as unknown. 9964 Notobatrachus has state 4 according to all figures. 9965 Ossinodus has state 1 or 2 (Warren, 2007). 9966 We have scored *Chroniosaurus as possessing state 0 or 4; state 4 occurs in the 9967 specimens described by Clack & Klembara (2009), state 0 possibly in quadratojugals 9968 attributed to “Jugosuchus”, some of which could be referable to *Chroniosaurus (Clack & 9969 Klembara, 2009: 17). 9970 *Nigerpeton has state 2. The fact (best visible in MNN MOR 108; D. M., pers. obs.) 9971 that the grooves lie on top of the sculpture instead of under it excludes states 0 and 1; the fact 9972 that the infranarial canal is visible in MNN MOR 69 but not the less eroded MNN MOR 70 9973 (D. M., pers. obs.) excludes state 3. 9974 State 3 cannot be excluded in *Saharastega (D. M., pers. obs. of MNN MOR 73); this 9975 means partial uncertainty between states 3 and 4. 9976 Beaumont & Smithson (1998: 191) stated about *Spathicephalus mirus: “In none of 9977 the skulls is there evidence of [the] lateral line canal system”. In his description of *S. 9978 pereger, Baird (1962: unnumbered table) did not mention the lateral lines at all, but showed a 9979 groove that seems to loop around the orbit and might have carried a lateral-line canal, if 9980 indeed it was continuous, which is hard to tell from the photograph. We have kept the score of 9981 the *Spathicephalus OTU as unknown.

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9982 *Sclerocephalus is apparently polymorphic, with some of the largest individuals 9983 showing state 3 (at least on part of the skull) and others state 4 (Schoch & Witzmann, 2009a). 9984 Gubin (1991: drawing 6) illustrated *Konzhukovia as having state 4, or rather did not 9985 shade the sculptured surface sufficiently to make the sulci stand out (some patterns in the 9986 sculpture vaguely suggest a few); following personal observation, Pereira Pacheco et al. 9987 (2016: appendix 2) reported state 3, which we have scored. 9988 The lateral-line canals of *Elginerpeton are wholly enclosed in the postorbital 9989 (Ahlberg, 1998) and almost wholly enclosed in the premaxilla (Ahlberg, 1995); the probable 9990 maxilla (Ahlberg, 1995: table 1) has not been described or illustrated, and other skull-roof 9991 bones are unknown. We have tentatively scored state 1. 9992 9993 101. SC 2: Mandibular canal totally enclosed (0), mostly enclosed with short sections in 9994 grooves (1), mostly in grooves with short sections enclosed (2), entirely in grooves (3), 9995 absent (4) (ordered). 9996 State 0 is present in Ventastega (see SC 1 above). 9997 Ichthyostega is best scored as possessing state 0 or 1 (Clack et al., 2012a). 9998 Whatcheeria should rather be scored as 1 than as 2 (Lombard & Bolt, 2006). 9999 Surprisingly, Milner & Lindsay (1998) did not comment on the presence or condition 10000 of lateral-line canals in the Baphetes specimen they described. Their fig. 4 seems to show the 10001 mandibular canal extending over most, perhaps all the length of the preserved part of the 10002 lower jaw; we have tentatively scored state 2 or 3. The specimen described by Milner, Milner 10003 & Walsh (2009) does not contradict this, but does not narrow it down either, showing state 1, 10004 2 or 3. 10005 Trimerorhachis has state 1, 2, or 3 (Milner & Schoch, 2013: fig. 7A). 10006 Langston (1953: 369) wrote about the lower jaw of Chenoprosopus: “Lateral line 10007 canals ill-defined: marginal sulcus [ = mandibular canal] appears on ventrolateral surface of 10008 angular, continuous forward across splenials following dentary-splenial sutures, terminates 10009 anteriorly at symphysis, perhaps continuous posteriorly with a shallow groove on ventral and 10010 posterior faces of surangular; dental sulcus [ = oral canal], if present, poorly developed.” 10011 Because we have not been able to find a statement in the literature that explicitly contradicts 10012 this, we have scored state 3. 10013 Isodectes was scored in RC07 as possessing state 1. There is, however, no clear 10014 evidence for enclosed canals anywhere on the animal; we have been cautious and scored the 10015 interrupted grooves (Sequeira, 1998) as state 2 or 3. 10016 Neldasaurus has state 2 or 3 as for the skull roof (Chase, 1965). 10017 Acheloma (Polley & Reisz, 2011) and Ecolsonia (D. M., pers. obs. of CM 38017 and 10018 CM 38024) have state 4. 10019 Traces of the lateral lines have never been mentioned or reconstructed for Broiliellus 10020 (Carroll, 1964; Schoch, 2012; Schoch & Milner, 2014). Because they would be preserved and 10021 visible, we have scored state 4. 10022 Schoch (2009b) did not mention the lower jaw of Micromelerpeton, but given the lack 10023 of lateral-line grooves on the skull in the adult stage, we have added state 4 to the observed 10024 uncertainty of state 2 or 3 of larvae (which was scored in RC07). 10025 Albanerpetidae has state 4 according to all literature about this taxon. 10026 Klembara et al. (2014) drew attention to a groove on the dentary of Gephyrostegus, 10027 wondering whether it was a lateral-line canal (state 3) or housed a blood vessel (state 4). We 10028 have kept the latter score, because the groove is discontinuous on both sides of the individual 10029 shown in their fig. 3, the rostralmost grooves ending in foramina as do several shorter 10030 grooves.

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10031 Except for Microbrachis, which was correctly scored as having state 3, and 10032 Rhynchonkos, which was correctly given state 4, all “microsaurs” were scored either as 10033 having state 0 or 1 (partial uncertainty) or as entirely unknown in RC07. This was not 10034 commented on by RC07 or Ruta, Coates & Quicke (2003), so we can only speculate that 10035 statements by CG78 about pits and grooves on lower jaws were misinterpreted as referring to 10036 lateral-line canals and led to the common score of 0 or 1. It is clear from context that these 10037 statements all refer to ornament and traces of nerves or blood vessels. CG78: 166 stated 10038 unambiguously that “Microbrachis is unique in having a lateral line canal groove, running 10039 along the ventral margin of the angular, the posterior splenial and the dentary.” This groove is 10040 illustrated in fig. 107A, and no such groove is shown on any other “microsaur” (fig. 103, 105, 10041 107). The correction to state 4 concerns Batropetes (Glienke, 2013: 81; 2015), Tuditanus 10042 (Carroll & Baird, 1968; CG78: fig. 4), Pantylus (Romer, 1969: 23), Asaphestera (CG78: fig. 10043 7; D. M., pers. obs. of NMC 10041), Saxonerpeton, Hapsidopareion, Micraroter, Pelodosotis, 10044 Cardiocephalus, Euryodus, Hyloplesion and Odonterpeton (specimen drawings in CG78). 10045 Olori (2015: 39, table S3) reported “distinct pores” on the dentary of Hyloplesion “which may 10046 also connect to the lateral line system” and scored state 3; we are unconvinced – pores could 10047 correspond to nerves or blood vessels, or to electroreceptory organs. 10048 Unknown in Scincosaurus (Milner & Ruta, 2009). 10049 Batrachiderpeton has state 3 (Bossy & Milner, 1998: 88, fig. 60C); so do Diplocaulus 10050 (Douthitt, 1917) and Diploceraspis (Beerbower, 1963). In the absence of evidence that any 10051 other diplocaulids had the (to our surprise) originally scored state 4, and given the facts that 10052 Bossy & Milner (1998) did not single out Batrachiderpeton as unusual and did not mention 10053 Diplocaulus or Diploceraspis in this context, we have scored them (i.e. Keraterpeton and 10054 Diceratosaurus) as unknown; see also SC 1 above. 10055 Notobatrachus has state 4 (Báez & Nicoli, 2004); apparently, so does Lethiscus (Pardo 10056 et al., 2017). 10057 Ossinodus has state 1 or 2; the material described by Warren (2007) is insufficient to 10058 distinguish between the two, so we have scored accordingly, but it should be mentioned that 10059 the distribution of pores and open grooves on the postsplenial hints at an ontogenetic 10060 transition from 2 to 1 (if not even 0). 10061 *Nigerpeton shows state 3; because not the entire lower jaw is preserved, state 2 10062 cannot be excluded (D. M., pers. obs. of MNN MOR 69, MNN MOR 70 and MNN MOR 10063 108), so we have scored partial uncertainty. 10064 The mandibular canal of the *St. Louis tetrapod appears to be (D. M., pers. obs. of 10065 MB.Am.1441.2) visible for a greater length than indicated by Clack et al. (2012b); we have 10066 scored state 2 rather than 1 or 2. 10067 Godfrey & Holmes (1989) tentatively implied state 3 for the *Parrsboro jaw; we have 10068 accepted this. 10069 The area that would have borne the mandibular canal is not preserved in 10070 *Australerpeton, but part of the oral canal is preserved as an open groove (Eltink & Langer, 10071 2014), so we have scored state 2 or 3. 10072 10073 102. VOM 1-13: Vomer approximately as wide as long or wider (0), intermediate (1), at 10074 least 2½ times longer than wide (2) (ordered). This is a merger of two correlated characters 10075 that described parts of a continuous character. 10076 Some snouts are so long and narrow that only state 2 is possible, making this character 10077 inapplicable. (The shape of the snout is not directly a character in this matrix, but correlates to 10078 varying extents with several characters.) This concerns Acheloma (Polley & Reisz, 2011), 10079 Archeria (already scored as unknown), *Archegosaurus, *Platyoposaurus and 10080 *Australerpeton. Furthermore, the combination of a long snout, round interpterygoid vacuities

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10081 and a vomer/pterygoid contact (states VOM 5-10/PTE 10-12-18/INT VAC 1(2 or lower) and 10082 INT VAC 3(1), which together imply short pterygoids and long vomers) likewise makes state 10083 2 of the present character inevitable; this concerns Chenoprosopus (Langston, 1953), 10084 Cochleosaurus (Sequeira, 2004), Neldasaurus (where “the vomers […] are approximately 10085 four times as long as they are wide” – Chase, 1965: 172), *Nigerpeton (Steyer et al., 2006) 10086 and, borderline, *Glanochthon (Schoch & Witzmann, 2009b). Note that in all of these the 10087 vomers are as wide as possible, occupying the entire space between the midline, the 10088 (pre)maxillae and the choanae. 10089 State 0 is found in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Colosteus 10090 (Hook, 1983: fig. 1), Eoscopus (Daly, 1994), and Ariekanerpeton (Klembara & Ruta, 2005a: 10091 fig. 13). 10092 State 1 occurs in Baphetes (Beaumont, 1977: fig. 19), Trimerorhachis (Milner & 10093 Schoch, 2013), Caerorhachis (Ruta, Milner & Coates, 2002: fig. 5c), Bruktererpeton (though 10094 almost state 2; Boy & Bandel, 1973: fig. 7), Batropetes (Glienke, 2013, 2015), Asaphestera 10095 (most likely; CG78: fig. 7), apparently Micraroter (CG78: fig. 53, 56), Rhynchonkos (CG78: 10096 fig. 63; Szostakiwskyj, Pardo & Anderson, 2015: fig. 3A), Diceratosaurus (Jaekel, 1903; D. 10097 M., pers. obs. of MB.Am.778), Capetus (Sequeira & Milner, 1993: fig. 9), Pederpes (as 10098 reconstructed by Clack & Finney, 2005: fig. 17), Silvanerpeton (Ruta & Clack, 2006: fig. 8), 10099 and Utegenia (Klembara & Ruta, 2004a: fig. 14) unless this is ontogenetic. CG78 (fig. 13, 14) 10100 depicted Hapsidopareion as having state 2, which was scored in RC07; however, the 10101 condition in *Llistrofus (Bolt & Rieppel, 2009), which falls near the upper end of state 1, 10102 strongly suggests that this was a misinterpretation partly due to damage to the 10103 Hapsidopareion specimens and that the correct score is 1. 10104 State 2 is present in Lethiscus (Pardo et al., 2017) and Orobates (Berman et al., 2004: 10105 fig. 3B). 10106 In Eoherpeton (Smithson, 1985: fig. 8) and Proterogyrinus (Holmes, 1984: fig. 3), the 10107 vomer is entirely unknown, but the skull is too narrow for state 0 given the shape of the 10108 palatine, so we have ascribed state 1 or 2 to both. 10109 As reconstructed (Panchen, 1972: fig. 7), Pholiderpeton attheyi has state 1 on the left 10110 and 2 on the right side. We have scored it as polymorphic. 10111 Gephyrostegus has state 2 (Klembara et al., 2014). 10112 The condition in Kotlassia is unknown (Bulanov, 2003). 10113 State 1 or 2 is present in Cardiocephalus (CG78: fig. 30) and Euryodus (CG78: fig. 10114 37, 38). 10115 The vomers of Microbrachis are so inclined (rostromedially to caudolaterally) that we 10116 cannot decide between states 0 and 1 (Vallin & Laurin, 2004: fig. 5). 10117 Ossinodus, too, has state 0 or 1 (Warren, 2007: fig. 6). 10118 The vomers of *Karpinskiosaurus are so inclined (rostromedially to caudolaterally) 10119 that we cannot decide between states 1 and 2 (Klembara, 2011: fig. 3C). 10120 *Chelotriton has state 1 when the toothed caudal processes that frame the cultriform 10121 process, characteristic of salamandrids, are taken into account, or 0 when they are ignored 10122 (Schoch, Poschmann & Kupfer, 2015); we have gone with the latter option in order to prevent 10123 a salamandrid autapomorphy from making *Chelotriton look less amphibamid-like. 10124 10125 103. VOM 3: Vomer with (0) or without (1) fangs comparable in size to, or larger than, 10126 marginal teeth (premaxillary or maxillary). 10127 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Acheloma 10128 (Polley & Reisz, 2011). 10129 Jarvik (1996) reconstructed Ichthyostega with state 1. Ahlberg, Lukševičs & Lebedev 10130 (1994) demonstrated that it has state 0 instead (which is also figured in the line drawing of

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10131 Blom, 2005: fig. 3). This is further confirmed by Jarvik’s (1996) own pl. 26:1 and by D. M.’s 10132 observations of TMM 41224-2, AMNH 23100 and MCZ 3361 – a total of five casts of the 10133 specimen figured in that plate (MGUH VP 6055). Clack & Milner (2015) mentioned this 10134 issue and provided further evidence for state 0, but did not make clear if specimens showing 10135 state 1 are known; for the time being, we have scored state 0. 10136 The most mature known individual of Amphibamus – the neotype, YPM 794 – has 10137 state 0 (if only on one side: Daly, 1994: 27). We regard this as the adult condition (see also 10138 Marjanović & Laurin, 2008: 193). Schoch & Milner (2014: 56) stated that Amphibamus lacks 10139 fangs on the vomer, palatine and ectopterygoid, but puzzlingly did not mention Daly (1994) in 10140 the context of Amphibamus at all, even though they of course mentioned YPM 794 and cited 10141 Daly (1994) as a source for Eoscopus. 10142 State 1 is found in Doleserpeton (Bolt, 1969; Sigurdsen & Bolt, 2010), Batropetes 10143 (Glienke, 2013, 2015), Hyloplesion (Olori, 2015), Diceratosaurus (Jaekel, 1903; D. M., pers. 10144 obs. of MB.Am.778 and CM 34656), Lethiscus (Pardo et al., 2017), Orobates (Nyakatura et 10145 al., 2015: digital reconstruction) and Ossinodus (Warren, 2007). Following the matrix of 10146 Pardo et al. (2017), we have also scored it for *Coloraderpeton. 10147 Apparently unknown in Broiliellus (Schoch, 2012: fig. 2F). 10148 The vomer is wholly unknown in Pelodosotis (CG78: 80–81). 10149 10150 104. VOM 4: Vomer without (0) or with (1) small teeth (denticles), the basal diameter 10151 and/or height of which is less than 30% of that of adjacent marginal teeth (premaxillary 10152 or maxillary) and remaining vomer teeth (if present). RC07 further specified for VOM 4 10153 that the denticles “form[…] [a] continuous shagreen or discrete, [sic] patches”, but denticles 10154 occur in other arrangements as well. The purely size-based distinction of “teeth” and 10155 “denticles” (here and in other characters below) may not be satisfactory, but in any case there 10156 is no histological difference (Gee, Haridy & Reisz, 2017). 10157 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Whatcheeria 10158 (Lombard & Bolt, 1995) and all preserved vomer fragments of Edops (D. M., pers. obs. of 10159 MCZ 1378 – the pterygoid fragments bear denticles throughout) as well as in Batropetes 10160 (Glienke, 2013, 2015), Scincosaurus (Milner & Ruta, 2009) and Tseajaia (Moss, 1972). 10161 The entire vomer (except the rostral edge and the intervomerine fossa) of Acheloma 10162 (Polley & Reisz, 2011), Broiliellus (Carroll, 1964) and Platyrhinops (Clack & Milner, 2010) 10163 is covered by denticles, giving them state 1. Limnoscelis (Berman, Reisz & Scott, 2010) and 10164 Ossinodus have state 1 as well (Warren, 2007). 10165 Although the vomerine denticles are restricted to a single ridge, they are present (state 10166 1) in Chenoprosopus (Hook 1993; D. M., pers. obs. of USNM 437646). 10167 The vomer of Bruktererpeton has two rows of denticles in its caudal corner (Boy & 10168 Bandel, 1973). We count this as state 1. 10169 Hapsidopareion (CG78: fig. 14E) has state 1; note that, on the morphologically left 10170 side of the latter, the vomer has a longitudinal break, and the medial fragment with its two 10171 remaining denticles was referred to the pterygoid by CG78. 10172 Diceratosaurus shows both states: the narrow-snouted morph, such as CM 34656, has 10173 a curled row of full-sized teeth on each vomer, while the broad-snouted morph, exemplified 10174 by CM 34670, CM 67157 and CM 81507 as well as MB.Am.778, instead has a field of 10175 denticles largely arranged in several parallel rows (D. M., pers. obs.). Ontogeny is an unlikely 10176 explanation: CM 67157 is larger than CM 34656 and CM 34670 but has the same skull length 10177 as the narrow-snouted CM 34696. In the absence of further evidence we have scored 10178 Diceratosaurus as polymorphic.

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10179 *Micropholis has a few scattered non-fang teeth on the vomer, but all appear to have a 10180 width well over 30% of that of the marginal teeth (Schoch & Rubidge, 2005: fig. 2B, ?D). It 10181 thus has state 0. 10182 Although this is not obvious from Maddin, Olori & Anderson (2011), *Carrolla has 10183 state 0 (D. M., pers. obs. of TMM 40031-54). We have followed the matrix of Pardo et al. 10184 (2017) in scoring state 0 for *Coloraderpeton as well. 10185 The vomer of *Glanochthon “is covered by numerous tubercles that could represent 10186 vestigial denticles” (Schoch & Witzmann, 2009b: 126). We have scored it as unknown, not 10187 counting the very small teeth (which may well qualify as denticles) of the parachoanal 10188 toothrow (see VOM 8). 10189 10190 105. VOM 5-10/PTE 10-12-18/INT VAC 1: Pterygoids sutured to each other plus 10191 contacting parasphenoid along entire length, interpterygoid vacuities therefore absent 10192 (0); pterygoids sutured only toward their rostral ends (1); contact between pterygoids 10193 absent, pterygoid/vomer suture still present (2); pterygoids do not contact vomers, but 10194 still overlap palatines medially for part of the palatines’ length (3); pterygoids entirely 10195 caudal to palatines, but still reach well mesial to subtemporal fenestrae (4); pterygoids 10196 do not extend mesially beyond their contribution (if any) to the rostral rims of the 10197 subtemporal fenestrae (5) (ordered). This is a fusion of six redundant characters that 10198 represent parts of a single continuous character, the gradual “retreat” of the palatal ramus of 10199 the pterygoid (from mesial to distal) coupled to size increase of the interpterygoid vacuities. 10200 The palatine, if present (see PAL 8 below), is excluded from contacting the interpterygoid 10201 vacuities or the parasphenoid in states 0 to 2 (VOM 10(0)) as opposed to states 3 and 4 (VOM 10202 10(1)). States 4 and 5 include the condition where the ectopterygoid participates in the margin 10203 of the interpterygoid vacuity, found in some temnospondyls that are not included in this 10204 matrix. State 5 is a rewording of PTE 18(1): “Pterygoid palatal ramus a robust, abbreviated, 10205 flange-like to digitiform structure, as long as or barely longer than combined length of 10206 quadrate ramus plus basicranial articulation”; note that it is not limited to caudates as 10207 originally scored, but also occurs in Broiliellus (borderline: Schoch, 2012: fig. 2F), Eocaecilia 10208 (Jenkins, Walsh & Carroll, 2007), Triadobatrachus (Roček & Rage, 2000; Ascarrunz et al., 10209 2016) and even Diploceraspis (Beerbower, 1963: fig. 4A). (Furthermore, it does not occur in 10210 the caudates *Beiyanerpeton and *Chelotriton [Roček & Wuttke, 2010; Gao & Shubin, 2012; 10211 Schoch, Poschmann & Kupfer, 2015]. We have, however, assigned state 5 to 10212 *Gerobatrachus, where the mesial end of the pterygoid is barely mesial to the mesial tip of 10213 the subtemporal fenestra, even though [much like in Broiliellus] the rostral rim of the fenestra 10214 is mostly formed by the ectopterygoid [Anderson et al., 2008a] – a bone caudates lack.) 10215 We have not directly represented VOM 5, “Vomer excluded from (0) or contributing 10216 to (1) interpterygoid vacuities”, although this distinction could be added to the present 10217 character as a split of state 2: it clearly depends at least in part on the width of the skull or that 10218 of the interpterygoid vacuities; if Scincosaurus or Bruktererpeton had wider skulls or 10219 interpterygoid vacuities, their vomers would end up forming the rostral margins of the 10220 interpterygoid vacuities, unless a neomorphic medial process appeared on the pterygoids. The 10221 width of the interpterygoid vacuities is coded here as INT VAC 2 and INT VAC 4. 10222 Ventastega has state 0 (Ahlberg, Lukševičs & Lebedev, 1994). 10223 Ichthyostega almost, but not quite, reaches state 0; it has state 1 (Jarvik, 1996: pl. 26– 10224 28; D. M., pers. obs. of TMM 41224-2 = AMNH 23100 = MCZ 3361, a total of five casts of 10225 MGUH VP 6055, which is the specimen figured in Jarvik, 1996: pl. 26:1). 10226 Whatcheeria has state 1 (Lombard & Bolt, 1995). 10227 Clack (2001: fig. 8) tentatively reconstructed state 1 for Eucritta under the assumption 10228 that the medial margin of the pterygoid (fig. 5) is complete as preserved. In seymouriamorphs,

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10229 the palate closes in ontogeny (see below), so it is possible that state 0 – which was scored in 10230 RC07 – would have arisen later in Eucritta; state 0 is indeed seen in Megalocephalus, though 10231 Baphetes retains state 1. We have assigned state 0 or 1 to Eucritta. 10232 States 2 and 3 are both found in Trimerorhachis (Milner & Schoch, 2013). 10233 McGowan (2002: 9) limited the possibilities for Albanerpetidae to state 1, 2, or 3. 10234 Although McGowan’s figures are coarse, his assessment is consistent with Maddin et al. 10235 (2013a: fig. 5H, I). 10236 Gephyrostegus has state 1 (Klembara et al., 2014). 10237 In seymouriamorphs the palate closes during ontogeny. Therefore we have assigned 10238 state 0 to Discosauriscus (Klembara, 1997: fig. 28, not fig. 24 or fig. 34; Klembara et al., 10239 2006: fig. 5B), and state 0 or 1 to Kotlassia (instead of just the observed state 1: Bulanov, 10240 2003: fig. 30) and also to Leptoropha (the pterygoid of which, not coded by RC07, is known: 10241 Bulanov, 2003: S33). Ariekanerpeton, Microphon and Utegenia were all given state 0, 1 or 2 10242 in RC07; given that only state 1 is observed in Ariekanerpeton (Klembara & Ruta, 2005a: 64, 10243 fig. 3B, 13A), Microphon (Bulanov, 2003: S40, S49) and apparently Utegenia (Klembara & 10244 Ruta, 2004a: fig. 11A, 14A), we have restricted all three to state 0 or 1 as well. 10245 Diadectes shows state 0 in some American species (Olson, 1947), state 1 or 2 in others 10246 (Case & Williston, 1912), and state 1 in D. absitus (Berman, Sumida & Martens, 1998). We 10247 have scored it as possessing states 0 and 1 because making partial uncertainty part of a 10248 polymorphism is not possible. 10249 Limnoscelis has state 1 (Berman, Reisz & Scott, 2010). 10250 It seems a safe assumption that Westlothiana possessed palatines (Smithson et al., 10251 1994). We have kept state 1 or 2, though whether 0 and 3 can really be excluded might be 10252 arguable. 10253 State 2 seems most likely in Batropetes (Glienke, 2013, 2015). 10254 State 1 is found in Microbrachis (Vallin & Laurin, 2004; Olori, 2015) and Hyloplesion 10255 (Olori, 2015). 10256 As reconstructed by Wellstead (1991) and Pardo & Anderson (2016), Brachydectes 10257 has a unique condition with an extremely broad parasphenoid that makes interpterygoid 10258 vacuities impossible. Regardless, it has state 2: there is a pterygoid/vomer contact rather than 10259 a palatine/parasphenoid contact, excluding states 3 and higher, and the pterygoids do not 10260 come anywhere near each other (being separated by the parasphenoid), excluding states 1 and 10261 0. 10262 The reconstruction and the specimen drawing of Adelospondylus (Andrews & Carroll, 10263 1991) are not very similar to each other. We have added state 0 to the uncertainty of states 1, 10264 2 or 3 scored in RC07. 10265 Diceratosaurus has state 1 (D. M., pers. obs. of CM 26231; compatible with the 10266 slightly disarticulated MB.Am.778, which was reconstructed as just reaching state 2 by 10267 Jaekel, 1903: pl. III). 10268 Lethiscus possesses state 1 or 2 (Pardo et al., 2017); Oestocephalus appears to have 10269 state 0, 1 or 2 (Carroll, 1998a: 153, fig. 2, 3). 10270 In Phlegethontia, the vomers and the palatines are absent. Technically, only states 0 10271 and 5 could therefore be excluded; however, given the length (rostral/mesial extent) of the 10272 “palatoquadrates” (Anderson, 2002, 2007a), we have scored state 1 or 2, because a palatine 10273 would have to be in a highly unusual position rostral to the “palatoquadrates”. 10274 Palatines (at least as separate bones) are likely also absent in Vieraella (Báez & Basso, 10275 1996); given again the length of the pterygoids, states 0, 1, 2 and 5 can be excluded, so we 10276 have scored state 3 or 4. The same applies to *Chelotriton, except that its pterygoid is so short 10277 (close to state 5, without reaching it: Roček & Wuttke 2010; Schoch, Poschmann & Kupfer, 10278 2015) that we have also excluded state 3, leaving state 4 for this OTU.

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10279 Ossinodus has state 0 or 1 (Warren 2007). 10280 States 3 and 4 both occur in *Micropholis (Schoch & Rubidge, 2005: fig. 2). 10281 We have included the condition of *Karpinskiosaurus (Klembara, 2011: fig. 3C) in 10282 state 0. 10283 The CT scans of *Carrolla (only known specimen: TMM 40031-54) by Maddin, Olori 10284 & Anderson (2011) seem to only distinguish finished bone surfaces from everything else, and 10285 not to distinguish spongy bone from the matrix. Thus, fig. 4F of Maddin, Olori & Anderson 10286 (2011) fails to show some bone that is clearly present – and also misses what must be the 10287 suture between vomer and pterygoid (D. M., pers. obs. of TMM 40031-54). The lateral 10288 elements of the palate have been pushed dorsally against the skull roof, breaking the 10289 pterygoid and rotating the palatine, but D. M. confirms the reconstruction of the palate by 10290 Maddin, Olori & Anderson (2011: fig. 7B) in this respect (see below for character PTE 3-9, 10291 however). *Carrolla thus has state 2. It is, however, noteworthy how thin (labiolingually) the 10292 mesial process of the pterygoid is (probably shared with Batropetes: Glienke, 2013, 2015). 10293 Fig. 14b of Werneburg (2012b) suggests state 3 for *Mordex, although fig. 14a (which 10294 does not show any sutures in the articulated palate of the smallest specimen) looks like state 2 10295 unless we assume that the palatine is split lengthwise and the lateral part alone is 10296 disarticulated. We have made this assumption and scored state 3. 10297 Following the matrix by Pardo et al. (2017), we have scored state 1 or 2 for 10298 *Coloraderpeton. 10299 10300 106. VOM 7: Vomer/maxilla suture anterior to the choana: absent (0); present (1). 10301 Whatcheeria (the premaxilla participates in the margin of the choana: Lombard & 10302 Bolt, 1995), Cochleosaurus (Sequeira, 2004), Trimerorhachis (Milner & Schoch, 2013), 10303 Acheloma (Polley & Reisz, 2011) and Batropetes (Glienke, 2013, 2015) have state 0. We 10304 have also scored state 0 for Silvanerpeton because the reconstruction by Ruta & Clack (2006: 10305 fig. 8) seems to make state 1 impossible. 10306 State 1 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Acanthostega 10307 (Porro, Rayfield & Clack, 2015: fig. 4C), Balanerpeton (Milner & Sequeira, 1994: 338), 10308 Dendrerpetidae (Dendrerpeton acadianum: Milner, 1996: fig. 6; in Dendrysekos the condition 10309 is unknown, but state 1 may well have been just barely present as in Balanerpeton: Holmes, 10310 Carroll & Reisz, 1998: fig. 4), apparently Diceratosaurus (D. M., pers. obs. of MB.Am.778), 10311 most likely Lethiscus (Pardo et al., 2017) and Ossinodus (Warren, 2007). 10312 Phonerpeton is apparently polymorphic: the previously scored state 0 was 10313 reconstructed by Dilkes (1990: fig. 1), but is almost certainly excluded by Dilkes (1993: fig. 10314 5) and by AMNH 7150 (D. M., pers. obs.). Dilkes (1993: fig. 4) also figured a clear case of 10315 state 0 in a specimen that cannot be referred to Phonerpeton with sufficient certainty (Dilkes, 10316 1993). 10317 The condition in Platyrhinops is unknown; it is possible that the palatine contacts the 10318 vomer lateral to the choana (Clack & Milner, 2010), and if so, the position of the suture 10319 between palatine and vomer lateral to the choana is unknown with respect to the maxilla 10320 (Clack & Milner, 2010). 10321 Unknown also in *Saharastega due to the problem of identifying the nasal passage (D. 10322 M., pers. obs. of MNN MOR 73). 10323 Schoch & Witzmann (2009b) scored both species of *Glanochthon as having a 10324 premaxillary contribution to the margin of the choana (state 0 of their character 32), which 10325 would mean state 0 of the present character. However, this contradicts their fig. 3D, which 10326 unambiguously shows state 1 in *G. angusta. Figure 3E, for *G. latirostris, does not show the 10327 maxilla/premaxilla suture, but if it was in about the same place as in *G. angusta, state 1 10328 would again result. We have scored state 1.

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10329 107. VOM 8: Vomer with (0) or without (1) lateral (parachoanal) toothrow. RC07 10330 specified a “toothed lateral crest” instead of a toothrow, but, firstly, the presence of the 10331 parachoanal toothrow – not otherwise represented in this matrix – is much easier to ascertain 10332 in published line drawings than the presence of a crest, and secondly, the alveoli of toothrows 10333 are usually (among taxa in this matrix) attached to a low but sharp labial crest, so that a 10334 toothrow without a crest is unlikely to occur. Incidentally, a crest without a toothrow is 10335 documented in Cochleosaurus (Sequeira, 2004), Phonerpeton (Dilkes, 1990: fig. 1; D. M., 10336 pers. obs. of MCZ 1485) and Eryops (D. M., pers. obs. of MCZ 1129 and MCZ 2766), all of 10337 which were scored 1 – we conclude that RC07 did not consider a crest covered with denticles 10338 “toothed”, and have kept these scores. 10339 We count oblique toothrows (oblique relative to the choanae) as VOM 9(0), not VOM 10340 8(0); see VOM 9. The OTUs concerned were already scored 1 or unknown for VOM 8. 10341 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Whatcheeria 10342 (Lombard & Bolt, 1995), Micromelerpeton (Boy, 1995), Rhynchonkos (CG78: fig. 63; 10343 Szostakiwskyj, Pardo & Anderson, 2015), Cardiocephalus (CG78), Lethiscus (Pardo et al., 10344 2017), Microphon (Bulanov, 2003, 2014), Ossinodus (Warren, 2007) and *Karpinskiosaurus 10345 (Klembara, 2011). We have further followed the matrix of Pardo et al. (2017) in scoring state 10346 0 for *Coloraderpeton. 10347 Acheloma (Polley & Reisz, 2011), Eoscopus (Daly, 1994), Bruktererpeton (Boy & 10348 Bandel, 1973), Gephyrostegus (Klembara et al., 2014), Batropetes (Glienke, 2013, 2015) and 10349 Diceratosaurus (at least the broad-snouted morph – in which, however, a suggestive 10350 extension of the denticle field is present: D. M., pers. obs. of MB.Am.778; idealized by 10351 Jaekel, 1903: pl. III) have state 1. Likewise, the pterygoid toothrows of Orobates do not 10352 continue onto the vomers (Nyakatura et al., 2015: digital reconstruction) 10353 Trimerorhachis is polymorphic, sometimes between the left and right sides of the 10354 same individual (Milner & Schoch, 2013: fig. 3C). 10355 In Eocaecilia, a single continuous toothrow extends along the labial margins of both 10356 vomers and palatines. Because the choanae lie lingual to it, we have kept the score of 1. 10357 This character and the next are hard to apply to Brachydectes: a toothrow spans the 10358 length of each vomer, but the teeth are so large and the vomers so narrow that the orientation 10359 of the toothrows is wholly dictated by that of the vomers (Pardo & Anderson, 2016). We have 10360 no non-phylogenetic arguments for either taking the parachoanal orientation of the toothrows 10361 at face value (state 0 of this character) or interpreting it as a salamandrid-like homolog of the 10362 interchoanal toothrow (state 0 of the next character), so we have had to score both as 10363 unknown. 10364 The vomer is wholly unknown in Pelodosotis (CG78: 80–81); the present character is 10365 also apparently unknown in Euryodus (CG78). 10366 10367 108. VOM 9: Vomer with (0) or without (1) transverse (interchoanal) toothrow. RC07 10368 specified “transversely orientated, anterior crest” and did not mention any teeth. Indeed, a 10369 toothless and (especially medially) largely rounded crest is present in Ichthyostega (Jarvik, 10370 1996: pl. 26:1; Clack & Milner, 2015: fig. 8C; D. M., pers. obs. of TMM 41224-2 = MCZ 10371 3361). A similar condition is found in Eryops, where this ridge additionally bears relatively 10372 large denticles that continue rostromedially but not caudally (D. M., pers. obs. of AMNH 10373 4673). A sharp ridge is found in Phonerpeton, where the entire vomer except for the floor of 10374 the rostral palatal vacuity bears scattered denticles (Dilkes, 1990: fig. 1; D. M., pers. obs. of 10375 MCZ 1485). Finally, Cochleosaurus has several denticle-bearing crests on the vomer, one of 10376 which is transverse (Sequeira, 2004). However, all four of these OTUs were scored 1 (which 10377 we have kept); we consider this evidence that RC07 actually had a crest bearing a toothrow in

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10378 mind, as they stated more clearly for VOM 8. For the same reasons as in VOM 8, we have 10379 scored the toothrow alone. 10380 Metamorphosed salamanders often have a transverse toothrow at the caudal end of the 10381 vomer; some clades instead have an S-shaped or straight toothrow that extends rostromedially 10382 to caudolaterally or caudally. These toothrows are homologous to each other and to the 10383 toothrows at the labial margin of the vomer seen in larvae and in neotenic adults that have not 10384 undergone complete metamorphosis: during metamorphosis, the part of the vomer lingual to 10385 the toothrow is destroyed, and the vomer grows on the labial side. For this reason we have 10386 scored the toothrows of Karaurus, Valdotriton (double to triple; see VOM 11), 10387 *Beiyanerpeton, *Pangerpeton and *Chelotriton (Schoch, Poschmann & Kupfer, 2015 – 10388 Roček & Wuttke, 2010: 323, appear to have assigned them to the inexistent palatine) all as 10389 representing state 0. We have done the same with Eocaecilia, where a single continuous 10390 toothed crest extends along the labial margins of both vomers and palatines. 10391 Because of this movement of the crest during salamander metamorphosis, and because 10392 the crest often lies about in the middle of the vomer in temnospondyls, we have scored the 10393 toothed crest of the frogs Notobatrachus (Báez & Nicoli, 2004), Vieraella (teeth unknown, 10394 but more ventral than the rest of the vomer: Báez & Basso, 1996) and *Liaobatrachus as 10395 constituting state 0 as well; in the latter, notably, the crest lies in the middle of the vomers 10396 rather than at their caudal edge (despite a general absence of paedomorphic features). The 10397 same applies to Batrachiderpeton, Diplocaulus and Diploceraspis (Williston, 1909; 10398 Beerbower, 1963; Bossy & Milner, 1998); Diceratosaurus is polymorphic between the broad- 10399 snouted and the narrow-snouted morph, see VOM 4. 10400 State 0 is further present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), 10401 Trimerorhachis (Milner & Schoch, 2013), Ptyonius (Bossy & Milner, 1998) and Ossinodus 10402 (Warren, 2007). We have also counted the rostralmost two teeth on the vomer of Lethiscus 10403 (Pardo et al., 2017) as forming a row; the vomer is too narrow for a longer transverse 10404 toothrow. Finally, we have assigned state 0 to Doleserpeton, see VOM 11. 10405 Acheloma (apparently: Polley & Reisz, 2011), Eoscopus (Daly, 1994), Bruktererpeton 10406 (Boy & Bandel, 1973), Batropetes (Glienke, 2013, 2015), Microphon (Bulanov, 2003) and 10407 Orobates (Nyakatura et al., 2015: digital reconstruction) have state 1. 10408 Unknown in Edops (D. M., pers. obs. of MCZ 1378); the vomer is wholly unknown in 10409 Pelodosotis (CG78: 80–81). 10410 State 0 is clearly present in juvenile *Glanochthon angusta (Schoch & Witzmann, 10411 2009b: fig. 3A), but its further fate in ontogeny is unclear from the description and the 10412 illustrations; because fig. 4D might show its persistence in adult *G. latirostris, we have 10413 provisionally scored state 0. 10414 10415 deleted VOM 11 10416 RC07 called this character “Vomer without (0) or with (1) nearly transverse patch 10417 of small teeth (denticles) lying posterome[d]ial to choana.” They stated that state 1 “is 10418 found in Doleserpeton and some basal salientians”, and scored it for Doleserpeton, the 10419 salientian Notobatrachus and the caudates Karaurus and Valdotriton. However, this is not 10420 defensible: 10421 Except for the pit that bears the fang-replacing toothrow, the entire vomer of 10422 Doleserpeton is covered by denticles (Sigurdsen & Bolt, 2010; already correctly scored as 10423 VOM 4(1)). There is thus no transverse patch, causing us to score state 0. 10424 Conversely, Notobatrachus and Karaurus lack denticles altogether. In Karaurus, the 10425 teeth that lie caudomedial to the choana have full size and are part of the transverse vomerine 10426 toothrow, far from being a patch of denticles (Ivachnenko, 1978: fig. 1b); those of 10427 Notobatrachus are smaller than the marginal teeth, but still rather too large for being

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10428 denticles, and form a straight row borne on a crest on each vomer (Báez & Nicoli, 2004). 10429 These teeth constitute VOM 9(0). 10430 Two to three rows of (small) teeth larger than the (tiny) marginal teeth are found on 10431 each otherwise toothless vomer of Valdotriton, and they lie rostromedial to the choana, which 10432 is not separate from the interpterygoid vacuity (Evans & Milner, 1996). This, too, constitutes 10433 state 0, even if the position of this double or triple toothrow would have changed in further 10434 ontogeny, corresponding as it does to what is seen halfway through metamorphosis in extant 10435 salamanders. While the toothrow shares the fact of not being single with a patch of denticles, 10436 denticles are defined in other characters of the present matrix as being much smaller than 10437 marginal teeth. 10438 Among the OTUs scored as unknown by RC07, state 0 is now known in Ventastega, 10439 Whatcheeria, Acheloma, Bruktererpeton and Ossinodus (see VOM 4) as well as 10440 Gephyrostegus (Klembara et al., 2014) and Capetus (Sequeira & Milner, 1993). 10441 State 0 was scored in RC07, but is in fact unknown, in Neldasaurus, for which Chase 10442 (1965: 176) specified: “The obstinate character of the matrix left no indication of palatal teeth 10443 in areas other than those described […], but the fragments of the pterygoid bones […] show 10444 that […] [parts of the pterygoid] are covered by a densely-packed shagreen of small teeth 10445 except at the medial edge of the bone.” Denticles are not mentioned anywhere else in the 10446 paper. We conclude that their presence, let alone arrangement, is unknown on the vomer – as 10447 already scored for the palatine (PAL 2) and the ectopterygoid (ECT 3). 10448 The vomers of Archeria and Pelodosotis, also originally scored 0, are entirely 10449 unknown (CG78: 80–81; Holmes, 1989). The state is also unknown in Hapsidopareion 10450 (CG78). 10451 In other words, once denticles are specified, state 1 does not occur in this matrix at 10452 all – except in *Gerobatrachus (Anderson et al., 2008a). In the wording of 2007, then, this 10453 character is parsimony-uninformative – quite apart from the issue of correlation with VOM 4. 10454 Ruta, Coates & Quicke (2003), however, did not specify denticles, and cited Bolt 10455 (1969, 1977, 1979, 1991) as support for their statement that state 1 is shared between 10456 Doleserpeton and various unspecified lissamphibians. This must refer to Bolt’s hypothesis 10457 that the short rows of full-sized (not “small”!) teeth found on the vomer, palatine and dentary 10458 of Doleserpeton in the positions (indeed in recognizable pits) where other temnospondyls bear 10459 fangs are homologous to lissamphibian toothrows. While we are skeptical about this idea, we 10460 have deleted the present character but scored Doleserpeton as having state VOM 9(0) to avoid 10461 bias against the TH. 10462 10463 109. VOM 12: Distinct posterolateral process of vomer bordering more than half of 10464 choana posterior margin: absent (0); present (1). 10465 State 0 is documented in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), 10466 Acheloma (Polley & Reisz, 2011), Bruktererpeton (Boy & Bandel, 1973), Diceratosaurus (D. 10467 M., pers. obs. of MB.Am.778), Lethiscus (Pardo et al., 2017) and Ossinodus (Warren, 2007). 10468 Breaks in MNN MOR 73 (D. M., pers. obs.) support the reconstruction of state 0 in 10469 *Saharastega by Damiani et al. (2006). 10470 State 1 must be scored for Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 2010). 10471 Rather than a caudal margin distinct from the medial one, the choana has a caudolateral point 10472 where the lateral edge of the vomer continues into a caudolateral process that extends all the 10473 way to the medial edge of the maxilla, excluding the palatine from the margin of the choana. 10474 State 1 is further present in Acanthostega (Porro, Rayfield & Clack, 2015) and in 10475 Batropetes as reconstructed by Glienke (2013). 10476 Unknown in Scincosaurus (Milner & Ruta, 2009); the vomer is wholly unknown in 10477 Pelodosotis (CG78: 80–81).

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10478 110. PAL 1: Palatine with (0) or without (1) fangs comparable in size to or larger than 10479 marginal teeth (premaxillary or maxillary). 10480 Jarvik (1996) reconstructed Ichthyostega with state 1. Ahlberg, Lukševičs & Lebedev 10481 (1994) demonstrated that it, as well as Ventastega, had state 0 instead. For Ichthyostega, this 10482 is confirmed by Jarvik (1996: pl. 26:1) and TMM 41224-2 = AMNH 23100 = MCZ 3361 (D. 10483 M., pers. obs.; five casts of the figured specimen MGUH VP 6055). Clack & Milner (2015) 10484 mentioned this issue and provided further evidence for state 0 in Ichthyostega, but did not 10485 make clear if specimens showing state 1 are known; for the time being, we have scored state 10486 0. 10487 The most mature known individual of Amphibamus – the neotype, YPM 794 – has 10488 state 0 (Daly, 1994: 27). We regard this as the adult condition (see also Marjanović & Laurin 10489 2008: 180). Schoch & Milner (2014: 56) stated that Amphibamus lacks fangs on the vomer, 10490 palatine and ectopterygoid, but puzzlingly did not mention Daly (1994) in the context of 10491 Amphibamus at all, even though they of course mentioned YPM 794 and cited Daly (1994) as 10492 a source for Eoscopus. 10493 State 0 is also found in Lethiscus (Pardo et al., 2017), Ossinodus (Warren, 2007) and 10494 Silvanerpeton (Ruta & Clack, 2006). 10495 Batropetes (Glienke, 2013), Diceratosaurus (Jaekel, 1903; D. M., pers. obs. of 10496 MB.Am.778), Orobates (Nyakatura et al., 2015: digital reconstruction) and Tseajaia (Moss, 10497 1972: 12) have state 1. 10498 This character is inapplicable to Notobatrachus, which lacks (separate) palatines (PAL 10499 8(1)). It also has to be scored as unknown for Vieraella, where the presence of palatines is 10500 unknown. 10501 10502 111. PAL 2: Palatine without (0) or with (1) small teeth (denticles), the basal diameter 10503 and/or height of which is less than 30% of that of adjacent marginal teeth (maxillary) 10504 and remaining palatine teeth (if present). See VOM 4; RC07 even wrote “remaining vomer 10505 teeth” instead of “remaining palatine teeth”. 10506 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Whatcheeria (Lombard & Bolt, 10507 1995), Batropetes (Glienke, 2013), apparently Oestocephalus (Carroll, 1998a), Orobates 10508 (Berman et al., 2004) and Tseajaia (Moss, 1972: 12) have state 0. Although this is not 10509 obvious from Maddin, Olori & Anderson (2011), so does *Carrolla (D. M., pers. obs. of 10510 TMM 40031-54). We further follow the matrix of Pardo et al. (2017) in scoring state 0 for 10511 *Coloraderpeton. 10512 Acheloma (Polley & Reisz, 2011), Broiliellus (Carroll, 1964), Platyrhinops (Clack & 10513 Milner, 2010), Limnoscelis (Fracasso, 1983: 121) and Diceratosaurus (at least the broad- 10514 snouted morph: Jaekel, 1903; D. M., pers. obs. of MB.Am.778) possess state 1, as does 10515 *Nigerpeton (D. M., pers. obs. of MNN MOR 69). The smallest teeth on the palatines of 10516 Pantylus (Romer, 1969; CG78) and Stegotretus (Berman, Eberth & Brinkman, 1988) qualify 10517 for state 1 as well. 10518 While CG78 did not mention or illustrate denticles for Hapsidopareion, this may be 10519 due to preservation or preparation issues; we have scored it as unknown. 10520 Unknown in Edops (D. M., pers. obs. of MCZ 1378). Probably also unknown in 10521 Kotlassia, judging from the comments on the preservation of the toothrow and on the 10522 pterygoid and parasphenoid (Bulanov, 2003: S55). 10523 The dots in the reconstruction of *Neopteroplax (Romer, 1963: fig. 5) appear to 10524 represent denticles, but there is no evidence for them in the specimen drawing (fig. 2) or the 10525 text; instead, in the specimen drawing, the denticle field has a very sharp edge that appears to 10526 coincide with the suture between pterygoid and palatine. We have therefore scored state 0. 10527

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10528 112. PAL 4: Palatine with (0) or without (1) row of teeth (3+) comparable in size to, or 10529 greater than, marginal teeth (maxillary) and parallel to these. 10530 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Microphon (Bulanov, 2014) and 10531 Ossinodus (Warren, 2007) have state 0. 10532 Phonerpeton (D. M., pers. obs. of AMNH 7150), Ecolsonia (D. M., pers. obs. of CM 10533 38017), Bruktererpeton (Boy & Bandel, 1973: 51), Batropetes (Glienke, 2013), 10534 Diceratosaurus (at least the broad-snouted morph: D. M., pers. obs. of MB.Am.778) and 10535 Tseajaia (Reisz, 2007) show state 1. 10536 Unknown in Asaphestera (CG78: 19). We follow the matrix of Pardo et al. (2017) in 10537 keeping the same score for Lethiscus, where both vomers are damaged labially (Pardo et al., 10538 2017: fig. 1, ext. data fig. 1). 10539 *Micropholis is polymorphic (Schoch & Rubidge, 2005), as (apparently) is 10540 *Sclerocephalus (Schoch & Witzmann, 2009a). 10541 Orobates has state 1 as originally scored (Nyakatura et al., 2015: digital 10542 reconstruction); however, this is impossible to see in Berman et al. (2004). 10543 10544 deleted PAL 6: Palatine articulates with maxilla only at anterior extremity of the 10545 former: absent (0); present (1). State 1 was scored in RC07 only for branchiosaurids and 10546 Petrolacosaurus. However, Werneburg (2012b: 43–44) reports that it is only known from 10547 larvae in the branchiosaurid Apateon – the skeletally most mature individuals of A. dracyi 10548 (neotenic), A. caducus (neotenic) and A. gracilis (metamorphosed) have state 0. Conversely, 10549 state 1 is present in larval but not metamorphosed Amphibamus (Milner, 1982; Werneburg, 10550 2012b: 44) and Platyrhinops (Werneburg, 2012b). It stands to reason that the observed state 1 10551 in Leptorophus and Schoenfelderpeton (and *Tungussogyrinus) is likewise larval or 10552 paedomorphic. This leaves state 1 to Petrolacosaurus alone (because of its suborbital 10553 fenestra), making this character parsimony-uninformative, so we have deleted it. We could 10554 instead have specified that state 1 only occurs in larvae – but the ontogeny of way too many 10555 taxa in this matrix is insufficiently known. 10556 Ventastega shows state 0 (Ahlberg, Lukševičs & Lebedev, 1994), as do 10557 Bruktererpeton (Boy & Bandel, 1973: 51), Lethiscus (Anderson, Carroll & Rowe, 2003; 10558 Pardo et al., 2017) and Ossinodus (Warren, 2007). 10559 Unknown in Adelogyrinus (Andrews & Carroll, 1991) and Orobates (Berman et al., 10560 2004); inapplicable to Phlegethontia, which lacks palatines (Anderson, 2002). 10561 10562 113. PAL 7: Palatines very wide, almost meeting in the midline (0); unremarkable (1); 10563 very narrow in any dimension (2) (ordered). State 0 of this potentially continuous character 10564 is new and accounts for the highly unusual condition of Eoherpeton (Smithson, 1985), 10565 Bruktererpeton (Boy & Bandel, 1973), Gephyrostegus (Klembara et al., 2014; Carroll, 1970, 10566 even reconstructed the palatines as meeting in one specimen), Pantylus (Romer, 1969; CG78), 10567 Stegotretus (Berman, Eberth & Brinkman, 1988) and *Sparodus (Carroll, 1988; D. M., pers. 10568 obs. of NHMW 1899/0003/0006). It does not seem to occur anywhere else in or close to our 10569 taxon sample, and there are no borderline cases we are aware of; the closest is Crassigyrinus, 10570 in which the palatines are roughly L-shaped and not much longer than wide, but nonetheless 10571 stay well away from the midline (Clack, 1998: fig. 4B). The distinction between states 1 and 2 10572 (originally 0 and 1), however, is harder to define; most likely, the coding remains rather 10573 subjective – the original wording (RC07: 100) is “Palatine shaped like a slender, strut-like 10574 bone: absent (0); present (1).” 10575 State 1 is in any case present in Ventastega (Ahlberg et al., 2008), Micromelerpeton 10576 (Boy, 1995; Schoch, 2009b: fig. 2c), Apateon (A. pedestris: Schoch & Milner, 2008; A. 10577 caducus: Fröbisch & Schoch, 2009b), arguably Leptorophus and Schoenfelderpeton (Boy,

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10578 1986), probably Batropetes (Glienke, 2013), Lethiscus (Anderson, Carroll & Rowe, 2003; 10579 Pardo et al., 2017) and Ossinodus (Warren, 2007). 10580 State 2 makes a surprise appearance in Acanthostega (Porro, Rayfield & Clack, 2015). 10581 In RC07, our state 1 was scored for Amphibamus. This is supported by Schoch (2001) 10582 and Schoch & Milner (2014: fig. 30B); but the individual drawn by Schoch (2002b) is not 10583 adult, because it lacks the palatal fangs noted by Daly (1994: 27) in the most mature known 10584 specimen (see VOM 7, PAL 1, ECT 2), and so does the composite reconstruction by Schoch 10585 & Milner (2014). Considering Schoch’s (2002b) reconstruction of the palate of Platyrhinops 10586 (though see Clack & Milner, 2010: fig. 9b) and the condition seen in *Iberospondylus (Laurin 10587 & Soler-Gijón, 2006), the shape of the palatine may depend on the presence of fangs; Daly 10588 (1994) did not illustrate it, so we have scored Amphibamus as unknown. 10589 Also unknown in Archeria (Holmes, 1989). 10590 We have scored state 1 or 2 for Diceratosaurus (D. M., pers. obs. of the crushed 10591 MB.Am.778) and for Brachydectes, whose palatines are arguably too short for these states to 10592 be distinguishable (Pardo & Anderson, 2016: fig. 10). 10593 *Saharastega is best scored as having state 0 or 1 (D. M., pers. obs. of MNN MOR 10594 73). 10595 10596 114. PAL 8: Separately ossified palatine: present (0); absent (1). 10597 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Batropetes (Glienke, 2013), 10598 Lethiscus (Anderson, Carroll & Rowe, 2003; Pardo et al., 2017) and Ossinodus (Warren, 10599 2007) have state 0. 10600 Unknown in Archeria (Holmes, 1989) and Vieraella (Báez & Basso, 1996), apparently 10601 also in Keraterpeton (Huxley & Wright, 1867; Jaekel, 1903). 10602 We accept the interpretation of Gao & Shubin (2012) and Wang, Dong & Evans 10603 (2015: 52) that a palatine is present (state 0) in the crown-group salamander *Beiyanerpeton. 10604 A palatine is also present in another Jurassic crown-group salamander, **Chunerpeton 10605 (unmarked and unmentioned in Gao & Shubin, 2003: fig. 1; mentioned by Wang, Dong & 10606 Evans, 2015: 52), and has recently been reported for a third one (**Qinglongtriton: Jia & 10607 Gao, 2016). It follows that we agree with Schoch (2014b) in rejecting Schoch’s earlier (1998) 10608 interpretation that the palatine is absent even in larval salamanders in which the 10609 “palatopterygoid”, homologous only to the pterygoid in that view, contacts the vomer. 10610 10611 115. ECT 1-4: Ectopterygoid at least as long as palatine (0); at least about a third as long 10612 as but shorter than palatine (1); at most about a third as long as palatine (2); absent (3) 10613 (ordered). ECT 1 concerned the presence (state 0) of an ectopterygoid, ECT 4 its size 10614 (“longer than/as long as (0) or shorter than (1) palatine”). We have merged both of them with 10615 character 8 of McGowan (2002) as revised by Marjanović & Laurin (2008): “Ectopterygoid at 10616 least about half as long as palatine (0), about a third as long as the palatine or shorter (1), or 10617 absent (2) (ordered)” to extract the maximum of phylogenetic signal while avoiding character 10618 correlation. The gap between states 0 and 1 of Marjanović & Laurin (2008) was an artefact of 10619 the small taxon sample; we now count this part of morphospace as part of our state 1. 10620 Unambiguous occurrences of state 2 are limited to Schoenfelderpeton and 10621 *Gerobatrachus; Doleserpeton (Sigurdsen & Bolt, 2010), Triadobatrachus (Ascarrunz et al., 10622 2016: fig. 4, 3D model 1), Eocaecilia (Jenkins, Walsh & Carroll, 2007; see Marjanović & 10623 Laurin, 2008: 181, for discussion of ectopterygoids in gymnophionomorphs) and 10624 Diploceraspis (Beerbower, 1963) have state 2 or 3. We have scored *Quasicaecilia the same 10625 way (Pardo, Szostakiwskyj & Anderson, 2015). *Carrolla has small, rounded ectopterygoids 10626 like taxa with state 2, but the palatine is itself so short that we have scored *Carrolla as 10627 possessing state 1.

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10628 Whatcheeria was scored as 0 for ECT 1 but unknown for ECT 4 in RC07. Lombard & 10629 Bolt (1995) did not mention the size of the ectopterygoid, technically excluding only state 3 10630 of the present character; however, they mentioned its dentition which make states 0 and 1 10631 probable, and would likely have mentioned if the ectopterygoid was unusually short. We have 10632 therefore scored state 0 or 1. 10633 Isodectes was scored the same way, but there is not enough space for our state 0 in the 10634 reconstruction by Sequeira (1998: fig. 9), while the presence of the ectopterygoid is uncertain 10635 (Sequeira, 1998); we have scored state 1, 2 or 3. 10636 We have accepted the score of 0 for Dendrerpetidae based on Godfrey, Fiorillo & 10637 Carroll (1987), judging from the text of which the reconstruction of the palate is probably 10638 justified even though the specimen drawing (fig. 1) only show the mere presence of the 10639 ectopterygoid. Other sources can only narrow the condition down to state 0 or 1 (Milner, 10640 1996: 90; Holmes, Carroll & Reisz, 1998). Similar considerations hold for the other ECT 10641 characters. 10642 Acheloma (Polley & Reisz, 2011), Anthracosaurus (Panchen, 1977) and Tseajaia 10643 (which has an unusually small palatine: Moss, 1972: 12) have state 0. 10644 Ecolsonia has state 0 or 1 (Berman, Reisz & Eberth, 1985: fig. 6). 10645 Broiliellus has state 1 according to Schoch (2012: fig. 2F). 10646 We assign state 1, 2 or 3 to Batropetes based on Glienke (2013: fig. 4A). 10647 Bruktererpeton has state 1 or 2; while the part of the palate that contains the suture 10648 between the ectopterygoid and the palatine is missing, enough of both bones appears to be 10649 known that the other states are impossible. The reconstruction (Boy & Bandel, 1973: fig. 7) 10650 further indicates that state 2 can be ruled out as well, but the text (p. 51) contradicts this by 10651 saying that only the caudal margin of the ectopterygoid is preserved. 10652 Seymouria sanjuanensis has state 1 as originally scored (Klembara et al., 2005), but S. 10653 baylorensis has state 0 (Laurin, 2000); Seymouria is thus polymorphic. 10654 Contra Marjanović & Laurin (2008: 181), Saxonerpeton (though borderline, if the 10655 ectopterygoid is correctly identified) and Hapsidopareion most likely have state 1 (CG78: 10656 figs. 14E, 21; already scored in RC07 for Hapsidopareion). 10657 Olori (2015) stated that the palatine of Hyloplesion was shorter than reconstructed by 10658 CG78; we have therefore scored state 1 or 2 (rather than only 2). 10659 Diplocaulus shows state 3 (Bossy & Milner, 1998), as do Sauropleura (Bossy & 10660 Milner, 1998), Oestocephalus (Carroll, 1998a) and Phlegethontia (Anderson, 2002). 10661 Bossy (1976) and Bossy & Milner (1998) reconstructed a suture on the palate of 10662 Ptyonius that would separate the vomer from the palatine in an odd place (quite some distance 10663 caudal to the choana). Therefore, they considered the next suture (even farther caudal to the 10664 choana) to be the one between palatine and ectopterygoid. That bone, however, looks exactly 10665 like the palatine of the closely related Sauropleura (and several other “nectrideans”) in their 10666 own reconstructions. Given the state of preservation of Ptyonius (Bossy, 1976), we prefer not 10667 to take the reconstruction at face value and have scored Ptyonius as unknown. It should be 10668 mentioned that ectopterygoids are otherwise absent in nectrideans (Bossy, 1976; Bossy & 10669 Milner, 1998) – Jaekel (1903: pl. III) reconstructed a suture between the palatine and the 10670 “transversum” (ectopterygoid) in Diceratosaurus, but we agree with RC07 in scoring 10671 Diceratosaurus as unknown because is hard to tell if MB.Am.778, the specimen on which the 10672 reconstruction is based, really possesses such a suture (D. M., pers. obs.). 10673 Lethiscus has state 1 (Pardo et al., 2017, excluding their matrix, where state 0 is 10674 scored). 10675 States 0 and 1 probably both occur in *Micropholis (Schoch & Rubidge, 2005: fig. 2).

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10676 Although the suture between the palatine and the ectopterygoid cannot be found in 10677 *Ymeria, the minimum length that includes all ectopterygoid teeth is longer than the length 10678 that remains for the palatine (Clack et al., 2012a: fig. 2), giving state 0 to *Ymeria. 10679 Werneburg (2012b: 12) stated that an ectopterygoid is not certainly preserved in 10680 *Branchiosaurus but may be present in fig. 6c, d. The bone in question is indeed most likely 10681 an ectopterygoid. Unfortunately, it may not be complete, and the length of the palatine is 10682 unknown, so we have scored state 0, 1 or 2. 10683 We have followed the matrix of Pardo et al. (2017) in scoring state 0 for 10684 *Coloraderpeton; the ectopterygoid is present (J. Pardo, pers. comm.), it is scored as reaching 10685 the subtemporal fenestra, and the space where it would lie is so long that state 0 seems 10686 inevitable. 10687 10688 116. ECT 2: Ectopterygoid with (0) or without (1) fangs comparable in size to or larger 10689 than marginal teeth (premaxillary or maxillary) and remaining ectopterygoid teeth (if 10690 present). 10691 Acanthostega (Clack, 1994b; Porro, Rayfield & Clack, 2015) and Acheloma (Polley & 10692 Reisz, 2011) show state 0, as does Phonerpeton (D. M., pers. obs. of MCZ 1485). We 10693 tentatively assign the same score to Trimerorhachis (Milner & Schoch, 2013); perhaps 10694 polymorphism would be better (Milner & Schoch, 2013: fig. 1, 5). 10695 The most mature known individual of Amphibamus – the neotype, YPM 794 – has 10696 state 0 (Daly, 1994: 27) as already scored in RC07. We regard this as the adult condition (see 10697 also Marjanović & Laurin, 2008: 180). Schoch & Milner (2014: 56) stated that Amphibamus 10698 lacks fangs on the vomer, palatine and ectopterygoid, but puzzlingly did not mention Daly 10699 (1994) in the context of Amphibamus at all, even though they of course mentioned YPM 794 10700 and cited Daly (1994) as a source for Eoscopus. 10701 Lethiscus (Pardo et al., 2017) and Tseajaia (Moss, 1972: 12) have state 1. We have 10702 followed the matrix of Pardo et al. (2017) in scoring it for *Coloraderpeton as well. 10703 Unknown in Bruktererpeton (Boy & Bandel, 1973: 51). 10704 Ichthyostega (Jarvik, 1996: pl. 26:1, 27:1; Blom, 2005; Clack et al., 2012a; Clack & 10705 Milner, 2015: fig. 8C) and *Lydekkerina (Shishkin, Rubidge & Kitching, 1996: fig. 7) are 10706 polymorphic. 10707 Orobates has state 1 as originally scored (Nyakatura et al., 2015: digital 10708 reconstruction); however, this is impossible to see in Berman et al. (2004). 10709 We interpret the name of this character as saying that ectopterygoid fangs have to be 10710 larger than the remaining ectopterygoid teeth; therefore *Glanochthon is polymorphic 10711 (Schoch & Witzmann, 2009b: figs. 3, 4) and *Australerpeton has state 1 (Eltink et al., 2016: 10712 848, fig. 6). *Platyoposaurus, while borderline, has state 0, however (Gubin, 1991: drawing 10713 3б); and we concur with Pereira Pacheco et al. (2016: appendix 2) in counting the borderline 10714 condition of *Konzhukovia (Gubin, 1991: drawing 15а) as state 0 as well. 10715 10716 117. ECT 3: Ectopterygoid without (0) or with (1) small teeth (denticles), the basal 10717 diameter and/or height of which is less than 30% of that of adjacent marginal teeth 10718 (maxillary) and remaining ectopterygoid teeth (if present). See VOM 4. 10719 Tseajaia shows state 0 (Moss, 1972: 12). 10720 State 1 occurs in Acheloma (Polley & Reisz, 2011) and Platyrhinops (Clack & Milner, 10721 2010). 10722 Probably unknown in Kotlassia, judging from the comments on the preservation of the 10723 toothrow and on the pterygoid and parasphenoid (Bulanov, 2003: S55). 10724 The ectopterygoid is too eroded to tell in the two *Nigerpeton specimens, MNN MOR 10725 69 and MNN MOR 70, that preserve it (D. M., pers. obs.).

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10726 Although this is not obvious from Maddin, Olori & Anderson (2011), *Carrolla has 10727 state 0 (D. M., pers. obs. of TMM 40031-54). We have followed the matrix of Pardo et al. 10728 (2017) in scoring it for *Coloraderpeton as well. 10729 The dots in the reconstruction of *Neopteroplax (Romer, 1963: fig. 5) appear to 10730 represent denticles, but there is no evidence for them in the specimen drawing (fig. 2) or the 10731 text; instead, in the specimen drawing, the denticle field has a very sharp edge that appears to 10732 coincide with the suture between pterygoid and ectopterygoid. We have therefore scored state 10733 0. 10734 10735 118. ECT 5: Ectopterygoid with (0) or without (1) row of teeth (3+) comparable in size to, 10736 or greater than marginal teeth (maxillary) and parallel to these. 10737 State 0 is found in Greererpeton (Smithson, 1982), Crassigyrinus (Clack, 1998), 10738 Trimerorhachis (Milner & Schoch, 2013), Kotlassia (Bulanov, 2003: S55, fig. 30), and 10739 Cardiocephalus (CG78) as well as *Coloraderpeton (Pardo et al., 2017: matrix; J. Pardo, 10740 pers. comm.). 10741 Acheloma (Polley & Reisz, 2011), Phonerpeton (D. M., pers. obs. of MCZ 1485), 10742 Ecolsonia (Berman, Reisz & Eberth, 1985; D. M., pers. obs. of CM 38017), Gephyrostegus 10743 (Carroll, 1970; Klembara et al., 2014), Limnoscelis (Fracasso, 1983; Reisz, 2007), 10744 Microbrachis (CG87; Vallin & Laurin, 2004; Olori, 2015), Lethiscus (Pardo et al., 2017) and 10745 Tseajaia (Moss, 1972: 12) show state 1. 10746 Unknown in Saxonerpeton (CG78). 10747 Orobates has state 1 as originally scored (Nyakatura et al., 2015: digital 10748 reconstruction); however, this is impossible to see in Berman et al. (2004). 10749 From comparisons to Colosteus and Greererpeton (Smithson, 1982; Hook, 1983) and 10750 after pers. obs. of MB.Am.1441.2 by D. M., we disagree with Clack et al. (2012b: 22) that 10751 “the right ectopterygoid is preserved in such a way that additional teeth would very likely 10752 have been evident if present” and have scored the *St. Louis tetrapod as unknown. 10753 10754 deleted ECT 6: Ectopterygoid/maxilla contact: present (0); absent (1). State 1, originally 10755 scored for the branchiosaurids, Petrolacosaurus, Hyloplesion and Odonterpeton, can mean 10756 different things: it can mean that the subtemporal fenestra extends all the way to the middle of 10757 the palatine (as it does in larval amphibamids, see above under PAL 6) or at least reaches the 10758 caudal end of the palatine (as CG78 reconstructed for Odonterpeton); or it can be due to the 10759 suborbital fenestra found in diapsids (represented in this matrix by Petrolacosaurus), which is 10760 separated from the subtemporal fenestra by an ectopterygoid-jugal (as in Petrolacosaurus) or 10761 ectopterygoid-maxilla contact (as in **crocodyliforms and some **dinosaurs, where the 10762 maxilla reaches the caudal margin of the suborbital fenestra); or, at least in theory, a long 10763 caudal extension of the palatine could intervene between the ectopterygoid and the maxilla. 10764 This last possibility was reconstructed by CG78 (fig. 89) for Hyloplesion. It looks, however, 10765 seriously weird. We have to wonder if the supposed ectopterygoid is actually the flange of the 10766 pterygoid (see PTE 3-9) that has broken off, and the real ectopterygoid is the fragment that 10767 lies rostrolateral to it in fig. 89E. (Compare the condition in Microbrachis: Vallin & Laurin 10768 2004: fig. 2C, 4B, 5B.) Olori (2015: 44) appeared to agree, stating that “the palatine 10769 terminates further anteriorly than was depicted by […] [CG78] in their figure 89H, and thus is 10770 shorter than the maxilla in anteroposterior length.” (The ectopterygoid is not otherwise 10771 mentioned or indicated in a figure.) Most likely, then, state 1 is limited to Petrolacosaurus 10772 and Odonterpeton, and the primary homology of their conditions is wide open to question. 10773 Should they be assigned separate states, the character would be parsimony-uninformative. 10774 In Odonterpeton, too, the situation is far from clear. First of all, if the reconstruction 10775 (CG78: fig. 99B) is correct, it may be due to skeletal immaturity, a condition that would be

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10776 unsurprising in this tiny specimen, in which case it should be scored as unknown (see PAL 6). 10777 The specimen drawings (CG78: fig. 98A, 99A), however, do not clearly support the 10778 reconstruction. In ventral view (right part of fig. 98A and 99A) all but the medial edge of the 10779 ectopterygoid – or perhaps the caudomedial edge of the palatine – is covered by the lower jaw 10780 on one side, and nothing is exposed on the other. The description (CG78: 145) reads in full: 10781 “The ectopterygoids are small bones. The lateral margin of the left ectopterygoid, seen in 10782 dorsal view through the orbit, does not appear to reach the maxilla.” It is not clear to us how 10783 this conclusion was reached; according to the specimen drawing in dorsal view (CG78: left 10784 part of fig. 98A and 99A), the lateral tip of the ectopterygoid lines up with the lateral margin 10785 of the palatine, or nearly so, and the disarticulated maxilla is only preserved in lateral view. 10786 Finally, not all of the sutures in these specimen drawings are accurate (see POSPAR 1-2 10787 above). 10788 Scoring Hyloplesion or Odonterpeton as anything other than unknown, thus, will have 10789 to await further inspection of specimens. (Unfortunately, D. M. had not yet considered this 10790 character during his visit to the USNM.) This leaves state 1 only to Petrolacosaurus, making 10791 the character parsimony-uninformative; we have deleted it. 10792 Acheloma (Polley & Reisz, 2011) and Tseajaia (Moss, 1972: 12), previously scored as 10793 unknown, show state 0. 10794 10795 deleted ECT 7: Ectopterygoid narrowly wedged between palatine and pterygoid: no (0); 10796 yes (1). RC07 explicitly ascribed state 1 to Odonterpeton and Hyloplesion, but Odonterpeton 10797 is reconstructed as having state 0 (CG78: fig. 99). This makes this character parsimony- 10798 uninformative (state 1 was not scored for any other OTUs, and we have not seen it in any of 10799 them), so we have deleted it. Additionally, we doubt whether state 1 occurs even in 10800 Hyloplesion, see ECT 6. 10801 10802 119. PTE 3-9: Flange on pterygoid: absent, pterygoid margin of subtemporal fenestra 10803 concave or straight throughout (0); rostrolateral-caudomedial orientation (1); 10804 mediolateral or rostromedial-caudolateral orientation (“transverse flange”), without 10805 row of large teeth (2); same with row of large teeth (3) (ordered). RC07 treated the 10806 “posterolateral flange” (PTE 9(1); our state 1) separately from the “transverse flange” (PTE 10807 3(1, 2); our states 2 and 3), but we think the “transverse flange” is only an extreme of a 10808 continuum the rest of which is called “posterolateral flange”. Indeed, the two flanges never 10809 occur together – except that our states 1 and 2 occur in different individuals of *Micropholis 10810 (Schoch & Rubidge, 2005: fig. 2) and apparently *Sclerocephalus (Schoch & Witzmann, 10811 2009a: fig. 4, 6), which we have both scored as having states 1 and 2. 10812 Interestingly, PTE 3 was called “Transverse flange of pterygoid absent (0), present 10813 without transverse tooth row (1), or present and carrying transverse tooth row.” – the number 10814 “(2)” was omitted. This may of course be a simple typographic error; notably, however, state 10815 2 did not occur in the matrix apart from the partial uncertainty (state 1 or 2) that was scored 10816 for Leptoropha and Tseajaia. 10817 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994). The condition 10818 of Caerorhachis is borderline (Ruta, Milner & Coates, 2002), but we have kept the score of 0. 10819 Trimerorhachis has a weak case of state 1 (Milner & Schoch, 2013), no weaker than 10820 that of Neldasaurus (already scored correctly; Chase, 1965). State 1 further appears in 10821 Micromelerpeton (close to state 2: Schoch, 2009b: fig. 2c), Apateon (Schoch & Milner, 2008), 10822 Leptorophus (Boy, 1986), Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015: fig. 3A), 10823 Lethiscus (Pardo et al., 2017), Oestocephalus (Carroll, 1998a), apparently Vieraella (Estes & 10824 Reig, 1973: fig. 1-2; Báez & Basso, 1996: fig. 6) and Silvanerpeton (Ruta & Clack, 2006). 10825 Broiliellus (Schoch, 2012: fig. 2F) and Tseajaia (Moss, 1972) have state 2.

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10826 If Hyloplesion was reconstructed correctly by CG78 (fig. 89H), this character is not 10827 applicable to it, because the pterygoid does not contribute to the subtemporal fenestra except 10828 by most of its quadrate ramus; if the unlikely positioned supposed ectopterygoid is part of the 10829 pterygoid instead (see ECT 6 above), Hyloplesion has state 2. We have gone with the latter 10830 option mainly because, even accepting all of the identifications by CG78, the left pterygoid 10831 (though perhaps not the right one) does go just around the corner between the medial and the 10832 rostral margin of the subtemporal fossa in one specimen (CG78: fig. 89E). This issue was not 10833 addressed or figured by Olori (2015). 10834 State 3 of the present character ( = state 2 of PTE 3) is present in Limnoscelis 10835 (Fracasso, 1983: fig. 2; Reisz, 2007; Berman, Reisz & Scott, 2010), Paleothyris (Carroll, 10836 1969a), and Petrolacosaurus (Reisz, 1981). 10837 The condition is entirely unknown in Colosteus (Hook, 1983: fig. 1B), Whatcheeria 10838 (the palate of which has not yet been described: Bolt & Lombard, 2000), Eucritta (the 10839 reconstruction, Clack, 2001: fig. 8, appears overly ambitious judging from the accompanying 10840 text and specimen drawings), Edops (D. M., pers. obs. of MCZ 1378; contra Romer & Witter, 10841 1942: fig. 3B), Batropetes (Carroll, 1991; Glienke, 2013, 2015), Asaphestera (CG78: fig. 6F), 10842 and apparently Pederpes (Clack & Finney, 2005). The palate of Keraterpeton appears to be 10843 entirely unknown (Huxley & Wright, 1867; Jaekel, 1903). 10844 Neither state 0 (already scored in RC07) nor state 1 can be excluded for Isodectes 10845 (Sequeira, 1998). For Scincosaurus, figures 2B and 3B of Milner & Ruta (2009) appear to 10846 contradict each other, at least on the anatomically left side: fig. 3B shows state 0 as already 10847 scored, while fig. 2B shows state 1, unless the bulge in question was dorsal rather than lateral 10848 in life; we have scored partial uncertainty here as well. 10849 State 0 can be ruled out for Bruktererpeton (Boy & Bandel, 1973: fig. 7); we have 10850 accordingly scored state 1, 2 or 3. 10851 Amphibamus (Bolt, 1979: fig. 6B; Milner, 1982: fig. 3b; Schoch & Milner, 2014: fig. 10852 30B) and Odonterpeton (CG78: fig. 99A) appear to have states 1 or 2. 10853 *Acanthostomatops has state 1, though it is close to state 2, at least in two dimensions 10854 (Witzmann & Schoch, 2006a). 10855 The reconstruction of *Carrolla by Maddin, Olori & Anderson (2011: fig. 7B) cannot 10856 be reconciled with the specimen (D. M., pers. obs. of TMM 40031-54): the drawing leaves 10857 practically no space for the subtemporal fenestra, in particular the coronoid process of the 10858 lower jaw which lies in this fenestra in the fossil, because it gives the pterygoid a large lateral 10859 extension, implying that the preserved lateral margin must be a break. In the specimen, the 10860 margin is finished and rounded, as is the cranial margin of the quadrate ramus; the margin 10861 implied by Maddin, Olori & Anderson (2011: fig. 4) should be taken at face value. 10862 Furthermore, the quadrate ramus is identified in fig. 4 and described, with its suture to the 10863 quadrate, several times in the text of Maddin, Olori & Anderson (2011), yet it is entirely 10864 absent from fig. 7B, where the pterygoid does not contact the quadrate at all! – One might 10865 wonder whether a transverse flange (state 2) might have merged with the equally transverse 10866 quadrate ramus immediately caudal to it; however, the pterygoid ramus of the quadrate 10867 articulates with the entire width of the quadrate ramus of the pterygoid, so that the flange 10868 would have to be extremely short and limited to the concave transition of the quadrate ramus 10869 to the rest of the pterygoid (D. M., pers. obs. of TMM 40031-54). *Carrolla thus has state 0. 10870 It remains to be seen whether this is size-related, however. 10871 “Large teeth” are not defined. Under the assumption that this simply means “not 10872 denticles”, the row of teeth found in *Archaeovenator qualifies for state 3, because the largest 10873 of those teeth are about the size of the smallest marginal teeth and distinctly larger than all 10874 denticles (Reisz & Dilkes, 2003: fig. 2). 10875

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10876 120. PTE 7: Pterygoid quadrate ramus orientated mostly caudally (0) or mostly laterally 10877 in ventral aspect (1); ramus absent, quadrate contacts central region of pterygoid (2) 10878 (ordered). State 0 was originally unspecified. State 2 is new and accounts for the condition 10879 seen in Batropetes (Glienke, 2013), Brachydectes (Wellstead, 1991; Pardo & Anderson, 10880 2016) and Scincosaurus (Milner & Ruta, 2009); the character is ordered because it is 10881 potentially continuous and reflects a widening of the parasphenoid and a rostral repositioning 10882 of the quadrates – although the correlation with JAW ART 1/SQU 2/DEN 8 (below) is not 10883 perfect. 10884 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Lethiscus 10885 (Pardo et al., 2017). 10886 Keraterpeton was scored in RC07 as having state 0. The palate appears to be entirely 10887 unknown (Huxley & Wright, 1867; Jaekel, 1903), and indeed state 1 would be expected from 10888 the proportions of the skull (Jaekel, 1903: fig. 1, 2); we have changed the score to unknown. 10889 State 1 is clearly found in Diceratosaurus (Jaekel, 1903: pl. III), Diplocaulus (Bossy 10890 & Milner, 1998) and Diploceraspis (Beerbower, 1963). In Batrachiderpeton (Bossy & 10891 Milner, 1998), the quadrate ramus is oriented much more laterally than caudally; we count 10892 this as state 1 as well. 10893 State 1 is also documented in *Chelotriton (Roček & Wuttke, 2010; Schoch, 10894 Poschmann & Kupfer, 2015); but in MB.Am.45, which is preserved in dorsal view only, state 10895 0 would be expected because the suspensoria extend far caudal to the occiput. We have scored 10896 partial uncertainty. 10897 We infer state 0 for the *St. Louis tetrapod because the lower jaw, and indeed its 10898 Meckelian fenestra, continues well distal to the basipterygoid process (Clack et al., 2012b). 10899 10900 121. PTE 11: Pterygoid/maxilla contact: absent (0); present (1). Because the ectopterygoid, 10901 if present, usually lies between the pterygoid and the maxilla, it would have been tempting to 10902 merge this character with ECT 1-4 (above), but Clack (1998: fig. 4B) suggests that the 10903 maxilla and the pterygoid could meet caudal to the ectopterygoid in Crassigyrinus (scored 10904 here as unknown), and indeed they meet caudal to the well developed ectopterygoid in 10905 Caerorhachis (see below) and Micraroter (CG78: 88; previously scored as unknown), so we 10906 have kept them separate. 10907 Acanthostega (Clack, 1994b), Acheloma (Polley & Reisz, 2011), Bruktererpeton (Boy 10908 & Bandel, 1973: fig. 7), Batropetes (Glienke, 2013) and Lethiscus (Anderson, Carroll & 10909 Rowe, 2003; Pardo et al., 2017) have state 0. 10910 Caerorhachis was scored 0 in RC07. Ruta, Milner & Coates (2002: fig. 4b), however, 10911 clearly showed state 1 on the right side of the specimen. On the left side of the same 10912 specimen, they reconstructed state 0 (fig. 5c); Ruta, Milner & Coates (2002) did not mention 10913 this discrepancy in the text. While it is possible that the left side had state 0, especially if the 10914 maxillary process of the pterygoid was genuinely absent and has not broken off, the left side 10915 of the palate is much too disarticulated to tell for sure; in particular, the ectopterygoid is 10916 missing on that side (fig. 3b, 5a). We have therefore scored state 1 alone. 10917 Unknown in Whatcheeria (Lombard & Bolt, 1995), Doleserpeton and 10918 Triadobatrachus, together with but not entirely dependent on the existence and extent of the 10919 ectopterygoid (Sigurdsen & Bolt, 2010; Ascarrunz et al., 2016: fig. 4, 12, 3D model 1; see 10920 also character ECT 1-4 above), apparently Keraterpeton (Huxley & Wright, 1867; Jaekel, 10921 1903) and Silvanerpeton (Ruta & Clack, 2006). 10922 The condition in Edops is likewise unknown (D. M., pers. obs. of MCZ 1378); RC07 10923 may have misplaced the question mark to the next character, the state of which is known (see 10924 below). 10925 For *Erpetosaurus and the *St. Louis tetrapod, see JUG 3 above.

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10926 We follow Pardo et al. (2017: matrix) in scoring state 0 for *Coloraderpeton. 10927 10928 122. PTE 13: Pterygoid without (0) or with (1) distinct, me[d]ially directed process for 10929 basipterygoid articulation. This character is only applicable when the interpterygoid 10930 vacuities are not too small; we have scored it as inapplicable where that condition is not 10931 fulfilled (this concerns a large majority of the OTUs scored 0 by RC07), as well as in a few 10932 other OTUs that lack space for such a process like Greererpeton or Limnoscelis (Reisz, 2007: 10933 fig. 6.1; Berman, Reisz & Scott, 2010: fig. 4A). 10934 State 1 is found in Acanthostega (weakly expressed: Porro, Rayfield & Clack, 2015), 10935 Edops (Romer & Witter, 1942: fig. 3B; D. M., pers. obs. of MCZ 1378), Neldasaurus (very 10936 weakly expressed: Chase, 1965), Trimerorhachis (weakly expressed: Milner & Schoch, 10937 2013), Balanerpeton (Milner & Sequeira, 1994), Pelodosotis (CG78: fig. 48), Rhynchonkos 10938 (Szostakiwskyj, Pardo & Anderson, 2015), Hyloplesion (in the largest of the three specimens 10939 drawn in CG78: fig. 89; photographed in Olori, 2015: fig. 30A), Diceratosaurus (Jaekel, 10940 1903: pl. III), Diplocaulus (Bossy & Milner, 1998: fig. 57C) where the process is very broad 10941 rostrocaudally but no less distinct than elsewhere, Diploceraspis (Beerbower, 1963: fig. 4A) 10942 where the same situation prevails (partly obscured by the fact that the quadrate ramus is 10943 situated so far rostrally), Ptyonius (Bossy, 1976: fig. 44, 49), and Capetus (Sequeira & 10944 Milner, 1993). The process is apparently very short but nonetheless distinct in Batropetes 10945 (Glienke, 2013), so we have assigned state 1 to it as well. 10946 The palate of Keraterpeton appears to be entirely unknown (Huxley & Wright, 1867; 10947 Jaekel, 1903). 10948 State 0 makes a surprise appearance in Lethiscus (Pardo et al., 2017). 10949 *Micropholis is polymorphic (Schoch & Rubidge, 2005). So is *Sclerocephalus 10950 (Schoch & Witzmann, 2009a: fig. 6). 10951 Although likely shorter than implied by Maddin, Olori & Anderson (2011: fig. 7B), 10952 the process is clearly present (state 1) in *Carrolla. 10953 We have also assigned state 1 to the special case of *Quasicaecilia, where the process 10954 is very long and clearly distinct, but points straight caudally because the jaw articulation is so 10955 far rostral (Pardo, Szostakiwskyj & Anderson, 2015). 10956 Although very wide rostrocaudally, the process is present (state 1) in *Australerpeton 10957 (Eltink & Langer, 2016). 10958 Even though this character is inapplicable to Hapsidopareion, *Llistrofus has state 1 10959 (Bolt & Rieppel, 2009). 10960 10961 123. PTE 14: Quadrate ramus of pterygoid more than (0) or at most twice as long as 10962 maximally broad (1). The original wording was more impressionistic: “Pterygoid quadrate 10963 ramus a robust structure, indistinctly merging into basal and palatal processes: absent (0); 10964 present (1)”, explained in the next sentence as the quadrate ramus being “a stout structure, 10965 slightly longer than wide and without a neat separation from the rest of the bone”. We have 10966 reduced this to the length/width ratio, which we have changed because the quadrate ramus is 10967 considerably longer than broad in most OTUs that were scored 1 in RC07 (all lissamphibians, 10968 Micromelerpeton, and all branchiosaurids were scored 1, everything else was given state 0). 10969 State 0 as defined by us occurs in Micromelerpeton (Boy, 1995), all branchiosaurids 10970 (Boy, 1986, 1987), and the lissamphibians Eocaecilia (Jenkins, Walsh & Carroll, 2007), 10971 Triadobatrachus (Roček & Rage, 2000; Ascarrunz et al., 2016; D. M. and M. L., pers. obs. of 10972 MNHN F.MAE.126), and Valdotriton (Evans & Milner, 1996) as well as *Liaobatrachus 10973 (Dong et al., 2013). Less surprisingly, it is known from Ventastega (Ahlberg, Lukševičs & 10974 Lebedev, 1994) and Lethiscus (Pardo et al., 2017).

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10975 We find state 1 in Baphetes (Beaumont, 1977), Eucritta (Clack, 2001), Isodectes 10976 (Sequeira, 1998), Platyrhinops (borderline; Clack & Milner, 2010), Caerorhachis (Ruta, 10977 Milner & Coates, 2002), Eoherpeton (Smithson, 1985), Pholiderpeton attheyi (Panchen, 10978 1972), Ph. scutigerum (Clack, 1987b), Asaphestera, Micraroter (marginally) and 10979 Cardiocephalus (CG78), Scincosaurus (Milner & Ruta, 2009), Batrachiderpeton (Bossy & 10980 Milner, 1998), Diceratosaurus (Jaekel, 1903), Diplocaulus (the pterygoids of which which 10981 look like those of the salamander Karaurus: Bossy & Milner, 1998), Diploceraspis 10982 (Beerbower, 1963), Capetus (Sequeira & Milner, 1993) and Silvanerpeton (Ruta & Clack, 10983 2006) as well as, unexpectedly, *Palaeoherpeton (Panchen, 1964: fig. 13). 10984 Euryodus is polymorphic (CG78). 10985 The condition is unknown in Anthracosaurus (Panchen, 1977), Odonterpeton (CG78: 10986 fig. 99A), Adelospondylus (Andrews & Carroll, 1991; it is too difficult to decide how to 10987 measure the reconstruction drawing and how to interpret it in relation to the specimen 10988 drawings), Keraterpeton (Huxley & Wright, 1867; Jaekel, 1903), and inapplicable in 10989 Batropetes, which likely lacks a quadrate ramus (Glienke, 2013), and Brachydectes, which 10990 clearly lacks a quadrate ramus (Wellstead, 1991; Pardo & Anderson, 2016), as well as in 10991 Oestocephalus (Carroll, 1998a), which lacks clear sutures between the pterygoid and other 10992 bones such as the epipterygoid and the quadrate. 10993 Apparently borderline in the incompletely preserved *Neopteroplax (Romer, 1963: 10994 fig. 2); we have scored it as unknown. 10995 10996 deleted PTE 15: Pterygoid quadrate ramus straight, rod-like and gently tapering distally 10997 in ventral aspect: absent (0); present (1). The ventral surface of the quadrate ramus further 10998 “is parallel-sided for most of its length and narrows smoothly in its rearmost part” in state 1, 10999 which is supposed to be present in “some dissorophoids and Eocaecilia”. This unquantified 11000 description, which is strongly reminiscent of PTE 14, turns out to be difficult to apply to 11001 many (if not most) OTUs, or at least to the line drawings that fail to show that the quadrate 11002 ramus is a more or less vertical lamina rather than a rod. The visible tapering of the process 11003 further depends strongly on diagenetic compression. We fail to see a difference between the 11004 conditions of Broiliellus (scored 0 by RC07), Platyrhinops (0), Eoscopus (1), Doleserpeton 11005 (1), or probably even Eocaecilia (1). For the time being, we have therefore deleted this 11006 character. 11007 11008 124. PTE 16: Pterygoid palatal ramus without (0) or with (1) distinct, anterior and 11009 unornamented digitiform process. State 1 requires that the pterygoids meet rostral to the 11010 parasphenoid; where this is not the case (VOM 5-10/PTE 10-12-18/INT VAC 1 having a state 11011 other than 0 or 1), this character is inapplicable. 11012 State 0 is found in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Microbrachis 11013 (Vallin & Laurin, 2004; Olori, 2015) and Ossinodus (Warren 2007). 11014 The condition of Westlothiana is unknown (Smithson et al., 1994) in addition to being 11015 inapplicable. The palate of Keraterpeton appears to be entirely unknown (Huxley & Wright, 11016 1867; Jaekel, 1903). 11017 We have counted the condition of *Chroniosaurus (Klembara, Clack & Čerňanský, 11018 2010) as state 1, although it may not be unornamented enough. 11019 11020 125. PTE 17: Basal region of pterygoid immediately anterior to quadrate ramus without 11021 (0) or with (1) sharply defined, elongate longitudinal groove. 11022 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994) and Lethiscus 11023 (Pardo et al., 2017).

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11024 State 1 is known in Euryodus (CG78) and makes a surprise appearance in 11025 *Liaobatrachus (Dong et al., 2013). 11026 Edops is probably best scored as unknown (D. M., pers. obs. of MCZ 1378). 11027 The palate of Keraterpeton appears to be entirely unknown (Huxley & Wright, 1867; 11028 Jaekel, 1903). 11029 11030 126. PTE 19: Robust, strut-like pterygoid–squamosal process providing support for 11031 quadrate: absent (0); present (1). This refers to the condition seen today in salamanders, 11032 where the quadrate process of the pterygoid is largely parallel to the ventrolateral process of 11033 the squamosal ( = its main body), and the two together almost completely encase the (often 11034 partly or wholly unossified) quadrate for its entire length or nearly so. 11035 State 0 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Lethiscus 11036 (Pardo et al., 2017) and, surprisingly, *Chelotriton (Schoch, Poschmann & Kupfer, 2015). 11037 As preserved, Triadobatrachus comes close to state 1; this is almost certainly due to 11038 crushing, however (Ascarrunz et al., 2016: 3D model 1), so we have kept state 0. 11039 The palate of Keraterpeton appears to be entirely unknown (Huxley & Wright, 1867; 11040 Jaekel, 1903). 11041 11042 127. INT VAC 2: Interpterygoid vacuities and cultriform process together occupy at 11043 least half of palatal width: absent (0); present (1). We have added the cultriform process of 11044 the parasphenoid to make clear that we measured the distance between the lateral extremities 11045 of the vacuities; as a side-effect, this increases the applicability of this character – specifically, 11046 Brachydectes has state 1 despite lacking interpterygoid vacuities (Wellstead, 1991; Pardo & 11047 Anderson, 2016). On the other hand, while a width of zero could be measured and scored, it 11048 follows automatically from state VOM 5-10/PTE 10-12-18/INT VAC 1(0); we have scored 11049 these OTUs as inapplicable, as RC07 did in a few cases. 11050 State 1 is also found in Cochleosaurus (Sequeira, 2004), Albanerpetidae (McGowan, 11051 2002; Maddin et al., 2013a: fig. 5H, I), Eocaecilia (Jenkins, Walsh & Carroll, 2007) and 11052 Batropetes, the only OTU in this matrix that is known to combine state 1 with convex 11053 pterygoid margins (INT VAC 3(0)) (Glienke, 2013). Lethiscus appears to reach state 1 as well 11054 (Pardo et al., 2017; J. Pardo, pers. comm.). 11055 Whatcheeria has state 0 (Lombard & Bolt 1995). So do Bruktererpeton (Boy & 11056 Bandel, 1973), Diadectes (Berman, Sumida & Martens, 1998) and Diceratosaurus (Jaekel, 11057 1903; D. M., pers. obs. of MB.Am.778). 11058 *Carrolla shares state 0: the vacuities are probably considerably less wide than half of 11059 the palate (D. M., pers. obs. of TMM 40031-54; contra Maddin, Olori & Anderson, 2011: fig. 11060 7B). 11061 The palate of Keraterpeton appears to be entirely unknown (Huxley & Wright, 1867; 11062 Jaekel, 1903). 11063 11064 128. INT VAC 3: Interpterygoid vacuities concave along their whole margins: absent (0); 11065 present (1). We count missing parts of margins as concave (for instance in salamanders 11066 where the palatine is absent and the pterygoid does not reach the maxilla). In the absence of 11067 interpterygoid vacuities, however (VOM 5-10/PTE 10-12-18/INT VAC 1(0)), this character is 11068 inapplicable. 11069 Batropetes is the only OTU in this matrix, with the possible exception of Eocaecilia, 11070 that combines convex pterygoid margins (state 0 of the present character) with vacuities that 11071 are together half as wide as the palate (INT VAC 2(1)) (Glienke, 2013). 11072 Albanerpetidae has state 0: the only known margins are very slightly convex in their 11073 caudal half (McGowan, 2002; Maddin et al., 2013a: PDF version of fig. 5H, I at 500%). So do

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11074 Bruktererpeton (Boy & Bandel, 1973), Diadectes (Berman, Sumida & Martens, 1998), 11075 Diceratosaurus (Jaekel, 1903; D. M., pers. obs. of MB.Am.778) and Lethiscus (Pardo et al., 11076 2017). 11077 Eocaecilia is borderline (Jenkins, Walsh & Carroll, 2007: fig. 3); we have scored it as 11078 unknown. Phlegethontia, too, is borderline (Anderson, 2002: fig. 8.2), so we have kept the 11079 score as unknown. 11080 State 1 is arguably found in Caerorhachis (Ruta, Milner & Coates, 2002: fig. 5c), 11081 apparently in Stegotretus (Berman, Eberth & Brinkman, 1988), almost certainly in 11082 Asaphestera (CG78: fig. 6F, 7), borderline but certainly in Ptyonius (Bossy & Milner, 1998: 11083 fig. 75B), perhaps less certainly but not borderline in Urocordylus (Bossy & Milner, 1998: 11084 fig. 55A), and definitely in Capetus (Sequeira & Milner, 1993: fig. 7, pl. 3). It further occurs 11085 in Tuditanus (Carroll & Baird, 1968: fig. 5); the reconstruction (fig. 9) shows state 1 on the 11086 anatomical right and 0 on the left side, but the left pterygoid is entirely unknown (fig. 5). 11087 *Sclerocephalus is polymorphic (Schoch & Witzmann, 2009a: fig. 4, 6). So is 11088 apparently Pantylus (left and right side of the specimen reconstructed by Romer, 1969: fig. 5; 11089 copied by CG78: fig. 25). 11090 *Carrolla has state 0: the vacuity margins are partly straight (D. M., pers. obs. of 11091 TMM 40031-54; only stippled by Maddin, Olori & Anderson, 2011: fig. 7B). 11092 Unknown in Eoherpeton (Smithson, 1985). The palate of Keraterpeton appears to be 11093 entirely unknown (Huxley & Wright, 1867; Jaekel, 1903). 11094 11095 129. INT VAC 4: Interpterygoid vacuities and cultriform process together broader than 11096 long: absent (0); present (1). We have added the cultriform process of the parasphenoid to 11097 make clear that we measured the distance between the lateral extremities of the vacuities; as a 11098 side-effect, it increases the applicability of this character – Brachydectes in particular has state 11099 0 (Wellstead, 1991; Pardo & Anderson, 2016). On the other hand, while a width of zero could 11100 be measured and scored, it is already coded as state VOM 5-10/PTE 10-12-18/INT VAC 1(0); 11101 we have scored these OTUs as inapplicable for the present character, as RC07 did in some 11102 cases. 11103 The combination of state 1 with INT VAC 3(0) does not occur in this matrix, but is 11104 known in larvae and some adults of **extant caecilians (Reiss, 1996); we have therefore not 11105 merged these characters. 11106 Cochleosaurus has state 0 (Sequeira, 2004), as do Bruktererpeton (Boy & Bandel, 11107 1973), Diadectes (Berman, Sumida & Martens, 1998), Batropetes (Glienke, 2013), 11108 Diceratosaurus (Jaekel, 1903; D. M., pers. obs. of MB.Am.778) and Lethiscus (Pardo et al., 11109 2017). 11110 State 1 is found in Albanerpetidae (McGowan, 2002; Maddin et al., 2013a: PDF 11111 version of fig. 5I at 500%), almost certainly in Asaphestera (CG78: fig. 6F, 7), and most 11112 likely in Hyloplesion (Olori, 2015: fig. 30C, ?A). 11113 The palate of Keraterpeton appears to be entirely unknown (Huxley & Wright, 1867; 11114 Jaekel, 1903). 11115 We have scored state 0 for *Coloraderpeton following the matrix by Pardo et al. 11116 (2017). 11117 11118 130. CHO 1: Choana wider in its anterior half than in its posterior half: no (0); yes (1). 11119 State 0 is found in Crassigyrinus (Clack, 1998), Platyrhinops (Clack & Milner, 2010), 11120 Albanerpetidae (Maddin et al., 2013a: PDF version of fig. 5I at 500%), Bruktererpeton (Boy 11121 & Bandel, 1973: 51), Kotlassia (Bulanov, 2003: fig. 30), Seymouria (Laurin, 2000; Klembara 11122 et al., 2007), Batropetes (most likely; Glienke, 2013, 2015), Lethiscus (Pardo et al., 2017),

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11123 Orobates (Nyakatura et al., 2015: digital reconstruction) and Silvanerpeton (Ruta & Clack, 11124 2006). 11125 State 1 occurs throughout Dendrerpetidae (Godfrey, Fiorillo & Carroll, 1987; Milner, 11126 1996; Holmes, Carroll & Reisz, 1998) and is shared by Acheloma (Polley & Reisz, 2011), 11127 Ecolsonia (Berman, Reisz & Eberth, 1985), Amphibamus (Schoch & Milner, 2014: fig. 30B), 11128 Doleserpeton (Sigurdsen & Bolt, 2010), Limnoscelis (Berman, Reisz & Scott, 2010), Pantylus 11129 (Romer, 1969; CG78) and Stegotretus (Berman, Eberth & Brinkman, 1988). Judging from the 11130 shape of the vomer, it is also a safe bet in Vieraella (Báez & Basso, 1996). 11131 Unknown in Saxonerpeton (CG78: fig. 21), Micraroter (CG78) and Scincosaurus 11132 (Milner & Ruta, 2009). 11133 *Sclerocephalus is polymorphic (Schoch & Witzmann, 2009a: fig. 4). 11134 11135 131. CHO 2: Choana expanded transversely along its medial margin: absent (0); present 11136 (1). We cannot see a difference between the taxa that were scored 1 and most of the ones that 11137 were scored 0. We have therefore tried to define state 1 as a choana that is wide linguolabially 11138 compared to the palatine and any teeth it may bear; there do not seem to be many borderline 11139 cases. 11140 We count the absence of a medial wall (as in Valdotriton) as state 1. 11141 Platyrhinops (Clack & Milner, 2010) and Bruktererpeton (Boy & Bandel, 1973: 51) 11142 have state 0. 11143 State 1 is found in Colosteus (Hook, 1983), Crassigyrinus (Clack, 1998), Edops 11144 (Romer & Witter, 1942; D. M., pers. obs. of MCZ 1378), Chenoprosopus (Langston, 1953), 11145 Cochleosaurus (Sequeira, 2004), Trimerorhachis (Milner & Schoch, 2013), Balanerpeton 11146 (Milner & Sequeira, 1994), Dendrerpetidae (Godfrey, Fiorillo & Carroll, 1987; Milner, 1996; 11147 Holmes, Carroll & Reisz, 1998), Eryops (Sawin 1941), Acheloma (Polley & Reisz, 2011), 11148 Phonerpeton (Dilkes, 1990), Ecolsonia (Berman, Reisz & Eberth, 1985), Broiliellus (even 11149 though the choana is extremely long and therefore looks narrow: Carroll, 1964: fig. 10; 11150 Schoch, 2012: fig. 2F), Micromelerpeton (Boy, 1995; Schoch, 2009b), Albanerpetidae 11151 (Maddin et al., 2013a: PDF version of fig. 5I at 500%), Caerorhachis (Ruta, Milner & Coates, 11152 2002), Eoherpeton (Panchen, 1975; Smithson, 1985), Proterogyrinus (Holmes, 1984), 11153 Pholiderpeton scutigerum (Clack, 1987b), Gephyrostegus (Klembara et al., 2014), Kotlassia 11154 (Bulanov, 2003: fig. 30), Discosauriscus and Seymouria (Klembara et al., 2007; though 11155 borderline in S. baylorensis: Laurin, 2000), Limnoscelis (Berman, Reisz & Scott, 2010), 11156 Batropetes (Glienke, 2013, 2015), Pantylus (CG78), Stegotretus (Berman, Eberth & 11157 Brinkman, 1988), apparently Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015), 11158 Brachydectes (Wellstead, 1991; Pardo & Anderson, 2016), Diceratosaurus (D. M., pers. obs. 11159 of MB.Am.778), Diplocaulus (Bossy & Milner, 1998), Diploceraspis (Beerbower, 1963), 11160 Lethiscus (Pardo et al., 2017), Orobates (Nyakatura et al., 2015: digital reconstruction) and 11161 Silvanerpeton (Ruta & Clack, 2006). Judging from the shape of the vomer, it is also a safe bet 11162 in Vieraella (Báez & Basso, 1996). *Saharastega most likely shared it (Damiani et al., 2006; 11163 D. M., pers. obs. of MNN MOR 73). 11164 Unknown in Pholiderpeton attheyi, where it may have been borderline (Panchen, 11165 1972); further unknown in Saxonerpeton (CG78: fig. 21), Micraroter (CG78) and 11166 Scincosaurus (Milner & Ruta, 2009). 11167 *Sclerocephalus is polymorphic (Schoch & Witzmann, 2009a: fig. 4). 11168 11169 132. ANT VAC 2: Anterior palatal vacuity present and single (0), present and double (1), 11170 or absent (2) (unordered). RC07 created this character by merging ANT VAC 1 and ANT 11171 VAC 2 of Ruta, Coates & Quicke (2003). We have not ordered this character because no

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11172 sequence is obvious. We interpret “vacuity” to mean “fenestra” exclusively; fossae not 11173 pierced by fenestrae are scored as state 2. 11174 State 0 or 1 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994). 11175 Colosteus (Hook, 1983) and Crassigyrinus (Clack, 1998) have state 1. 11176 Not described or illustrated in Whatcheeria (Lombard & Bolt, 1995; Bolt & Lombard, 11177 2000). 11178 One specimen of Megalocephalus has state 1, unlike the others that have state 0 11179 (Beaumont, 1977) as previously scored; we have changed the score to polymorphism. 11180 Karaurus was scored as possessing state 2 in RC07, but has only been reconstructed 11181 (Ivachnenko, 1978) with a very large, single vacuity, thus state 0; Bruktererpeton shares state 11182 0 (Boy & Bandel, 1973: 51), and apparently so does Vieraella (Báez & Basso, 1996: fig. 5, 11183 7). 11184 State 2 is known in Batropetes (Glienke, 2013), Diceratosaurus (D. M., pers. obs. of 11185 MB.Am.778) and Orobates (Nyakatura et al., 2015: digital reconstruction). 11186 Lethiscus appears to have state 0 (Pardo et al., 2017; also scored in their matrix). 11187 The condition is unknown in Edops (Romer & Witter, 1942; D. M., pers. obs. of MCZ 11188 1378 – the tip of the snout consists only of plaster), Gephyrostegus (Klembara et al., 2014: 11189 fig. 2), Scincosaurus (Milner & Ruta, 2009), Silvanerpeton (Ruta & Clack, 2006) and 11190 Tseajaia (Moss, 1972: 12). 11191 States 0 and 2 are both known to occur in *Micropholis (Schoch & Rubidge, 2005). 11192 State 0 was reconstructed for *Liaobatrachus (L. zhaoi: Dong et al., 2013: fig. 7B), 11193 but the photos show that the vacuity, if present, must have been smaller than reconstructed; 11194 because the text does not mention the vacuity at all, we have scored it as unknown. 11195 For *Pholidogaster we have followed Panchen (1975: 625), who considered state 1 11196 “the most probable” condition. For *Coloraderpeton we have followed the matrix of Pardo et 11197 al. (2017) in scoring state 0. 11198 11199 133. SUPOCC 1: Caudal exposure of separately ossified supr[…]occipital: absent (0); 11200 present (1). The caudal exposure has to be specified because a suproccipital – or in any case 11201 an ossification of the synotic tectum – can be present and form the roof of the braincase 11202 without being visible from the outside at all (Olson, 1941: 162, fig. 8; Bystrow, 1944; 11203 Berman, Eberth & Brinkman, 1988; Maddin, Reisz & Anderson, 2010; Polley & Reisz, 2011, 11204 and references therein – though some of these cases may represent the suprotic rather than the 11205 suproccipital: compare Grande & Bemis, 1998, and Cubbage & Mabee, 1996). 11206 Damiani et al. (2006) cited Sequeira (1998) for the claim that Isodectes has a caudally 11207 exposed suproccipital (though not necessarily as a separate bone, and thus not necessarily 11208 state 1 of the present character). Not only did Sequeira (1998) not mention or illustrate such 11209 an ossification, but her fig. 4B shows a median suture between the exoccipitals dorsal to the 11210 foramen magnum, continuous with the median suture between the postparietals, leaving no 11211 space for a suproccipital. We have therefore kept the score of 0 for Isodectes. 11212 State 0 is apparently present in Dendrerpetidae (Robinson, Ahlberg & Koentges, 2005) 11213 and Diplocaulus (Douthitt, 1917). 11214 Bolt (1969: 889) stated explicitly that Doleserpeton clearly shows state 0: “There is no 11215 supraoccipital bone, and indeed no room for one, as the opisthotics cover the tops of the 11216 exoccipitals and, in maturer specimens, fuse above the foramen magnum.” This is confirmed 11217 by Sigurdsen (2008) and Sigurdsen & Bolt (2010). 11218 Eocaecilia shares state 0, as demonstrated by the median dorsal suture in the braincase 11219 (Jenkins, Walsh & Carroll, 2007) – the suproccipital is a single median bone and would make 11220 such a suture impossible. The same holds for Notobatrachus, at least in the reconstructions by

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11221 Estes & Reig (1973) and Báez & Nicoli (2004), but apparently also in fig. 4 of the latter (a 11222 photograph of a cast of the holotype). 11223 Although Stegotretus has a suproccipital (or some other ossification in that area), it 11224 appears not to have been exposed, but completely covered by the postparietals in caudal view 11225 (Berman, Eberth & Brinkman, 1988: 310). This constitutes state 0. 11226 Euryodus was scored as unknown in RC07, but we cannot distinguish its condition 11227 from that of Cardiocephalus which was scored 0 (both according to CG78); we have assigned 11228 state 0 to both. 11229 Unknown in Eusthenopteron, where the entire braincase is fused (Carroll & Chorn, 11230 1995), Megalocephalus (similarly due to fusion: Beaumont, 1977: 65f.), Phonerpeton (Dilkes, 11231 1990), Eoscopus, where “[b]raincase bones […] were unossified in all specimens” (Daly, 11232 1994: 8), Platyrhinops (Clack & Milner, 2010), Eoherpeton (Holmes, 1984: fig. 4; Smithson, 11233 1985), Westlothiana, where the bone interpreted as such by Smithson et al. (1994) could just 11234 as well be e.g. a part of the otic capsules (as previously noted by Laurin & Reisz, 1999), and 11235 Lethiscus (Pardo et al., 2017; as already scored) and Phlegethontia (Anderson, 2002), where 11236 the braincase roof is thin but fused. 11237 Panchen (1964) first described state 1 in *Palaeoherpeton, but later regarded this as 11238 “an artefact of preservation” (Clack & Holmes, 1988: 91). We have scored state 0. 11239 11240 134. EXOCC 2-3-4-5/BASOCC 1-5: Basioccipital not restricting notochord (0); single 11241 occipital cotyle (with or without notochordal funnel) (1); single occipital condyle (with or 11242 without notochordal pit) (2); exoccipital articulating surfaces dorsolateral or lateral to 11243 basioccipital, basioccipital cotyle articulating with interglenoid tubercle (3); 11244 basioccipital not participating in articulation or absent, two exoccipital condyles or flat 11245 surfaces not touching each other (4); two condyles or flat surfaces touching each other, 11246 “exoccipital-basioccipital complex” without sutures (5) (stepmatrix). We have merged six 11247 correlated characters (see below for the seventh), each of which had only one of its two states 11248 described; state 1 of each of these characters made state 1 of all five (indeed six) others 11249 impossible. State 0 of the present character is BASOCC 1(0), which was originally called 11250 “basioccipital notochordal”, an imprecise term; state 5 is a modification of EXOCC 2(1) and 11251 EXOCC 5(1) and occurs in Acheloma (Olson, 1941: fig. 8; Polley & Reisz, 2011), 11252 Phonerpeton (Dilkes, 1990; D. M., pers. obs. of MCZ 2313), Ecolsonia (Berman, Reisz & 11253 Eberth, 1985; D. M., pers. obs. of CM 38017) and Doleserpeton (Sigurdsen, 2008) as well as 11254 *Konzhukovia (with a dorsal incisure that connects to the notochordal pit) and 11255 *Platyoposaurus (Gubin, 1991). See below for Eryops. The stepmatrix for this character is 11256 Appendix-Table 4. 11257 Within state 1, it might be possible to distinguish a closed cotyle from a deep funnel as 11258 found in the aïstopods (Lethiscus: Pardo et al., 2017; Oestocephalus: Carroll, 1998a; 11259 Phlegethontia: Anderson, 2002, and references therein). We speculate that this distinction 11260 may have been the original point of BASOCC 6 (see below). However, incomplete 11261 ossification, bad preservation and inadequate illustration would prevent us from scoring 11262 almost any other of the OTUs currently scored 1 as having a cotyle or a funnel. 11263 OTUs known to possess an intercotylar tubercle on the atlas (CER VER 4(1), see 11264 character 253) are scored as having state 1, 3, 4 or 5 of the present character if it is in fact 11265 unknown, because only these four states can occur in that case. The only occurrences of this 11266 situation are Saxonerpeton (made explicit by CG78: 34), *Gerobatrachus (Anderson et al., 11267 2008a) and *Beiyanerpeton (Gao & Shubin, 2012: fig. 3). 11268 Because four (and not just one) states can occur together with it, we have not merged 11269 CER VER 4 with the present character. For convenience, however, we have ignored the fact 11270 that CER VER 4(0) makes state 3 of the present character impossible (a partial uncertainty of

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11271 five states is probably more trouble than it is worth, and the two states in question occur in 11272 separate areas of the tree). 11273 State 1 is present in Dendrerpetidae (Robinson, Ahlberg & Koentges, 2005). It also 11274 appears to occur in Ariekanerpeton (Klembara & Ruta, 2005a) and probably Utegenia 11275 (Klembara & Ruta, 2004a); the same seems to hold for Discosauriscus, where the poorly 11276 ossified basioccipital is a caudally flat plate, but the exoccipitals appear to participate in the 11277 cotyle (Klembara, 2007). 11278 The taphonomically crushed Tseajaia appears to possess state 2, as far as we can tell 11279 from Moss (1972). 11280 We have also assigned state 2 to Captorhinus because it has a condyle, even though no 11281 sutures can be traced in its “exoccipital-basioccipital complex”, and to Orobates, even though 11282 the notochordal pit, though shallow, is large and even though the digital reconstruction by 11283 Nyakatura et al. (2015) does not show sutures (generally) and does not compensate for all 11284 deformation and disarticulation. 11285 Hapsidopareion and *Llistrofus (CG78: 27, 28; Bolt & Rieppel, 2009) are borderline 11286 between states 3 and 4, but we have stayed conservative and assigned state 3 to both because 11287 the basioccipital does seem to have participated in the articulation. 11288 Szostakiwskyj, Pardo & Anderson (2015) contradicted themselves: in their description 11289 of Rhynchonkos, they stated that only a flat eroded surface is preserved, which would mean 11290 that the range of possibilities for this character could only be narrowed down to state 1, 2, 3 or 11291 4, while in their discussion, they stated that state 3 is present. J. Pardo (pers. comm. 2015) 11292 confirms the latter: although the area is eroded, state 3 is still visible. 11293 State 4 is found in Batropetes (Carroll, 1991: fig. 5; Glienke, 2013: fig. 4, showing a 11294 ventral suture between the exoccipitals) and Diceratosaurus (D. M., pers. obs. of CM 72608). 11295 Outside the original taxon sample, it is standard in lissamphibians and also occurs in most 11296 *stereospondylomorph temnospondyls. 11297 Asaphestera has a unique state (D. M., pers. obs. of NMC 10041 with J. Anderson). 11298 The drawing of the same specimen in CG78 (fig. 6E) is accurate as a two-dimensional 11299 projection in strict caudal view. In other words, state 3 (which RC07 had scored) is not 11300 reached: on its ventral side, the basioccipital sends a prong far caudal, while the dorsal side is 11301 flat until very far rostral, where it curves dorsally. To articulate with this latter surface, an 11302 interglenoid tubercle would have had to be much longer than known in any other vertebrates; 11303 realistically, only the dorsal surface of the prong could have articulated with the ventral side – 11304 not the rostral end – of such a tubercle on the atlas. We have scored state 4: although the 11305 basioccipital is present and bears the mentioned large caudal process, it does not participate in 11306 an articular surface together with the widely spaced exoccipitals. 11307 Eryops appears to be quite variable and generally transitional. A dorsoventrally 11308 compressed, bilobed version of state 1, with a median constriction, is known to occur (Sawin, 11309 1941; D. M., pers. obs. of the large skull TMM 40349-20 and the smaller skull MCZ 2766); 11310 however, TMM 31226-12 and MCZ 1129 have state 4, AMNH 23529 has state 5 (unless it 11311 can be interpreted as having state 2 with a very large notochordal pit), AMNH 4673 has state 11312 5 bordering on 4, the partially encrusted AMNH 4180 most likely has state 4 or 5, as does 11313 AMNH 4186, AMNH 4183 has 5 or possibly 1, and the uncatalogued USNM specimens 11314 “Texas ’84 #40” and “Texas ’86 #77” have or come close to states 4 and/or 5 (all pers. obs. 11315 by D. M.). It should be investigated whether all these skulls should continue to be referred to 11316 the same species. Unfortunately we have not been able to rigorously examine whether this 11317 variation correlates with the neat division into a narrow-headed and a broad-headed morph 11318 (Werneburg, 2007a; Schoch & Milner, 2014; D. M., pers. obs. of USNM, TMM, AMNH and 11319 MCZ specimens), although there is currently no reason to think it does: for example, AMNH 11320 4673, AMNH 4180 and AMNH 4183 are narrow-headed, while the enormous AMNH 4186 is

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11321 broad-headed. Incomplete ossification and difficult preservation (such as the common 11322 presence of an ironstone crust) contribute to the confusion; unfortunately, this is the case for 11323 the type specimen of the type and possibly only species E. megacephalus, the narrow-headed 11324 AMNH 4189, which could have any of the three states in question (D. M., pers. obs.). For the 11325 time being, we have scored Eryops as possessing all three states: 1, 4 and 5. 11326 Entirely unknown in Baphetes (Beaumont, 1977), apparently Amphibamus (Watson, 11327 1940; Carroll, 1964; Daly, 1994), Caerorhachis (Ruta, Milner & Coates, 2002) and 11328 Hyloplesion (CG78). Contrary to Carroll (1970: 274, fig. 5), Klembara et al. (2014: 787–788) 11329 have further argued that the entire braincase is unknown in Gephyrostegus. 11330 Cochleosaurus has state 1 or 3 (Sequeira, 2004). 11331 Platyrhinops appears to have state 4 or 5 (Clack & Milner, 2010). 11332 Diadectes may be said to change from state 1 to state 2 in ontogeny. In AMNH 4839 11333 (D. M., pers. obs.), the convexity that defines state 2 is hard to find, only what must be the 11334 incompletely ossified exoccipitals are slightly convex in lateral view; the articulation as a 11335 whole may be interpreted as state 2 with a giant conical notochordal pit that takes almost all 11336 the convexity away. This interpretation is confirmed by the considerably larger specimen 11337 AMNH 4352 (D. M., pers. obs.), in which the notochordal pit is considerably smaller and 11338 surrounded by a thick convex rim. We have thus kept state 2 for Diadectes. 11339 The preservation of Limnoscelis (Berman, Reisz & Scott, 2010: fig. 10, 12) is 11340 insufficient to distinguish states 1, 2, 3 and 5. We have scored partial uncertainty. 11341 Interestingly, Berman, Reisz & Scott (2010: fig. 4) reconstructed a condition intermediate 11342 between all four of those states – a flat plate with the notochordal pit that is visible in the 11343 specimen (fig. 10, 12). 11344 Odonterpeton has state 1 or 3; CG78 (145) suggested that it has 2, but that is almost 11345 certainly incorrect – the most evident candidate for a median condyle is simply the 11346 anatomically left rim of the cotyle, against which the vertebral column has slipped to the right 11347 (D. M., pers. obs. of USNM 4465+4467). The other candidate consists of two tiny grains that 11348 are probably not part of a condyle. – As mentioned above, fig. 99A of CG78 is idealized and 11349 simplified to the extent of being unreliable. 11350 We have scored Ptyonius, Sauropleura and Urocordylus as possessing state 1 or 3 11351 based on Bossy & Milner (1998: 86, 91). Bossy & Milner (1998: 91) appear to rule out state 4 11352 shortly after mentioning that the median part of the cranial face of the atlas centrum can be 11353 “somewhat protruding” in some or all of these taxa; probably this only means that the 11354 interglenoid tubercle (see character CER VER 4) cannot be as large as it often is in 11355 “microsaurs” – it is quite small in many lissamphibians and in the “microsaur” Odonterpeton 11356 (see character CER VER 4 below). 11357 Silvanerpeton has state 0 or 1 (Ruta & Clack, 2006). 11358 State 1 is almost certain in *Nigerpeton (D. M., pers. obs. of MNN MOR 69 and MNN 11359 MOR 70). 11360 *Iberospondylus appears to have the version of state 1 sometimes seen in Eryops (D. 11361 M., pers. obs. of PU-ANF 15 with Rodrigo Soler-Gijón). 11362 *Utaherpeton, which has lateral facets for the exoccipitals on the basioccipital, is 11363 scored 1 or 3 because Carroll, Bybee & Tidwell (1991) did not explicitly argue against the 11364 version of state 2 sometimes seen in Eryops. 11365 *Sparodus appears to have states 3 or 4 (Carroll, 1988: fig. 1A), although a suture 11366 between the possible occipital condyles and the postparietals cannot be determined (D. M., 11367 pers. obs. of NHMW 1899/0003/0006). 11368 We have assigned states 3, 4 or 5 to *Acanthostomatops because its basioccipital was 11369 probably small, judging from the size of the facet for it on the parasphenoid (Witzmann & 11370 Schoch, 2006a).

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11371 The CT scans of *Carrolla (only known specimen: TMM 40031-54) by Maddin, Olori 11372 & Anderson (2011) seem to only distinguish finished bone surfaces from everything else, and 11373 not to distinguish spongy bone from the matrix. Thus, the figures of Maddin, Olori & 11374 Anderson (2011), including the reconstruction (fig. 7B), fail to show some bone that is clearly 11375 present. This includes unfinished bone between the finished lateral extremities of the occipital 11376 articulation (D. M., pers. obs. of TMM 40031-54). As there is no interruption in the almost 11377 flat unfinished surface of this articulation, while there is a strong median constriction, the 11378 state shown by the only known specimen of *Carrolla is best called 5, making *Carrolla the 11379 only non-temnospondyl in this matrix to possess this state. However, it is entirely possible 11380 that further ossification would have transformed this into state 4. We have scored this as 11381 partial uncertainty. The strong constriction makes it unlikely that state 3 (expected for a 11382 “microsaur”) would have developed. 11383 11384 For Analysis EB, this character was split as follows: 11385 BASOCC 1-5: Occipital articulation absent (unrestricted notochord) (0); concave 11386 (occipital cotyle) (1); convex (occipital condyle) (2) (ordered). These states correspond to 11387 states 0, 1+3 and 2+3+4+5 of the merged character, respectively; state 3 of the merged 11388 character is scored as partial uncertainty of the present one. 11389 EXOCC 2-3-5: Occipital articulation single (0); bilobed (1); double (2) (ordered). These 11390 states correspond to states 1+2, 3+5 and 3+4 of the merged character, respectively. The 11391 present character is inapplicable to OTUs with state 0 of the preceding and thus the merged 11392 character; state 3 of the merged character is scored as partial uncertainty of the present one. 11393 EXOCC 4: Basioccipital participates in articulation: yes (0); no (1). Only applicable to 11394 double occipital articulations, so that the states correspond to states 3 and 4 of the merged 11395 character. 11396 11397 Appendix-Table 4: Stepmatrix for character 134 (EXOCC 2-3-4-5/BASOCC 1-5). 11398 from ↓ to → 0 1 2 3 4 5 0 0 1 2 2 3 3 1 1 0 1 1 2 2 2 2 1 0 2 2 1 3 2 1 2 0 1 2 4 3 2 2 1 0 1 5 3 2 1 2 1 0 11399 11400 deleted BASOCC 6: Articulation surface of the basioccipital circular and recessed: 11401 absent (0); present (1). This character was originally explained as follows: “In aïstopods and 11402 adelospondyls, the basioccipital has a circular outline and carries a funnel-like excavation.” 11403 Specifically, state 1 was assigned to Oestocephalus, Phlegethontia and Adelogyrinus; the 11404 other aïstopods and adelospondyls were (correctly) scored as unknown. However, 11405 Oestocephalus and Phlegethontia (with the possible exception of one specimen: Anderson, 11406 2002) lack sutures in the braincase, making it impossible to determine which bones make up 11407 their circular occipital cotyle; they have to be scored as unknown as well. (The same holds for 11408 Lethiscus, which was already scored as unknown: Pardo et al., 2017.) This leaves state 1 to 11409 Adelogyrinus alone (if that, given the damage mentioned by Andrews & Carroll, 1991: 250), 11410 rendering the character parsimony-uninformative. We have accordingly deleted it. 11411

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11412 135. OPI 2, POSPAR 5: Exoccipitals contact postparietals or parietals (0); opisthotics 11413 and/or suproccipital separating exoccipitals from postparietals or parietals (1); separate 11414 opisthotics absent (2) (unordered). No sequence for ordering suggests itself. 11415 OPI 2 was originally worded “Opisthotic[s] forming a thickened plate together with 11416 the supraoccipital, preventing the exoccipitals from contacting the skull table: absent (0); 11417 present (1)” in RC07: 102, but whether a “plate” is present depends on PTF 1, and the 11418 presence of the suproccipital is already another character (SUPOCC 1), so, in order to avoid 11419 redundancy, it should not be mentioned here. 11420 POSPAR 5 was worded “Postparietal/exoccipital suture: absent (0); present (1)” in 11421 RC07:96. This was not applicable to taxa without postparietals (POSPAR 1-2(2)), but 11422 otherwise identical to OPI 2 with inverted state numbers: when the postparietals contact the 11423 exoccipitals (POSPAR 5(1)), OPI 2(1) is impossible, and when they do not (POSPAR 5(1)), 11424 OPI 2(1) is unavoidable – once the “thickened plate” and the suproccipital are removed from 11425 consideration – because nothing other than the opisthotics and/or the suproccipital ever 11426 intervenes between the postparietals (or parietals when postparietals are absent) and the 11427 exoccipitals. 11428 Merging the present character with SUPOCC 1 is not an option, because Archeria 11429 (which was correctly scored as having state OPI 2(1), POSPAR 5(0)) possesses huge 11430 opisthotics that separate the postparietals from the exoccipitals, but there is just a narrow 11431 unossified slit where a cartilaginous suproccipital may have been (Holmes, 1989: fig. 10A), 11432 showing that SUPOCC 1(0) and OPI 2, POSPAR 5(1) can occur together. 11433 State 2 is new and accounts for taxa in which the opisthotics are absent or fused to the 11434 exoccipitals, including of course those with completely fused otoccipital parts of the 11435 braincase. These are Eusthenopteron (Carroll & Chorn, 1995), Ichthyostega (reconstruction 11436 drawing and photo in Jarvik, 1996, assuming the coarse-grained photo which does not show 11437 any sutures can be taken at face value; also suggested by Clack et al., 2003: fig. 3a, c; not 11438 mentioned or illustrated by Clack & Milner, 2015), Albanerpetidae (Maddin et al., 2013a), 11439 Eocaecilia, Valdotriton, Lethiscus (Pardo et al., 2017), Oestocephalus, Phlegethontia, and 11440 Notobatrachus (Estes & Reig, 1973; Báez & Nicoli, 2004, did not mention opisthotics, but 11441 mentioned that the exoccipitals usually fuse to the prootics in adults, which implies there were 11442 no opisthotics in between) as well as *Liaobatrachus, *Carrolla and *Chelotriton; state 0 or 2 11443 occurs in Odonterpeton (CG78: 145f.), *Sclerocephalus and *Australerpeton. 11444 State 0 occurs in Chenoprosopus (Hook, 1993), Dendrerpetidae (Robinson, Ahlberg & 11445 Koentges, 2005), Pelodosotis (CG78: fig. 48), apparently Hyloplesion (CG78: 137), 11446 Batrachiderpeton if the opisthotic is correctly identified (Bossy & Milner, 1998: fig. 57B) and 11447 Ariekanerpeton (made explicit by Klembara & Ruta, 2005a) as well as *Lydekkerina 11448 (Hewison, 2007: 26–27). 11449 Greererpeton was reconstructed as having state 0 by Smithson (1982) based on 11450 crushed specimens; less crushed ones have revealed state 1 (Bolt & Lombard, 2001: 1041; 11451 Clack, 2003b). State 1 is also present in Acanthostega and Whatcheeria according to the latter 11452 paper. 11453 Eoherpeton was scored in RC07 as POSPAR 5(?) (presence of exoccipital/postparietal 11454 suture unknown), but OPI 2(1). The latter is correct, except that the presence of a 11455 suproccipital cannot be ascertained (Smithson, 1985: 338; already correctly scored as 11456 SUPOCC 1(?)); we have therefore scored state 1 of the present character. 11457 We have assigned state 1 to Batropetes: although the exoccipitals and the opisthotics 11458 fuse dorsally, the suture persists ventrally, and in caudal or dorsal view it seems that the 11459 exoccipitals are growing around the foramen magnum much as in later ontogenetic stages of 11460 Acheloma (Maddin, Reisz & Anderson, 2010).

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11461 State 1 also occurs in Brachydectes (Pardo & Anderson, 2016) and Tseajaia (Moss, 11462 1972). 11463 Ptyonius appears to have state 0 or 1 on account of having separate opisthotics (Bossy 11464 & Milner, 1998: 86). The same appears to hold for *Palaeoherpeton (compare Panchen, 11465 1964: fig. 2, to Clack & Holmes, 1988: 91, fig. 1). 11466 We have scored Doleserpeton as possessing state 0 or 2. The postparietals have tall 11467 occipital flanges that overlie the opisthotics caudally and reach the exoccipitals (Sigurdsen & 11468 Bolt, 2010; Sigurdsen & Green, 2011), corresponding to state 0; however, in the most mature 11469 specimens, the dorsal parts of the exoccipitals fuse to the opisthotics (Sigurdsen, 2008; 11470 Sigurdsen & Bolt, 2010), raising the question if Doleserpeton should be considered to have 11471 state 2. 11472 Perhaps similarly, Diplocaulus is illustrated as having state 2 by Bossy & Milner 11473 (1998: fig. 57C), but Beerbower (1963: 59) reports that “[a]lthough Douthitt reports the 11474 exoccipital and opisthotic as fused in Diplocaulus, sutures can be distinguished in many 11475 specimens of that genus”, frustratingly not mentioning if there are any in which fusion can be 11476 ascertained. We have scored Diplocaulus as having state 0 or 2. 11477 Unknown in Proterogyrinus (Holmes, 1984: fig. 4) and Pederpes (Clack & Finney, 11478 2005). 11479 11480 136. PASPHE 1: Cultriform process gradually tapering to a rostral point (0) or parallel- 11481 sided along most of its length (1). This is a rewording of the original name of this character 11482 and its explanation; the process cannot help being “elongate”, because taxa where it does not 11483 reach the vomers are not included in this matrix. State 1 includes cases where the process is 11484 biconcave, wider at its rostral end than in the middle. 11485 Ventastega (Ahlberg, Lukševičs & Lebedev, 1994), Doleserpeton (Sigurdsen & Bolt, 11486 2010), Solenodonsaurus (Danto, Witzmann & Müller, 2012) and Lethiscus (Anderson, Carroll 11487 & Rowe, 2003) have state 0. State 0 is also found in Leptorophus tener (Schoch & Milner, 11488 2008); L. raischi does have state 1 (Schoch, 2014a) as scored in RC07, but because it is only 11489 known from skeletally less mature (and smaller) specimens than L. tener, we have scored 11490 Leptorophus as having state 0. 11491 Ruta, Coates & Quicke (2003) and Ruta & Coates (2007) scored all PASPHE 11492 characters of Phlegethontia as unknown (even PASPHE 11, which does not depend on the 11493 presence of the parasphenoid). Anderson (2002), however, maintained that the parasphenoid, 11494 although indistinguishably fused to the endochondral braincase, is present in Phlegethontia: in 11495 particular, there is a cultriform process (Anderson, 2002: fig. 4.2, 4.3, 8.2). Ruta, Coates & 11496 Quicke (2003) cited Anderson (2002 – as “in press”) as their source for several scores of 11497 Phlegethontia, but did not cite it in any context involving the parasphenoid. We have 11498 therefore scored those few parasphenoid characters that do not depend on where the 11499 boundaries of the basal plate were. (Comparison to other aïstopods – Pardo et al., 2017 – 11500 suggests that the basal plate was much smaller than expected.) For the present character, 11501 Phlegethontia has state 0. 11502 State 1 is present in Greererpeton (Smithson, 1982; D. M., pers. obs. of TMM 41574- 11503 1), Karaurus (biconcave: Ivachnenko, 1978: fig. 1b!), Triadobatrachus (Roček, 2000; 11504 Ascarrunz et al., 2016), Valdotriton (Evans & Milner, 1996), Hyloplesion (Olori, 2015: fig. 11505 30A, table S3) and arguably Notobatrachus (Báez & Nicoli, 2004); *Liaobatrachus has state 11506 0, however (Dong et al., 2013). 11507 Microbrachis is somewhat borderline (Olori, 2015: fig. 10); following the 11508 recommendation of Olori (2015: 56), we have scored state 0. 11509 Not described or illustrated in Whatcheeria (Lombard & Bolt, 1995; Bolt & Lombard, 11510 2000); unclear in Hapsidopareion (CG78: fig. 13A, 14E; Bolt & Rieppel, 2009: 475).

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11511 Given the state of preservation of *Quasicaecilia (Pardo, Szostakiwskyj & Anderson, 11512 2015: fig. 2, 4), we have scored this character as unknown rather than going with the 11513 reconstruction (fig. 3, which shows state 0 without indicating any uncertainty) or the 11514 statement on p. 12 that the process is “parallel-sided”. 11515 11516 137. PASPHE 2-12: Base of cultriform process and area between basipterygoid 11517 processes: no ridges (0); rostromedian-to-caudolateral ridges forming a V (1); state 1 11518 plus a caudal ridge, together delimiting a raised triangular area (2) (ordered). State 1 is 11519 the “anterior wedge-like process” of Klembara & Ruta (2004a), which can hardly be called a 11520 process. It occurs in several seymouriamorphs, but so does state 2 contrary to the scoring of 11521 RC07. 11522 States 1 and 2 cannot be distinguished when the median depression (PASPHE 6(1)) is 11523 too large. This is the case in several taxa that (contrary to the scoring of RC07) clearly do not 11524 have state 0, namely Proterogyrinus (Holmes, 1984), Archeria (Clack & Holmes, 1988), 11525 Pholiderpeton scutigerum (Clack, 1987b) and Limnoscelis (Berman, Reisz & Scott, 2010), 11526 and also in *Chroniosaurus (Clack & Klembara, 2009). 11527 The raised area in state 2 usually bears denticles, and usually the rest of the 11528 parasphenoid is then toothless. Limnoscelis is an exception where the raised area is rough but 11529 apparently toothless (Berman, Reisz & Scott, 2010), and in Utegenia the area is almost 11530 toothless while the cultriform process is (otherwise) densely denticulated (Klembara & Ruta, 11531 2004a: fig. 10, 14). RC07 treated the raised area and its dentition as a single character (which 11532 may be the reason why they gave our state 1 to Utegenia); these are clearly two independent 11533 characters, so we have excluded the dentition from consideration. We have, somewhat 11534 similarly, assigned state 2 to Trimerorhachis where it is not known if a denticle field was 11535 present (Milner & Schoch, 2013: 107, fig. 1D), and to *Glanochthon, where a well-defined 11536 triangular denticle field was lost in ontogeny but a well-defined raised area which we count as 11537 triangular persisted in adults (Schoch & Witzmann, 2009b: 126, fig. 4C, D). Further, we 11538 assign state 2 to Balanerpeton (Milner & Sequeira, 1994: fig. 1A). 11539 State 0 is present in Ventastega (Ahlberg et al., 2008), apparently Ecolsonia (D. M., 11540 pers. obs. of CM 38017), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Solenodonsaurus 11541 (Danto, Witzmann & Müller, 2012), seemingly Kotlassia (Bulanov, 2003: S54, fig. 30), 11542 Diceratosaurus (D. M., pers. obs. of several CM specimens), Lethiscus (Pardo et al., 2017), 11543 Phlegethontia (Anderson, 2002: fig. 4.2), Microphon (Bulanov, 2003) and Tseajaia (Moss, 11544 1972). 11545 Schoch & Milner (2014: fig. 30) reconstructed a condition for Amphibamus that may 11546 count as state 2, but we count the condition in the most mature known specimen (Daly, 1994: 11547 fig. 21 right side) as state 1. State 1 is furthermore found in Caerorhachis (Ruta, Milner & 11548 Coates, 2002), Pholiderpeton attheyi (Panchen, 1972) and Gephyrostegus (Klembara et al., 11549 2014). 11550 State 2 is not limited to temnospondyls. Apart from Utegenia, it makes surprise 11551 appearances in Pelodosotis (CG78: fig. 48) and Rhynchonkos (Szostakiwskyj, Pardo & 11552 Anderson, 2015) and shows up in later ontogenetic stages of Discosauriscus (Klembara et al., 11553 2006) as well as its fellow seymouriamorphs *Karpinskiosaurus (Klembara, 2011) and 11554 **Biarmica (Bulanov, 2003). 11555 Using a generous interpretation, we have assigned state 2 to *Acanthostomatops; some 11556 specimens fit even under a strict one (Witzmann & Schoch, 2006a). State 2 is also seen in 11557 *Platyoposaurus: although the area is not triangular, all three ridges are present (Eltink et al., 11558 2016: fig. 12B). 11559 Unknown in Colosteus (Hook, 1983: 16) and Anthracosaurus (Panchen, 1977: 469). 11560

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11561 138. PASPHE 3: Parasphenoid without (0) or with (1) a pair of posterolaterally 11562 orientated, ventral thickenings (ridges ending in basal tubera). This character is only 11563 applicable to OTUs whose parasphenoids are long enough caudally, i.e. those that have or 11564 may have PASPHE 9(2). 11565 Greererpeton has state 1 (Smithson, 1982; D. M., pers. obs. of TMM 41574-1). So do 11566 the largest specimens of Acheloma (Olson, 1941; Maddin, Reisz & Anderson, 2010), making 11567 the scores of many other temnospondyls suspect. Indeed, MNN MOR 70 appears to have state 11568 1, and so might MNN MOR 69 (D. M., pers. obs.); we have scored state 1 for *Nigerpeton. 11569 State 1 further makes a surprise appearance in *Liaobatrachus (Dong et al., 2013: fig. 6B). 11570 State 0 is known in Albanerpetidae (Estes & Hoffstetter, 1976; Maddin et al., 2013a). 11571 In Asaphestera, a partial parasphenoid is preserved in NMC 10041 (D. M., pers. obs. with J. 11572 Anderson) and seems to show state 0 as well. 11573 We have assigned state 1 to Gephyrostegus, which has very pronounced ridges, 11574 although they fade into flat, short triangular processes caudally and basal tubera are absent 11575 (Klembara et al., 2014). 11576 Inapplicable to Phlegethontia (as already scored), where there is no space for such 11577 ridges (Anderson, 2002: fig. 4.2, 4.3). 11578 The drawings and even the photos by Moss (1972) are not three-dimensional enough 11579 to show which state Tseajaia has, and the text does not mention it; in CM 38033 (D. M., pers. 11580 obs.), most of the palate is covered by the lower jaws, matrix, and miscellaneous fragments; 11581 we have therefore scored Tseajaia as unknown. 11582 The basal tubera are apparently unknown in *Archegosaurus, but the ridges are there 11583 (Witzmann, 2006). 11584 Incompletely ossified (Maddin, Reisz & Anderson, 2010) but present in 11585 *Erpetosaurus (Milner & Sequeira, 2011: fig. 2C). 11586 11587 139. PASPHE 4: Parasphenoid without elongate, broad posterolateral processes (0), or 11588 with processes that are less than (1), or at least half as wide as (2) the parasphenoid plate 11589 (ordered). We have ordered this character because it is continuous. This character is only 11590 applicable to OTUs whose parasphenoids are long enough caudally, i.e. those that have or 11591 may have PASPHE 9(2). It is further inapplicable in taxa where the fenestrae ovales/vestibuli 11592 are (proportionally) too large to allow anything other than state 0, like Albanerpetidae (Estes 11593 & Hoffstetter, 1976; Maddin et al., 2013a; already scored as unknown), Triadobatrachus 11594 (where, in addition, the margins of the putative fenestra ovalis are unossified: Ascarrunz et al., 11595 2016) or Hyloplesion (CG78: fig. 89E, H); similarly, there is no space for processes in 11596 Eocaecilia (Jenkins, Walsh & Carroll, 2007). 11597 State 0 occurs in Batropetes (Glienke, 2013, 2015). 11598 State 1 is found in Greererpeton (D. M., pers. obs. of TMM 41574-1), Edops (D. M., 11599 pers. obs. of USNM 23309), apparently Cochleosaurus (Sequeira, 2004), Balanerpeton 11600 (Milner & Sequeira, 1994), Dendrerpetidae (Robinson, Ahlberg & Koentges, 2005), Eryops 11601 (Sawin, 1941: pl. 2, 8), Acheloma (Olson, 1941; Maddin, Reisz & Anderson, 2010), 11602 Broiliellus (Schoch, 2012: fig. 2F), Gephyrostegus (Klembara et al., 2014), *Nigerpeton (D. 11603 M., pers. obs. of MNN MOR 69 and MNN MOR 70), *Platyoposaurus (Eltink et al., 2016: 11604 fig. 12B) and *Australerpeton (Eltink et al., 2016: fig. 9A). 11605 Microbrachis has state 2 (Vallin & Laurin, 2004: fig. 4A; Olori, 2015: fig. 12A). 11606 The state is apparently unknown in Megalocephalus (Beaumont 1977: 63), Ecolsonia 11607 (Berman, Reisz & Eberth, 1985: fig. 6) and Hapsidopareion (CG78: fig. 13A); it has also not 11608 been described or illustrated in Whatcheeria (Lombard & Bolt, 1995; Bolt & Lombard, 2000). 11609 *Erpetosaurus seems to just reach state 2 (Milner & Sequeira, 2011: fig. 2, 5). 11610

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11611 140. PASPHE 6: Parasphenoid without (0) or with (1) single median depression. Clack et 11612 al. (2016) merged this character with the following one (as their character 77), and indeed no 11613 taxon in our matrix is known to have state 1 of both; it is not clear to us whether such a 11614 condition is impossible, however, or whether paired lateral depressions can form by 11615 subdivision of a median one (or vice versa), so we prefer to keep these characters separate for 11616 now. 11617 Albanerpetidae has state 0 (Estes & Hoffstetter, 1976; Maddin et al., 2013a), as do 11618 Solenodonsaurus (Danto, Witzmann & Müller, 2012), Lethiscus (Pardo et al., 2017) and 11619 apparently Phlegethontia (Anderson, 2002: fig. 4.2). 11620 State 1 is known in Broiliellus (Schoch, 2012: fig. 2F), most likely Gephyrostegus 11621 (Klembara et al., 2014), Seymouria (Laurin, 1996c, 2000) and Limnoscelis (Berman & 11622 Sumida, 1990) as well as *Platyoposaurus (Eltink et al., 2016: fig. 12B) and apparently 11623 *Coloraderpeton (Pardo et al., 2017: video). 11624 Inapplicable to Acanthostega, where the parasphenoid is not long enough (Porro, 11625 Rayfield & Clack, 2015); not described or illustrated in Whatcheeria (Lombard & Bolt, 1995; 11626 Bolt & Lombard, 2000). 11627 We have scored state 0 for *Diploradus after Clack et al. (2016: matrix). 11628 11629 141. PASPHE 7: Parasphenoid without (0) or with (1) paired lateral depressions. 11630 Cochleosaurus has state 0 (Sequeira, 2004). So do Albanerpetidae (Estes & 11631 Hoffstetter, 1976; Maddin et al., 2013a), Gephyrostegus (Klembara et al., 2014), 11632 Solenodonsaurus (Danto, Witzmann & Müller, 2012) and Lethiscus (Pardo et al., 2017). 11633 State 1 makes a surprise appearance in *Liaobatrachus (Dong et al., 2013: fig. 6B). 11634 Inapplicable to Acanthostega, where the parasphenoid is not long enough (Porro, 11635 Rayfield & Clack, 2015); not described or illustrated in Whatcheeria (Lombard & Bolt, 1995; 11636 Bolt & Lombard, 2000). 11637 We have scored state 0 for *Diploradus after Clack et al. (2016: matrix). 11638 11639 142. PASPHE 9: Intracranial joint (0); ventral cranial suture visible in ventral view, 11640 caudal margin of parasphenoid lying rostral to or at it (1); parasphenoid extending 11641 caudal to suture (2) (ordered). We have reworded this character to make clear what state 2, 11642 originally “Ventral cranial fissure […] not traceable”, means in practice – fusion of the 11643 basisphenoid and the basioccipital is rare, and when it occurs, it is hardly ever determinable in 11644 a fossil (except by tomography), let alone described or illustrated, but the caudal extent of the 11645 parasphenoid is fairly readily observable (except in Phlegethontia, which we have kept as 11646 unknown even though no trace remains of any cranial fissure). Because the states of this 11647 character form a sequence of progressively firmer immobilization of the ventral cranial fissure 11648 (which forms part of a joint in Eusthenopteron and Panderichthys), we have ordered the 11649 character. 11650 Ventastega (Ahlberg et al., 2008), Ichthyostega (Clack, 2000) and Lethiscus (Pardo et 11651 al., 2017) show state 1; although apparently not sutured, the fissure of Lethiscus is not a joint, 11652 so we have not scored state 0. 11653 The suture between basisphenoid and basioccipital is still partially exposed in the 11654 smallest specimen of Acheloma shown by Maddin, Reisz & Anderson (2010: fig. 4, 5), as 11655 well as in one of the largest ones (fig. 4). In those specimens the parasphenoid only covers the 11656 median third of the suture; the parasphenoid completely overgrows it in some but not all of 11657 the largest specimens (fig. 4, 5). Nonetheless, the definition of state 2 is fulfilled, so we have 11658 kept the score of 2. 11659 The braincase is probably altogether unknown in Gephyrostegus (Klembara et al., 11660 2014).

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11661 Diadectes is polymorphic, having states 1 and 2 (Moss, 1972), with only state 1 being 11662 documented in D. absitus (Berman, Sumida & Martens, 1998). 11663 Limnoscelis has state 1 or 2 (Berman, Reisz & Scott, 2010: fig. 4A, 10). 11664 Asaphestera (D. M., pers. obs. of NMC 10041 with J. Anderson) and Pelodosotis 11665 (CG78: fig. 48) have state 2. 11666 Unknown in Adelospondylus; Adelogyrinus appears to have state 1 or 2 (Andrews & 11667 Carroll, 1991). 11668 Pederpes was scored 1 in RC07, but may just as well have had state 0, because the 11669 basioccipital is not preserved (Clack & Finney, 2005); we have accordingly scored partial 11670 uncertainty. 11671 Tseajaia has state 1 (Moss, 1972: fig. 2, 4A, 15B; pl. 4; and various allusions in the 11672 text). 11673 We have scored state 1 for *Pseudophlegethontia: a line that may be the ventral 11674 cranial suture is visible between the two caudal processes of the parasphenoid (Anderson, 11675 2003b: fig. 2A), much like in *Coloraderpeton (Pardo et al., 2017), and in any case the gap 11676 between these two processes extends very far rostral. 11677 11678 143. PASPHE 11: Basipterygoid processes of the basisphenoid shaped like 11679 anterolaterally directed stalks, subtriangular to rectangular in ventral view and 11680 projecting anterior to the insertion of the cultriform process: absent (0); present (1). 11681 This is one of the more unnerving characters: state 1 is a carefully explained combination of 11682 states of two characters (shape and orientation of basipterygoid processes) which may or may 11683 not correlate – no demonstration of this was attempted by RC07 or Ruta, Coates & Quicke 11684 (2003) –, and state 0 comprises everything else, potentially a large number of distinguishable 11685 states. More attention will have to be paid to the present character (and to its conditions of 11686 applicability) in the future. 11687 Naturally, the basisphenoid is seldom observable; in such cases we have resorted to 11688 the parasphenoid (to which the basisphenoid very often fuses indistinguishably). 11689 Microbrachis shows state 1 (Olori, 2015: fig. 12A), as apparently does the larger 11690 Hapsidopareion individual illustrated by CG78 (fig. 14E). Very mild cases are present in 11691 Platyrhinops (Clack & Milner, 2010) and Batropetes (Glienke, 2013, 2015); we have scored 11692 these as state 1 in order to retain this score for Doleserpeton (see Sigurdsen & Bolt, 2010: fig. 11693 4) and especially Karaurus, which barely counts at best (Ivachnenko, 1978: fig. 1b). 11694 State 0 is present in Ventastega (Ahlberg et al., 2008), Albanerpetidae (Maddin et al., 11695 2013a), Lethiscus (Pardo et al., 2017) and Phlegethontia (Anderson, 2002). 11696 Thoroughly obscured by crushing, breakage and the large fenestrae ovales in 11697 Triadobatrachus (Ascarrunz et al., 2016: 3D model 1). 11698 Danto, Witzmann & Müller (2012) scored Solenodonsaurus as having state 0, while 11699 noting in the text that the basipterygoid processes and indeed the basisphenoid as a whole are 11700 not preserved; likewise, the pertinent parts of the parasphenoid are unknown (Danto, 11701 Witzmann & Müller, 2012: fig. 8A). Clearly, the correct score is unknown (unchanged from 11702 RC07). It is likewise unknown in Scincosaurus (Milner & Ruta, 2009) and inapplicable to 11703 Brachydectes (Pardo & Anderson, 2016). 11704 Micraroter and Cardiocephalus are both polymorphic (CG78: fig. 30, 52, 55). 11705 A very wide version of state 1 is found in *Liaobatrachus zhaoi (Dong et al., 2013: 11706 fig. 6B – differing greatly from the reconstruction in fig. 7B); *L. macilentus (fig. 5B), 11707 however, has a different shape, so we have scored polymorphism. 11708 *Palaeoherpeton appears to have a mild case of state 1 (Panchen, 1964: fig. 13). 11709

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11710 144. PASPHE 13: Parasphenoid much wider than long immediately posterior to level of 11711 basal articulation: absent (0); present (1). 11712 State 0 is found in Ventastega (Ahlberg et al., 2008), Platyrhinops (Clack & Milner, 11713 2010), Gephyrostegus (Klembara et al., 2014) and Lethiscus (Anderson, Carroll & Rowe, 11714 2003; Pardo et al., 2017). 11715 Acheloma (Polley & Reisz, 2011) and Albanerpetidae (Estes & Hoffstetter, 1976; 11716 Maddin et al., 2013a) have state 1. *Nigerpeton very clearly shares it (D. M., pers. obs. of 11717 MNN MOR 69 and MNN MOR 70). 11718 Not applicable to Phlegethontia (as already scored in RC07; Anderson, 2002: fig. 4.2, 11719 4.3), *Beiyanerpeton (Gao & Shubin, 2012: fig. 3) and apparently *Chelotriton (Schoch, 11720 Poschmann & Kupfer, 2015), where the area in question is taken up by the fenestrae ovales. 11721 11722 145. PASPHE 14: Ventral plate of parasphenoid (caudal to basal articulations) more or 11723 less triradiate/triangular (0), rectangular (1), or rectangular with a caudal lobe (2) 11724 (unordered). Dividing this character into states (RC07 distinguished only two: 11725 “subrectangular” and everything else) is difficult because such a wide continuum of shapes 11726 exists – notably, state 2 includes pentaradiate conditions that can look like part of an octogon, 11727 as well as hexaradiate shapes, and state 0 encompasses di-, tri-, and tetraradiate shapes; this 11728 diversity of shapes is also why we have not ordered this character. 11729 We have ignored the relatively huge fenestrae ovales of salientians and albanerpetids 11730 for the purposes of scoring this character. This allows state 1 in Triadobatrachus and 11731 Notobatrachus (Estes & Reig, 1973; Báez & Nicoli, 2004) and 1 or 2 in Albanerpetidae 11732 (Estes & Hoffstetter, 1976; Maddin et al., 2013a). Much smaller excavations of the 11733 parasphenoid plate for the fenestrae ovales occur in Archeria (Holmes, 1989) and the 11734 temnospondyl **Tersomius (Carroll, 1964). 11735 State 0: Greererpeton, Crassigyrinus, Whatcheeria (Lombard & Bolt, 1995), 11736 Baphetes, Megalocephalus, Eucritta if the reconstruction by Clack (2001) can be trusted, 11737 Isodectes, Neldasaurus, Anthracosaurus (Panchen, 1977), Pholiderpeton scutigerum, 11738 apparently Gephyrostegus (Klembara et al., 2014), Discosauriscus, Seymouria, Captorhinus, 11739 Paleothyris, Petrolacosaurus, Tuditanus, Pantylus, Saxonerpeton, Pelodosotis, 11740 Cardiocephalus, Ariekanerpeton, Leptoropha, Microphon (borderline; Bulanov, 2003), 11741 Pederpes, Tseajaia (Moss, 1972: fig. 2), Utegenia. 11742 State 1: the four OTUs mentioned above, Panderichthys (though the plate is very 11743 short), Edops (Romer & Witter, 1942; D. M., pers. obs of USNM 23309), Chenoprosopus 11744 (Langston, 1953), Cochleosaurus (Sequeira, 2004), Trimerorhachis (Milner & Schoch 2013), 11745 Eryops (Sawin, 1941), Phonerpeton (Dilkes, 1990: fig. 1B), Ecolsonia (Berman, Reisz & 11746 Eberth, 1985), Broiliellus (Schoch, 2012: fig. 2F), Amphibamus (Daly, 1994: fig. 21 right 11747 side), Doleserpeton, Micromelerpeton, Apateon, Leptorophus and Schoenfelderpeton (Boy, 11748 1987), Eoherpeton, Proterogyrinus, Pholiderpeton attheyi, Micraroter, Rhynchonkos 11749 (Szostakiwskyj, Pardo & Anderson, 2015), Brachydectes, Scincosaurus, Sauropleura. 11750 State 2: Platyrhinops (Clack & Milner, 1994, 2010), Karaurus, Valdotriton, 11751 Batropetes (Carroll, 1991; Glienke, 2013; D. M., pers. obs. of MB.Am.1232 contradicting 11752 Glienke, 2015: fig. 3F), Microbrachis (Olori, 2015: fig. 12A), Diploceraspis, Oestocephalus 11753 (Carroll, 1998a). 11754 Dendrerpetidae is polymorphic, having states 1 and 2 (Godfrey, Fiorillo & Carroll, 11755 1987; Milner, 1996; Robinson, Ahlberg & Koentges, 2005); Euryodus is likewise 11756 polymorphic, with E. dalyae possessing state 2 and E. primus displaying state 0. 11757 Acheloma has a condition intermediate between states 0 and 1 (Olson, 1941: fig. 8; 11758 Maddin, Reisz & Anderson, 2010: fig. 5I); we have scored partial uncertainty.

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11759 Similarly, Balanerpeton is reconstructed as intermediate between states 1 and 2 11760 (Milner & Sequeira, 1994); we have scored partial uncertainty. 11761 Unknown (and not already so scored in RC07): Eusthenopteron (inapplicable because 11762 there only are two caudal processes that are together narrower than at the basal articulation: 11763 Ahlberg, Clack & Lukševičs, 1996), Acanthostega (inapplicable because the parasphenoid 11764 barely extends caudally beyond the basal articulation: Clack, 1994b; Porro, Rayfield & Clack, 11765 2015), Ichthyostega (inapplicable because the parasphenoid does not extend caudally beyond 11766 the basal articulation at all), Hapsidopareion (CG78: fig. 13A, 14E), Adelospondylus 11767 (Andrews & Carroll, 1991: fig. 13C), Batrachiderpeton, Lethiscus (the parasphenoid – 11768 parabasisphenoid? – is too short and caudally pointed: Pardo et al., 2017) and Capetus 11769 (Sequeira & Milner, 1993). 11770 Vieraella has state 1 or 2 (Báez & Basso, 1996). 11771 State 1, implied by Damiani et al. (2006: fig. 4B), is probably safe to score for 11772 *Saharastega (D. M., pers. obs. of MNN MOR 73). Following the text of Gubin (1991), we 11773 have also assigned state 1 to *Konzhukovia, though the state shown in drawing 15 is 11774 borderline to state 0. 11775 Schoch, Poschmann & Kupfer (2015) figured state 1 in a specimen drawing, but state 11776 2 in two reconstructions; given the state of preservation of the specimens, we have scored 11777 partial uncertainty for *Chelotriton. 11778 11779 146. JAW ART 1/SQU 2/DEN 8: Jaw articulation lying caudal to (0), level with (1), or 11780 rostral to occiput but with rostrodorsally to caudoventrally inclined or vertical 11781 caudolateral edge of squamosal (2), or caudolateral edge of squamosal caudodorsally to 11782 rostroventrally inclined (3), or even dentary shorter than half of distance between snout 11783 and occiput (4) (ordered). State 3, the previous SQU 2(1), required JAW ART 1(2), and 11784 state 4, the previous DEN 8(1) which is limited to Batropetes and Brachydectes in the original 11785 taxon sample, required SQU 2(1), so we have merged these characters. (State 4 is also found 11786 in *Carrolla [Maddin, Olori & Anderson, 2011] and is inevitable in *Quasicaecilia, where 11787 the lower jaw is almost wholly unknown but the distance between the tip of the snout and the 11788 jaw joints is less than that between the jaw joints and the occiput [Pardo, Szostakiwskyj & 11789 Anderson, 2015].) Because the present character is continuous, we have ordered it and 11790 interpreted state 1 as meaning that the distance between the midpoints of the jaw joints and 11791 the occipital condyle(s)/cotyle is less than 5% of the distance between the latter and the tip of 11792 the snout; this gives state 1 to Eoherpeton (Smithson, 1985: fig. 8A), which was originally 11793 scored as unknown for JAW ART 1. 11794 RC07 commented JAW ART 1 (their character 187) as follows: “There appears to be 11795 no clear signal associated with the distribution of different character-states, even within the 11796 same clade.” Indeed, this character is somewhat labile. Still, states other than 0 occur (in the 11797 original taxon sample) only in Eusthenopteron, Eoherpeton, Cochleosaurus, Trimerorhachis, 11798 Isodectes and the seymouriamorph-diadectomorph-amniote-amphibian clade, augmented in 11799 the expanded taxon sample only by the temnospondyls *Saharastega, *Lydekkerina, 11800 *Palatinerpeton and *Acanthostomatops and the chroniosuchian *Bystrowiella; states 2 and 3 11801 are limited to amphibians, Orobates and Isodectes, and state 0 occurs at least twice in the 11802 urocordylid-aïstopod clade. Despite its five states, the present character has only 38 steps on 11803 the shortest trees from Analysis R4; reversals from state 1 to 0 are only seen six times, state 2 11804 appears seven or eight times and reverses at most twice, state 3 or higher appears five or six 11805 times and reverses at most once, state 4 appears once and never reverses. This is far from a 11806 random distribution. 11807 State 0 is found in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994; Ahlberg et al., 11808 2008), Phonerpeton (Dilkes, 1990), Eoscopus (Daly, 1994), Bruktererpeton (Boy & Bandel,

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11809 1973: pl. 7), Gephyrostegus (Carroll, 1970: fig. 6A; D. M., pers. obs. of TMM 41773-1), 11810 Westlothiana (Smithson et al., 1994: text and fig. 2), and Oestocephalus (Carroll, 1998a). 11811 Cochleosaurus (Sequeira, 2004), Trimerorhachis (Milner & Schoch, 2013), Lethiscus 11812 (Pardo et al., 2017; J. Pardo, pers. comm.) and Tseajaia (Moss, 1972: fig. 2; Berman, Sumida 11813 & Lombard, 1992: fig. 9; D. M., pers. obs. of CM 38033) have state 1. 11814 Isodectes (Sequeira, 1998) and Keraterpeton (Bossy & Milner, 1998: fig. 57A, 78) 11815 show state 2. So does even the largest known skull of Orobates (Berman et al., 2004: fig. 8A). 11816 State 3 occurs in Albanerpetidae, Karaurus, Valdotriton and Scincosaurus, as well as 11817 in *Beiyanerpeton. 11818 Batrachiderpeton, Diplocaulus and Diploceraspis possess state 2 or 3; Diceratosaurus 11819 has state 3 or 4. 11820 Urocordylus has state 0, 1, or 2. 11821 The condition is entirely unknown in Dolichopareias (Andrews & Carroll, 1991). 11822 States 2 and 3 cannot be distinguished in Phlegethontia due to the unique shape of the 11823 squamosal (Anderson, 2002). 11824 Many taxa go from a higher to a lower state in ontogeny. Accordingly, we have scored 11825 Schoenfelderpeton as possessing state 0, 1, or 2 (instead of just the observed 2). 11826 Micromelerpeton (Boy, 1995) and Apateon (Schoch & Fröbisch, 2006) are scored 0 based on 11827 the most mature specimens. Leptoropha and Microphon are scored as unknown because the 11828 halfway complete skull roofs known of them do not come from adult individuals (Bulanov, 11829 2003). 11830 *Gerobatrachus has state 0 or 1 based on the different possibilities for where the 11831 occiput could have been in life. 11832 In *Lydekkerina, the occipital condyles lie rostral to the jaw joints, but the distance is 11833 less than 5% of the distance between the jaw joints and the rostral end of the skull (Shishkin, 11834 Rubidge & Kitching, 1996; Jeannot, Damiani & Rubidge, 2006); we have scored this as state 11835 1. 11836 State 4 can be excluded for the *St. Louis tetrapod; the other four states remain 11837 possible (Clack et al., 2012b: fig. 2A). 11838 *Bystrowiella almost certainly falls within the range of state 1 (Witzmann & Schoch, 11839 2017: fig. 15). 11840 11841 147. PSYM 1: Parasymphysial plate: present (0); absent (1). 11842 State 1 is found in Acheloma (Polley & Reisz, 2011), apparently Schoenfelderpeton 11843 (Boy, 1986: 154, fig. 15b), Limnoscelis (Berman & Sumida, 1990: fig. 5A), Batropetes 11844 (Glienke, 2013, 2015) and Notobatrachus (Báez & Nicoli, 2008). 11845 Kotlassia was scored as unknown in RC07. Ruta, Coates & Quicke (2003) cited 11846 Bystrow (1944) as their only source for scoring Kotlassia; they did not mention having seen 11847 any specimens. Bystrow (1944: fig. 6) very clearly illustrated state 1; unfortunately, as we 11848 have not seen specimens either, we have no way of telling to which extent that figure can be 11849 trusted on features that are not mentioned in the text. None of the figures of Bystrow (1944) 11850 indicate any part of the skull or lower jaw as unknown; there is no indication in the legends or 11851 in the illustrations themselves as to which, if any, extent they are reconstructions or specimen 11852 drawings. – Because Bystrow (1944: fig. 6) illustrated state 1, the text (p. 389–390) does not 11853 explicitly mention any part of the lower jaw as unknown and says that “a complete 11854 description of the structural details of the lower jaw” is possible, and RC07 and Ruta, Coates 11855 & Quicke (2003) did not indicate any reason for why they scored this character as unknown 11856 instead, we have changed the score to 1. We are aware, however, that the skull roof is not as 11857 well preserved as Bystrow (1944) drew it (Bystrow, 1944: 409; Bulanov, 2003). – Bystrow 11858 (1944) did not distinguish Kotlassia from *Karpinskiosaurus, but used (p. 389) the holotypes

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11859 of both Ko. prima and *Ka. secundus for describing the lower jaw, and the possibly 11860 composite drawing (fig. 6) labeled “Lower jaw of Kotlassia prima” shows clear differences to 11861 the reconstruction of *Karpinskiosaurus by Klembara (2011: fig. 9D, E), so we infer that the 11862 lower jaw of Kotlassia is reasonably well known in general; furthermore, Klembara (2011) 11863 did not use the holotype of *Ka. secundus in his reconstruction of the lower jaw, which he 11864 based on two other specimens, leading us to conclude that the holotype does not provide 11865 much information on the lower jaw. 11866 For the time being, we accept the interpretation that the lump of bone in Lethiscus and 11867 *Coloraderpeton visible not only in dorsal and lingual, but even ventral and labial views is a 11868 huge toothless parasymphysial (Pardo et al., 2017) and have therefore scored state 0 for both 11869 OTUs. However, we consider it at least as likely that this bone is a mentomandibular (an 11870 ossification of the mesial end of Meckel’s cartilage). 11871 We have been very cautious in interpreting the lower jaw of *Carrolla, in which some 11872 fragments are missing and several bones are distorted (Maddin, Olori & Anderson, 2011); for 11873 example, we have scored the present character as unknown. 11874 However, we accept the “brassicate structure” at the symphysis of the *St. Louis 11875 tetrapod (Clack et al., 2012b; D. M., pers. obs. of MB.Am.1441) as evidence of state 0. 11876 Sutures around this “structure” cannot be seen, but sutures cannot be seen almost anywhere 11877 else on the specimen either. 11878 11879 148. PSYM 2: Parasymphysial plate without (0) or with (1) paired fangs, comparable in 11880 size with or greater than dentary teeth. 11881 RC07 cited Ahlberg & Clack (1998) as saying that Megalocephalus has state 1, but 11882 Milner & Lindsay (1998: 220) stated that it has state 0 and cited a pers. comm. by Ahlberg & 11883 Clack. We have accordingly changed the score of Megalocephalus to 0. 11884 Lethiscus shares state 0 (Pardo et al., 2017; see PSYM 1). 11885 Bolt & Lombard (2001) stated in table 1 that *Deltaherpeton (FM PR 1637) lacks 11886 parasymphysial fangs like all other colosteids. The text (p. 1036), however, maintains that this 11887 cannot be determined. Their fig. 7 does not help, so we have gone with the text rather than the 11888 table and have scored *Deltaherpeton as unknown. 11889 11890 149. PSYM 3: Parasymphysial plate without (0) or with (1) anteroposterior tooth row 11891 oriented subparallel to marginal dentary teeth and the basal diameter and/or height of 11892 which [ = of the teeth in the parasymphysial toothrow] is 30 % or greater than that of 11893 marginal teeth and twice or more that of denticles, if present. 11894 Lethiscus has state 0 (Pardo et al., 2017; see PSYM 1). 11895 Bolt & Lombard (2001) stated in table 1 that *Deltaherpeton (FM PR 1637) possesses 11896 two parasymphysial teeth like all other colosteids. The text (p. 1036), however, maintains that 11897 this cannot be determined. Figure 7 does not help, so we have gone with the text rather than 11898 the table and have scored *Deltaherpeton as unknown. 11899 *Ymeria is probably polymorphic (Clack et al., 2012a). 11900 11901 150. PSYM 4: Parasymphysial plate with (0) or without (1) small teeth (denticles) 11902 forming continuous shagreen or discrete patches and the basal diameter and/or height of 11903 which is less than 30% of that of adjacent marginal dentary teeth. 11904 The resolution of the scans published by Pardo et al. (2017; see PSYM 1) is low 11905 enough that we keep this character unknown for Lethiscus. 11906 On the only known parasymphysial of *Densignathus, there is just a single denticle 11907 (Daeschler, 2000); because denticles are usually completely absent when they are not 11908 “forming continuous shagreen or discrete patches”, we have scored state 0.

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11909 deleted DEN 1: Dentary with (0) or without (1) accessory toothrows. According to RC07, 11910 state 0 occurs in Captorhinus and Pantylus. In fact, Pantylus has a single toothrow on the 11911 dentary – the additional toothrows (insofar as rows can be recognized) of the lower jaw all lie 11912 on the (single) coronoid (Williston, 1916: fig. 27; Romer, 1969: fig. 14; CG78: fig. 25 bottom 11913 middle, 25 bottom right, and 114C). This makes the character parsimony-uninformative, so 11914 we have deleted it. For the sake of completeness, we would further like to mention that state 0 11915 is limited to one of the three species of Captorhinus and not plesiomorphic for the genus as a 11916 whole (Kissel, Dilkes & Reisz, 2002); the other clade (!) of captorhinids with multiple 11917 toothrows is not included in this matrix. 11918 “The dorsal edge of the dentary carries a marginal row of closely spaced homodont 11919 teeth. Some, but apparently not all, individuals have a secondary row of much smaller teeth 11920 outside the principal row” in Panderichthys (Ahlberg & Clack, 1998: 14). By comparison to 11921 other characters in this matrix, we consider the “smaller teeth” denticles, so Panderichthys, 11922 originally scored as polymorphic, has only state 1 of this character. Alternatively, it may be 11923 that Ruta, Coates & Quicke (2003) intended state 0 to mean the condition of some 11924 Panderichthys individuals (and a few taxa not included in the matrix of RC07, like the 11925 explicitly mentioned *Elginerpeton: Ahlberg, 1995; Ahlberg & Clack, 1998); but if so, 11926 Captorhinus could not be counted, and Pantylus would have state 1 anyway, rendering the 11927 character parsimony-uninformative again (state 0 would be restricted to part of one OTU). 11928 Our addition of *Elginerpeton has not rendered this character parsimony-informative 11929 if Panderichthys is scored as polymorphic, because PAUP* cannot reconstruct ancestors as 11930 polymorphic: even if Panderichthys and *Elginerpeton were sister-groups, two steps (one of 11931 them within Panderichthys) would be needed to explain the distribution of state 1 regardless 11932 of which state their last common ancestor would have had. 11933 11934 151. DEN 2: Dentary with anterior fangs generally comparable in size with, or greater 11935 than, other dentary teeth and lying close to symphysial region and lingual to marginal 11936 dentary teeth (0); with fangs/tusks/incisiforms that are part of the marginal toothrow 11937 (1); without fangs (2) (unordered). Instead of “lingual”, RC07 had “mesial”. The distinction 11938 between states 0 and 1 is new; state 1 occurs in Ichthyostega (Jarvik, 1996: fig. 31, pl. 31; 11939 Clack et al., 2012a: fig. 5C), Colosteus (Hook, 1983), Greererpeton and *Deltaherpeton (Bolt 11940 & Lombard, 2001), Diadectes, Limnoscelis, Captorhinus, Pantylus, Stegotretus and Orobates. 11941 (The caniniform teeth of some Oedaleops specimens [Sumida, Pelletier & Berman, 2014] are 11942 too far from the symphysis to count as state 1; we have scored state 2 for *Caseasauria. The 11943 same holds for the caniniform region of Hapsidopareion (already scored in RC07) and 11944 *Llistrofus [CG78: fig. 13F; Bolt & Rieppel, 2009].) 11945 Eusthenopteron has state 2 (Ahlberg & Clack, 1998: 15); so do Triadobatrachus 11946 (Ascarrunz et al., 2016), Solenodonsaurus (Danto, Witzmann & Müller, 2012), Microbrachis 11947 (CG78: fig. 80) and Scincosaurus (Milner & Ruta, 2009). 11948 Baphetes has state 0 (Milner & Lindsay, 1998; Milner, Milner & Walsh, 2009), as do 11949 Acheloma (Polley & Reisz, 2011), Ecolsonia (D. M., pers. obs. of CM 38017 and CM 38024), 11950 Eoscopus (Daly, 1994: 10), Platyrhinops (Clack & Milner, 2010), Schoenfelderpeton (Boy, 11951 1986: 154, fig. 15b) and Gephyrostegus (Klembara et al., 2014). 11952 Archeria shows both state 0 and state 2 in different individuals (Holmes, 1989). 11953 Anthracosaurus appears to have had state 1 and state 2 in different individuals 11954 (Panchen, 1977: 475). 11955 Kotlassia was scored as unknown in RC07. Following Bystrow (1944: 392, fig. 6), we 11956 have changed the score to 2, but see character PSYM 1. 11957 Acherontiscus was scored as having state 0; state 2 is much more likely (Carroll, 11958 1969b).

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11959 Unknown in Leptoropha (Bulanov, 2003) and Silvanerpeton (Ruta & Clack, 2006). 11960 *Glanochthon has two teeth per dentary that lie lingual to the mesialmost marginal 11961 teeth but are only as tall as the smallest (distalmost) marginal dentary teeth. Still, we count 11962 this as “generally comparable in size with […] other dentary teeth” and have assigned state 0 11963 to *Glanochthon. 11964 We accept the inference of state 0 in *Erpetosaurus from the holes in the ventral and 11965 the dorsal surface of the premaxillae (Milner & Sequeira, 2011). 11966 Panchen (1975: 619) considered the inference of a tusk in *Pholidogaster somewhat 11967 uncertain; however, we consider the damage to the roof of the snout (Panchen, 1975: 617; 11968 compare Bolt & Lombard, 2010) evidence for state 0 or 1. 11969 *Platyoposaurus and *Australerpeton have states 0 and 1: there are tusks both in the 11970 toothrow and lingual to it (Gubin, 1991; Eltink & Langer, 2014). 11971 11972 152. DEN 3: Dentary without (0) or with (1) ‘chamfered’ margin. 11973 State 0 is documented in Cochleosaurus (Sequeira, 2004), Solenodonsaurus (Danto, 11974 Witzmann & Müller, 2012), Scincosaurus (Milner & Ruta, 2009) and Lethiscus (Pardo et al., 11975 2017), and also known in *Nigerpeton (D. M., pers. obs. of MNN MOR 70). 11976 “In some Ichthyostega specimens, it [the chamfered margin] seems restricted to the 11977 posterior portion of the dentary” (Clack et al., 2012a: 77). This strongly implies that state 1 is 11978 always present. 11979 Not applicable to Phlegethontia, where all dermal postdentary bones are absent 11980 (Anderson, 2002, and references therein). 11981 11982 153. DEN 4: Dentary without (0) or with (1) U-shaped notch for premaxillary tusks. 11983 Karaurus has state 0 (D. M., pers. obs. of unnumbered MNHN cast of PIN 2585/2); so 11984 do Solenodonsaurus (Danto, Witzmann & Müller, 2012) and Lethiscus (Pardo et al., 2017). 11985 *Nigerpeton has a condition similar to but different from state 1 (D. M., pers. obs. of 11986 MNN MOR 108); we have scored this as state 0. 11987 We accept the interpretation by Clack et al. (2012b) that the *St. Louis tetrapod has 11988 state 1, though the notch is shaped less like a U and more like an asymmetric W; a similar 11989 shallow but sharp-edged notch may even be visible in the same position on the other dentary 11990 (D. M., pers. obs. of MB.Am.1441.2). 11991 11992 154. DEN 7: Dentary toothed (0) or toothless (1). 11993 State 0 is documented in Chenoprosopus (Hook, 1993), Solenodonsaurus (Danto, 11994 Witzmann & Müller, 2012) and Scincosaurus (Milner & Ruta, 2009), and also known in 11995 *Saharastega (pers. obs. of MNN MOR 73). 11996 Kotlassia was scored as unknown in RC07. However, Bystrow (1944: 390) stated: 11997 “There is a row of conical slightly recuved sharp teeth all along the upper edge of the 11998 dentary.” We have changed the score to 0; see PSYM 1 for discussion. 11999 12000 155. SPL 2: Posteriormost extension of splenial lingual lamina closer to anterior margin 12001 of adductor fossa than to anterior extremity of jaw, when the lower jaw ramus is 12002 observed in me[d]ial aspect and in anatomical connection (i.e. symphysial region 12003 orientated towards the observer): absent (0); present (1). We follow RC07 and many other 12004 sources in homologizing the single splenial of amniotes, diadectomorphs and others with the 12005 presplenial and not the postsplenial, though we are not aware of any evidence for or against 12006 this other than the fact that this single splenial often participates in the symphysis. Unlike all 12007 other amniotes, Petrolacosaurus was reported to possess a (uniquely small) postsplenial 12008 (Reisz, 1981); following a pers. comm. by R. R. Reisz in about 2008, we have kept POSPL

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12009 1(0) for Petrolacosaurus, but we still wonder if the supposed postsplenial might actually be a 12010 fragment of the angular instead. 12011 Whatcheeria has state 1 (Lombard & Bolt, 2006). So do Limnoscelis (Reisz, 2007; 12012 Berman, Reisz & Scott, 2010), Batropetes (Glienke, 2015), Diplocaulus (Douthitt, 1917) and 12013 Lethiscus (Pardo et al., 2017: ext. data fig. 6, contradicting their matrix). 12014 Inapplicable (unknown) in all lissamphibians, because there is no evidence for a 12015 splenial in any of them. (The occasional reports from caecilian ontogeny in fact refer to a 12016 coronoid: Müller, Oommen & Bartsch, 2005; Müller, 2006.) 12017 Kotlassia was scored as unknown in RC07. Following Bystrow (1944: fig. 6), we have 12018 changed the score to 1, but see character PSYM 1. 12019 No splenials can be confidently identified in Rhynchonkos (Szostakiwskyj, Pardo & 12020 Anderson, 2015); we have therefore scored all SPL and POSPL characters as well as 12021 PREART 5 (all below) as unknown. 12022 Remarkably, state 0 was scored in RC07 for Phlegethontia, which has just two bones 12023 in the lower jaw (Anderson, 2002, and references therein): one is the dentary, the other is 12024 most likely a purely Meckelian ossification – no lamina and no splenial are remotely 12025 identifiable, leaving us no way to apply this character. 12026 It appears (D. M., pers. obs. of MB.Am.1441.2) that the *St. Louis tetrapod had a long 12027 distal process of the splenial overlying the prearticular near the dorsomesial edge of the 12028 Meckelian fenestra, very similar to what is seen in Greererpeton (Bolt & Lombard, 2001: fig. 12029 5.2). We have therefore scored state 1. 12030 12031 156. SPL 3-4: Splenial separated from anterior and middle coronoids by prearticular 12032 (0); splenial contacts anterior but not middle coronoid (1); splenial contacts both 12033 anterior (if present) and middle coronoid (2) (ordered). The splenial never contacts the 12034 middle coronoid without also contacting the anterior one (even though the latter contact lies 12035 entirely on the symphysial surface in *Platyoposaurus: Gubin, 1991: drawing 20) unless of 12036 course if the anterior one is absent; the ordering reflects a gradual shortening of the 12037 prearticular. 12038 We assume that the three denticle-covered areas in the coronoid series of Platyrhinops 12039 (Clack & Milner, 2010) correspond to the three coronoids; this allows us to keep state 2. 12040 Milner & Schoch (2013: fig. 7B) reconstructed state 0, which was scored in RC07, for 12041 Trimerorhachis without mentioning this character in the text; following a pers. comm. by R. 12042 Schoch (April 2015), however, we have scored Trimerorhachis as unknown. 12043 State 0 is, however, found in *Sclerocephalus (Schoch & Witzmann, 2009a; 12044 tentatively confirmed by D. M., pers. obs. of MB.Am.1346) and in the *Parrsboro jaw: the 12045 denticulated mystery element that could be part of the prearticular or of the splenial (Sookias, 12046 Böhmer & Clack, 2014) appears continuous, except for diagenetic deformation, with the 12047 prearticular (the middle part of which has been bent deep into the Meckelian fenestra), and 12048 Caerorhachis (Ruta, Milner & Coates, 2002) is the only case known to us where the denticle 12049 field of the lower jaw extends, just barely, onto the splenial, while in the *Parrsboro jaw a 12050 large area is covered by denticles. 12051 Acanthostega has state 1 (Porro, Rayfield & Clack, 2015), as does Whatcheeria 12052 (Lombard & Bolt, 2006). Edops shares state 1, though for an unusual reason: the suture 12053 between the anterior and the middle coronoid and the one between splenial and postsplenial 12054 are about at the same level, but separated by the posterior coronoid, which has a long suture 12055 with the anterior one (D. M., pers. obs. of USNM 23309, impossible to tell in MCZ 1378; not 12056 described by Romer & Witter, 1942, not visible in their fig. 3A). This condition (and thus 12057 state 1) is also found in Eryops (Sawin, 1941), Pholiderpeton attheyi (Panchen, 1972), 12058 Anthracosaurus (Panchen, 1977) and possibly Proterogyrinus (compare Holmes, 1984: fig.

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12059 15, to Panchen, 1972 and 1977), though we have kept partial uncertainty (state 1 or 2) for the 12060 last of these. 12061 Kotlassia was scored as unknown in RC07. Following Bystrow (1944: fig. 6), we have 12062 changed the score to 2, but see character PSYM 1. 12063 Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 2010), Ariekanerpeton (Klembara 12064 & Ruta, 2005: fig. 6D) and Tseajaia (Moss, 1972: 19) show state 2 as well. We have further 12065 scored state 2 for Lethiscus; although the middle coronoid has not been identified, there is a 12066 large distance between the mesial end of the prearticular and the distal end of the putative 12067 anterior coronoid, all of it filled by the lingual lamina of the splenial (Pardo et al., 2017). 12068 Acheloma has state 1 or 2 (Polley & Reisz, 2011). 12069 *Nigerpeton has state 1 (D. M., pers. obs. of MNN MOR 70), as does *Saharastega 12070 (pers. obs. of MNN MOR 73). 12071 It appears that the prearticular separates the splenial from the anterior coronoid in 12072 *Elginerpeton (Ahlberg & Clack, 1998: fig. 12B; Ahlberg, Friedman & Blom, 2005: fig. 2B), 12073 so we have scored state 0. 12074 *Lydekkerina (Jeannot, Damiani & Rubidge, 2006: fig. 4D) and *Australerpeton 12075 (Eltink & Langer, 2014) have a point contact between the splenial, the postsplenial and both 12076 pertinent coronoids; we have scored state 1 or 2 for both. 12077 *Aytonerpeton appears to have state 0 (Clack et al., 2016: fig. 4c, supplementary video 12078 2). 12079 12080 157. POSPL 1: Separately ossified postsplenial: present (0); absent (1). 12081 State 0 is, surprisingly, found in Diplocaulus (Douthitt, 1917). It is further said to be 12082 present in *Densignathus (Daeschler, 2000); we have followed this, although the illustrations 12083 do not show the suture to the angular (except as a stippled line in reconstructions). 12084 *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. M., pers. obs. of 12085 MNN MOR 73) have state 0 as well. 12086 Batropetes has state 1 (Glienke, 2013). We have also followed Pardo et al. (2017) in 12087 scoring it for Lethiscus, although fully articulated sutures are at best difficult to identify in 12088 their scans; their extended data figure 2 and the accompanying supplementary videos show a 12089 failed attempt to identify separate postsplenials (in pink). In *Coloraderpeton, absence of the 12090 postsplenial is indicated by the long distance between the splenial (and its facet) and the 12091 angular. Note that all this contradicts the matrix by Pardo et al. (2017), where both Lethiscus 12092 and *Coloraderpeton are scored as having two splenials. 12093 Based on the figures and videos of Clack et al. (2016), we tentatively accept state 0 for 12094 *Aytonerpeton. 12095 12096 158. POSPL 2: Postsplenial without (0) or with (1) lingual lamina. 12097 Whatcheeria has state 0 (Lombard & Bolt, 2006). 12098 State 1 is just barely found in Chenoprosopus (D. M., pers. obs. of USNM 437646) 12099 and clearly in Isodectes (D. M., pers. obs. of unnumbered MCZ cast of AMNH 6935 before 12100 etching), Doleserpeton (Sigurdsen & Bolt, 2010: fig. 3B), Gephyrostegus (Klembara et al., 12101 2014), Diplocaulus (Douthitt, 1917), *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and 12102 *Saharastega (D. M., pers. obs. of MNN MOR 73). 12103 12104 159. POSPL 3: Postsplenial with (0) or without (1) pit line. 12105 State 1 is found in Whatcheeria (Lombard & Bolt, 2006), Ecolsonia (D. M., pers. obs. 12106 of CM 38024), Doleserpeton (Sigurdsen & Bolt, 2010: fig. 3B) and apparently Diplocaulus 12107 (Douthitt, 1917). 12108 Unknown in Panderichthys (Ahlberg & Clack, 1998) and Ossinodus (Warren, 2007).

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12109 160. ANG 1: Separately ossified angular: present (0); absent (1). 12110 State 0 is known in Baphetes (Milner & Lindsay, 1998: fig. 5; Milner, Milner & 12111 Walsh, 2009), Diceratosaurus (D. M., pers. obs. of CM 72608), Diplocaulus (Douthitt, 1917) 12112 and Lethiscus (Anderson, Carroll & Rowe, 2003). 12113 State 1 is found in Albanerpetidae (Estes & Hoffstetter, 1976; Gardner, 2001; Venczel 12114 & Gardner, 2005). 12115 Unclear in Triadobatrachus (Ascarrunz et al., 2016). 12116 Schoch, Poschmann & Kupfer (2015) described a bone in *Chelotriton that they 12117 identified as the surangular. According to their reconstruction (Schoch, Poschmann & Kupfer, 12118 2015: fig. 4f), however, this bone lies unambiguously in the position of an angular, at the 12119 ventral edge of the lower jaw, entirely ventral to the prearticular and the articular. “The 12120 angular and surangular” are mentioned in the text (p. 82), but there is no “angular” in the 12121 illustrations, the list of abbreviations, or anywhere in the text outside the above quote. 12122 Personal communication of D. M. with R. Schoch has not so far clarified this matter; for the 12123 time being, we therefore interpret *Chelotriton as possessing an angular – unique though this 12124 is among urodeles, as discussed by Marjanović & Witzmann (2015) – and lacking a 12125 surangular; we have scored state 0 of the present character and have also scored *Chelotriton 12126 for other ANG characters based on the supposed “surangular”. 12127 Judging from the starburst ornamentation (supplementary video 2), the suture between 12128 the angular and the postsplenial of *Aytonerpeton postulated in fig. 4b of Clack et al. (2016) 12129 goes straight through the angular. 12130 12131 161. ANG 2-3: Angular-prearticular contact: entirely at caudoventral edge of jaw (0); 12132 absent, Meckelian bone or cartilage continuously exposed from the jaw joint to the 12133 splenial (1); on the lingual side, where the angular has a lingual lamina (2) (unordered). 12134 The contact (explicitly called a suture) and the lingual (“mesial”) lamina of the angular were 12135 treated as separate characters by RC07, but the latter never seems to occur without the former; 12136 we therefore follow Ahlberg, Clack & Blom (2005) and the matrix of Ahlberg et al. (2008), 12137 Callier, Clack & Ahlberg (2009) and Clack et al. (2012a) in merging these characters. 12138 State 0 is now known in Lethiscus (Pardo et al., 2017). 12139 RC07 claimed that the absence of a contact (ANG 3(1)) was limited to Acanthostega 12140 in their taxon sample; had that been correct, the character would have been parsimony- 12141 uninformative. However, state 1 does occur in Eusthenopteron (Zupiņš, 2008: fig. 4) and 12142 Whatcheeria (Lombard & Bolt, 2006), where the surangular, the angular and the postsplenial 12143 are wholly separated from the prearticular by exposed Meckelian bone continuous with the 12144 articular, and in Pederpes, where the prearticular, “[a]s its ventral border is very simple and 12145 delicate, it clearly did not suture with the surangular or angular and possibly not with the 12146 postsplenial” (Clack & Finney, 2005). Incidentally, state 1 appears plesiomorphic for 12147 Sarcopterygii (Worobjewa, 1975: fig. 3; Long, Barwick & Campbell, 1997: fig. 38; Friedman, 12148 2007: fig. 5). 12149 State 2 is known to occur in Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 12150 437646, though the sutures are difficult to trace), Isodectes (D. M., pers. obs. of unnumbered 12151 MCZ cast of AMNH 6935 before etching, though the sutures are nigh impossible to trace), 12152 Doleserpeton (Sigurdsen & Bolt, 2010; Sigurdsen & Green, 2011: appendix 2), 12153 Gephyrostegus (Klembara et al., 2014), Batropetes (Glienke, 2013, 2015), Cardiocephalus 12154 (CG78) and Diplocaulus (Douthitt, 1917). 12155 Inapplicable in Albanerpetidae, see ANG 1; “always unclear” (Bossy & Milner, 1998: 12156 87) in Sauropleura (which was already scored as unknown for ANG 2, but not for ANG 3). 12157 Following Ahlberg, Friedman & Blom (2005), we have scored state 1 for 12158 *Elginerpeton.

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12159 There may not be a prearticular in *Coloraderpeton or *Pseudophlegethontia: the 12160 supposed fusion of the prearticular and the Meckelian bone in the former (Pardo et al., 2017) 12161 is probably just Meckelian bone, and the supposed suture at the cranial end of the supposed 12162 left prearticular of the latter (absent on the right side; Anderson, 2003b: fig. 2A) could be a 12163 break in the Meckelian bone. However, the angular clearly lacks a lingual lamina, so we have 12164 scored state 0 or 1 for both. 12165 12166 162. ANG 4: Angular not reaching (0) or reaching (1) lower jaw posterior end. 12167 Baphetes has state 0 (Milner, Milner & Walsh, 2009). So do Chenoprosopus (Hook, 12168 1993) and Platyrhinops (Clack & Milner, 2010). 12169 State 1 is found in Batropetes (Glienke, 2015), Diceratosaurus (D. M., pers. obs. of 12170 CM 72608), Diplocaulus (Douthitt, 1917) and Lethiscus (Pardo et al., 2017). 12171 Kotlassia was scored as unknown in RC07. Following Bystrow (1944: fig. 6), we have 12172 changed the score to 0, but see character PSYM 1. 12173 The condition of Westlothiana is probably not known, judging from the specimen 12174 drawings in Smithson et al. (1994). 12175 12176 163. SURANG 1: Separately ossified surangular: present (0); absent (1). 12177 State 0 is documented in Whatcheeria (Lombard & Bolt, 2006), Baphetes (Milner, 12178 Milner & Walsh, 2009), Batropetes (Glienke, 2015), Diceratosaurus (D. M., pers. obs. of CM 12179 72608), and Lethiscus (Anderson, Carroll & Rowe, 2003; Pardo et al., 2017). 12180 Diplocaulus and Diploceraspis have state 1; we have, however, kept the scores of 12181 SURANG 3 and 5 for the latter and scored the former (which was scored as unknown in 12182 RC07 for most of the lower jaw) because at least part of the unitary “articular” must be 12183 homologous to the surangular (Douthitt, 1917; Beerbower, 1963: 68, fig. 7). 12184 Schoch, Poschmann & Kupfer (2015) described a bone in *Chelotriton that they 12185 identified as the surangular. According to their reconstruction (Schoch, Poschmann & Kupfer, 12186 2015: fig. 4f), however, this bone lies unambiguously in the position of an angular, at the 12187 ventral edge of the lower jaw, entirely ventral to the prearticular and the articular. “The 12188 angular and surangular” are mentioned in the text (p. 82), but there is no “angular” in the 12189 illustrations, the list of abbreviations, or anywhere in the text outside the above quote. 12190 Personal communication of D. M. with R. Schoch has not clarified this matter; for the time 12191 being, we therefore interpret *Chelotriton as possessing an angular – unique though this is 12192 among urodeles, as discussed by Marjanović & Witzmann (2015) – and lacking a surangular 12193 like all other lissamphibians; we have, in short, scored state 1 of the present character, and 12194 have correspondingly scored the other SURANG characters as unknown. 12195 Like Witzmann & Schoch (2017), we infer the presence of the surangular in 12196 *Bystrowiella from the serrated, apparently sutural dorsal margin of the angular. 12197 12198 164. SURANG 3: Surangular with (0) or without (1) pit line. Ahlberg, Friedman & Blom 12199 (2005) suggested that the surangular pit line was homologous with the oral sulcus of the 12200 lateral-line system; this is clearly not the case, because Eusthenopteron possesses both 12201 (Schultze & Reed, 2012: fig. 10A). 12202 Whatcheeria has state 1 (Lombard & Bolt, 2006), as do Baphetes (Milner, Milner & 12203 Walsh, 2009), Batropetes (Glienke, 2015), Diplocaulus (Douthitt, 1917), apparently Lethiscus 12204 (Pardo et al., 2017; though scored as unknown in their matrix) and Ossinodus (Warren, 2007: 12205 fig. 8A) – judging from their fig. 7P, the “pit line” mentioned by Warren & Turner (2004: 12206 158) refers to the two pores that are part of the lateral-line system in the surangular figured by 12207 Warren (2007: fig. 8A) and do not lie in a position where a pit line would be expected. We 12208 have followed the matrix of Pardo et al. (2017) in scoring state 1 for *Coloraderpeton.

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12209 Kotlassia was scored as unknown in RC07. Following Bystrow (1944: fig. 6), we have 12210 changed the score to 1, but see character PSYM 1. 12211 Unknown in Westlothiana where the surface of the bone is unknown (Smithson et al., 12212 1994). 12213 12214 165. SURANG 5: Surangular lateral exposure much smaller than angular lateral 12215 exposure: no (0); yes (1). 12216 Whatcheeria has state 0 (Lombard & Bolt, 2006), as do Baphetes (Milner, Milner & 12217 Walsh, 2009), Batropetes (Glienke, 2015), Brachydectes (Wellstead, 1991; Pardo & 12218 Anderson, 2016), Diplocaulus (Douthitt, 1917) and Lethiscus (Anderson, Carroll & Rowe, 12219 2003; Pardo et al., 2017). Following the illustrations by Berman et al. (2004) against the text, 12220 we have also scored Orobates as possessing state 0. 12221 State 1 is found in Cochleosaurus (Sequeira, 2004) and Diploceraspis (Beerbower, 12222 1963: 68). 12223 Kotlassia was scored as unknown in RC07. Following Bystrow (1944: fig. 6), we have 12224 changed the score to 0, but see character PSYM 1. 12225 12226 166. PREART 5: Prearticular/splenial suture: present (0); absent (1). The possible 12227 correlations with SPL 3-4 and POSPL 1 remain to be investigated; more states of this 12228 character and/or SPL 3-4 should perhaps be distinguished. 12229 State 0 is found in Whatcheeria (Lombard & Bolt, 2006), Diplocaulus (Douthitt, 12230 1917) and Lethiscus (Pardo et al., 2017). We have also scored it for *Coloraderpeton (Pardo 12231 et al., 2017), though there it seems likely that the prearticular is altogether absent rather than 12232 fused to Meckel’s bone (Pardo et al., 2017: video). 12233 Sigurdsen & Green (2011) reported state 1 in Doleserpeton. State 1 also occurs in 12234 *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. M., pers. obs. of 12235 MNN MOR 73). 12236 Cochleosaurus bohemicus was scored in RC07 as having state 0, possibly after the 12237 reconstruction of C. florensis by Godfrey & Holmes (1995: fig. 5); however, the text (p. 17) 12238 and the specimen drawing (fig. 2) make clear that the area in question is not preserved. In her 12239 description of the skull of C. bohemicus, Sequeira (2004) showed a clear case of state 1 (fig. 12240 12D) in a specimen that appears to be split through the bone, so it may not show the sutures at 12241 the lingual surface (fig. 12B); in another specimen, Sequeira (2004: fig. 13) showed a point 12242 contact if the dashed suture between the splenial and the postsplenial is taken for granted, did 12243 not elaborate on this in the reconstruction (fig. 8C), and mentioned in the text (p. 30) that 12244 “[a]n elongate prearticular extends beneath [ = ventral to] the short posterior coronoid and 12245 continues forward for some distance beneath the middle coronoid, apparently terminating 12246 close to the common splenial suture [between splenial and postsplenial] in a subadult 12247 specimen (Fig. 13)”. We have changed the score of the Cochleosaurus OTU to unknown. 12248 Following a pers. comm. by R. Schoch (April 2015), we have scored Trimerorhachis 12249 as unknown. 12250 12251 167. ANT COR 1: Separately ossified anterior coronoid: present (0); absent (1). 12252 Acheloma has state 0 (Polley & Reisz, 2011), as do Lethiscus (apparently: Pardo et al., 12253 2017), *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. M., pers. obs. 12254 of MNN MOR 73). 12255 Hook (1983) stated: “The sutures subdividing the coronoid series cannot be traced and 12256 the tusk-bearing anterior coronoid of Greererpeton is not preserved [in Colosteus].” 12257 Nevertheless, we agree with RC07 that all three coronoids were probably present: the mesial 12258 end of the coronoid series as preserved, whether complete or not, is very far mesial, easily far

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12259 enough to belong to the anterior coronoid, while the distal end of the lower-jaw fragment in 12260 Hook (1983: fig. 3A) is too far distal to belong to the anterior coronoid by comparison to e.g. 12261 Greererpeton (Bolt & Lombard, 2001); another lower-jaw fragment shows that the coronoid 12262 series reached the adductor fossa (Hook, 1983: fig. 9), so that the posterior coronoid should 12263 have been present; and a complete lower jaw (Hook, 1983: fig. 6B) does not show any 12264 interruption in the middle of the coronoid series. 12265 State 1 is found in Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 2010) and 12266 apparently Batropetes (Glienke, 2013, 2015). 12267 Daly (1994: 11) described the situation in Eoscopus as follows: “Sharp, recurved 12268 denticles cover the dorsomedial part of the jaw and extend from the region of the symphysis 12269 to the presumed position of the adductor fossa. The coronoid bones that bear the denticles 12270 cannot be described because of their position.” To be on the safe side, we have kept only the 12271 scores for the presence and the denticles of the posterior coronoid of Eoscopus, and have 12272 changed all other coronoid characters to unknown. 12273 All ANT COR and MID COR characters as well as POST COR 2, 3 and 4 were scored 12274 as unknown in Kotlassia. However, Bystrow (1944: 390) described “three toothless 12275 coronoids” and added (p. 414): “All endeavors to find traces of teeth on any of the coronoids 12276 of Kotlassia have yielded no results.” We have scored all eleven characters accordingly; see 12277 PSYM 1. 12278 Szostakiwskyj, Pardo & Anderson (2015) identified two coronoids in Rhynchonkos, 12279 separated by a large gap and a break in the specimen. It remains possible that all three 12280 fragments belonged to a single bone (J. Pardo, pers. comm., 2015); however, if they do 12281 represent two separate coronoids, it is not clear if the mesial one is the anterior coronoid or 12282 the middle coronoid. We have accordingly scored all ANT COR and MID COR characters as 12283 unknown. 12284 Douthitt (1917: 17) stated that the anterior and middle coronoids of Diplocaulus were 12285 most likely absent. Considering how unusually wide the dentary is in dorsal view (Douthitt, 12286 1917: fig. 2.5) and that the area is damaged in all specimens (Douthitt, 1917: 17), we prefer to 12287 keep ANT COR 1 and MID COR 1 as unknown: maybe part of the “dentary” actually belongs 12288 to a coronoid or several, and the suture is too eroded to remain visible. 12289 Unknown in Dendrerpetidae (Godfrey, Fiorillo & Carroll, 1987; Holmes, Carroll & 12290 Reisz, 1998), Doleserpeton (Sigurdsen & Bolt, 2010) and Orobates (Berman et al., 2004). 12291 We have scored all three coronoids as present in *Ymeria as suggested by Clack et al. 12292 (2012a). 12293 Similarly, while the illustrations of *Densignathus (Daeschler, 2000) do not show the 12294 sutures (except as stippled lines in the reconstructions), the text is so confident about their 12295 locations that we have scored all three coronoids as present in *Densignathus. Daeschler 12296 (2000: 304) even stated: “Coronoids.—There are three coronoids. The posterior coronoid is 12297 the longest and […]” (italics in the original). 12298 The same may hold for *Mordex, where the sutures are not shown in the specimen 12299 drawings (there are no reconstructions) by Milner & Sequeira (2003) or Werneburg (2012b), 12300 but the latter (p. 27) stated that all three coronoids bear denticles all over; we have thus scored 12301 all three as present, consistent with the fact that the denticle field extends from the adductor 12302 fossa to the symphysis (Werneburg, 2012b: fig. 19c). 12303 Clack et al. (2012b: 22) confidently stated that “a fragment of the first coronoid, 12304 bearing denticles, is visible” in the *St. Louis tetrapod, but their fig. 2C only labels it 12305 “?coronoid”, and no denticles are indicated. It appears (D. M., pers. obs. of MB.Am.1441.2) 12306 that the labial (as well as the lingual) margin of the parasymphysial is visible. Labial to it, the 12307 ragged edge of the “?coronoid” (Clack et al., 2012b: fig. 2C) actually consists of spikes that 12308 may well be denticles, although the pterygoid denticles are hemispherical; this morphology is

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12309 readily interpretable by comparison to Greererpeton (Bolt & Lombard, 2001: fig. 5.2, 5.3). 12310 We have thus scored state 0 of the present character and of ANT COR 3. 12311 In *Coloraderpeton it seems to be impossible to tell if there were sutures in the “long 12312 coronoid series” (Pardo et al., 2017: 643, ext. data fig. 6, video); however, the series is so long 12313 that we have scored all three coronoids as present (as Pardo et al., 2017, did in their matrix). 12314 We have done the same for the similar situations of *Doragnathus and *Diploradus 12315 (Smithson, 1980; Clack et al., 2016). 12316 “Cor 2 tooth” of *Aytonerpeton (Clack et al., 2016: fig. 4c) is the fang on the fairly 12317 well discernible anterior, not middle, coronoid; we have scored state 0 of this and the next 12318 character. 12319 12320 168. ANT COR 2: Anterior coronoid with (0) or without (1) fangs comparable in size to 12321 or larger than marginal dentary teeth. 12322 State 0 makes a surprise appearance in Leptorophus (Boy, 1986: 144, fig. 7b). 12323 Acheloma (Polley & Reisz, 2011), Platyrhinops (Clack & Milner, 2010), Lethiscus 12324 (Pardo et al., 2017), *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. 12325 M., pers. obs. of MNN MOR 73) have state 1. 12326 Best scored as unknown in Colosteus, where the pertinent part of the anterior coronoid 12327 may have broken off (Hook, 1983). 12328 The part of the coronoid where the fangs would be expected is not preserved in 12329 MB.Am.1441 (D. M., pers. obs.), unless a mysterious multipartite hole is part of an alveolus; 12330 we have scored the *St. Louis tetrapod as unknown. 12331 12332 169. ANT COR 3: Anterior coronoid with (0) or without (1) small teeth (denticles) 12333 forming continuous shagreen or discrete patches and the basal diameter and/or height of 12334 which is less than 30% of that of adjacent marginal dentary teeth. 12335 Clack et al. (2016: 6) wrote: “Some colosteids lack coronoid teeth, and instead bear 12336 shagreen, a variable condition among individuals”, citing Bolt & Lombard (2001), who in fact 12337 reported no such individual variation, indeed no variation at all between the specimens they 12338 studied except for the presence of “denticles” on the middle coronoid in *Deltaherpeton and 12339 their absence in Greererpeton (Bolt & Lombard, 2001: table 1: character 89); “teeth” on the 12340 middle coronoid are present in both taxa (character 87), and in both taxa the “smallest teeth” 12341 on that bone are arranged in more than one row (character 88). While RC07 used 30% of the 12342 size of the marginal teeth as the cutoff point between “teeth” and “denticles”, Bolt & 12343 Lombard (2001) used 10%. Accepting, like RC07, the inference (Bolt & Lombard, 2001, 12344 based on comparison to *Deltaherpeton) that Greererpeton had both middle and posterior 12345 coronoids, we find that RC07 scored the denticles and toothrows of Greererpeton accurately 12346 except for missing the rows of very small teeth, which nonetheless seem to count as such 12347 under their/our definition, on the middle and posterior coronoids (see MID COR 4 and POST 12348 COR 4 below). 12349 We have kept state 1 for the toothrow of Colosteus; although the teeth are small 12350 enough to count as denticles when compared to the dentary teeth, many or all of the upper 12351 marginal teeth would be denticles by comparison to the dentary teeth as well. Because the 12352 dentary teeth of Colosteus are unusually large, we have ignored the size criterion in this 12353 instance. 12354 State 0 is known in Acheloma (Polley & Reisz, 2011), Platyrhinops (Clack & Milner, 12355 2010) and *Saharastega (D. M., pers. obs. of MNN MOR 73). 12356 Whatcheeria has state 1 (Lombard & Bolt, 2006), as does Trimerorhachis (Milner & 12357 Schoch, 2013). 12358 Eryops is polymorphic (Werneburg, 2007a).

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12359 The coronoid teeth of *Sigournea, *Diploradus and arguably *Doragnathus are (just 12360 barely) large enough not to be considered denticles (Bolt & Lombard, 2006: fig. 2; Clack et 12361 al., 2016: fig. 3d; Smithson, 1980: fig. 2); we have scored absence of denticles and presence 12362 of a toothrow (see below) for all three OTUs and all three coronoids, even though 12363 *Diploradus and, for a short stretch on the middle coronoid, *Sigournea have two rows 12364 instead of the usual one. 12365 12366 170. ANT COR 4: Anterior coronoid with (0) or without (1) anteroposterior tooth row 12367 orientated sub-parallel to marginal dentary teeth and the basal diameter and/or height 12368 of which is 30% or greater than that of marginal teeth and twice or more that of 12369 denticles, if present. 12370 State 1 is now documented in Trimerorhachis (Milner & Schoch, 2013), Acheloma 12371 (Polley & Reisz, 2011), Platyrhinops (Clack & Milner, 2010) and Lethiscus (Pardo et al., 12372 2017) and is also preserved in *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and 12373 *Saharastega (D. M., pers. obs. of MNN MOR 73). 12374 Jeannot, Damiani & Rubidge (2006: 831) stated that *Lydekkerina has state 0; 12375 Hewison (2007: 35) quoted that, but illustrated state 1 in fig. 34. Given the polymorphism that 12376 *Lydekkerina shows in many other characters (such as POST COR 4), we have tentatively 12377 scored polymorphism here as well. 12378 12379 171. MID COR 1: Separately ossified middle coronoid: present (0); absent (1). 12380 Baphetes has state 0 (Milner, Milner & Walsh, 2009), as do *Nigerpeton (D. M., pers. 12381 obs. of MNN MOR 70) and *Saharastega (D. M., pers. obs. of MNN MOR 73). 12382 Batropetes apparently has state 1 (Glienke, 2013, 2015), as does Orobates (Berman, 12383 Reisz & Scott, 2010). 12384 Unknown in Dendrerpetidae (Godfrey, Fiorillo & Carroll, 1987; Holmes, Carroll & 12385 Reisz, 1998); see ANT COR 1 for Diplocaulus. 12386 Pardo et al. (2017) reconstructed only one coronoid (here interpreted as the anterior 12387 one, see above) in Lethiscus, followed distally by a long gap. This gap may of course have 12388 been filled in life by further coronoids which may well be too crushed to identify in the CT 12389 scan; we have therefore kept the middle and the posterior coronoid as unknown. Note that 12390 Pardo et al. (2017) scored Lethiscus as having three coronoids without discussing this 12391 decision. 12392 12393 172. MID COR 2: Middle coronoid with (0) or without (1) fangs comparable in size to or 12394 larger than marginal dentary teeth. 12395 State 0 makes a surprise appearance in AMNH 4565, the type specimen of 12396 Trimerorhachis insignis (D. M., pers. obs.), and most likely in AMNH 4572. This was scored 12397 as MID COR 4(0) in RC07, but does not fulfill its definition: the fang is not larger than the 12398 marginal teeth. – At the same time, Milner & Schoch (2013) strongly implied the absence of 12399 fangs in a different specimen; we have scored Trimerorhachis as polymorphic. The mention 12400 of “no coronoid fangs” in their diagnosis of Trimerorhachis (p. 115) may assume a different 12401 definition of “fang” than the strictly size-based one used by RC07. 12402 Accepting, like RC07, that the middle coronoid is present in Colosteus (see ANT COR 12403 1 above), state 1 is strongly suggested by Hook (1983: fig. 3A, 6B). 12404 Balanerpeton (Milner & Sequeira, 1994), Doleserpeton (Sigurdsen & Bolt, 2010), 12405 *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. M., pers. obs. of 12406 MNN MOR 73) have state 1 in any case. 12407 Ahlberg & Clack (1998: fig. 10A) explicitly indicated a pair of fangs on the middle 12408 coronoid of *Elginerpeton, but stated in the text (p. 27): “The middle and posterior coronoids

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12409 do not carry distinct fang pairs.” Because not only the two teeth indicated in the figure, but 12410 the entire toothrow (MID COR 4) would count as fangs under the definition used here, we 12411 have scored state 0; we have scored POST COR 2 as unknown, because the part of the 12412 posterior coronoid where fangs would be expected is not known (Ahlberg, Friedman & Blom, 12413 2005). 12414 12415 173. MID COR 3: Middle coronoid with (0) or without (1) small teeth (denticles) forming 12416 continuous shagreen or discrete patches and the basal diameter and/or height of which 12417 is less than 30% of that of adjacent marginal dentary teeth. 12418 Baphetes has state 0 (Milner, Milner & Walsh, 2009). So do Trimerorhachis (Milner 12419 & Schoch, 2013; D. M., pers. obs. of AMNH 4565) and *Saharastega (D. M., pers. obs. of 12420 MNN MOR 73). 12421 Eryops is polymorphic (Werneburg, 2007a). 12422 “The middle coronoid of Doleserpeton has either large denticles or small teeth”, so 12423 Sigurdsen & Green (2011: appendix 2: 14) recommended to score it as unknown; we have 12424 followed this. 12425 12426 174. MID COR 4: Middle coronoid with (0) or without (1) anteroposterior tooth row 12427 orientated subparallel to marginal dentary teeth and the basal diameter and/or height of 12428 which is 30% greater than that of marginal teeth and twice or more that of denticles, if 12429 present. 12430 State 0 is apparently found in Greererpeton, in that some of the teeth in the row fulfill 12431 the size criterion (Bolt & Lombard, 2001: fig. 1, 2, 5). We have also scored it in Colosteus 12432 (Hook, 1983: fig. 3A, 6B; see ANT COR 1, ANT COR 3 and MID COR 2 above). 12433 Trimerorhachis has state 1, see MID COR 2. So do Balanerpeton (Milner & Sequeira, 12434 1994), *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. M., pers. obs. 12435 of MNN MOR 73). 12436 “The middle coronoid of Doleserpeton has either large denticles or small teeth”, so 12437 Sigurdsen & Green (2011: appendix 2: 14) recommended to score it as unknown; we have 12438 followed this. 12439 12440 175. POST COR 1: Separately ossified posterior coronoid: present (0); absent (1). 12441 Baphetes has state 0 (Milner, Milner & Walsh, 2009), as do Trimerorhachis (Milner & 12442 Schoch, 2013; D. M., pers. obs. of AMNH 4565), Brachydectes (Pardo & Anderson, 2016) 12443 and likely Diplocaulus (Douthitt, 1917: 17), although we prefer to keep all POST COR 12444 characters unknown for the latter. 12445 Batropetes apparently has state 1 (Glienke, 2013, 2015). 12446 The coronoid of Pantylus is so large that it may well represent a fusion of all three 12447 coronoids, or the crowded teeth may simply obscure the sutures between two or three 12448 coronoids; but because it has not been possible to trace sutures (Romer, 1969: 24; CG78) and 12449 because the coronoid participates in the coronoid process, we here homologize it with the 12450 posterior coronoid and have scored the other two coronoids as absent (keeping the scores of 12451 RC07 for ANT COR 1, MID COR 1 and POST COR 1). 12452 The evidence for any coronoids in *Sparodus is limited to a pair of tusks (Fig. 4; 12453 Carroll, 1988) and a probable suture between the bone that bears them and the dentary (D. M., 12454 pers. obs. of NHMW 1899/0003/0006; Fig. 4). Parsimoniously, we assume that these tusks 12455 are homologous to those of Pantylus, so we have scored *Sparodus as possessing a posterior 12456 coronoid and fangs on it (see POST COR 2 below) and have scored all other coronoid 12457 characters as unknown.

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12458 As Stegotretus had coronoid tusks that look homologous to those of Pantylus and 12459 *Sparodus (see POST COR 2), we have assigned state 0 to Stegotretus as well. 12460 It is not clear which coronoid(s) is/are preserved in the *Goreville microsaur 12461 (Lombard & Bolt, 1999), but the posterior one is probably the safest bet because it is the most 12462 common one to occur in complete specimens of other OTUs. 12463 Similarly, Diceratosaurus has two toothrows in each lower jaw ramus, and sutures are 12464 not visible (D. M., pers. obs. of CM 29593, CM 29876 and CM 34668); because they extend 12465 equally far caudally, we assign the lingual one to the posterior coronoid. 12466 12467 176. POST COR 2: Posterior coronoid with (0) or without (1) fangs comparable in size to 12468 or larger than marginal dentary teeth. 12469 RC07 copied the scores of Ahlberg & Clack (1998), but used a different definition of 12470 “fangs”. Character 15 of Ahlberg & Clack (1998: 43) reads: “Fangs on posterior coronoid 12471 recognisable because much bigger than marginal teeth: yes (0); no (1).” Under the definition 12472 of RC07, Ventastega has state 0, because the largest two alveoli on the posterior coronoid are 12473 much larger than most and larger than most or all alveoli on the dentary (Ahlberg & Clack, 12474 1998: fig. 14B), in addition to being much larger than all other alveoli on the posterior 12475 coronoid itself. They are part of the toothrow on that bone, but this is also the case for the 12476 considerably larger fang pairs on the other two coronoids, which were scored as fangs. 12477 State 0 makes a surprise appearance in AMNH 4565, the type specimen of 12478 Trimerorhachis insignis (D. M., pers. obs.): the caudalmost member of the denticle field 12479 reaches the size of a dentary tooth. This is not apparent from the illustration of this specimen 12480 – or at least a specimen with the same number – by Milner & Schoch (2013: fig. 7C), where 12481 the entire field is only shown as black spots symbolizing alveoli, or in their reconstruction 12482 (fig. 7B). As explained under MID COR 2, we have scored Trimerorhachis as possessing 12483 state 0. 12484 Boy (1986: fig. 15b) showed one tooth on the posterior coronoid of 12485 Schoenfelderpeton; he called it “a large denticle” on p. 154, but added that it is “not smaller 12486 than the dentary teeth”. It is thus large enough to count as state 0 of this character. 12487 Unfortunately it is not clear if the preservation of that specimen is good enough to rule out a 12488 toothrow (POST COR 4(0)), but in the drawing the sutures between the dentary, the posterior 12489 coronoid and the prearticular are shown as unbroken lines well anterior (mesial) to the tooth, 12490 implying that the space where a toothrow would have one or two alveoli is preserved and does 12491 not bear teeth. We have scored state 0 for Schoenfelderpeton. 12492 State 0 is moreover found in Pantylus, Stegotretus and *Sparodus (see POST COR 1 12493 above). 12494 Whatcheeria (Lombard & Bolt, 2006) and Doleserpeton (Sigurdsen & Bolt, 2010) 12495 have state 1, as do Brachydectes (Pardo & Anderson, 2016) and Diceratosaurus (see POST 12496 COR 1). 12497 Under the present definition, at least the first two teeth on the posterior coronoid of 12498 *Densignathus are fangs (Daeschler, 2000: fig. 2). 12499 We have scored *Elginerpeton as unknown (see MID COR 2), although most of the 12500 toothrow (POST COR 4) counts as fangs under the definition used here. 12501 12502 177. POST COR 3: Posterior coronoid with (0) or without (1) small teeth (denticles) 12503 forming continuous shagreen or discrete patches and the basal diameter and/or height of 12504 which is less than 30% of that of adjacent marginal dentary teeth. 12505 Baphetes has state 0 (Milner, Milner & Walsh, 2009). So do Dendrerpetidae (Godfrey, 12506 Fiorillo & Carroll, 1987) and Pantylus (see POST COR 1 above).

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12507 Doleserpeton (Sigurdsen & Bolt, 2010), Diadectes (Berman, Sumida & Martens, 12508 1998: fig. 11), Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015) and Brachydectes 12509 (Pardo & Anderson, 2016) show state 1. 12510 Colosteus may have a double toothrow like *Diploradus; whether additional denticles 12511 were present is not clear from the published drawing (Hook, 1983: fig. 9). Ignoring the size 12512 criterion (see ANT COR 3 above), we have therefore scored Colosteus as unknown. 12513 12514 178. POST COR 4: Posterior coronoid with (0) or without (1) anteroposterior tooth row 12515 orientated sub-parallel to marginal dentary teeth and the basal diameter and/or height 12516 of which is 30% or greater than that of marginal teeth and twice or more that of 12517 denticles, if present. 12518 Greererpeton has a row of three fairly large teeth and thus state 0 (Bolt & Lombard, 12519 2001). 12520 Colosteus lacks that row, but may have a double row of smaller teeth like *Diploradus 12521 (Hook, 1983: fig. 9; see POST COR 3 immediately above); we have scored it as unknown. 12522 Trimerorhachis (Milner & Schoch, 2013; D. M., pers. obs. of AMNH 4565) and 12523 Doleserpeton (Sigurdsen & Bolt, 2010) have state 1, as do Anthracosaurus (Panchen, 1977: 12524 fig. 10), Limnoscelis (Reisz, 2007; Berman, Reisz & Scott, 2010), Rhynchonkos 12525 (Szostakiwskyj, Pardo & Anderson, 2015) and Brachydectes (Pardo & Anderson, 2016). 12526 Pantylus has state 0 (Romer, 1969; CG78 – at least the labialmost seven teeth may be 12527 considered a row), as do Batrachiderpeton (Bossy & Milner, 1998 – two rows surrounding a 12528 denticle field) and Diceratosaurus (see POST COR 1 above). 12529 *Glanochthon is polymorphic, with *G. latirostris having state 1 and *G. angusta 12530 having state 0 (Boy, 1993; Schoch & Witzmann, 2009b). 12531 *Lydekkerina appears to be polymorphic as well (Hewison, 2007). 12532 12533 179. POST COR 5-7: Posterior coronoid without posterodorsal process (0); with a 12534 process that does not contribute to the tallest point of lateral margin of adductor fossa 12535 (1); or with a process that does (2) (ordered). This is a continuous character (gradual 12536 enlargement of the posterodorsal process). 12537 Whatcheeria has state 2 (Lombard & Bolt, 2006), and so do Isodectes (D. M., pers. 12538 obs. of unnumbered MCZ cast of AMNH 6935 before etching), Ecolsonia (D. M., pers. obs. 12539 of CM 38024), Doleserpeton (Sigurdsen & Bolt, 2010: fig. 3C), Brachydectes (Pardo & 12540 Anderson, 2016) and *Nigerpeton (D. M., pers. obs. of MNN MOR 70). 12541 Cochleosaurus has state 1 (Sequeira, 2004), as do Limnoscelis (Reisz, 2007) and 12542 Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015). 12543 State 0 is found in Trimerorhachis (Milner & Schoch, 2013; D. M., pers. obs. of 12544 AMNH 4565). 12545 Gephyrostegus has state 1 or 2 (Klembara et al., 2014: fig. 3, 6). 12546 We follow the text (p. 509) rather than the label in fig. 4D of Schoch & Rubidge 12547 (2005) in scoring state 2 for *Micropholis. 12548 Hewison (2007) claimed state 0 for *Lydekkerina. The accompanying reconstruction 12549 drawing (Hewison, 2007: fig. 34), however, shows state 2, even though the process is very 12550 low. 12551 The lower jaw of *Neopteroplax is so strongly C-shaped that the meaning of “tallest 12552 point” is unclear. Measuring more or less along the curve, we have scored state 2, in keeping 12553 with the fact that the surangular crest is unusually low for an anthracosaur (Romer, 1963: 429, 12554 fig. 6). 12555 12556

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12557 180. POST COR 6: Posterior coronoid exposed in lateral view: no (0); yes (1). 12558 Baphetes has state 0 (Milner, Milner & Walsh, 2009). So do Edops (as far as D. M. 12559 can tell from pers. obs. of MCZ 1378, where the area is partly covered by upper-jaw 12560 fragments), Cochleosaurus (Sequeira, 2004), Limnoscelis (Reisz, 2007; Berman, Reisz & 12561 Scott, 2010), Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015) and Tseajaia (Berman, 12562 Reisz & Scott, 2010). 12563 Phonerpeton (D. M., pers. obs. of MCZ 1414), Ecolsonia (D. M., pers. obs. of CM 12564 38024), Doleserpeton (Sigurdsen & Bolt, 2010: fig. 3C), Pantylus (Romer, 1969: 24), 12565 Brachydectes (Pardo & Anderson, 2016), Orobates (Berman, Reisz & Scott, 2010) and 12566 *Nigerpeton (D. M., pers. obs. of MNN MOR 70) show state 1. 12567 We follow the text (p. 509) rather than the label in fig. 4D of Schoch & Rubidge 12568 (2005) in scoring state 2 for *Micropholis. 12569 12570 181. ADD FOS 1: Adductor fossa facing dorsally (0) or lingually (1). This is actually a 12571 continuous character, and it is not clear where the line is supposed to be drawn. Fairly much is 12572 visible of the adductor fossa of Whatcheeria in medial view, yet Lombard & Bolt (2006: 26f.) 12573 stated that “[t]he adductor fossa opens mostly dorsally, as in other early tetrapods and the 12574 osteolepiform sarcopterygians related to them”, in other words counting Whatcheeria as 12575 possessing state 0 (as scored by RC07). 12576 Even so, state 1 is found in Greererpeton (Bolt & Lombard, 2001), Baphetes (Milner, 12577 Milner & Walsh, 2009), Doleserpeton (Sigurdsen & Bolt, 2010), Lethiscus (Pardo et al., 2017 12578 – contrary to their matrix), and Eocaecilia (Jenkins, Walsh & Carroll, 2007), although we 12579 wonder if the latter should be scored as inapplicable because its subtemporal fenestra faces 12580 labioventrally rather than just ventrally. 12581 Yet, state 0 occurs in Albanerpetidae (Albanerpeton inexpectatum: Estes & 12582 Hoffstetter, 1976: pl. VII; Gardner, 2001: fig. 5), Batropetes (Glienke, 2013, 2015), Pantylus 12583 (Romer, 1969: fig. 15), Rhynchonkos (Szostakiwskyj, Pardo & Anderson, 2015: fig. 5D – the 12584 labial rim is drawn out into a tall crest, but the lingual rim is straight rather than embayed 12585 ventrally), Brachydectes (Pardo & Anderson, 2016), Batrachiderpeton (Bossy & Milner, 12586 1998), Diplocaulus (Douthitt, 1917), *Carrolla (Maddin, Olori & Anderson, 2011) and 12587 *Chelotriton (Schoch, Poschmann & Kupfer, 2015). 12588 Following the reconstructions in CG78: fig. 114, we have also tentatively assigned 12589 state 0 to Hapsidopareion (which was scored as unknown in RC07), Micraroter, 12590 Cardiocephalus and Euryodus, where the labial rim of the adductor fossa is much taller than 12591 the lingual one only because of the tall coronoid process, while the lingual rim is more or less 12592 on the same level with the articular and the toothrow. 12593 Bystrow (1944: fig. 6) showed state 0 in Kotlassia as well. Note that this is not shared 12594 by *Karpinskiosaurus (Klembara, 2011: fig. 9D, E). 12595 Unknown in Stegotretus (Berman, Eberth & Brinkman, 1988). 12596 *Lydekkerina appears to change from state 1 (Jeannot, Damiani & Rubidge, 2006: fig. 12597 4D) to state 0 as seen in Whatcheeria (Hewison, 2007: fig. 34) in ontogeny. We have scored 12598 state 0. 12599 12600 182. TEETH 1: Marginal tooth pedicely at any point in ontogeny: absent (0); present (1). 12601 This character is usually difficult to score in small animals unless sections and electron 12602 micrographs are made – or unless the tooth crowns have fallen off post mortem, leaving the 12603 pedicels in place (a very common occurrence in lissamphibian fossils). When the tooth 12604 crowns are in place, ambiguity is common. As an example, there is a consensus (Clack & 12605 Milner, 2010: 288, fig. 6, 8; and references therein) that Platyrhinops shows state 0 (as scored 12606 by RC07 – Pardo, Small & Huttenlocker [2017: supplementary information part E] mentioned

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12607 state 1 in passing, but this is an error). Yet, the lingual side of CM 72646 (a natural mold of 12608 the mesial part of a lower jaw; D. M., pers. obs.) has two mesiodistal breaks, one distal to the 12609 other, that run through several teeth each, giving the impression of pedicely at first glance. 12610 These breaks, however, continue through the matrix between the teeth and have crooked, 12611 jagged, parallel edges instead of straight or rounded smooth ones. They probably follow, more 12612 or less, the labial jaw margin, which is much taller than the lingual one; the labial side of the 12613 specimen shows no breaks and preserves only the tips of the teeth. In a smaller specimen, 12614 where the edges of the breaks would be more difficult to see and/or there would be less space 12615 between the teeth, it might not be possible to determine whether the teeth were pedicellate. 12616 Most OTUs that are potentially relevant to lissamphibian origins remain to be 12617 investigated. 12618 We have added the specification about ontogeny because pedicely often appears 12619 during lissamphibian ontogeny and is commonly absent in neotenic salamanders. 12620 Bolt (1979: 545) wrote about the teeth of Amphibamus: “Some appear to be 12621 pedicellate (see Fig. 8 and discussion below), although it is difficult to be sure of this on the 12622 basis of a cast.” The cited fig. 8 shows what looks at least as much like a break as like an 12623 unmineralized zone. We therefore follow Sigurdsen & Bolt (2010) and Sigurdsen & Green 12624 (2011: appendix 2) in scoring Amphibamus as unknown. 12625 Apateon and Schoenfelderpeton were scored as unknown, but the only published 12626 report of pedicely in any branchiosaurid specimen (Apateon: Schoch & Carroll, 2003) looks 12627 very much like a preservational artefact to us. We have therefore scored both taxa as having 12628 state 0. 12629 We have kept state 0 for Diceratosaurus, but it is noteworthy that each of its teeth is 12630 ringed by a constriction near the tip; postmortem breakage at this point, while by no means 12631 universal within an individual, appears to be common (D. M., pers. obs. of several CM 12632 specimens). Indeed, all marginal teeth of MB.Am.778 (D. M., pers. obs.) are broken at what 12633 seems to be the same height, making at least the anatomical left side look like most jaw 12634 specimens of fossil lissamphibians or Doleserpeton. 12635 The mode of preservation suggests state 0 in Lethiscus and *Coloraderpeton (Pardo et 12636 al., 2017). 12637 Carroll (1998a: fig. 4B, 8A) illustrated a dentary and maxillae of Oestocephalus where 12638 many teeth appear to be broken at the same level, as if the crowns had fallen off of pedicels, 12639 and mentioned this similarity on p. 158. We have scored Oestocephalus as unknown, even 12640 though other specimens (such as CM 29596, CM 29891 and CM 68353; D. M., pers. obs.) do 12641 not show evidence of pedicely. 12642 Germain (2008b) cautiously suggested on the basis of electron micrographs that the 12643 teeth of Phlegethontia could be pedicellate, interpreting two possible breaks as the separation 12644 between tip and pedicel and between tooth and jawbone. We have therefore scored it as 12645 unknown. 12646 Notobatrachus has state 0 (Báez & Nicoli, 2004), a likely reversal also found in the 12647 **pipoids and **Ascaphus. We have further assigned state 0 to *Liaobatrachus, where all 12648 tooth crowns appear to be preserved and there is no evidence for pedicels (figures in Dong et 12649 al., 2013), although Dong et al. (2013), surprisingly, did not mention this question at all. 12650 Anderson et al. (2008a) reported pedicely in *Gerobatrachus. However, as pointed out 12651 previously (Marjanović & Laurin, 2008), not one of the teeth is preserved as a lone pedicel – 12652 there are only complete teeth and empty alveoli. Given the facts that the resolution of the 12653 photo (fig. 3a) is too low to tell, that we have not seen the specimen (the forthcoming detailed 12654 description by Anderson et al. will doubtless provide additional information) and that the 12655 single known specimen does not provide ontogenetic information, we have scored it as 12656 unknown, even though pedicellate teeth would not be surprising in a close relative of

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12657 Doleserpeton (where they are indeed present, as scored by RC07 [Bolt, 1991: fig. 4; 12658 Sigurdsen & Bolt, 2010]) – and even though Sigurdsen & Bolt (2010), who had seen the 12659 specimen, considered it to lack pedicely. – Very recently, Pardo, Small & Huttenlocker (2017: 12660 supplementary information part E) reported that “[p]edicellate morphology, but no clear 12661 dividing zone between pedicel and crown, is seen in […] Gerobatrachus”, which – in the 12662 absence of ontogenetic information – confirms that the correct score is unknown. 12663 Although most tooth crowns are not preserved, *Saharastega has state 0 (D. M., pers. 12664 obs. of MNN MOR 73). 12665 We interpret the complete teeth and empty alveoli of *Sparodus (Carroll, 1988) as the 12666 unsurprising absence of pedicely in this “microsaur”. 12667 We follow Maddin, Olori & Anderson (2011) in interpreting the teeth of *Carrolla as 12668 possibly pedicellate, i.e., unknown for this character. 12669 One of the two lower jaws known from *Diploradus was not figured by Clack et al. 12670 (2016), so we do not know if it preserves complete teeth, which are shown in the 12671 reconstruction drawing (bottom of fig. 3d). The lower jaw of the type specimen, drawn above 12672 the reconstruction, seems to show all teeth broken at a similar level. We have scored the 12673 present character (as well as the other tooth-tip characters: TEETH 3, 6, 7, 10) as unknown. 12674 12675 183. TEETH 3: Maximum number of labiolingually arranged cusps per tooth at any 12676 point in ontogeny: one cusp (0); a ridge (1); two or three separate cusps (2) (ordered). 12677 We have ordered this partially meristic, partially continuous character. 12678 The original wording was: “Marginal teeth without (0) or with (1) two cuspules 12679 labiolingually arranged.” RC07 went on to state that the mesiodistally arranged cusps of 12680 Batropetes and Albanerpetidae “cannot be treated as an alternative state, as they are not 12681 readily comparable”. The two OTUs in question were scored 0. We do not understand why 12682 this condition was not treated as a third state of the same character (as done by Marjanović & 12683 Laurin, 2008); however, given the diversity of cusp arrangements among the OTUs of this 12684 matrix (especially the OTUs we have added), we have instead split this character, treating the 12685 number of labiolingually (TEETH 3) and mesiodistally arranged cusps (the new character 12686 TEETH 10) separately. Taxa that have two or more cusps in both directions do not occur in 12687 this matrix, but exist – “HOMO noſce Te ipsum”, as Linnaeus (1758) wrote (“**human, learn 12688 to know yourself”; capitals and italics in the original). 12689 State 1 occurs in “cf. Broiliellus sp.” according to Bolt (1977). Because Carroll (1964) 12690 explicitly reported state 0 for Broiliellus brevis, we think that the specimen Bolt described 12691 does not belong to the latter species, for which we have therefore kept the score of 0. State 1 12692 is, however, found in Cardiocephalus (Anderson & Reisz, 2003; Anderson, 2007b); as 12693 Anderson & Reisz (2003) pointed out, this state may be much more widespread but widely 12694 overlooked. 12695 State 2 is found in Diadectes (which has three cusps in a labiolingual row: Berman et 12696 al., 2004) and Orobates (Berman et al., 2004). 12697 Lethiscus has state 0 (Pardo et al., 2017). 12698 Unknown in Pederpes (Clack & Finney, 2005: 322). 12699 *Saharastega has state 0 (D. M., pers. obs. of MNN MOR 73). 12700 *Carrolla has two cusps per teeth; according to Maddin, Olori & Anderson (2011), it 12701 is not clear if they were arranged labiolingually or mesiodistally in life. As for character 12702 TEETH 10, we have therefore assigned state 0 or 2 to *Carrolla. 12703 Because crown-group salamanders replace mono- by bicuspid teeth during 12704 metamorphosis, we have scored the neotenic *Beiyanerpeton, which has monocuspid teeth, as 12705 unknown. 12706

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12707 184. TEETH 4: Conspicuous peak involving one or more anterior maxillary teeth: absent 12708 (0); present (1). 12709 Acanthostega has state 1: a clear caniniform region is preserved in the holotype of the 12710 only species, A. gunnari (D. M., pers. obs. of TMM 41766-1, a cast of MGUH VP 6033). This 12711 may also have been noted by Clack & Milner (2015: 18), who noted that the maxillary teeth 12712 are “largest at positions 7 to 11” (even though that contradicts their fig. 3A and 6A), and 12713 possibly by Porro, Rayfield & Clack (2015: 10). Given the (already scored) presence of state 12714 1 in Ventastega, Ichthyostega and Whatcheeria, this is less surprising than it might look at 12715 first glance. 12716 Chenoprosopus shares state 1 (Hook, 1993), and so do Cochleosaurus (Sequeira, 12717 2004), Acheloma (Dilkes & Reisz, 1987: fig. 3), and Phonerpeton (Dilkes, 1990: fig. 1) as 12718 well as Discosauriscus (borderline: Klembara, 1997), Ariekanerpeton and Utegenia (Bulanov, 12719 2003; figures in Klembara & Ruta, 2004a, 2005a). Bruktererpeton (Boy & Bandel, 1973) and 12720 Hapsidopareion (CG87: fig. 14D) have a weak version of state 1. 12721 Cardiocephalus has state 0 (CG78), as do Lethiscus (Anderson, Carroll & Rowe, 12722 2003; Pardo et al., 2017) and Vieraella (Báez & Basso, 1996). 12723 Euryodus is polymorphic; whether the caniniform tooth of one of the two species 12724 counts as “anterior” is debatable, but the number of maxillary teeth rostral to it is low. 12725 Scincosaurus is unknown for this character (Milner & Ruta, 2009). 12726 We have assigned state 0 to *Nigerpeton because its huge maxillary tusks are not part 12727 of the marginal toothrow in MNN MOR 70 (D. M., pers. obs.). This amounts, however, to an 12728 ontogenetic hypothesis: the maxillary tusks are part of the toothrow in the smaller MNN 12729 MOR 69 and not preserved in the intermediate-sized MNN MOR 108 (D. M., pers. obs.). 12730 Judging from the reconstruction by Klembara (2011: fig. 3B), *Karpinskiosaurus had 12731 a very prominent caniniform region (state 1) in the adult stage; unfortunately, neither 12732 Klembara (2011) nor Bulanov (2003) mentioned this character at all, and no photographs or 12733 specimen drawings that would show it appear to have been published – the published 12734 illustrations (Bulanov, 2003; Klembara, 2011) all show younger individuals which had state 12735 0. We have provisionally scored state 1. 12736 States 0 and 1 appear to be found in different individuals of *Lydekkerina (Jeannot, 12737 Damiani & Rubidge, 2006; Hewison, 2007). 12738 Unclear in the *St. Louis tetrapod; it is even possible that there was a caniniform 12739 region on the left but not the right side of the only known specimen (Clack et al., 2012b: fig. 12740 2A; D. M., pers. obs. of MB.Am.1441.2). We have scored it as unknown. 12741 12742 185. TEETH 5: Dentary teeth larger than maxillary teeth: no (0); yes (1). 12743 We have scored Crassigyrinus as having state 1 because almost all dentary teeth are 12744 larger than all maxillary ones (Clack, 1998). A very similar condition, which we have also 12745 scored as state 1, is found in Dendrerpetidae (Godfrey, Fiorillo & Carroll, 1987) and 12746 Caerorhachis (Ruta, Milner & Coates, 2002). 12747 In Neldasaurus, only ⅓ to ½ of its dentary teeth are larger than the maxillary teeth 12748 (Chase, 1965: fig. 2, 6), but we count this as state 1 because the larger teeth do not form a 12749 specialized caniniform (or other) region. 12750 Trimerorhachis has state 1 (Case, 1935: fig. 13, pl. VII; Milner & Schoch, 2013), as 12751 does Platyrhinops (Clack & Milner, 2010). 12752 “The individual teeth are definitely longer and have a greater diameter than those of 12753 the upper jaw” (CG78); we have accordingly scored state 1 for Micraroter. 12754 State 0 is shown for Bruktererpeton in table 7 of Boy & Bandel (1973). It is also 12755 present in Solenodonsaurus (where the maxillary teeth are indeed larger than the dentary 12756 ones: Danto, Witzmann & Müller, 2012), Scincosaurus (from comparing fig. 2A and fig. 4 of

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12757 Milner & Ruta, 2009), Diceratosaurus (D. M., pers. obs. of CM 67169), Lethiscus (Pardo et 12758 al., 2017), *Nigerpeton (D. M., pers. obs. of MNN MOR 70) and *Saharastega (D. M., pers. 12759 obs. of MNN MOR 73). 12760 Following Bystrow (1944) and DEN 7 (see above), we have scored state 0 for 12761 Kotlassia. 12762 Orobates was scored as polymorphic in RC07, presumably due to its long incisiform 12763 dentary teeth that are longer than the maxillary teeth (and oppose similarly long incisiform 12764 teeth on the premaxilla). We exclude incisiform teeth (a very rare specialization in this 12765 matrix) from consideration and therefore score Orobates as possessing only state 0. 12766 Sequeira & Milner (1993) reconstructed Capetus with a mild version of state 1 (in 12767 more than half of the toothrow). 12768 *Crinodon is apparently borderline; we have scored it as unknown. 12769 The dentary teeth of *Palatinerpeton (Boy, 1996) vary in size, being smaller opposite 12770 the caniniform region of the maxilla and premaxilla but larger elsewhere. Many are larger 12771 than most of its right maxillary teeth, but this may not hold for the left side; we have scored 12772 *Palatinerpeton as unknown. 12773 The few exposed dentary teeth of *Erpetosaurus are no larger than the tiny maxillary 12774 teeth (Milner & Sequeira, 2011); however, the dentary teeth of the same region of Isodectes 12775 are no larger than the maxillary teeth either, while the remaining ones are easily twice as large 12776 (Sequeira, 1998), so we have scored *Erpetosaurus as unknown. 12777 State 1 is strongly suggested for *Pholidogaster by Romer (1964: fig. 3, alone and in 12778 comparison with pl. 1); we have scored *Pholidogaster accordingly, even though Romer 12779 (1964) nowhere mentioned this character in the text. 12780 Unless the distalmost teeth in the right maxilla are all much less far erupted than the 12781 dentary teeth opposite them, the *St. Louis tetrapod has state 1; the discrepancy is larger than 12782 shown by Clack et al. (2012b: fig. 2A, B), because those are ventral and ventrolabial views 12783 rather than strictly labial ones (D. M., pers. obs. of MB.Am.1441.2). However, the 12784 discrepancy is still noticeably smaller than in Greererpeton (let alone Colosteus; Smithson, 12785 1982; Hook, 1983); in addition, the dentary teeth are distinctly smaller than the ectopterygoid 12786 fang next to them, quite unlike in Greererpeton and Colosteus. In order to emphasize this 12787 difference, we have accepted the claim of “no clear discrepancy in tooth size between upper 12788 and lower jaw rami” (Clack et al., 2012b: 22) and scored state 0. 12789 12790 186. TEETH 6: Marginal tooth crowns chisel-tipped: no (0); yes (1). 12791 Lethiscus has state 0 (Pardo et al., 2017), as does *Saharastega (D. M., pers. obs. of 12792 MNN MOR 73). 12793 Oestocephalus was scored in RC07 as having state 0 or 1; it has 0 and 1, respectively, 12794 in different specimens (species?) from different sites (Carroll, 1998a), so we have scored 12795 polymorphism. 12796 12797 187. TEETH 7: Marginal tooth crowns without (0) or with (1) ‘dimple’. 12798 *Saharastega has state 0 (D. M., pers. obs. of MNN MOR 73). 12799 12800 188. TEETH 8: Marginal tooth crowns robust and conical: absent (0); present (1). Such 12801 teeth require so much space that not many of them fit into a maxilla (apparently never more 12802 than 12 or perhaps 15), so that state 1 makes TEETH 9 inapplicable. Simply adding this state 12803 to TEETH 9, however, is not an option: in Batropetes, each maxilla bears 4 to 6 mostly 12804 cylindrical teeth (mostly or entirely individual variation) and is small enough to only have 12805 space for 10, yet the teeth are thin and cylindrical except for an expanded, tricuspid tip 12806 (Glienke, 2013, 2015); in Brachydectes and *Carrolla, each maxilla holds only 5–8 relatively

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12807 enormous teeth that are pointed but recurved and much taller (thus thinner) than in taxa with 12808 state 1 (Maddin, Olori & Anderson, 2011; Pardo & Anderson, 2016); in Scincosaurus, there 12809 are 8 slender, stalked teeth per maxilla (Bossy & Milner, 1998; Milner & Ruta, 2009); 12810 Keraterpeton, Batrachiderpeton and Diceratosaurus have similarly few teeth of entirely 12811 plesiomorphic shape and size (Bossy & Milner, 1998; D. M., pers. obs. of Diceratosaurus 12812 specimens), while those of Diploceraspis are large and have an intermediate shape 12813 (Beerbower, 1963) – when teeth are very few in number, they are not necessarily robust and 12814 conical. 12815 Carroll (1969b) reconstructed Acherontiscus as having 15 maxillary teeth; the 12816 preserved teeth – the last 4 – are robust and bluntly conical. We count this as state 1. 12817 12818 189. TEETH 9: Number of maxillary teeth greater than 40 (0), between 30 and 40 (1), 12819 between 13 and 29 (2); smaller than 13 (3) (ordered). As this is a meristic (practically 12820 continuous) character, we have ordered it. Indeed, unambiguous changes between states 0 and 12821 2 are seen only three times in the shortest trees from Analysis R4, and state 3 only changes to 12822 (once) and from state 2 (twice), while the character as a whole has 48 steps. 12823 Even apart from this, the distribution of the states is nowhere near random. State 1 or 12824 higher is an autapomorphy (reversed a minimum of nine times) of the smallest clade that 12825 contains *Ymeria and the crown-group; state 2 is rare in temnospondyls, and state 3 is limited 12826 to two clades of amphibians, while almost all members of the seymouriamorph- 12827 diadectomorph-amniote-amphibian clade have state 2 or 3 (where applicable – see above). 12828 Clearly, the claim that this character contains “little phylogenetic signal” (RC07) is not 12829 tenable. 12830 State 3 is new, and found in Batropetes, Brachydectes, Scincosaurus, Keraterpeton, 12831 Batrachiderpeton, Diceratosaurus, Diploceraspis and *Carrolla (see TEETH 8); state 2 of 12832 RC07 was simply “smaller than 30”. The cutoff is chosen so that Albanerpeton inexpectatum 12833 retains state 2; it has 15 to 23 teeth per maxilla (Estes & Hoffstetter, 1976: 312), while no 12834 OTU in this matrix seems to have 13 or 14. 12835 Colosteus has at least 34 maxillary teeth (Hook, 1983: fig. 1), giving it state 0 or 1. 12836 Isodectes seems to have state 1 or 2 (Sequeira, 1998: 252 and fig. 9B, C). 12837 Trimerorhachis has state 0 (Milner & Schoch, 2013). 12838 Acheloma seems to have had 30 maxillary teeth at the most (Polley & Reisz, 2011), 12839 giving it state 1 or 2. 12840 Micromelerpeton was scored as unknown in RC07. Boy (1972: 25) reported state 1, 12841 agreeing with the reconstruction (fig. 5) and possibly with a specimen drawing (fig. 4p) in the 12842 same paper, so we have scored state 1. 12843 Apateon, too, was scored as unknown. Schoch & Milner (2008: fig. 4E) reconstructed 12844 A. pedestris with 25 teeth on one maxilla and 26 on the other; this resolves to state 2. Boy 12845 (1987: 84; translated by D. M.), however, ascribed “maximally 23–35 teeth” to A. pedestris, 12846 spanning states 1 and 2. State 2 was also reported for A. dracyi (as “A. dracyiformis”) by Boy 12847 (1986: 158, 1987: 90), although this may be due to skeletal immaturity (the maxilla is very 12848 short); state 1 was confirmed for A. caducus by Boy (1987: 88 – “Long, slender maxilla […] 12849 bears more than 30 teeth”; translated by D. M.). Metamorphosed A. gracilis, however, has 12850 state 0 with about 50 maxillary teeth (Werneburg, 1991: 82); indeed, the maxilla grows with 12851 positive allometry (Werneburg, 1991: 82). We have scored state 0, because A. gracilis is the 12852 only species of A. known to undergo metamorphosis. 12853 Leptorophus tener has state 0 or 1: “maxilla with maximally 37–42 teeth” (Boy, 1986: 12854 139; translated by D. M.). L. raischi has “space for about 30 teeth” in the maxilla (Schoch, 12855 2014a: 231), which would translate to state 1 or 2. Because the shorter snout of L. raischi 12856 compared to L. tener is a sign of relative skeletal immaturity and because polymorphism with

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12857 partial uncertainty is impossible in PAUP*, we have ignored the possibility of state 2 and 12858 have scored Leptorophus as having states 0 and 1; Schoch (2014a) pointed out, however, that 12859 the teeth of L. raischi are larger than those of L. tener, so if the former continued to grow to 12860 the latter’s snout length, it would still have fewer teeth. 12861 Bruktererpeton has “ca. 40 teeth” in the maxilla, giving it state 0 or 1 (Boy & Bandel, 12862 1973: 50, translation by D. M.). 12863 In Kotlassia, “the number of marginal teeth remains uncertain” due to incomplete 12864 preservation and incompetent preparation (Bulanov, 2003); Kotlassia was accordingly scored 12865 as unknown. However, a few maxillary teeth remain in the holotype (Bulanov, 2003); we 12866 therefore trust Bystrow’s (1944: fig. 2) reconstruction of state 1 even though the exact number 12867 of maxillary teeth is uncertain. 12868 State 2 is found in Cochleosaurus (Sequeira, 2004), Valdotriton (Evans & Milner, 12869 1996), apparently Lethiscus (Pardo et al., 2017) and Leptoropha (Bulanov, 2003). 12870 *Micropholis is polymorphic, showing states 0 and 1 (Schoch & Rubidge, 2005). 12871 We estimate 20 to 25 maxillary teeth, thus state 2, for the *Goreville microsaur 12872 (Lombard & Bolt, 1999: fig. 2). 12873 We have scored *Sigournea as possessing state 0. The maxilla is unknown, but the 12874 dentary has so many tooth positions (88) that any other state would require the maxillary teeth 12875 to be implausibly large and/or widely spaced (Bolt & Lombard, 2006). The same holds for the 12876 98 to 100 tooth positions in the dentary of *Doragnathus (Smithson, 1980) and the about 90 12877 to 100 known tooth positions in the dentary of *Elginerpeton (Ahlberg, 1995; Ahlberg & 12878 Clack, 1998; Ahlberg, Friedman & Blom, 2005). 12879 Because of its paedomorphically short maxilla, we have scored *Beiyanerpeton as 12880 having state 0 or the observed uncertainty of state 1 or 2. 12881 States 1 and 2 are known in adult *Glanochthon (Schoch & Witzmann, 2009b: figs. 3, 12882 4). 12883 Panchen (1964: fig. 13) reconstructed space for 32 teeth in *Palaeoherpeton; we have 12884 cautiously scored state 1 or 2. 12885 12886 190. TEETH 10: Maximum number of mesiodistally arranged cusps per marginal tooth 12887 at any point in ontogeny: 1 (0), lozenge-shaped crown with mesial and distal ridges that 12888 lead to the mesial and distal corners or very short cusps (1), 3 (2), more (3) (ordered). 12889 This character is ordered for the same reasons as TEETH 3, from which it is split. 12890 State 0 is the plesiomorphy, found in all OTUs that preserve tooth crowns (including 12891 *Saharastega: D. M., pers. obs. of MNN MOR 73) except for the following: 12892 State 1 is found in Discosauriscus (at least in the tooth in the third alveolus in fig. 10 12893 of Klembara 1997) and Scincosaurus (Milner & Ruta, 2009). 12894 State 2 occurs in Batropetes (Carroll, 1991; Glienke, 2013, 2015) and 12895 *Tungussogyrinus (Werneburg, 2009). 12896 State 3 is limited to Leptoropha and Microphon (Bulanov, 2003) in the present matrix. 12897 Albanerpetidae is polymorphic, with Anoualerpeton possessing state 1 (Gardner, 12898 Evans & Sigogneau-Russell, 2003) and its sister-group, composed of Celtedens and 12899 Albanerpeton, showing state 2 (e.g. Estes & Hoffstetter, 1976; Fox & Naylor, 1982; 12900 McGowan, 2002). 12901 Westlothiana shows partial uncertainty between states 0 and 1 (Smithson et al., 1994). 12902 *Carrolla has two cusps per tooth; according to Maddin, Olori & Anderson (2011), it 12903 is not clear if they were arranged labiolingually or mesiodistally in life. As for character 12904 TEETH 3, we have therefore assigned state 0 or 2 to *Carrolla (3 cusps are the closest 12905 condition to 2). 12906

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12907 191. CLE 1: T-shaped dorsal expansion of cleithrum: absent (0); present (1). 12908 State 0 is known in Ventastega (Ahlberg et al., 2008), Baphetes (Milner & Lindsay, 12909 1998), Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of CM 81512 and CM 12910 81430) and Doleserpeton (Sigurdsen & Bolt, 2010). 12911 CG78 (p. 60, fig. 31) identified an L- to C-shaped bone as the cleithrum in 12912 Cardiocephalus. We do not understand why and have kept the scores of all three CLE 12913 characters as unknown. It might be a clavicle (if so, we still cannot score the only CLA 12914 character) or an unrelated part of the fissure-fill taphocoenosis at Fort Sill. 12915 12916 192. CLE 2: Cleithrum with (0) or without (1) postbranchial lamina. Probably unlike 12917 RC07, we count everything that is primarily homologous to a postbranchial lamina as state 0; 12918 this includes laminae that may have the wrong size or shape to function as a postbranchial 12919 lamina, so we do not hypothesize on which of the taxa we have scored 0 actually possessed 12920 internal gills in life. What sizes and shapes are possible for a functional postbranchial lamina 12921 has not, to the best of our limited knowledge, ever been investigated; conversely, the lamina is 12922 clearly not necessary for internal gills to function – even the lamina “of Eusthenopteron is 12923 very narrow and poorly differentiated from the cleithral blade” (Ahlberg, 1998: 113). 12924 Moreover, cleithra of limbed vertebrates are almost never illustrated or described in cranial or 12925 caudal view (the postbranchial lamina is impossible to see in lateral view, and difficult or 12926 impossible to recognize in medial view at least in drawings); sometimes, like in the 12927 description of the postcranium of Greererpeton by Godfrey (1989), the lamina has been 12928 illustrated but not recognized (as previously noted by Lebedev & Coates, 1995, and Coates, 12929 1996). We suspect therefore that state 0 is more widespread than we have been able to score. 12930 Character 43 of Coates (1996) was called “Post-branchial lamina: present (0); absent 12931 (1)” in the character list (p. 417), but in the text Coates (1996: 400) specified “a broad 12932 postbranchial lamina (character 43)” (without attempting to define “broad”). This supports 12933 our interpretation that RC07 scored laminae that do not fulfill unspecified criteria of size 12934 and/or shape as state 1. 12935 Under our possibly expanded definition, state 0 is present in Ventastega (Ahlberg et 12936 al., 2008: fig. 2b, 3e – contradicting the text which evidently uses a stricter definition), 12937 Baphetes (Milner & Lindsay, 1998; Milner, Milner & Walsh, 2009), and Archeria (Pawley, 12938 2006: fig. 70-2.4); compare the conditions of Ichthyostega (Jarvik, 1996: pl. 45) and 12939 Greererpeton (Godfrey, 1989: fig. 17b), which were already scored 0. 12940 Ossinodus has a candidate lamina. Warren & Turner (2004) identified that lamina as 12941 the sutural surface for the clavicle; it is clear from Bishop (2014), however, that this can only 12942 be true for the ventralmost part, leaving the rest to function as a postbranchial lamina and us 12943 to score it as state 0. The similarity between the cleithra of Ossinodus (Warren & Turner, 12944 2004: fig. 9B, C; Bishop, 2014: fig. 8B, E) and Archeria (Pawley, 2006: fig. 70-2.4) is 12945 striking; contrast Eryops (Pawley & Warren, 2006: 4), which has state 1 as already scored. 12946 Crassigyrinus was scored as unknown in RC07. Laurin (2011: 57) wrote that it had a 12947 postbranchial lamina, citing Coates (1996) as his source, yet Coates (1996) did not mention 12948 Crassigyrinus in his discussion of the postbranchial lamina and scored it in his data matrix as 12949 lacking the lamina. Given that our definition of the postbranchial lamina is less strict than that 12950 of Coates (1996), we have kept the score as unknown. 12951 State 1 is preserved in Cochleosaurus (Sequeira, 2009: fig. 6, 7) and Doleserpeton 12952 (Sigurdsen & Green, 2011: appendix 2). In Gephyrostegus, state 1 seems to be preserved in 12953 TMM 41773-1, so we have scored state 1 as present, though crushing and the fact that this 12954 specimen is a cast leave doubts about this, in particular about the interpretation of the 12955 cleithrum as being preserved in medial view.

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12956 Clack & Finney (2005) stated that the postbranchial lamina is absent in Pederpes, and 12957 illustrated this with a cross-section of the cleithrum (fig. 11 B). It is not at all obvious from 12958 the figure (including the photo: fig. 11 A) or the text if the very tall ridge is medial (thus 12959 potentially a postbranchial lamina) or lateral; however, personal observation by D. M. of the 12960 only known specimen (GLAHMS 100815) on exhibit in the Hunterian Museum, Glasgow, 12961 shows that it is lateral, meaning that there is no postbranchial lamina, so the score of 1 in 12962 RC07 is correct despite the occurrence of state 0 in Whatcheeria and Ossinodus. 12963 Unknown (or at least not sufficiently well illustrated and described) in Proterogyrinus 12964 (Holmes, 1984), Pholiderpeton scutigerum (Clack, 1987b), Bruktererpeton (Boy & Bandel, 12965 1973), Kotlassia (Bystrow, 1944) and Adelogyrinus (Andrews & Carroll, 1991: 252). 12966 Perhaps surprisingly, *Casineria has state 0 (Fig. 7), which we have therefore scored. 12967 The condition appears to be quite similar to that seen in Archeria (Pawley, 2006: fig. 70-2.4); 12968 see Discussion: Phylogenetic relationships: The interrelationships of Anthracosuria, 12969 Silvanerpeton, Caerorhachis, Gephyrostegidae, Casineria and Temnospondyli. 12970 12971 193. CLE 3: Cleithrum co-ossified with scapulocoracoid: yes (0); no (1). 12972 State 0 is present in Ventastega (Ahlberg et al., 2008). 12973 Whatcheeria is polymorphic (Coates, 1996: 409). Surprisingly, so is Eryops (Pawley 12974 & Warren, 2006). 12975 Baphetes has state 1 (Milner & Lindsay, 1998; Milner, Milner & Walsh, 2009), as do 12976 Cochleosaurus (Sequeira, 2009) and Isodectes (D. M., pers. obs. of CM 81430). 12977 Inapplicable to salamanders, which lack cleithra entirely, and to aïstopods, which lack 12978 scapulocoracoids entirely. 12979 “In late adult individuals, the two bones are probably fused to each other” in 12980 *Sclerocephalus (Meckert, 1993: 123; translation by D. M.); we have stayed conservative and 12981 scored *Sclerocephalus as possessing state 1. 12982 12983 194. CLA 3: meet anteriorly: yes (0); no (1). 12984 State 0 occurs in Diadectes (Case, 1911: 79, fig. 26) and Orobates (Berman et al., 12985 2004: fig. 2B). It is most likely shared by Chenoprosopus, judging from the disarticulated 12986 clavicle of USNM 437646 (Hook, 1993: fig. 2; D. M., pers. obs.). 12987 State 1 is present in Ventastega (Ahlberg, Lukševičs & Lebedev, 1994; Ahlberg et al., 12988 2008). Baphetes shares state 1 (Milner & Lindsay, 1998), as do Cochleosaurus (Sequeira, 12989 2009), Isodectes (D. M., pers. obs. of USNM 4471, CM 81512 and CM 81430), Leptorophus 12990 (Werneburg, 2007b), Ossinodus (Bishop, 2014) and, judging from the shapes of clavicle and 12991 interclavicle, Doleserpeton (Sigurdsen & Bolt, 2010) and *Sparodus (Carroll, 1988). Clack & 12992 Milner (2010) implied it for Platyrhinops. 12993 Unclear in Kotlassia (Bystrow, 1944: fig. 15); best scored as unknown in 12994 *Chroniosaurus and *Bystrowiella (Witzmann & Schoch, 2017). 12995 Apparently unknown in Notobatrachus (Báez & Nicoli, 2004); *Liaobatrachus has 12996 state 0 (Dong et al., 2013). 12997 *Lydekkerina is polymorphic (Shishkin, Rubidge & Kitching, 1996; Pawley & 12998 Warren, 2005; Hewison, 2007: 42). 12999 13000 195. INTCLA 1-2: Interclavicle posterior margin not drawn out into parasternal process 13001 (0), with parasternal process that is not parallel-sided (1), or with elongate, slender 13002 process that is parallel-sided for most of its length (2) (unordered). Although called 13003 INTCLA 1 by RC07, this character is a composite of INTCLA 1 and INTCLA 2 of Ruta, 13004 Coates & Quicke (2003), which were still kept separate by Pawley (2006: 350). For the time

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13005 being, we have not ordered it because we have yet to compare the data on its changes in 13006 ontogeny and phylogeny. 13007 State 0 is found in Cochleosaurus (Sequeira, 2009) and Doleserpeton (Sigurdsen & 13008 Bolt, 2010). 13009 Ventastega (Ahlberg et al., 2008) and Batropetes (Glienke, 2013, 2015) have state 1. 13010 Limnoscelis (Kennedy, 2010) and Tseajaia (Moss, 1972) show state 2; the process has 13011 a unique club-shaped expansion at the caudal end, but is otherwise parallel-sided. 13012 Baphetes (Milner, Milner & Walsh, 2009: fig. 3A, 4B) and Hyloplesion (Olori, 2015: 13013 57) have state 1 or 2. 13014 13015 196. INTCLA 3: Interclavicle wider than long (excluding parasternal process, if present): 13016 absent (0); present (1). 13017 Ventastega (Ahlberg et al., 2008), Cochleosaurus (Sequeira, 2009) and Bruktererpeton 13018 (Boy & Bandel, 1973: fig. 10) have state 0. 13019 As reconstructed by Pawley & Warren (2006) and mentioned in the text of their 13020 publication, Eryops shows state 1. The fimbriate rostral margin indicates that growth may 13021 have continued till state 0 was reached, and indeed state 0 is not far away, but there is no 13022 evidence that this happened, the known individuals all seem well advanced in age, and the 13023 fimbriation is much weaker than in Microbrachis or Hyloplesion. We have therefore scored 13024 Eryops as indeed possessing state 1. 13025 State 1 is further present in Limnoscelis (Kennedy, 2010), Hyloplesion (CG78: fig. 13026 87B; Olori, 2015) and Orobates (Nyakatura et al., 2015: digital reconstruction). 13027 We have scored Schoenfelderpeton as unknown due to its pronounced 13028 paedomorphosis. 13029 State 1 was scored for Ossinodus in RC07, but as preserved (Warren & Turner, 2004) 13030 the incomplete interclavicle shows state 0; because of its broken margins we have scored it as 13031 unknown. 13032 13033 197. INTCLA 4: Caudal part of interclavicle (excluding parasternal process, if present) 13034 longer (0) or shorter (1) than cranial part. The original wording was: “Interclavicle 13035 rhomboidal with posterior part longer (0) or shorter (1) than anterior part”, but it is usually 13036 possible to distinguish the parts even when the interclavicle lacks the plesiomorphic deltoid 13037 shape, the boundary being the mediolateral line along which the interclavicle is widest. We 13038 have added the mention of the parasternal process. 13039 Ventastega (Ahlberg et al., 2008) and Limnoscelis (Kennedy, 2010) have state 0, as do 13040 Tuditanus and Pantylus (CG78) and Orobates (Nyakatura et al., 2015: digital reconstruction). 13041 Cochleosaurus shows a mild case of state 1 (Sequeira, 2009), as, surprisingly, 13042 Doleserpeton (Sigurdsen & Bolt, 2010) seems to. Eryops is an unambiguous example of state 13043 1, with the caudal part only about 2/3 as long as the cranial part (Pawley & Warren, 2006). 13044 State 1 is further found in Archeria (Romer, 1957: fig. 1C), Kotlassia (Bystrow, 1944: fig. 15) 13045 and Seymouria (White, 1939: fig. 21). 13046 *Sclerocephalus passes from state 0 to state 1 in ontogeny (Meckert, 1993: fig. 1, 4; 13047 Schoch & Witzmann, 2009a: fig. 6A, D, E). 13048 13049 198. INTCLA 5: Transversely elongate grooves and ridges on central part of interclavicle 13050 ventral surface: absent (0); present (1). 13051 Ventastega (Ahlberg et al., 2008), Chenoprosopus (Hook, 1993; D. M., pers. obs. of 13052 USNM 437646), Cochleosaurus (Sequeira, 2009), Trimerorhachis (Pawley, 2007) and 13053 Doleserpeton (Sigurdsen & Bolt, 2010) have state 0, as do Solenodonsaurus (Danto, 13054 Witzmann & Müller, 2012) and Limnoscelis (Kennedy, 2010).

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13055 Whatcheeria was scored 0 in RC07. We have changed it to unknown, because 13056 ornamentation is entirely absent not only on the skull but also on the shoulder girdle of 13057 Whatcheeria (Lombard & Bolt, 1995: 483–484), making state 0 predictable and thus this 13058 character inapplicable. 13059 State 1 is, surprisingly, found in Eryops (Pawley & Warren, 2006). 13060 Panchen (1975) described an interclavicle as belonging to *Pholidogaster even though 13061 it was isolated and not found at the type locality. Clack & Milner (2015: 49) pointed this out 13062 and added that this interclavicle “is unlike undisputed colosteid interclavicles in shape”, 13063 casting doubt on its referral. This refers to the fact that it has state INTCLA 4(0) (see above), 13064 the plesiomorphy, while the two other colosteids that preserve interclavicles – Colosteus and 13065 Greererpeton – have state 1. However, the interclavicle of the holotype, which is partially 13066 covered by the clavicles and partially preserved as an impression, does have state 0 of that 13067 character (Romer, 1964). This is not surprising for a colosteid that lies outside the smallest 13068 clade formed by Colosteus and Greererpeton. For the moment, we accept Panchen’s (1975) 13069 referral and have used the interclavicle he described to score *Pholidogaster where that of the 13070 holotype does not suffice; this concerns only the present character (state 0). 13071 13072 199. SCACOR 1: Separate scapular ossification: absent (0); present (1). As previously 13073 pointed out (e.g. Marjanović & Laurin, 2008: 185), ontogenetic fusion makes this character 13074 difficult to interpret. Also, the taxon sample is perhaps somewhat unfortunate – the 13075 salamanders in this matrix (Karaurus, Valdotriton, *Beiyanerpeton, *Pangerpeton and 13076 *Chelotriton) all have state 0, but **Kokartus, a close relative of Karaurus, shows state 1 in 13077 an apparently immature specimen (Averianov et al., 2008: 480, fig. 7B), as do adults of the 13078 extant paedomorphic salamanders **Amphiuma and **Siren (Goodrich, 1930). 13079 Nonetheless, we have scored Ventastega (Ahlberg et al., 2008), Platyrhinops (implied 13080 by Carroll, 1964, and Clack & Milner, 2010) and Micromelerpeton (implied by Boy, 1995: 13081 444) as possessing state 0. 13082 In contrast, we have not been able to find any mention of the endochondral shoulder 13083 girdle of Amphibamus in the literature (Carroll’s [1964] “Amphibamus lyelli” is Platyrhinops) 13084 and have therefore scored it as unknown. 13085 Where known (Celtedens: McGowan, 2002), albanerpetids have state 1. So do 13086 Eocaecilia (Jenkins, Walsh & Carroll, 2007), Diplocaulus (Douthitt, 1917) and Orobates 13087 (Nyakatura et al., 2015: digital model). 13088 In Bruktererpeton the condition is unknown because the region is entirely 13089 unossified (Boy & Bandel, 1973). 13090 Captorhinus was scored 0 in RC07. Fox & Bowman (1966) insisted several times that 13091 it has state 1, but provided no evidence other than a notch which supposedly marked the 13092 otherwise obliterated suture between the procoracoid and the metacoracoid. It is quite likely 13093 that Captorhinus changed from state 1 to state 0 in ontogeny, but in the absence of a reference 13094 for state 1, we have kept state 0. 13095 Unknown in Trimerorhachis, where of the entire scapulocoracoid only the central part 13096 of the scapula ever ossifies (Pawley, 2007), and in Brachydectes (Wellstead, 1991), where the 13097 same seems to be the case. Also unclear in Microbrachis, where a break in an unusually well 13098 ossified specimen may or may not correspond to a suture (Olori, 2015). 13099 Danto, Witzmann & Müller (2012) identified a small bone of Solenodonsaurus that, as 13100 far as preserved, does not participate in the glenoid as a coracoid would; despite this 13101 uncertainty, they scored Solenodonsaurus as having state 1 of this character. We side with the 13102 uncertainty of the text and fig. 4 and have scored Solenodonsaurus as unknown. 13103 Based on the report of a longitudinal groove which may be “a partially co-ossified 13104 suture” (Schoch & Rubidge, 2005: 511), we have assigned state 1 to *Micropholis.

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13105 200. SCACOR 2: Glenoid subterminal: yes (0); no (1). This character describes whether the 13106 coracoid part of the scapulocoracoid is at least partly ventral (state 1) or purely medial to the 13107 glenoid (state 0); it is not applicable to taxa with unossified , unless the clavicles and 13108 the interclavicle allow a 3D reconstruction. 13109 State 0 occurs in Ventastega (Ahlberg et al., 2008), Cochleosaurus (Sequeira, 2009), 13110 Doleserpeton (Sigurdsen & Bolt, 2010), Eoscopus (Daly, 1994: 16) and Diplocaulus 13111 (Williston, 1909), likely also in Apateon (Werneburg, 1991: fig. 5b). 13112 State 1 is found in Eryops (Pawley & Warren, 2006; D. M., pers. obs. of TMM 31227- 13113 14), Albanerpetidae (McGowan, 2002), Eocaecilia (Jenkins, Walsh & Carroll, 2007), 13114 Scincosaurus (Milner & Ruta, 2009), Orobates (Nyakatura et al., 2015: digital model) and 13115 Ossinodus (Warren & Turner, 2004: fig. 9I; Bishop, 2014: fig. 12). 13116 Glienke (2013: fig. 5K) reconstructed state 1 for Batropetes niederkirchensis; Glienke 13117 (2015: fig. 5B) reconstructed state 0 for B. palatinus; Glienke (2015: fig. 8G) reconstructed 13118 state 1 for B. appelensis. In B. niederkirchensis and B. palatinus, the coracoid portion is 13119 preserved and shows state 1, which may be due to diagenetic pressure; in B. appelensis, the 13120 coracoid portion was unossified, but the clavicles and the interclavicle allow a 3D 13121 reconstruction. It is not clear from Glienke (2015: fig. 5) or from MB.Am.1232 (D. M., pers. 13122 obs.) whether this is also the case for B. palatinus; for the time being, we have scored 13123 Batropetes as polymorphic. 13124 13125 201. SCACOR 3: Enlarged glenoid foramen: absent (0); present (1). “Loss of an enlarged 13126 glenoid foramen occurs sporadically and does not show any clear phylogenetic signal” 13127 (RC07: 105, 106) – it only happens at most once on the shortest trees from Analysis R6 (in 13128 Pantylus; unknown in Stegotretus) and at most twice in R4 and R5 (Pantylus and Batropetes 13129 + Lissamphibia; unknown in Brachydectes and many other “microsaurs”), for a constant total 13130 of four steps under the LH, the TH and the PH. Presence of the enlarged foramen, however, 13131 may keep several “microsaurs” together with each other (Asaphestera, Pelodosotis, 13132 *Trihecaton; unknown in most others) and with Diplocaulus. 13133 Doleserpeton (Sigurdsen & Bolt, 2010, Sigurdsen & Green, 2011: appendix 2), 13134 apparently Apateon (Werneburg, 1991: fig. 5b), Eocaecilia (Jenkins, Walsh & Carroll, 2007), 13135 apparently Triadobatrachus (Ascarrunz et al., 2016: 3D model 1), Valdotriton (Evans & 13136 Milner, 1996: fig. 11a), Batropetes (Carroll, 1991; Glienke, 2013, 2015), Notobatrachus 13137 (Báez & Nicoli, 2004: fig. 3B) and Orobates (Nyakatura et al., 2015: digital model) have state 13138 0; the notch cranial of the glenoid of Notobatrachus should correspond to the coracoid 13139 foramen, not the glenoid foramen, judging from Pawley & Warren (2006: fig. 5). 13140 State 1 is present in Ventastega, assuming this is what “glenoid canal” means (Ahlberg 13141 et al., 2008). The condition in Diplocaulus (Williston, 1909: pl. 4a) may also count. 13142 Unknown in Trimerorhachis (Pawley, 2007), Scincosaurus (Milner & Ruta, 2009) and 13143 Ossinodus (Warren & Turner, 2004: 166). 13144 13145 202. SCACOR 4: Ventrome[d]ially extended infraglenoid buttress: absent (0); present 13146 (1). 13147 State 0 is present in Ventastega (Ahlberg et al., 2008). 13148 Doleserpeton has state 1 (Sigurdsen & Bolt, 2010, Sigurdsen & Green, 2011: appendix 13149 2). State 1 is also known in Eocaecilia (most likely: Jenkins, Walsh & Carroll, 2007: fig. 40), 13150 Triadobatrachus (Ascarrunz et al., 2016: 3D model 1), Westlothiana (Smithson et al., 1994: 13151 392), Diplocaulus (Williston, 1909: pl. 4a) and Orobates (Nyakatura et al., 2015: digital 13152 model). 13153 13154

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13155 203. ANOCLE 1: Anocleithrum: present (0); absent (1). 13156 State 0 is present in Ventastega (Ahlberg et al., 2008). 13157 State 1 looks like a safe interpretation of Cochleosaurus (Sequeira, 2009: fig. 2, 4, 6). 13158 Complete articulated skeletons of Celtedens, with even the scales in place, 13159 demonstrate state 1 for Albanerpetidae (McGowan, 2002). 13160 The dorsal end of the cleithrum of Tseajaia is known and lacks a contact surface for an 13161 anocleithrum (Moss, 1972), so we have taken the absence of a preserved anocleithrum at face 13162 value and scored Tseajaia as possessing state 1. 13163 Only a small part of the cleithrum has ever been found in any of the many specimens 13164 of Trimerorhachis (Pawley, 2007); we therefore cannot (except by phylogenetic bracketing) 13165 feel safe about taking the lack of an anocleithrum at face value and have changed the score to 13166 unknown. 13167 13168 204. HUM 1: Latissimus dorsi process offset anteriorly relative to the ectepicondyle (0) 13169 or aligned with the latter (1). 13170 This character and HUM 4 are inapplicable to Ichthyostega, where the attachment 13171 surface for the latissimus dorsi isn’t much of a process. Ahlberg (2011) stated that the M. 13172 latissimus dorsi probably attached to process 1; however, even if so, process 1 can hardly be 13173 considered homologous with the latissimus dorsi process or ridge in other OTUs in this matrix 13174 (Callier, Clack & Ahlberg, 2009: supp. inf.; Ahlberg, 2011: fig. 1; Clack et al., 2012a). It is 13175 confusing, though, that Ahlberg is a coauthor of Callier, Clack & Ahlberg (2009) as well as of 13176 Clack et al. (2012a), and that his 2011 paper was both submitted and accepted while the 13177 manuscript of Clack et al. (2012a) was in review. 13178 State 0 is now known in Ossinodus (Bishop, 2014). It also appears to be present in 13179 Panderichthys (Boisvert, Mark-Kurik & Ahlberg, 2008: supplementary movie 4); a possible 13180 process for the M. latissimus dorsi can be seen in a location similar to where the process is in 13181 Acanthostega (Coates, 1996: fig. 16d), distal to a foramen – the feature labeled “ldp” by 13182 Coates (1996: fig. 35i) is instead a part of the ectepicondyle ridge. Instead of a process, 13183 Ahlberg (2011) figures several ridges as the attachment area for the M. latissimus dorsi; these 13184 are offset anteriorly (preaxially) from the ectepicondyle as well. 13185 State 1 is documented in all but the smallest specimens of Trimerorhachis (Pawley, 13186 2007) and appears to occur in Isodectes (D. M., pers. obs. of USNM 4474) and in Karaurus 13187 (D. M., pers. obs. of unnumbered MNHN cast of PIN 2585/2). 13188 13189 205. HUM 2: Distinct “supinator” (brachioradialis) process projecting anteriorly: absent 13190 (0); present (1). See Bishop (2014) for the homology of this feature. 13191 State 0 occurs in Baphetes (Milner & Lindsay, 1998), Doleserpeton (Sigurdsen & 13192 Bolt, 2009; D. M., pers. obs. of AMNH 29466) and Eocaecilia (Jenkins, Walsh & Carroll, 13193 2007). 13194 Lebedev & Coates (1995: 316) described a not particularly pointed, but large 13195 “supinator” process in Tulerpeton; it even appears to be visible in distal view (Lebedev & 13196 Coates, 1995: fig. 5D). A pathetic version of this is seen in the most ossified specimen of 13197 Archeria (Romer, 1957: fig. 4B, D, 5E). Chase (1965: 200) reported the presence of a 13198 “supinator” process (state 1) in Neldasaurus. Trimerorhachis shows state 1 in presumably 13199 subadult and adult specimens (Pawley, 2007); similarly, state 1 is seen in the most mature 13200 specimens of Micromelerpeton (Boy, 1995). Notably, it is shared by Ariekanerpeton 13201 (Klembara & Ruta, 2005b: fig. 6A). 13202 Danto, Witzmann & Müller (2012: 49) stated that the “supinator” process is absent in 13203 Solenodonsaurus. Even as preserved, the process is clearly present (Danto, Witzmann &

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13204 Müller, 2012: fig. 1, 4, 5A); it may have been longer, with the rest of the impression being 13205 part of the lost counterpart. 13206 State 1 is further found in Captorhinus (Fox & Bowman, 1966: fig. 28). 13207 CG78 figured a corner in the position where the “supinator” process would be 13208 expected (from comparison to Smithson et al., 1994: fig. 12) in Tuditanus (CG78: fig. 5D) 13209 and Asaphestera (CG78: fig. 8E). For Tuditanus, this appears to be confirmed by the 13210 photograph in Carroll & Baird (1968: fig. 4 right side) – the specimen drawing (fig. 5) 13211 disagrees, but is clearly reconstructed in several places. We have tentatively scored state 1 for 13212 both Tuditanus and Asaphestera; the specimens of both should clearly be restudied, however. 13213 Like those of Apateon, Leptorophus, Schoenfelderpeton (Boy, 1986, 1987; 13214 Werneburg, 2007b; Schoch, 2014a) and Discosauriscus (Klembara & Bartík, 2000), the 13215 humerus of *Chroniosaurus (Clack & Klembara, 2009: fig. 9) and that of *Micropholis 13216 figured by Schoch & Rubidge (2005: fig. 6A) are too poorly ossified to possess a “supinator” 13217 process (Pawley & Warren, 2006); we have scored all OTUs mentioned in this paragraph as 13218 unknown. Similarly, we have scored Amphibamus as unknown: Gregory (1950: 850) 13219 described a specimen where the ends of the humeri “are imperfectly ossified”; Daly (1994: 13220 fig. 18) presented a photograph of the largest Amphibamus specimen, which clearly has 13221 completely ossified humeri (with a distal end much wider than in the closely related 13222 Doleserpeton), but it remains impossible to determine from this photograph whether 13223 “supinator” processes were present. 13224 Preservation and ossification conspire in Balanerpeton to make it impossible to 13225 determine the state of this character, at least from the published figures (Milner & Sequeira, 13226 1994); we have scored Balanerpeton as unknown. 13227 Carroll (1967) stated that his dendrerpetid material lacked the “supinator” process. 13228 However, a minimally ossified process might even be present in the incompletely ossified 13229 humerus drawn in his fig. 15D, judging from comparison to the less incompletely ossified one 13230 of Ariekanerpeton which was labeled by Klembara & Ruta (2005b: fig. 6A) as possessing the 13231 process. A more or less fully ossified humerus is preserved in the specimen described by 13232 Holmes, Carroll & Reisz (1998), but there the area where the process would be has not been 13233 prepared out of the matrix. We have scored Dendrerpetidae as unknown. 13234 About Broiliellus, Carroll (1964: 200) stated: “The left humerus is complete except for 13235 the ectepicondylar process distal to the middle of the articulating surface for the radius.” His 13236 fig. 10B, however, suggests that the distal end is quite incompletely ossified. We have scored 13237 Broiliellus as unknown. 13238 Probably not visible in Eoscopus (Daly, 1994: fig. 11, 14). 13239 Diplocaulus was scored in RC07 as having state 0; the only figured humerus 13240 (Williston, 1909; Douthitt, 1917) is not quite well enough ossified to tell, however, and the 13241 ectepicondyle projects so far that state 1 actually seems quite likely. We have changed the 13242 score to unknown. 13243 We have kept state 1 for Orobates, although the process is very small indeed 13244 (Nyakatura et al., 2015: digital model). 13245 The area where the process would be – indeed the entire proximal, preaxial and ventral 13246 edge of the humerus – is not ossified in Pederpes (Clack & Finney, 2005: fig. 13). We have 13247 therefore changed the score to unknown. 13248 The area is preserved in *Casineria, and the humerus is well ossified, but the 13249 specimen is split through the bone so that the “supinator” process, if present, is deeply buried 13250 in matrix (D. M., pers. obs. of NMS G 1993.54.1) and cannot be scored. 13251 13252

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13253 206. HUM 3: Sharp-edged ventral humeral ridge: present (0); absent (1). RC07 had a 13254 comma after “sharp-edged”, but the ventral humeral ridge is present and blunt in Edops (D. 13255 M., pers. obs. of MCZ 1781) and Eryops (Pawley & Warren, 2006), whose scores we keep as 13256 1. 13257 State 0 is known from Tulerpeton and Eoherpeton (Milner & Lindsay, 1998), 13258 Whatcheeria and Ossinodus (Bishop, 2014) and Pederpes (Clack & Finney, 2005). 13259 Isodectes (D. M., pers obs. of USNM 4471 and USNM 4474), Trimerorhachis 13260 (Pawley, 2007), Acheloma (Polley & Reisz, 2011), Doleserpeton (Sigurdsen & Bolt, 2009), 13261 Platyrhinops (Clack & Milner, 2010), Albanerpetidae (McGowan, 2002), Eocaecilia (Jenkins, 13262 Walsh & Carroll, 2007), Diplocaulus (Williston, 1909; Douthitt, 1917), Orobates (Nyakatura 13263 et al., 2015: digital model) and Tseajaia (Moss, 1972: fig. 9A) have state 1. 13264 Unknown or at least not illustrated or described in Kotlassia (Bystrow, 1944: fig. 16). 13265 13266 207. HUM 4: Latissimus dorsi process confluent with (0) or distinct from (1) 13267 deltopectoral crest. 13268 State 1 is found in Panderichthys (Boisvert, 2009), Isodectes (D. M., pers. obs. of 13269 USNM 4474) and Ossinodus (Bishop, 2014). 13270 13271 208. HUM 5: Entepicondyle foramen: present (0); absent (1). 13272 State 0 is known in Hyloplesion (Olori, 2015) and Ossinodus (Bishop, 2014). 13273 Diplocaulus was scored in RC07 as having state 1, in keeping with the claim that the humerus 13274 of Scincosaurus “is unique among nectrideans in having an entepicondylar foramen” (Bossy 13275 & Milner, 1998: 97); it has state 0 instead (Williston, 1909; Douthitt, 1917). We note that 13276 Bossy & Milner (1998) did not mention or illustrate the humerus of Diplocaulus at all. 13277 Orobates was correctly (Nyakatura et al., 2015: digital model) scored as having state 0 13278 in RC07, even though the condition was neither described nor illustrated by Berman et al. 13279 (2004) and RC07 (appendix 1) did not claim to have seen specimens. 13280 Unknown in Colosteus (Hook, 1983). 13281 13282 209. HUM 6: Ectepicondyle foramen: present (0); absent (1). See Bishop (2014) for the 13283 homology of this feature; the foramen found in many amniotes happens not to occur in the 13284 present matrix. 13285 The idea that this character might be size-dependent (loss of the foramen at a certain 13286 size: Sequeira, 2009) seems unlikely to us, because very small amphibamids including 13287 branchiosaurids lack this foramen as well as the much larger Eryops, Trimerorhachis and 13288 *Sclerocephalus. 13289 State 1 is found in Scincosaurus (Milner & Ruta, 2009) and Ossinodus (Bishop, 2014). 13290 Orobates was correctly (Nyakatura et al., 2015: digital model) scored as having state 13291 1, even though the condition was neither described nor illustrated by Berman et al. (2004) and 13292 RC07 (appendix 1) did not claim to have seen specimens. 13293 We keep the score of Cochleosaurus as unknown; the foramen is present in small 13294 humeri, while in the largest one it is absent – if, that is, the quality of the plaster cast that is all 13295 which remains of that specimen can be trusted (Sequeira, 2009). 13296 13297 210. HUM 7-8: Ectepicondyle ridge present, not reaching distal humeral end (0); 13298 present, reaching distal end (1); absent (2) (unordered). State 0, originally HUM 8(0), was 13299 originally scored only for Eusthenopteron, Notobatrachus and Vieraella – but the latter two 13300 have state 2 instead, which limited state 0 to Eusthenopteron and thus made character HUM 8 13301 uninformative. However, Panderichthys shares state 0 (Boisvert, 2009). 13302 Platyrhinops has state 1 (Hook & Baird, 1984: fig. 1).

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13303 State 2 is known in Eocaecilia (Jenkins, Walsh & Carroll, 2007), Batropetes (Glienke, 13304 2015: fig. 6) and Microbrachis (Olori, 2015). 13305 Unclear in Eoscopus (Daly, 1994). 13306 We have changed the score of Isodectes from entirely unknown to state 0 or 1. This 13307 must be based on D. M.’s pers. obs. of the specimens mentioned for other characters here, but 13308 if so, D. M. forgot to document this. The area where the ridge should be is preserved in 13309 several specimens, and the distal end is never ossified (D. M., pers. obs.), so the new score is 13310 most likely correct. 13311 We have tentatively kept the score of 2 for Micromelerpeton and all branchiosaurids, 13312 because there is no evidence of another state in the literature; however, we wonder if this 13313 could be due to insufficient ossification. Unfortunately, fig. 5b of Werneburg (1991) is not 13314 clear enough to tell if it can be known which state the skeletally most mature individual of 13315 Apateon had. 13316 13317 211. HUM 9: Distal extremity of ectepicondyle ridge: aligned with ulnar articulation (0); 13318 between ulnar articulation and radial condyle (1); aligned with radial condyle (2) 13319 (ordered). This continuous character is inapplicable when the ectepicondyle ridge is absent 13320 (HUM 7-8(2)); RC07 already scored accordingly. We use the term “ulnar articulation” instead 13321 of “ulnar condyle” because the articular surface for the ulna on the humerus is a trochlea 13322 rather than a condyle in most OTUs of this matrix (see Sigurdsen & Bolt, 2009) to the extent 13323 that it is even ossified. 13324 Eucritta (Clack, 2001: fig. 7, in comparison with Baphetes: Milner & Lindsay, 1998: 13325 fig. 9), Isodectes (D. M., pers. obs. of USNM 4471 and USNM 4474), Platyrhinops (Hook & 13326 Baird, 1984), Diplocaulus (Williston, 1909; Douthitt, 1917) and Silvanerpeton (Ruta & Clack, 13327 2006) show state 2. 13328 Bishop (2014: 217, fig. 12) reconstructed state 0 in Ossinodus. 13329 We tentatively score state 1 or 2 for the incompletely ossified *Erpetosaurus (Milner 13330 & Sequeira, 2011: fig. 8). 13331 Unknown in Eoscopus (Daly, 1994: fig. 11, 14). 13332 13333 212. HUM 10: Humerus without (0) or with (1) waisted shaft. 13334 Ossinodus has state 0 (Bishop, 2014). 13335 Cochleosaurus (Sequeira, 2009) and Isodectes (D. M., pers. obs. of USNM 4471, 13336 USNM 4474, USNM 4555, and CM 81430) have state 1, and so do Cardiocephalus (CG78: 13337 fig. 31), Microbrachis (CG78; Olori, 2015) and, somewhat surprisingly, Diplocaulus 13338 (Williston, 1909; Douthitt, 1917). 13339 Sigurdsen & Green (2011: appendix 2) stated, in agreement with Romer (1946), that 13340 Limnoscelis lacks a humeral shaft, and changed the score from 1 to 0. The humerus is still, 13341 however, strongly constricted in the middle, where the proximal expansion (the head with the 13342 deltoid and pectoral processes) and the distal expansion (with the epicondyles and the 13343 “supinator” process) meet at a right angle in the widespread tetrahedral shape (Romer, 1946; 13344 Berman & Sumida, 1990: 331, fig. 12A; Kennedy, 2010), so we regard Limnoscelis as 13345 combining state 1 with an unusually short humerus (in particular HUM 12-15(0), see below); 13346 humeri with state 0 look quite different. This is also in accordance with the , which 13347 Berman & Sumida (1990) described as follows: “The proximal and distal ends are widely 13348 expanded and joined by an extremely short and moderately stout shaft, giving the femur a 13349 deeply waisted appearance.” 13350 Sigurdsen & Green (2011: appendix 2) went on to state that “Seymouria has a very 13351 porrly [sic] developed shaft”, which they scored as polymorphic – they appear not to have 13352 distinguished polymorphism from partial uncertainty, although we still wonder why they

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13353 would have wanted to score “partial” uncertainty for a binary character –; White (1939: fig. 13354 23) clearly figured a short waisted shaft, so we retain state 1 here as well. 13355 13356 213. HUM 11: Position of radial condyle: terminal (0); ventral (1). 13357 “It seems very likely” that Ossinodus had state 0 (Bishop, 2014: 217). 13358 State 1 is documented in Doleserpeton (Sigurdsen & Bolt, 2009; D. M., pers. obs. of 13359 AMNH 29466), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Archeria (Romer, 1957: fig. 13360 4D), Kotlassia (Bystrow, 1944: fig. 16), Westlothiana (Smithson et al., 1994: fig. 12), 13361 Hyloplesion (Olori, 2015) and Orobates (Nyakatura et al., 2015: digital model). Sigurdsen & 13362 Green (2011: appendix 2) further reported it for Triadobatrachus; this seems at least plausible 13363 from the inclination of the ossification front shown in Sigurdsen, Green & Bishop (2012: fig. 13364 7C) and Ascarrunz et al. (2016: 3D model 1). It also seems to be present in Isodectes (D. M., 13365 pers. obs. of USNM 4555). In Balanerpeton, the quite small attachment area for the condyle 13366 is well visible on the ventral side (Sequeira & Milner, 1994: fig. 12A, B), and the forelimb of 13367 Dendrysekos (Dendrerpetidae) described by Holmes, Carroll & Reisz (1998: fig. 8) is 13368 preserved in such a strongly flexed position that the probably unossified condyle must have 13369 been on the ventral side; we have therefore scored state 1 for both Balanerpeton and 13370 Dendrerpetidae. 13371 The entire area did not ossify in the known specimens of Neldasaurus (Chase, 1965), 13372 Trimerorhachis (Pawley, 2007; D. M., pers. obs. of TMM 40031-80 and TMM 40031-81), 13373 Discosauriscus (Klembara & Bartík, 2000), Ariekanerpeton (Klembara & Ruta, 2005b) and 13374 apparently Tuditanus (Carroll & Baird 1968, CG78). Even in Eoherpeton, comparison to the 13375 best-ossified specimen of Archeria (Romer, 1957: 118, fig. 4, 5E; Smithson, 1985: fig. 25) 13376 makes it likely that the articular surface for the humerus was incompletely ossified, so we 13377 have scored it as unknown as well. The area is furthermore not exposed in Silvanerpeton 13378 (Ruta & Clack, 2006). 13379 13380 214. HUM 12-15: Humerus L-shaped, postaxial margin proximal to entepicondyle 13381 shorter than or subequal to length of proximal margin of entepicondyle (0); 13382 intermediate (1); slender and elongate, total length more than three times maximum 13383 width of distal end (2) (ordered). 13384 HUM 15 was originally called “Width of entepicondyle greater (0) or smaller (1) than 13385 half humerus length”. Ruta, Coates & Quicke (2003) did not explain how these measurements 13386 should be taken, though the name of the character seems obvious enough. RC07 (p. 106) 13387 provided fairly precise instructions: “The entepicondyle width is measured in the plane of the 13388 entepicondyle flattening, as the distance between its free margin and a line parallel to the 13389 humerus greater axis and passing through the point of attachment of the entepicondyle 13390 posterior margin into the general surface of the bone. The humerus length is the maximum 13391 distance between its proximal and distal extremities.” If defined this way, state 0 may not 13392 occur in this matrix at all. All OTUs that were scored HUM 15(0) have HUM 15(1) according 13393 to the usual sources, except apparently Tulerpeton (Lebedev & Coates, 1995; but note the 13394 incomplete ossification of the head, while the entepicondyle is fully ossified) and maybe 13395 Keraterpeton (Jaekel, 1903: fig. 3). 13396 Among those previously scored as unknown, HUM 15(0) has not shown up either, 13397 while HUM 15(1) is found in Panderichthys (Coates, 1996: fig. 35i; Boisvert, Mark-Kurik & 13398 Ahlberg, 2008; Boisvert, 2009), Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. 13399 of USNM 4471, USNM 4474 and USNM 4555), Karaurus (D. M., pers. obs. of unnumbered 13400 MNHN cast of PIN 2585/2), Archeria (Romer, 1957), Paleothyris (D. M., pers obs. of TMM 13401 45955-2, a cast of MCZ 3482), Ossinodus (unless the ossification was very unequally 13402 incomplete: Bishop, 2014) and Tseajaia (Moss, 1972: 32).

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13403 Rather than deleting HUM 15 as uninformative, we strongly suspect that the 13404 explanation by RC07 is wrong and Ruta, Coates & Quicke (2003) actually measured 13405 something else, perhaps the length-to-width ratio of the humerus (width including but not 13406 limited to the entepicondyle) or the ratio of the lengths of the proximal margin of the 13407 entepicondyle and the adjacent postaxial margin of the humerus proximal to the 13408 entepicondyle. For ease of scoring, we have decided in favor of the latter, drawing the line 13409 close to a ratio of 1 : 1. State 0 of the present character thus occurs in Acanthostega and 13410 Ichthyostega (Callier, Clack & Ahlberg, 2009), Tulerpeton (Lebedev & Coates, 1995), 13411 Greererpeton (Godfrey, 1989), Crassigyrinus (Panchen, 1985), Whatcheeria (Lombard & 13412 Bolt, 1995), Baphetes (Milner & Lindsay, 1998), Eoherpeton (Smithson, 1985), 13413 Proterogyrinus (Holmes, 1984), Limnoscelis (Kennedy, 2010), Keraterpeton (Jaekel, 1903: 13414 fig. 3), Diceratosaurus (D. M., pers. obs. of MB.Am.776; note that the proximal end of the 13415 humerus is better preserved than drawn by Jaekel, 1903: pl. IV), Orobates (Nyakatura et al., 13416 2015: digital model), Ossinodus (Bishop, 2014), Pederpes (Clack & Finney, 2005) and *NSM 13417 994 GF 1.1 (Holmes & Carroll, 2010). “Defined” this way, HUM 15 had to be merged with 13418 HUM 12 (which was defined as absence/presence of state 2 of the present potentially 13419 continuous character), because states 0 and 2 of the present character cannot occur in the same 13420 humerus. However, the present character remains independent of HUM 16 both in theory 13421 (unlike state 0 of the present character, HUM 16(0) does not require a wide entepicondyle, 13422 and unlike state 1 of the present character, HUM 16(1) does not require a narrow one) and in 13423 practice. 13424 Of the OTUs that were originally scored as unknown for HUM 12 and are not listed 13425 above as having state 0, state 1 of the present character is found in Cochleosaurus (Sequeira, 13426 2009) and Isodectes (D. M., pers. obs. of USNM 4471, USNM 4474, USNM 4555, CM 13427 81512 and CM 81430). Cardiocephalus has state 1 or 2 (CG78: fig. 31). 13428 Because of incomplete ossification (Clack, 2001), we cannot determine if Eucritta has 13429 state 0 or 1. 13430 13431 215. HUM 13: Posterolateral margin of entepicondyle lying distal relative to plane of 13432 radial and ulnar facets: yes (0); no (1). 13433 Trimerorhachis shows state 0 in large specimens (Pawley, 2007), highlighting the fact 13434 that this character can only be scored for well ossified humeri. 13435 We have also assigned this state to Edops, because MCZ 1781 appears to show a weak 13436 case of it (less weak in extensor view) despite being incompletely ossified (D. M., pers. obs.), 13437 and tentatively to Greererpeton based on the incompletely ossified humerus pictured in 13438 Godfrey (1989: fig. 19g, h). It is further found in Acanthostega (Coates, 1996: fig. 15, 16 13439 contra fig. 35j!; Callier, Clack & Ahlberg, 2009: fig. 2B, note that 2C = 4E is reconstructed), 13440 at least marginally in Whatcheeria (Lombard & Bolt, 1995: fig. 7B), Ecolsonia (Berman, 13441 Reisz & Eberth, 1985: fig. 11D), Eoherpeton (Smithson, 1985: fig. 25), Proterogyrinus 13442 (Holmes, 1984: fig. 26), Archeria (Romer, 1957), Pholiderpeton scutigerum (borderline, but 13443 incompletely ossified: Clack, 1987b: fig. 30), apparently Solenodonsaurus (Danto, Witzmann 13444 & Müller, 2012: fig. 5A), Kotlassia (Bystrow, 1944: fig. 16), Seymouria (White, 1939: fig. 13445 23), Diadectes (Berman, Sumida & Martens, 1998), Limnoscelis (Berman & Sumida, 1990; 13446 Kennedy, 2010), Captorhinus (just barely: Fox & Bowman, 1966: fig. 28), Sauropleura 13447 (Bossy & Milner, 1998: fig. 66C) and Orobates (Nyakatura et al., 2015: digital model). 13448 State 1 is found in Panderichthys (Coates, 1996: fig. 35i; Boisvert, Mark-Kurik & 13449 Ahlberg, 2008; Boisvert, 2009) and Karaurus (D. M., pers. obs. of unnumbered MNHN cast 13450 of PIN 2585/2). We have kept the score of 1 for Ichthyostega because, although the 13451 entepicondyle projects distal to the ulnar facet, the radial facet is so much more proximal – 13452 much like in Panderichthys (Ahlberg, 2011) – that the entepicondyle at most reaches the

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13453 oblique plane in which the two facets lie (Callier, Clack & Ahlberg, 2009: fig. 1, 4D); this 13454 situation is in fact quite similar to that seen in Paleothyris (Carroll, 1969a: fig. 7E). 13455 Unknown due to insufficient ossification in Crassigyrinus (Panchen, 1985: fig. 22), 13456 Baphetes (Milner & Lindsay, 1998), Eucritta (Clack, 2001), Neldasaurus (Chase, 1965: fig. 13457 12), Balanerpeton (Milner & Sequeira, 1994), Dendrerpetidae (Carroll, 1967; Holmes, Carroll 13458 & Reisz, 1998), Apateon (Werneburg, 1991: fig. 5b), Triadobatrachus (Sigurdsen, Green & 13459 Bishop, 2012: fig. 7C; Ascarrunz et al., 2016: 3D model 1), Discosauriscus (Klembara & 13460 Bartík, 2000), Brachydectes (Wellstead, 1982), Diplocaulus (Williston, 1909; Douthitt, 1917), 13461 Ariekanerpeton (Klembara & Ruta, 2005b), Pederpes (Clack & Finney, 2005), Silvanerpeton 13462 (Ruta & Clack, 2006) and Utegenia (Klembara & Ruta, 2004b). 13463 Unclear (at least from published illustrations) in Ptyonius and Urocordylus (Bossy & 13464 Milner, 1998: fig. 66A, B) as well as Tseajaia (where the text and the illustration of Moss 13465 [1972] appear to contradict each other, and the illustration is at an oblique angle). 13466 13467 216. HUM 14: Posterolateral margin of the entepicondyle markedly concave: yes (0); no 13468 (1). Apparently this describes whether the distal margin is straight or forms a distal hook. If 13469 so, Panderichthys has state 0 (Boisvert, 2009). 13470 Cochleosaurus (Sequeira, 2009), Eoscopus (Daly, 1994: fig. 11, 14) and Karaurus (D. 13471 M., pers. obs. of unnumbered MNHN cast of PIN 2585/2) have state 1. 13472 Insufficiently ossified to score in Triadobatrachus (Ascarrunz et al., 2016: 3D model 13473 1). 13474 13475 217. HUM 16: Portion of humerus […] length proximal to entepicondyle smaller (0) or 13476 greater (1) than humerus head width. 13477 State 0 looks very likely in Ossinodus (Bishop, 2014). 13478 State 1 is found in Eusthenopteron (just barely: Coates, 1996: fig. 35h), Panderichthys 13479 (Coates, 1996: fig. 35i; Boisvert, Mark-Kurik & Ahlberg, 2008), Baphetes (perhaps just 13480 barely: Milner & Lindsay, 1998), Edops (D. M., pers. obs. of MCZ 1781), Isodectes (D. M., 13481 pers. obs. of USNM 4471, USNM 4474 and USNM 4555), Balanerpeton (Sequeira & Milner, 13482 1994: fig. 12), Dendrerpetidae (Holmes, Carroll & Reisz, 1998: fig. 8), Eryops (Pawley & 13483 Warren, 2006), Karaurus (D. M., pers. obs. of unnumbered MNHN cast of PIN 2585/2), 13484 Solenodonsaurus (Danto, Witzmann & Müller, 2012), Kotlassia (Bystrow, 1944: 409), 13485 Paleothyris (D. M., pers obs. of TMM 45955-2, a cast of MCZ 3482), Cardiocephalus 13486 (CG78: fig. 31), Diplocaulus (Williston, 1909; Douthitt, 1917) and Orobates (Nyakatura et 13487 al., 2015: digital model). 13488 We have scored Eucritta as unknown because the measurements are about equal 13489 (Clack, 2001) and the proximal end of the humerus seems incompletely ossified. 13490 The state in the largest specimen of Cochleosaurus is unclear; smaller ones are rather 13491 borderline (Sequeira, 2009). We have therefore kept its score as unknown. Proterogyrinus is 13492 likewise borderline (Holmes, 1984: fig. 26), so we have scored it as unknown as well; taking 13493 the width in fig. 26(c) at face value, P. would just barely have state 1, rather than 0 as 13494 originally scored. 13495 Unknown in Scincosaurus (Milner & Ruta, 2009). 13496 13497 218. HUM 17: Accessory foramina on humerus: present (0); absent (1). 13498 State 1 occurs in Tulerpeton (Lebedev & Coates, 1995), Cochleosaurus (Sequeira, 13499 2009), Paleothyris (D. M., pers obs. of TMM 45955-2, a cast of MCZ 3482) and Ossinodus 13500 (Bishop, 2014). Germain (2008a) correctly scored state 1 in Isodectes (D. M., pers. obs. of 13501 USNM 4471, USNM 4474, and USNM 4555), but did not mention this in the text; instead he

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13502 intended (Germain, 2008a: 185) to change the score of the next character from unknown to 1, 13503 but did not do this in the matrix. Evidently, the right score ended up in the wrong column. 13504 13505 219. HUM 18/DIG 1: Forelimb absent (0); humerus present, length smaller (1) or greater 13506 (2) than combined length of two and a half mid-trunk vertebrae (ordered). State 0 13507 corresponds to part of state DIG 1(0) of RC07; for the other part see state DIG 1-2-3-4(0) in 13508 our character 276. States 1 and 2 correspond to states HUM 18(0,1) of RC07 – who had 13509 exchanged the states in the text but not in the matrix, except maybe for the taxa they added. 13510 State 2 is found in Whatcheeria (strongly implied by Lombard & Bolt, 1995), 13511 Baphetes (Milner & Lindsay, 1998 – the longest intercentrum is 22 mm long, the humerus 13512 somewhere around 85; this should ensure state 2 even if the vertebrae were very 13513 rhachitomous), Eucritta (Clack, 2001), Edops (Romer & Witter, 1942), Cochleosaurus 13514 (Sequeira, 2009), Isodectes (Sequeira, 1998; Germain, 2008a: 185 – see HUM 17; D. M., 13515 pers. obs. of CM 81512), Acheloma (Polley & Reisz, 2011), Phonerpeton (Dilkes, 1990), 13516 Ecolsonia (Berman, Reisz & Eberth, 1985), Doleserpeton (Sigurdsen & Bolt, 2010), 13517 Leptorophus (Boy, 1986; Werneburg, 2007b), Triadobatrachus (all literature and pers. obs.), 13518 Eoherpeton (Smithson, 1985: compare fig. 19, 24, 25), Pholiderpeton scutigerum (Clack, 13519 1987b), Diadectes (all literature), Cardiocephalus (CG78: fig. 31), Notobatrachus and 13520 Vieraella (Estes & Reig, 1973; Báez & Basso, 1996), Orobates (Berman et al., 2004: fig. 1), 13521 Pederpes (Clack & Finney, 2005), Silvanerpeton (Ruta & Clack, 2006), and Tseajaia (Moss, 13522 1972: pl. 2; D. M., pers. obs. of CM 38033). We have kept state 1 or 2 for the very poorly 13523 ossified Schoenfelderpeton (Boy, 1986). 13524 RC07 scored Acherontiscus and all adelogyrinids as unknown for the presence of 13525 limbs; Ruta, Coates & Quicke (2003: 263) commented on the adelogyrinids (there is no 13526 comment specifically on Acherontiscus): “Limb absence may well be a preservational artifact, 13527 especially because of the very few specimens known.” However, we find it difficult to 13528 imagine that the forelimbs and, notably, the endochondral shoulder girdle would have just 13529 fallen off the specimen of Adelogyrinus drawn by Andrews & Carroll (1991: fig. 6), where 13530 the ribs, the dermal shoulder girdle and even the hyobranchial apparatus are hardly 13531 disarticulated and well preserved. Andrews & Carroll (1991: 252) commented on that 13532 specimen: “No unidentified bone is present in the area of the dermal shoulder girdle and none 13533 could possibly be confused with the endochondral girdle or fore limbs. All bone present is 13534 well preserved, although it has suffered surface damage. The specimen is broken through the 13535 area of the shoulder girdle so that a cross-section of the bones is visible. If the endochondral 13536 shoulder girdle had been ossified, it is difficult to imagine how it could fail to be preserved 13537 with the rest of the girdle, ribs and vertebrae. One can only assume that these bones were 13538 unossified (cartilaginous) or missing in the living animal. The scapulocoracoid is slow to 13539 ossify in small labyrinthodonts and microsaurs, but the remainder of the skeleton suggests that 13540 this specimen is mature. The dermal elements are typical of other early tetrapods in their 13541 proportions and configuration.” We have therefore scored Adelogyrinus as limbless (state 0), 13542 although we have kept the question mark for the less well articulated Acherontiscus, the much 13543 less well articulated Adelospondylus, and of course Dolichopareias which is exclusively 13544 known from skull bones. 13545 *Utaherpeton changes from state 2 to state 1 in ontogeny (Carroll & Chorn, 1995: 13546 table 1). We have only considered the adult condition. 13547 *Sclerocephalus has state 2, but just barely (Schoch & Witzmann, 2009a: fig. 9D), at 13548 least as far as the ossified part of the humerus is concerned. 13549 In spite of having only 13 presacral vertebrae, *Chelotriton has state 1 (Schoch, 13550 Poschmann & Kupfer, 2015), showing that state 1 does not always correlate with trunk 13551 elongation.

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13552 220. HUM 19: Process ‘2’ on humerus: absent (0); present (1). Sigurdsen & Green (2011) 13553 suspected that this process is homologous to the latissimus dorsi process, but they are both 13554 present and lie on different sides of the ectepicondyle ridge in Acanthostega (Coates, 1996: 13555 fig. 16) and Ossinodus (Bishop, 2014) for example; Pawley (2006: fig. 72.2.1) figured and 13556 labeled them both on a humerus of Proterogyrinus. 13557 Isodectes has state 0 (D. M., pers. obs. of USNM 4471 and USNM 4474). 13558 Panderichthys and even Eusthenopteron have a candidate process (figures in Boisvert, 13559 2009, and Ahlberg, 2011) which we have scored as state 1. 13560 In Acanthostega, process 2 seems to disappear during ontogeny (Callier, Clack & 13561 Ahlberg, 2009: fig. 2), which is not known to happen in any other taxon; we have kept state 1 13562 for the time being because process 2 is not mentioned in the figures, text or supplementary 13563 information of Callier, Clack & Ahlberg (2009) and because the drawing is not completely 13564 unambiguous, but we would like to draw attention to this question. 13565 Ichthyostega was scored in RC07 as having state 0; but the term “process 2” was first 13566 invented for Ichthyostega (Jarvik, 1996: 62). In Ichthyostega, unlike in the other OTUs that 13567 have it, process 2 is only identifiable in postaxial/posterior view (Jarvik, 1996: fig. 45), hiding 13568 between the ectepicondyle ridge (“dorsal ridge” of Jarvik, 1996) and the entepicondyle; in 13569 extensor/dorsal view, the large process 1 covers it, while in flexor/ventral view, it lies behind 13570 the oblique ridge that forms the proximal edge of the entepicondyle (compare Jarvik, 1996: 13571 fig. 45F and Callier, Clack & Ahlberg, 2009: fig. 1 left side for two slightly different 13572 interpretations of exactly which angle is “ventral view”). It is not common for the humeri of 13573 early tetrapods to be figured in postaxial/posterior view; Callier, Clack & Ahlberg (2009) and 13574 Ahlberg (2011), for example, did not bother. – In short, Ichthyostega has state 1. 13575 Tulerpeton was scored as unknown, and RC07 stated without further comment that the 13576 presence of process 2 was “uncertain”. Ruta & Clack (2006), however, claimed that 13577 Tulerpeton had state 1 and cited Lebedev & Coates (1995). The latter did not mention process 13578 2; from their fig. 5 it seems that a rather indistinct process is present. We have therefore 13579 changed the score to 1. 13580 The process of Crassigyrinus that Panchen (1985) identified as the insertion point of 13581 M. subscapularis and Lebedev & Coates (1995: fig. 6F) labeled as the insertion point of M. 13582 latissimus dorsi appears to be process 2 by comparison to Acanthostega (Coates, 1996; 13583 Callier, Clack & Ahlberg, 2009) and Ossinodus (Bishop, 2014). 13584 It is unclear from Milner & Lindsay (1998: fig. 9) whether Baphetes had a small 13585 process 2; we have changed the score to unknown. 13586 Not preserved in Eucritta, apart from the early ontogenetic stage of the individual 13587 (Clack, 2001: fig. 7). 13588 Fig. 13 of Romer & Witter (1942) is a reconstruction; the area where process 2 would 13589 be is not preserved in any known specimen of Edops (D. M., pers. obs.), which we have 13590 therefore scored as unknown. 13591 State 1 is further known in Ossinodus (Bishop, 2014); Silvanerpeton has a possibly 13592 slightly less weak version of state 1 than Tulerpeton (Ruta & Clack, 2006). 13593 About Pederpes, Clack & Finney (2005: 330) stated: “There is no equivalent to 13594 ‘process 2’ of Ichthyostega (Jarvik, 1996) or Acanthostega (Coates, 1996).” We do not think, 13595 however, that this can be stated with reasonable certainty when the area where the process 13596 would be has not been fully prepared and the humerus was even less well ossified (Clack & 13597 Finney, 2005: fig. 13) than that of Ossinodus (Bishop, 2014). We have therefore changed the 13598 score to unknown. 13599 13600 13601

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13602 221. RAD 1: Radius or radioulna longer (0) or shorter (1) than humerus. 13603 Baphetes has state 1 (Milner & Lindsay, 1998), as do Edops (D. M., pers. obs. of MCZ 13604 1769), Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of USNM 4471, USNM 13605 4474, USNM 4555 and CM 81430), Doleserpeton (Sigurdsen & Bolt, 2009, 2010), 13606 Cardiocephalus (CG78: fig. 31), Notobatrachus (Báez & Nicoli, 2004) and Vieraella (Báez & 13607 Basso, 1996). 13608 13609 222. RAD 2: Radius longer than (0), as long as (1), or shorter than (2) ulna (ordered). 13610 This is a continuous character. 13611 State 1 is found in Doleserpeton (Sigurdsen & Green, 2011: appendix 2), 13612 Albanerpetidae (McGowan, 2002), Eocaecilia (Jenkins, Walsh & Carroll, 2007) and 13613 apparently Cardiocephalus (CG78: fig. 33C). 13614 Edops has state 2 (D. M., pers. obs. of MCZ 1769), as do Cochleosaurus (Sequeira, 13615 2009), Isodectes (D. M., pers. obs. of USNM 4471 and CM 81430), Trimerorhachis (Pawley, 13616 2007), Triadobatrachus (Ascarrunz et al., 2016: 3D model 1), Valdotriton (Evans & Milner, 13617 1996: fig. 7), Microbrachis (Olori, 2015: fig. 20C, D, 27C) and Diplocaulus (Williston, 1909; 13618 Douthitt, 1917). Radius and ulna remain distinguishable in a fused radioulna (RAD 3(1)); 13619 state 2 is shared by Notobatrachus (Báez & Nicoli, 2004) and probably Vieraella (Báez & 13620 Basso, 1996: fig. 6). 13621 Olori (2015: 58, table S3) has stated that Microbrachis and Hyloplesion have state 1. 13622 This must reflect a more generous definition of that state than what we have used. As 13623 mentioned, we consider three photographs of Microbrachis in Olori (2015) to show state 2. 13624 The most mature forearm of Hyloplesion depicted in that study, Olori (2015: fig. 33C), indeed 13625 shows state 1, but the ulna has almost no olecranon, and the caption states: “Beyond this 13626 [ontogenetic] stage, the olecranon becomes a rounded, distinct process.” This strongly implies 13627 that state 2 was reached later in ontogeny. For this reason we have kept state 2 for 13628 Hyloplesion, which is unambiguously depicted in the drawings in CG78: fig. 90D, E. 13629 Unknown in Solenodonsaurus (Danto, Witzmann & Müller, 2012) and Euryodus 13630 (CG78). 13631 As preserved, *Erpetosaurus has state 1 (Milner & Sequeira, 2011: fig. 8), but scoring 13632 it that way would assume that the olecranon process is fully ossified, which is unlikely in the 13633 light of the clearly incompletely ossified humerus. We have therefore scored state 1 or 2. 13634 From Paton, Smithson & Clack (1999: fig. 3) it may seem that *Casineria has state 2; 13635 however, radius and ulna are so incompletely ossified and preserved (split lengthwise; D. M., 13636 pers. obs. of NMS G 1993.54.1p) that we have to keep the score as unknown. 13637 13638 223. RAD 3: Compound radio-ulna: absent (0); present (1). 13639 Baphetes is known to have state 0 (Milner & Lindsay, 1998), as are Edops (D. M., 13640 pers. obs. of MCZ 1769), Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of 13641 USNM 4471, USNM 4474 and CM 81430) and Cardiocephalus (CG78: fig. 31). 13642 13643 224. ULNA 1: Olecranon process: absent (0); present (1). 13644 Incompletely ossified proximal ends of ulnae that do not show a process should of 13645 course not be scored 0, but unknown. This affects Crassigyrinus (Panchen, 1985), 13646 Schoenfelderpeton (Boy, 1986: fig. 10), Pederpes (Clack & Finney, 2005), Silvanerpeton 13647 (Ruta & Clack, 2006: fig. 6), and even the most mature known specimens of Discosauriscus 13648 (Klembara & Bartík, 2000) and Utegenia (Klembara & Ruta, 2004b) that preserve an ulna. In 13649 Leptorophus, a rudimentary process might sometimes be present (Boy, 1986: fig. 10), but 13650 more likely the ulna is again too incompletely ossified to tell (supported for Leptorophus by 13651 Werneburg, 2007b, and Schoch, 2014a). The same holds for Micromelerpeton (Boy, 1972:

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13652 37, fig. 20) and Odonterpeton (CG78: 147, fig. 98, 99). We have scored all OTUs mentioned 13653 in this paragraph as unknown. 13654 Edops (D. M., pers. obs. of MCZ 1769 and MCZ 7143), Cochleosaurus (Sequeira, 13655 2009), Isodectes (D. M., pers. obs. of USNM 4471 and CM 81430), Apateon (metamorphosed 13656 A. gracilis: Fröbisch & Schoch, 2009b), Albanerpetidae (Celtedens ibericus: McGowan, 13657 2002: fig. 6C), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Microbrachis (Olori, 2015), 13658 Diplocaulus (Williston, 1909; Douthitt, 1917) and Ariekanerpeton (Klembara & Ruta, 2005b) 13659 have state 1. Apparently, so do the incompletely ossified Valdotriton (Evans & Milner, 1996: 13660 fig. 7, 8) and the incompletely preserved Cardiocephalus (CG78: fig. 31). 13661 “In Acanthostega the ulna lacks an olecranon process” (Coates, 1996: 386), and indeed 13662 Acanthostega was scored as having state 0 in RC07. But on the same page (Coates, 1996: fig. 13663 17g–l), the left ulna of Acanthostega is illustrated as having a quite large process that 13664 continues the large flange proximal to the ossification front of the proximal articular end. 13665 Comparison to the right ulna of Greererpeton (Godfrey, 1989: fig. 20g–l) and to skeletal 13666 restorations (Godfrey, 1989: fig. 1c; Coates, 1996: fig. 18) does not show any reason not to 13667 consider this process homologous to an olecranon process. The only clear difference to 13668 Greererpeton (scored 1 in RC07) is that, in Acanthostega, the proximal surface of this process 13669 is entirely unfinished (it looks like a cross-section) and continuous with the equally unfinished 13670 surface of the articulation for the humerus; this is not a sufficient reason to score state 0. We 13671 thus agree with Ahlberg (2011) that the olecranon process is present in Acanthostega and 13672 have changed the score to 1. 13673 Somewhat similarly, Notobatrachus should be considered to have state 1 (Báez & 13674 Nicoli, 2004: 167, fig. 2, 4, 5). 13675 CG78 stated on p. 32 that there is no “distinct olecranon” in *Llistrofus. The base of 13676 an olecranon process is, however, shown in their fig. 15, so we have scored state 1. Given the 13677 wide-open skull sutures, the neurocentral sutures, the absence of preserved carpals and the 13678 apparently rather featureless radius, we consider the lack of further ossification of the 13679 olecranon to be most likely a juvenile feature. 13680 13681 225. ILI 3: Dorsal iliac process: absent (0); present (1). Judging from various “microsaurs” 13682 like Tuditanus and Sparodus, this process is homologous to the preacetabular process of 13683 (many) amniotes. 13684 Frogs generally have only one process which is directed cranially. We wonder if the 13685 tuber superius of Triadobatrachus, Notobatrachus, **Gobiates and **some other salientians 13686 (Roček & Rage, 2000; Ascarrunz et al., 2016; Báez & Nicoli, 2004; Roček, 2008) – though 13687 not all others; *Liaobatrachus lacks it (Dong et al., 2013) – is homologous to the caudal 13688 process, and have therefore scored the two mentioned OTUs as having state 1. 13689 Ventastega shares state 1 (Ahlberg et al., 2008). So do Edops (D. M., pers. obs. of 13690 MCZ 6489; also implied by Romer & Witter, 1942), Chenoprosopus (Hook, 1993; D. M., 13691 pers. obs. of USNM 437646), Isodectes (D. M., pers. obs. of USNM 4474), Neldasaurus 13692 (Chase, 1965), Trimerorhachis (well developed: Pawley, 2007), Dendrerpetidae (less distinct, 13693 but still clear: Milner, 1996; Holmes, Carroll & Reisz, 1998; Pawley, 2006: 183, fig. 58), 13694 Acheloma (Olson, 1941), Broiliellus (D. M., pers. obs. of MCZ 3272; also suggested by the 13695 illustration of that specimen in Carroll, 1964: fig. 11), Doleserpeton (Sigurdsen & Bolt, 13696 2010), Eoscopus (Daly, 1994), Platyrhinops (Hook & Baird, 1984; Werneburg, 2012b; D. M., 13697 pers. obs. of AMNH 2002), Apateon (Werneburg, 1991: fig. 8d), Leptorophus (Werneburg, 13698 2007b: fig. 3), Batropetes (Glienke, 2013, 2015), Saxonerpeton, Hapsidopareion, Micraroter 13699 and Euryodus (CG78: fig. 126), Pelodosotis (CG78: 85), Hyloplesion (in later ontogeny: 13700 Olori, 2015), Scincosaurus, Diceratosaurus, Ptyonius, Sauropleura and Urocordylus (Bossy 13701 & Milner, 1998: fig. 67), and Ariekanerpeton and Utegenia (Klembara & Ruta, 2004b,

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13702 2005b). An extremely short but otherwise well developed dorsal process is found in 13703 *Chroniosaurus (Clack & Klembara, 2009: fig. 8, left side); we have scored this as state 1 as 13704 well. 13705 Eryops was scored as having state 0 in RC07. However, if anything, the caudal 13706 process is absent, not the dorsal one (Romer, 1957: 117; Pawley, 2006: 183, fig. 58; Pawley 13707 & Warren, 2006; D. M., pers. obs. of specimens in USNM, TMM, AMNH and elsewhere), 13708 leading us to score state 1. The caudal process may well be present as the corner called “sacral 13709 flange” by Pawley (2006: fig. 58) and Pawley & Warren (2006). 13710 The albanerpetid Celtedens appears to have a dorsal process and maybe a small caudal 13711 one (McGowan, 2002: fig. 9); we have therefore assigned state 1 to Albanerpetidae. 13712 The unusual-looking fig. 8 of Watson (1940), recommended by Daly (1994), suggests 13713 that Amphibamus may have had state 1 rather than 0 as scored by RC07, especially when 13714 compared to Eoscopus (Daly, 1994: fig. 13); we have scored it as unknown. “[T]he rear parts 13715 of the body are missing” in all known specimens of Schoenfelderpeton (Boy, 1986: 155; 13716 translated by D. M.), almost the entire ilium is unknown in Valdotriton (Evans & Milner, 13717 1996), and the situation is unclear (probably the ilium is too poorly ossified) in Keraterpeton 13718 (Bossy & Milner, 1998: fig. 67). 13719 The ilium of Cochleosaurus (Sequeira, 2009) apparently has an unusual ontogeny 13720 which begins at a shape very similar to that of Eryops but ends at a long, almost parallel- 13721 sided, caudodorsally directed rod as seen in Isodectes and *Erpetosaurus. However, as we 13722 count both of those conditions as state 1, we have assigned state 1 to Cochleosaurus as well. 13723 In *Gerobatrachus, “[t]he ilium lacks the posterior process common to temnospondyls 13724 but the presence of an anterior process, a salientian character, is obscured by an overlying 13725 fragment of the femur” (Anderson et al., 2008a: 516). Because the caudal process is absent, 13726 we have tentatively scored state 1. 13727 The situation in *Micropholis is borderline, but we interpret the low dorsal bulge 13728 (Schoch & Rubidge, 2005: fig. 6G) as the dorsal process and have thus scored state 1. 13729 13730 226. ILI 4: Caudal iliac process tapers to a single point or is rounded (0); ends in two 13731 corners (1). The original wording, “Posterior iliac process subhorizontal, stout, abbreviated 13732 posteriorly and tapering rearward in lateral aspect: absent (0); present (1)”, is a garbled hash 13733 of four statements on size and shape, using “abbreviated” to indicate that the process is 13734 metaphorically ‘shortened’ by being metaphorically ‘cut off’, giving it a more or less caudal 13735 edge (sometimes vertical as in Limnoscelis and Discosauriscus) with two corners instead of 13736 one. Notably, caudal processes with state 1 usually do not taper, but have a more or less 13737 constant width throughout. – Judging from various “microsaurs” like Tuditanus and 13738 Sparodus, this process is homologous to the postacetabular process of (many) amniotes. 13739 State 0 is present in Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 13740 437646), Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of USNM 4474), 13741 Platyrhinops (Hook & Baird, 1984), Leptorophus (Werneburg, 2007b) and Kotlassia 13742 (Bystrow, 1944: 409). 13743 State 1, at least under our definition, is found in Petrolacosaurus (Reisz, 1981), 13744 probably Westlothiana (Smithson et al., 1994: fig. 11A, 14A, B, 15B), and, more surprisingly, 13745 Acheloma (Olson, 1941: fig. 12A), Archeria (Romer, 1957), Sauropleura (Bossy & Milner, 13746 1998), *Archegosaurus (Witzmann & Schoch, 2006), *Mordex (lectotype: Werneburg, 13747 2012b: fig. 31f) and *Australerpeton (Eltink & Langer, 2014). By comparison to younger 13748 individuals of *Mordex (Werneburg, 2012b: fig. 31b–d), we have scored *Branchiosaurus 13749 (Werneburg, 2012b: fig. 30b, d, f) as unknown. 13750 Batropetes appears to be polymorphic (Glienke, 2015: fig. 5).

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13751 Unknown in Ecolsonia (Berman, Reisz & Eberth, 1985: fig. 12A); almost the entire 13752 ilium is unknown in Valdotriton (Evans & Milner, 1996). If the tuber superius of 13753 Triadobatrachus is homologous to the caudal iliac process, it is nonetheless too small and 13754 possibly incompletely ossified for this character to be applicable (Ascarrunz et al., 2016: 3D 13755 model 1). 13756 13757 227. ILI 6: Supr[…]acetabular iliac buttress less (0) or more (1) prominent than 13758 postacetabular buttress. 13759 State 0 is found in Orobates (Nyakatura et al., 2015: digital model). 13760 Cochleosaurus has state 1 (Sequeira, 2009), as do Doleserpeton (D. M., pers. obs. of 13761 BEG 40882-25), apparently Platyrhinops (Hook & Baird, 1984) and (weakly expressed) 13762 Triadobatrachus (Ascarrunz et al., 2016: 3D model 1). We have also kept this state for 13763 Eoscopus, because Daly (1994: 17, fig. 13) mentioned and possibly drew “projecting rims 13764 dorsally and ventrally” on the acetabulum, with no indication of a caudal one; Daly (1994: 17) 13765 went on to state that “there is no supra-acetabular buttress”, but clearly such a buttress and the 13766 projecting dorsal rim are homologous. 13767 Eryops was scored as having state 1 in RC07. Pawley & Warren (2006: figs. 8.2 and 13768 8.4, based entirely on specimens not mentioned below) reconstructed state 0 instead. This is 13769 not likely to be ontogenetic, because the large specimens TMM 31225-3 and TMM 31225-9 13770 show state 1 while the likewise large MCZ 1126, MCZ 1536, MCZ 2588 and MCZ 2638 13771 share state 0 with the middle-sized MCZ 2682 and the small TMM 31225-33, though other 13772 differences between the large specimens leave open the possibility of sexual or similar 13773 dimorphism. Such dimorphism is well known for the skulls, which are not preserved in these 13774 specimens: there is a narrow-headed and a round-headed morph independently of absolute 13775 size (Werneburg, 2007a; D. M., pers. obs. of USNM, TMM, AMNH and MCZ specimens; 13776 considered two species by Schoch & Milner, 2014). In any case, we have scored Eryops as 13777 polymorphic. 13778 Diagenetic crushing can further make this character difficult to code; the left side of 13779 the Diadectes specimen AMNH 23761 shows (if somewhat borderline) state 1 as scored, 13780 while on the right side the ilium is bent ventromedially, creating state 0. (We have kept state 1 13781 for Diadectes.) 13782 The postacetabular buttress is unossified in Chenoprosopus (Hook, 1993: fig. 3B; D. 13783 M., pers. obs. of USNM 437646) and Trimerorhachis (Pawley, 2007). The same appears to be 13784 the case in *Sclerocephalus (Schoch & Witzmann, 2009a: fig. 8F), *Archegosaurus 13785 (Witzmann & Schoch, 2006b: fig. 7), *Erpetosaurus (Milner & Sequeira, 2011: fig. 10A), 13786 and to a lesser extent *Australerpeton (Eltink & Langer, 2014). 13787 13788 228. ILI 7: Transverse pelvic ridge: absent (0); present (1). 13789 State 0 is found in Ventastega (Ahlberg et al., 2008) and Cochleosaurus (Sequeira, 13790 2009). 13791 State 1 is documented in Edops (D. M., pers. obs. of MCZ 6489), in at least some 13792 large specimens of Trimerorhachis (Pawley, 2007) and in Acheloma (Polley & Reisz, 2011), 13793 and was apparently also present in Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 13794 437646), Kotlassia (Bystrow, 1944: fig. 17) and Tuditanus (D. M., pers. obs. of CM 29592). 13795 We further agree with Romer (1957) that the transverse ridge of Ichthyostega (Jarvik, 1996) 13796 constitutes state 1. 13797 13798 13799

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13800 229. ILI 9: Ilium shaped like an elongate rod directed anteriorly/anterodorsally: absent 13801 (0); present (1). We have deliberately kept this character independent of the putative 13802 homology of the rod, in particular the question of whether it is the dorsal or the caudal process 13803 (ILI 3), in order to allow the homology hypotheses to compete. 13804 State 0 is present in Ventastega (Ahlberg et al., 2008), Edops (D. M., pers. obs. of 13805 MCZ 6489), Chenoprosopus (Hook, 1993), Cochleosaurus (Sequeira, 2009), Isodectes (D. 13806 M., pers. obs. of USNM 4474), Platyrhinops (Hook & Baird, 1984; Clack & Milner, 2010), 13807 Leptorophus (Werneburg, 2007b) and probably Cardiocephalus (CG78: fig. 31). 13808 “[T]he rear parts of the body are missing” in all known specimens of 13809 Schoenfelderpeton (Boy, 1986: 155; translated by D. M.); almost the entire ilium is unknown 13810 in Valdotriton (Evans & Milner, 1996). 13811 *Tungussogyrinus has an intermediate condition that we count as state 1, following 13812 Werneburg (2009). The same appears to be the case in *Beiyanerpeton (Gao & Shubin, 2012: 13813 fig. 2). 13814 13815 deleted ILI 10: Acetabulum directed posteriorly/posterolaterally (0) or laterally (1). As 13816 RC07 pointed out, this character is parsimony-uninformative, so we have deleted it. 13817 Boisvert (2005) stated three times that Panderichthys, which was scored as unknown 13818 in RC07, has state 0, referring twice to her fig. 1d. That, however, is a line drawing which 13819 does not show the acetabulum, but instead shows the whole area as damaged. The photograph 13820 (Boisvert, 2005: fig. 1c) which the drawing interprets appears to show that the entire surface 13821 of the pelvis and of the proximal half or so of the femur is damaged; no acetabulum can be 13822 discerned. We therefore keep the score as unknown; state 0 thus remains restricted to 13823 Eusthenopteron, and this character remains parsimony-uninformative. 13824 “[T]he rear parts of the body are missing” in all known specimens of 13825 Schoenfelderpeton (Boy, 1986: 155; translated by D. M.). 13826 13827 deleted ISC 1: Ischium contributing to pelvic symphysis: no (0); yes (1). As RC07 pointed 13828 out, this character is parsimony-uninformative, so we have deleted it. 13829 13830 230. PUB 1: Number of pubic obturator foramina: multiple (0), single (1), or absent (2) 13831 (ordered). We have ordered this meristic character. 13832 Eryops (Pawley & Warren, 2006), Acheloma (Polley & Reisz, 2011), Phonerpeton (D. 13833 M., pers. obs. of MCZ 1548), Doleserpeton (Sigurdsen & Bolt, 2010), Eoscopus (Daly, 1994) 13834 and Cardiocephalus (CG78: fig. 31) display state 1. 13835 The three pubes catalogued as MCZ 7158 have been assigned to Edops. Only one of 13836 them clearly shows a foramen. Right next to it (craniodorsally), there is another hole of about 13837 the same size; however, we interpret it as damage, because it seems to have a solid floor of 13838 spongy bone (unlike the more likely foramen, which is filled with matrix to at least a deeper 13839 level) and because the bone surface around it, including the area between the two holes, is 13840 damaged (D. M., pers. obs.). We have therefore scored state 1 for Edops. 13841 Platyrhinops has state 1 or 2; we can exclude the possibility of state 0 (D. M., pers. 13842 obs. of AMNH 2002). 13843 Batropetes palatinus shows states 1 and 2 in different specimens (Glienke, 2015). 13844 Because only state 1 is documented in the other three species (Glienke, 2013, 2015), we have 13845 kept the score of 1, although this may yet turn out to be an artefact: B. niederkirchensis and B. 13846 appelensis are known from a single specimen each, and the specimens of B. fritschi and B. 13847 appelensis are less well preserved and ossified than those of the other two species (Glienke, 13848 2013, 2015).

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13849 Clearly, the absence of pubic bones in the *Lydekkerina specimens described by 13850 Hewison (2008) is due to immaturity, while the specimen described by Pawley & Warren, 13851 (2005) is more mature and has a short but ossified pubis which bears an obturator foramen on 13852 its ventral surface (Pawley & Warren, 2005: fig. 6F–H). We have scored state 1. 13853 13854 231. FEM 1-2-6: Internal trochanter does not project (0); projects proximally, enclosing 13855 (with the head) an indentation (often rounded) in the “ventral” margin of the femur (1); 13856 projects only “ventrally”, so that its proximal edge forms an angle of at least 90° with 13857 the shaft (2) (unordered). It may be further possible to distinguish lack of projection (which 13858 appears to occur e.g. in Ichthyostega; Pierce, Clack & Hutchinson, 2012: supplementary 13859 movies) from complete absence, but it appears that absence is only documented in 13860 Eusthenopteron in the present taxon samples (Coates, 1996: fig. 36i). 13861 State 2 is our reinterpretation of FEM 6(1), which was scored only for Eocaecilia and 13862 Valdotriton in RC07. In those two OTUs (Evans & Milner, 1996; Jenkins, Walsh & Carroll, 13863 2007), the internal trochanter is very large in relation to the femoral head, projects “ventrally”, 13864 and is not continued distally by an adductor blade, making it even more conspicuous; but the 13865 lack of the adductor blade seems to be the only distinction to the condition found in Eryops 13866 (Pawley & Warren, 2006; D. M., pers. obs. of TMM 31227-11 and TMM 31227-14), 13867 Diadectes (Berman, Sumida & Martens, 1998: fig. 18A) or Ossinodus (Warren & Turner, 13868 2004), to all of which we have therefore also assigned state 2. We note that FEM 6(0) was 13869 redundantly scored instead of FEM 6(?) for all OTUs with FEM 1(0) – “Internal trochanter 13870 raised as a distinct protuberance: absent” – except Notobatrachus. 13871 The original FEM 2 was confusing: its name was “Internal trochanter separated from 13872 the general surface of the femur shaft by a distinct, trough-like space: absent (0); present (1)”, 13873 but the explanation (RC07: 107) referred to “a deeply notched web of bone”, strongly 13874 implying that the “trough-like space” lies proximodorsal to the trochanter, between it and the 13875 head, rather than “dorsal” or “ventral” from it. Complete absence of this notch is 13876 indistinguishable from FEM 1(0), while conversely the notch can occupy the entire space 13877 where the web would be, which is always the case in taxa with state 2 of the present merged 13878 character – including Eocaecilia and Valdotriton (see above). Clearly, the three characters had 13879 to be merged. Neither the sequence 0-1-2 nor 0-2-1 represents increasing size as far as we can 13880 tell, so we have not ordered this character. 13881 State 0 is present in Edops (D. M., pers. obs. of MCZ 6493) and Saxonerpeton (CG78: 13882 38). 13883 State 1 is found in Cochleosaurus (Sequeira, 2009: fig. 11), the largest specimen of 13884 Trimerorhachis (Pawley, 2007), Pholiderpeton attheyi (Panchen, 1972: fig. 14b) and 13885 Gephyrostegus (D. M., pers. obs. of MB.Am.641). Following Kennedy (2010: fig. 9D), we 13886 have also scored state 1 for Limnoscelis; the internal trochanter is in any case present 13887 (Kennedy, 2010: 217). 13888 Kotlassia (Bystrow, 1944: fig. 19) and Seymouria (D. M., pers. obs. of BEG 30966- 13889 176) are probably best scored as showing state 2, which they share with Microphon (Bulanov, 13890 2014). State 2 is further seen in Dendrerpetidae (Carroll, 1967: fig. 18), Acheloma (Olson, 13891 1941: fig. 12; Polley & Reisz, 2011: fig. 14), Ecolsonia (Berman, Reisz & Eberth, 1985: 23, 13892 fig. 12D), Doleserpeton (Sigurdsen & Bolt, 2010: fig. 11B), Platyrhinops (Hook & Baird, 13893 1984: fig. 1), Archeria (Romer, 1957), Batropetes (Glienke, 2013: fig. 8Q; D. M., pers. obs. 13894 of MB.Am.1232; unclear if 1 or 2 from Glienke, 2015), Diplocaulus (Williston, 1909; 13895 Douthitt, 1917), Orobates (Berman et al., 2004: fig. 15; Nyakatura et al., 2015: digital model), 13896 Tseajaia (Moss, 1972) and *Beiyanerpeton (Gao & Shubin, 2012), although we caution that 13897 in some of these cases it is not certain whether the trochanter was fully ossified. In contrast, 13898 an unambiguous case of state 2 occurs in *Lydekkerina (Pawley & Warren, 2005: fig. 6).

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13899 Urocordylus seems to have state 0 or 2 (Bossy, 1976: 228). 13900 It appears from comparisons that the supposedly left femur of *Platyoposaurus shown 13901 by Gubin (1991: drawing 35) is a right one, and that the supposed fourth trochanter (tr) is 13902 actually the entire adductor blade. Under this assumption, it is not quite clear whether state 1 13903 or 2 is present, but state 2 appears more likely. The text does not mention the internal 13904 trochanter. 13905 Incomplete ossification prevents us from determining whether Neldasaurus (Chase, 13906 1965), Proterogyrinus (Holmes, 1984), Bruktererpeton (Boy & Bandel, 1973), Tuditanus, 13907 Micraroter, Pelodosotis, Microbrachis (CG78: 99, 124, fig. 5I, 50F, 83, 127; D. M., pers. obs. 13908 of MB.Am.840.2, the specimen figured in Olori, 2015: fig. 24F) and Brachydectes 13909 (Wellstead, 1991) had state 1 or 2; we have scored partial uncertainty. Broiliellus is 13910 apparently not well enough preserved to decide between the same two states (Carroll, 1964). 13911 Amphibamus may be well enough preserved, but Daly’s (1994) fig. 18 is unclear, and no 13912 better reference appears to exist, so we have scored the same uncertainty; similarly, we have 13913 assigned state 1 or 2 to Petrolacosaurus (Reisz, 1981: fig. 22). Being unaware of a sufficient 13914 illustration of a femur of Euryodus, we have also scored it the same way; the only 13915 Scincosaurus specimen that appears to preserve a femur, MB.Am.29, is damaged in that area 13916 (D. M., pers. obs.), so we have scored it the same way as well. 13917 Wholly inapplicable to the insufficiently ossified femora of Discosauriscus (Klembara 13918 & Bartík, 2000: fig. 25). 13919 13920 232. FEM 3: Fourth trochanter of femur with distinct rugose area: no (0); yes (1). We 13921 have not investigated whether this character is size-related or how distinct the area can be. 13922 Phonerpeton shows state 0 (D. M., pers. obs. of MCZ 1771 and MCZ 2474, several 13923 small and incompletely ossified femora), as do Doleserpeton (Sigurdsen & Bolt, 2010), 13924 Diplocaulus (Williston, 1909; Douthitt, 1917) and Microphon (Bulanov, 2014). 13925 We have scored state 1 for *Nigerpeton because there is a distinct process; whether it 13926 was rugose before erosion is impossible to tell (D. M., pers. obs. of MNN MOR 82). 13927 13928 233. FEM 4: Proximal end of femur adductor crest reaching midshaft length: no (0); yes 13929 (1). 13930 Diplocaulus has state 0 (Williston, 1909; Douthitt, 1917). 13931 State 1 is found in Edops (D. M., pers. obs. of MCZ 7264), Chenoprosopus (Hook, 13932 1993), Cochleosaurus (Sequeira, 2009), Trimerorhachis (Pawley, 2007), Phonerpeton (D. M., 13933 pers. obs. of MCZ 1771 and MCZ 2474), Diadectes (Case, 1911: fig. 30a; Berman, Sumida & 13934 Martens, 1998: fig. 18A; D. M., pers. obs. of BEG 31222-56), Microphon (Bulanov, 2014) 13935 and Orobates (Berman et al., 2004). 13936 13937 234. FEM 5: Femur shorter than (0), as long as (1), or longer than humerus (2) 13938 (ordered). This is a continuous character. 13939 State 0 is found in Panderichthys (Boisvert, 2005) and Ichthyostega (Coates & Clack, 13940 1995, and references therein; Pierce, Clack & Hutchinson, 2012: fig. 1, supplementary text 13941 1.1, supplementary movies), making the distinction between states 0 and 1 potentially useful. 13942 In RC07, state 0 was restricted to Eusthenopteron. 13943 Acanthostega (Coates, 1996: 389: “The femur is about 25% longer than the 13944 humerus”!), Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of CM 81430 and 13945 USNM 4474), Trimerorhachis (Pawley, 2007), Doleserpeton (Sigurdsen & Bolt, 2010: fig. 1; 13946 Sigurdsen & Green, 2011: appendix 2) and Leptorophus (Werneburg, 2007b) have state 2. 13947 State 1 makes surprise appearances in Acheloma (specimen WM 1756: Olson, 1941: 13948 fig. 11D, E, 12B–D) and *Lydekkerina (Pawley & Warren, 2005: fig. 6).

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13949 Batropetes was scored as having states 1 and 2 in RC07. State 2 is limited to the left 13950 side of one specimen (Glienke, 2015: appendix 1). On the right side, the same specimen has 13951 state 1; state 1 is further found in one or two other specimens of B. palatinus and maybe one 13952 of B. fritschi. All others have state 0 (Glienke, 2013: appendix; 2015: appendix 1). Because 13953 state 0 is so common, we have assigned it to Batropetes without polymorphism. 13954 13955 235. TIB 6: Outline of tibia medial margin shaped like a distinct, subsemicircular 13956 embayment contributing to interepipodial space and the diameter of which is less than 13957 one-third of bone length: absent (0); present (1). 13958 Since almost any condition is by definition state 0, it is not surprising that state 0 is 13959 known to occur in Panderichthys (Boisvert, 2005), Edops (D. M., pers. obs. of MCZ 7162), 13960 Cochleosaurus (Sequeira, 2009: fig. 11), Isodectes (D. M., pers. obs. of USNM 4474), 13961 Doleserpeton (Sigurdsen & Bolt, 2010; D. M., pers. obs. of AMNH 24969), Platyrhinops 13962 (Clack & Milner, 2010), Albanerpetidae (McGowan, 2002) and Karaurus (Ivachnenko, 1978; 13963 D. M. and M. L., pers. obs. of unnumbered MNHN cast of PIN 2585/2). 13964 Strangely, Warren (2007: fig. 11) did not color the tibia of Ossinodus in her skeletal 13965 reconstruction to mark it as known. The shape of the reconstructed tibia, however, agrees with 13966 the better preserved one of the two described by Warren & Turner (2004), so we assume the 13967 lack of color is unintentional and have kept the scores for this and the following character. 13968 13969 236. TIB 7: Tibia without (0) or with (1) flange along its posterior edge. 13970 Like Panderichthys (Boisvert, 2005), Cochleosaurus (Sequeira, 2009: fig. 11), 13971 Isodectes (D. M., pers. obs. of USNM 4474), Doleserpeton (Sigurdsen & Bolt, 2010; D. M., 13972 pers. obs. of AMNH 24969) and Karaurus (D. M., pers. obs. of unnumbered MNHN cast of 13973 PIN 2585/2), Orobates has state 0 (Nyakatura et al., 2015: digital model). 13974 We count the crest of *Archegosaurus (Witzmann & Schoch, 2006b: fig. 9B), and by 13975 extension Edops (D. M., pers. obs. of MCZ 7162 and MCZ 7259), as state 1. 13976 13977 237. FIB 1: Fibula waisted: no (0); yes (1). 13978 State 0 is found in Panderichthys (Boisvert, 2005). 13979 Edops possesses state 1 (D. M., pers. obs. of MCZ 1782 and 7258), and so do 13980 Cochleosaurus (Sequeira, 2009: fig. 11), Isodectes (D. M., pers. obs. of CM 81430), 13981 Doleserpeton (Sigurdsen & Bolt, 2010; D. M., pers. obs. of AMNH 29470), Platyrhinops 13982 (Hook & Baird, 1984; Clack & Milner, 2010) and Leptorophus (Werneburg, 2007b). We have 13983 also assigned state 1 to Notobatrachus because its tibiofibula is strongly waisted (Báez & 13984 Nicoli, 2004). 13985 The fibula is entirely unknown in Ossinodus (Warren & Turner, 2004; Warren, 2007: 13986 fig. 11). 13987 All of the bones lying around in fig. 10A of Milner & Sequeira (2011) are waisted; 13988 judging from their sizes and positions, one of them is bound to be the fibula. We have 13989 therefore scored state 1 for *Erpetosaurus. 13990 13991 238. FIB 3: Ridge near posterior edge of fibula flexor surface: absent (0); present (1). 13992 Orobates has state 0 (Berman et al., 2004; Nyakatura et al., 2015: digital model). 13993 Trimerorhachis (Pawley, 2007: fig. 15.2.3; D. M., pers. obs. of TMM 40998-39) and 13994 Doleserpeton (Sigurdsen & Bolt, 2010) show state 1. (The Doleserpeton specimen AMNH 13995 29470 has state 0 [D. M., pers. obs.], but this could be ontogenetic.) State 1 further shows up 13996 in *Australerpeton (Eltink & Langer, 2014). 13997 Sigurdsen & Green (2011: appendix 2) recommended to score Valdotriton as 13998 unknown; we have followed this.

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13999 The fibula is entirely unknown in Ossinodus (Warren & Turner, 2004; Warren, 2007: 14000 fig. 11). 14001 14002 239. FIB 4: Rows of tubercles near posterior edge of fibula flexor surface: absent (0); 14003 present (1). 14004 Doleserpeton (Sigurdsen & Bolt, 2010) and Orobates (Berman et al., 2004; Nyakatura 14005 et al., 2015: digital model) have state 0. 14006 State 1 is found in Eryops (Pawley & Warren, 2006). 14007 The fibula is entirely unknown in Ossinodus (Warren & Turner, 2004; Warren, 2007: 14008 fig. 11). 14009 14010 240. TAR 2: Separate tibiale, intermedium and/or centrale 4 (0); astragalus (1). The 14011 original wording counted the “[p]roximal tarsal ossifications: absent (0); presence of single 14012 ossification (1); presence of more than two ossifications (2)”. This did not distinguish 14013 incomplete ossification of the tarsus from fusion of individual tarsals. The degree of 14014 ossification depends both on ontogeny and on lifestyle (with aquatic taxa ossifying the 14015 proximal tarsus later and/or to a lesser degree than terrestrial ones). Furthermore, incomplete 14016 ossification and incomplete preservation can only be distinguished in articulated skeletons. 14017 Finally, the astragalus usually comes with a calcaneum ( = fibulare), so there are two 14018 “[p]roximal tarsal ossifications” – yet no state was available between “single” and “more than 14019 two”! Of the OTUs with an astragalus, Captorhinus, Paleothyris and Petrolacosaurus were 14020 scored as having state 2 in RC07, while Diadectes, Tuditanus and Pantylus were scored as 14021 having state 1 or 2! We do not consider this tenable and have redefined the character to 14022 consider fusion only. 14023 Of the OTUs previously scored as unknown or partially uncertain, Albanerpetidae has 14024 state 0 (McGowan, 2002), as do Eocaecilia (Jenkins, Walsh & Carroll, 2007), 14025 Triadobatrachus (Roček & Rage, 2000; Ascarrunz et al., 2016), Kotlassia (Bystrow, 1944: 14026 406), most likely Limnoscelis (Kennedy, 2010), Batropetes (Glienke, 2013), Microbrachis 14027 (CG78: 124; Olori, 2015) and Scincosaurus (Milner & Ruta, 2009). Apparently, so does 14028 Platyrhinops (Hook & Baird, 1984; Clack & Milner, 2010: fig. 1a). We have also scored state 14029 0 for Ossinodus, where Warren (2007: fig. 11) figured a tibiale in a skeletal restoration 14030 without mentioning it in the text (the possible fibulare of Warren & Turner [2004], which has 14031 a quite different shape, is not shown), and *Pholidogaster, where the largest preserved tarsal 14032 (on both sides), which is clearly proximal, is much smaller than expected for an astragalus 14033 (Romer, 1964: fig. 1B). 14034 We count Gephyrostegus as possessing state 1: the tibiale and the intermedium are 14035 (although incompletely) fused, and the lateralmost centrale in fig. 9 of Carroll (1970) should 14036 be the centrale 3, not 4. 14037 In Euryodus the condition is unknown (CG78: 65). 14038 14039 241. TAR 3: L-shaped proximal tarsal element: absent (0), present (1). 14040 Albanerpetidae and Eocaecilia have state 0 (McGowan, 2002; Jenkins, Walsh & 14041 Carroll, 2007), as do Limnoscelis (Kennedy, 2010), Microbrachis (Olori, 2015) and Tseajaia, 14042 assuming that Moss (1972) has interpreted the tarsus correctly (the shapes of the tibiale and 14043 the intermedium are rather unusual). 14044 Tuditanus shows state 1 (Carroll & Baird, 1968: fig. 10B). 14045 14046 14047

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14048 242. TAR 4: Distal tarsal ossifications between fibulare and digits: absent (0); present 14049 (1). RC07 (p. 108) stated that this character and TAR 5 have the same distribution. We would 14050 have merged the characters in that case; however, Scincosaurus and Orobates break the 14051 pattern (see below). 14052 Platyrhinops (D. M., pers. obs. of AMNH 2002) and Albanerpetidae (McGowan, 14053 2002) have state 1. 14054 Remarkably, Scincosaurus shows state 0 (Milner & Ruta, 2009). 14055 14056 243. TAR 5: Distal tarsal ossifications between tibiale and digits: absent (0); present (1). 14057 State 1 is known in Platyrhinops (D. M., pers. obs. of AMNH 2002), Albanerpetidae 14058 (McGowan, 2002), Batropetes (Glienke, 2015) and Scincosaurus (Milner & Ruta, 2009). 14059 Orobates has state 0; of all distal tarsals only the fourth is ossified (Berman et al., 14060 2004). 14061 14062 244. RIB 1: Anterior and posterior process of ribs: both absent (0); anterior process 14063 present, posterior process absent (1); both present, ribs k-shaped in at least part of the 14064 trunk (2) (ordered). RC07 compared the shape to a capital K, but the ventrolateral ramus is 14065 distinctly longer than the others, so we follow the comparison by Anderson (2002, 2003a, b) 14066 and Anderson, Carroll & Rowe (2003). While RC07 only contrasted state 2 with the others in 14067 a binary character, we prefer to code the fact that Lethiscus has half of the k-shape (Anderson, 14068 Carroll & Rowe, 2003). State 1 is not known elsewhere (the anterior process may be 14069 homologous with the capitulum, but differs in not articulating with a vertebra); ribs with a 14070 posterior but no anterior process appear to be entirely unknown, justifying ordering of this 14071 character. 14072 Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of USNM 4555, CM 14073 81430 and CM 81512), Archeria (D. M., pers. obs. of MCZ 2049 and others) and 14074 Cardiocephalus (CG78: fig. 31) have state 0. 14075 14076 245. RIB 2: “Cervical” (“pectoral”) ribs with (0) or without (1) flattened distal ends. 14077 Unknown in Ossinodus (Warren & Turner, 2004; Warren, 2007). 14078 Cochleosaurus has state 0 (Sequeira, 2009), and so do Isodectes (D. M., pers. obs. of 14079 USNM 4474 and CM 81430), Doleserpeton (Sigurdsen & Bolt, 2010), Cardiocephalus 14080 (CG78: fig. 31) and Ptyonius (D. M., pers. obs. of MCZ 3721, a cast of “AMNH 6871 14081 (85466)”). 14082 Trimerorhachis has state 1 where known (Milner & Schoch, 2013). So do 14083 Oestocephalus (Anderson, 2003a: fig. 4B) and Phlegethontia (Anderson, 2002). We further 14084 follow Pardo et al. (2017: matrix) in scoring state 1 for Lethiscus and *Coloraderpeton. 14085 14086 246. RIB 3: Ribs mostly straight (0) or ventrally curved in at least part of the trunk (1). 14087 The “first dorsal rib” of Tseajaia has “cervical rib” morphology (Moss, 1972); this 14088 may be why it (and it alone) was scored as polymorphic by RC07. The definition refers to “at 14089 least part of the trunk”, however, meaning that Tseajaia has state 1. 14090 So do Isodectes (D. M., pers. obs. of USNM 4474, CM 81430 and CM 81512) and 14091 Cardiocephalus (CG78). 14092 State 0 is found in Cochleosaurus (Sequeira, 2009). We follow Pardo et al. (2017: 14093 matrix) in scoring state 0 for *Coloraderpeton. 14094 Schoch & Rubidge (2005: figs. 5B, 7A) showed curvature in *Micropholis, but did not 14095 explain if it is ventral or only caudal in direction. We have scored *Micropholis as unknown. 14096 14097

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14098 247. RIB 4: Broad rectangular flanges in at least some trunk ribs: absent (0); present (1). 14099 Like Cochleosaurus (Sequeira, 2009), Archeria (D. M., pers. obs. of MCZ 2049 and 14100 others), Kotlassia (Bystrow, 1944) and Cardiocephalus (CG78: fig. 31), Lethiscus has state 0 14101 (Anderson, Carroll & Rowe, 2003). 14102 *Nigerpeton has state 1 (D. M., pers. obs. of MNN MOR 83). In *Platyoposaurus, the 14103 flanges are somewhat narrow, but clearly present as well (Konzhukova, 1955; Gubin, 1991). 14104 14105 248. RIB 5: Triangular spur-like posterodorsal process in at least some trunk ribs: 14106 absent (0); present (1). 14107 Baphetes shows state 1 (Milner & Lindsay, 1998), as do Gephyrostegus (Godfrey & 14108 Reisz, 1991) and Kotlassia (Bystrow, 1944). 14109 Like Cochleosaurus (Sequeira, 2009), Archeria (D. M., pers. obs. of MCZ 2049 and 14110 others) and Cardiocephalus (CG78: fig. 31), Lethiscus has state 0 (Anderson, Carroll & 14111 Rowe, 2003), and so does *Nigerpeton (D. M., pers. obs. of MNN MOR 83). 14112 14113 249. RIB 6: Elongate posterodorsal triangular flange in the midtrunk ribs: absent (0); 14114 present (1). 14115 Like Cochleosaurus (Sequeira, 2009), Archeria (D. M., pers. obs. of MCZ 2049 and 14116 others) and Cardiocephalus (CG78: fig. 31), Lethiscus has state 0 (Anderson, Carroll & 14117 Rowe, 2003), and so does *Nigerpeton (D. M., pers. obs. of MNN MOR 83). 14118 14119 250. RIB 7: Trunk ribs longer (0) or shorter (1) than three successive articulated 14120 vertebrae in adults. The measured vertebrae should be from the same region of the trunk as 14121 the vertebrae. 14122 RC07 added the unquantified terms “poorly ossified” and “slender” to the definition of 14123 state 1 and did not test if all three traits are correlated. We have reduced the character to 14124 length alone, making it identical to McGowan’s (2002) character 1 as modified by Marjanović 14125 & Laurin (2008: 177f.). Thus, we have scored Micromelerpeton as possessing state 0 which, 14126 according to R. Schoch (pers. comm. to Marjanović & Laurin, 2008: 178), is observed in the 14127 metamorphosed specimens announced by Lillich & Schoch (2007) and Schoch (2009b), and 14128 we have scored Balanerpeton (Milner & Sequeira, 1994), Dendrerpetidae (Holmes, Carroll & 14129 Reisz, 1998), Acheloma (Case, 1911: fig. 46), Cardiocephalus (borderline; CG78: fig. 31), 14130 Odonterpeton (CG78), Lethiscus (the longest preserved rib seems not to reach state 0, 14131 although it comes close: Wellstead, 1982: fig. 8B), Oestocephalus (Carroll, 1998a; Anderson, 14132 2003a) and Phlegethontia (both species; Anderson, 2002: fig. 10) as having state 1. 14133 Importantly, Acheloma (Case, 1911: fig. 46) demonstrates that this character is not 14134 correlated to absolute body size, even though *Utaherpeton adds to the already known sample 14135 of taxa which change from state 1 to (barely) state 0 in their ontogeny (Carroll, Bybee & 14136 Tidwell, 1991; Carroll & Chorn, 1995). 14137 State 0 is further found in Baphetes (Milner & Lindsay, 1998), Cochleosaurus 14138 (Sequeira, 2009) and Isodectes (D. M., pers. obs. of CM 81512) as well as *Nigerpeton (D. 14139 M., pers. obs. of MNN MOR 83). It furthermore occurs (just barely) in Adelospondylus and 14140 Adelogyrinus (Andrews & Carroll, 1991; contra Marjanović & Laurin, 2009), while 14141 Acherontiscus, in which the ribs are as long as 2½ vertebrae, has state 1 (Carroll, 1969b). 14142 Unknown in Phonerpeton (Dilkes, 1990) and in Westlothiana where it is too 14143 borderline to tell (Smithson et al., 1994). 14144 14145 14146 14147

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14148 251. CER VER 1: Halves of atlas neural arch unfused (0) or fused (1). 14149 Edops has state 0 (D. M., pers. obs. of MCZ 7197), as do Cochleosaurus (Sequeira, 14150 2009), Trimerorhachis (Pawley, 2007; Milner & Schoch, 2013), Acheloma (Polley & Reisz, 14151 2011), Triadobatrachus (Ascarrunz et al., 2016) and Batropetes (Glienke, 2013: 81; 2015). 14152 Euryodus is polymorphic, with E. dalyae having state 0 as scored, but E. primus 14153 showing state 1 (CG78: fig. 115). 14154 State 1 is found in Diplocaulus (Williston, 1909: pl. 3; Douthitt, 1917: fig. 4). We 14155 have scored *Gerobatrachus as possessing state 1, following the matrix by Anderson et al. 14156 (2008a), surprising though this is (Doleserpeton has state 0, as was correctly scored: Bolt, 14157 1991: fig. 5; Sigurdsen & Bolt, 2010). 14158 The situation in Microbrachis is unclear; in the other vertebrae the halves seem to 14159 have fused in later ontogeny (Olori, 2015). We have scored it as unknown. 14160 We follow Pardo et al. (2017: matrix) in scoring state 1 for Lethiscus and 14161 *Coloraderpeton. 14162 14163 252. CER VER 3: Axis arch not fused (0) or fused (1) to axis (pleuro)centrum. 14164 Trimerorhachis (Pawley, 2007) shows state 0, as does Acheloma (Polley & Reisz, 14165 2011). 14166 Eocaecilia has state 1 (Jenkins, Walsh & Carroll, 2007), as do Triadobatrachus 14167 (Ascarrunz et al., 2016: fig. 7), Kotlassia (Bystrow, 1944: 394, fig. 8), apparently Batropetes 14168 (Glienke, 2013) and Cardiocephalus (there is only “a trace of suture”: CG78: 58). We have 14169 also scored it for Hyloplesion, following Olori (2015: table S3), coherent with a statement on 14170 p. 57 of that paper but apparently contradicting another on p. 46. 14171 We also ascribe state 1 to Albanerpetidae because we strongly suspect that the entirely 14172 arch-less “axis”, which often fuses to the “third cervical”, is in fact the axis intercentrum, and 14173 the “third cervical” is the axis pleurocentrum + neural arch (Material and methods: 14174 Modifications to individual cells: The albanerpetid neck). 14175 In Brachydectes, however, we have scored state 0: while we have not been able to find 14176 a statement concerning specifically the axis, neurocentral sutures are ubiquitous in both the 14177 atlas and other vertebrae (Wellstead, 1991; Pardo & Anderson, 2016: fig. 15), so state 1 14178 would be rather surprising. 14179 State 0 is documented in subadult specimens of Doleserpeton, but the condition in 14180 adult individuals is apparently unknown; given state TRU VER 11(1), it is possible that they 14181 had state 1 of this character (Sigurdsen & Bolt, 2010), so we follow Sigurdsen & Green 14182 (2011) in keeping Doleserpeton scored as unknown. 14183 State 0 is also seen in the only known axis of Microphon (Bulanov, 2014); given the 14184 immature or paedomorphic (Bulanov, 2003) status of that specimen, we retain the original 14185 score of unknown. 14186 Given that the arch is fused to the centrum both in the atlas and in the trunk (Pardo et 14187 al., 2017: characters 111 and 132 in their matrix), state 1 seems likely enough in Lethiscus 14188 and *Coloraderpeton for us to score it. 14189 14190 253. CER VER 4: Odontoid process, or tuberculum interglenoideum, on anterior surface 14191 of atlas body: absent (0); present (1). It is a good question if this process – also called 14192 “intercotylar tubercle”; not homologous to the odontoid process of mammals, which consists 14193 of the entire atlas pleurocentra that are fused to the axis – should be considered homologous 14194 regardless of whether the “atlas body” consists of pleuro- or intercentra. Unfortunately, 14195 whether the atlantes of, say, lissamphibians consist of pleuro- or intercentra is itself a difficult 14196 question, so we have followed RC07 in considering all such processes primarily homologous.

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14197 We have scored this character as unknown for OTUs which are known to have any 14198 state of EXOCC 2-3-4-5/BASOCC 1-5 other than 4 or 5, because the process does not (as far 14199 as known) and probably cannot occur together with states 0, 1 or 2 of EXOCC 2-3-4- 14200 5/BASOCC 1-5-6 and by definition occurs with state 3 (where the cotyle of the basioccipital 14201 articulates with it). The great exception to this rule is Phlegethontia, which has state 1 of that 14202 character, but nonetheless displays a long odontoid process; this is made possible by the 14203 surprising gap between the skull and the atlas that is bridged by the long proatlas dorsally and, 14204 at least in part, by the odontoid process ventrally (Anderson, 2002; D. M., pers. obs. of 14205 USNM 17097, where the proatlas is not preserved). Although the process is an extension of 14206 the ventral surface in Phlegethontia, it has a more dorsal, more lissamphibian-like location in 14207 the closely related *Pseudophlegethontia (Anderson, 2003b), so we see no reason not to 14208 consider it primarily homologous and have scored state 1. 14209 Furthermore, this character is inapplicable to Doleserpeton, in which the area where a 14210 tubercle could lie is occupied by the huge notochordal canal (Bolt, 1991: fig. 5; Sigurdsen & 14211 Bolt, 2010). Similarly, the presacral centra of *Sclerocephalus are very incompletely ossified 14212 (Schoch & Witzmann, 2009a); *Platyoposaurus (Gubin, 1991: drawing 27) shows a well- 14213 defined but huge notochordal notch similar to that of Doleserpeton despite being a much 14214 larger animal. 14215 The illustrations of Acheloma supplied by Polley & Reisz (2011) are, unfortunately, 14216 not three-dimensional enough to tell; however, because Polley & Reisz (2011) did not 14217 mention the presence of a process, we have scored Acheloma as possessing state 0. 14218 We cannot find a description or illustration of the atlantes of Amphibamus or 14219 Eoscopus; the most likely source, Daly (1994), did not describe any atlas centra, except for 14220 mentioning the very existence of one in Platyrhinops (which RC07 already scored as 14221 unknown). We have therefore scored both as unknown. 14222 The condition is further unknown in Hyloplesion (CG78: 131). 14223 Odonterpeton was scored as unknown in RC07. CG78: 167 implied state 0, but this 14224 refers to a large process as commonly found in “microsaurs”; the process can be very small in 14225 lissamphibians, and indeed CG78: fig. 99C (repeated as fig. 116L) depicted state 1. Personal 14226 observation by D. M. of USNM 4465+4467 (the holotype and probably only known 14227 specimen) shows that this is correct – although only as an outline drawing; the process is not 14228 part of the ventral surface of the atlas, but has a considerably more dorsal position, making the 14229 atlas much less unusual than implied by CG78. 14230 State 1 is found in Diplocaulus (Williston, 1909: pl. 3), as well as in Triadobatrachus 14231 (very weakly ossified: Ascarrunz et al., 2016: 3D model 1), Notobatrachus (Báez & Basso, 14232 1996; Báez & Nicoli, 2004), *Liaobatrachus (figures in Dong et al., 2013) and other frogs 14233 like **Gobiates (Roček, 2000: fig. 16; 2008: fig. 2E). We further follow Pardo et al. (2017: 14234 matrix) in scoring it for Lethiscus and *Coloraderpeton. 14235 14236 254. TRU VER 1: Extra articulations above zygapophyses in at least some trunk and 14237 caudal vertebrae: absent (0); present (1). 14238 Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of CM 81512) and 14239 Cardiocephalus (CG78: fig. 31) have state 0. 14240 14241 255. TRU VER 2: Neural and haemal spines rectangular to fan-shaped in lateral view: 14242 no (0); yes (1). 14243 Chenoprosopus shows state 0 (D. M., pers. obs. of USNM 437646), as do 14244 Cardiocephalus (CG78: fig. 31), Phlegethontia (Anderson, 2002), Ossinodus (Warren, 2007) 14245 and *Nigerpeton (D. M., pers. obs. of MNN MOR 83).

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14246 Pardo et al. (2017: supp. inf.) scored *Coloraderpeton as having state 0 of their 14247 character 115: “Neural spine shape in lateral view (HPSA 153): (0) anterior and posterior 14248 sides parallel, forming a rectangular surface; (1) non-parallel, triangular”. We interpret this as 14249 our state 1. 14250 14251 256. TRU VER 3: Neural and haemal spines aligned dorsoventrally: absent (0); present 14252 (1). 14253 Hyloplesion (Olori, 2015) and Ossinodus (Warren, 2007) have state 0. 14254 The entire tail is unknown in Colosteus (Hook, 1983), Crassigyrinus (Panchen, 1985), 14255 Neldasaurus (Chase, 1965), Broiliellus (Carroll, 1964), Eoherpeton (Smithson, 1985), 14256 Pholiderpeton scutigerum (Clack, 1987b), Gephyrostegus (Carroll, 1970; Godfrey & Reisz, 14257 1991), Solenodonsaurus (Laurin & Reisz, 1999; Danto, Witzmann & Müller, 2012), 14258 Stegotretus (Berman, Eberth & Brinkman, 1988), and Ariekanerpeton (Klembara & Ruta, 14259 2005b). Similarly, no hemal arches are preserved in Triadobatrachus (Roček & Rage, 2000), 14260 and none were ossified in described specimens of Apateon or Leptorophus. 14261 Doleserpeton has state 0 as scored, but one wonders how this was done before 14262 Sigurdsen & Bolt (2010) described (any part of) the tail for the first time in a publication; 14263 Ruta, Coates & Quicke (2003) did not claim to have seen specimens and did not cite Bolt’s 14264 unpublished thesis (which dates to 1964). 14265 14266 257. TRU VER 4: Haemal spines not fused (0) or fused (1) to caudal centra. According to 14267 RC07, state 1 is “observed almost exclusively in nectrideans”, but this statement does not 14268 seem defensible to us. 14269 Importantly, hemal arches are not homologous to intercentra or parts thereof (contra, 14270 e.g., Williston, 1912: 466; Carroll, 1968: 1177, 1188–1189, 1969b: 545; Carroll & Chorn, 14271 1995: 49; Palci, Caldwell & Nydam, 2013: 1339; Olori, 2015: 57). This is demonstrated by 14272 the separate hemal arches and intercentra of animals like the temnospondyls 14273 *Acanthostomatops (Witzmann & Schoch, 2006a), *Lydekkerina (Pawley & Warren, 2005) 14274 and **Trematolestes (Schoch, 2006: fig. 6H) or the anthracosaurs **RM 206859 (Holmes & 14275 Carroll, 2010) and apparently **CM 34638 (Clack, 2011a). Therefore, this character cannot 14276 be interpreted as “hemal spines not/fused to caudal pleurocentra”. It is also, unfortunately, not 14277 a cheap way of determining whether an animal has intercentra (see TRU VER 7, 8, 9, 13-14). 14278 State 1 is thus present at a minimum in Eusthenopteron and Acanthostega (Coates, 14279 1996), probably Ichthyostega (Jarvik, 1996: pl. 38), Greererpeton (Godfrey, 1989), Edops (D. 14280 M., pers. obs. of MCZ 7128), Trimerorhachis (Pawley, 2007), Dendrerpetidae (Holmes, 14281 Carroll & Reisz, 1998: fig. 1), Eryops (Moulton, 1974: fig. 6–8), Acheloma (Case, 1911: 135), 14282 Phonerpeton (Dilkes, 1990: fig. 10), Ecolsonia (Berman, Reisz & Eberth, 1985), 14283 Amphibamus and Eoscopus (Daly, 1994), Platyrhinops (Hook & Baird, 1984), Karaurus 14284 (Ivachnenko, 1978: 366; D. M., pers. obs. of unnumbered MNHN cast of PIN 2585/2), 14285 Caerorhachis (Ruta, Milner & Coates, 2002), Proterogyrinus (Holmes, 1984), Archeria 14286 (Holmes, 1989), Pholiderpeton attheyi (Panchen, 1972), Bruktererpeton (Boy & Bandel, 14287 1973: fig. 8), Kotlassia (Bystrow, 1944), Discosauriscus (Klembara & Bartík, 2000), 14288 Seymouria (White, 1939: 356), Diadectes (Berman, Sumida & Martens, 1998: 78), 14289 Limnoscelis (Williston, 1912: 466, fig. 25; Berman & Sumida, 1990: 326), Captorhinus 14290 (Dilkes & Reisz, 1986: 1294), Petrolacosaurus (Reisz, 1981: 36), Westlothiana (Smithson et 14291 al., 1994), Micraroter (CG78: 97, fig. 58), Orobates (Nyakatura et al., 2015: digital model), 14292 Ossinodus (Warren, 2007), Silvanerpeton (Ruta & Clack, 2006) and Utegenia (Klembara & 14293 Bartík, 2000: fig. 30). It is also suggested for Balanerpeton by fig. 10C of Milner & Sequeira 14294 (1994); we have accepted this at face value. 14295 Hyloplesion has state 0 (Olori, 2015).

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14296 A large number of taxa where the tail is poorly or not known were scored as having 14297 state 0 by RC07. This includes Colosteus (Hook, 1983), Crassigyrinus (Panchen, 1985), 14298 Neldasaurus (Chase, 1965), Broiliellus (Carroll, 1964), Eoherpeton (Smithson, 1985), 14299 Pholiderpeton scutigerum (Clack, 1987b), Gephyrostegus (Carroll, 1970; Godfrey & Reisz, 14300 1991), Solenodonsaurus (Laurin & Reisz, 1999; Danto, Witzmann & Müller, 2012), 14301 Stegotretus (Berman, Eberth & Brinkman, 1988) and Ariekanerpeton (Klembara & Ruta, 14302 2005b). 14303 Further unknown in Baphetes (Milner & Lindsay, 1998: fig. 8), Albanerpetidae 14304 (McGowan, 2002) and Paleothyris (Carroll, 1969a); inapplicable to Triadobatrachus which 14305 does not preserve any hemal arches (Roček & Rage, 2000; Ascarrunz et al., 2016). 14306 Doleserpeton has a truly remarkable tail in which all elements of each vertebra – 14307 neural arch, pleurocentrum, intercentrum, and hemal arch – are fused into a single bone 14308 (Sigurdsen & Bolt, 2010). This constitutes state 1; it is probably not even possible to 14309 distinguish if the hemal arches are fused to the intercentra alone or to both inter- and 14310 pleurocentra, though Sigurdsen & Bolt (2010) suggested that the latter has happened. 14311 We interpret *Archaeovenator (Reisz & Dilkes, 2003: fig. 1) as having fused hemal 14312 arches and intercentra, thus state 1. 14313 14314 258. TRU VER 5: Extra articulations on haemal spines: absent (0); present (1). 14315 State 0 is now known in Hyloplesion (Olori, 2015), Orobates (Nyakatura et al., 2015: 14316 digital model) and Ossinodus (Warren, 2007). 14317 State 1 is found in Scincosaurus (Milner & Ruta, 2009). 14318 The entire tail is unknown in Colosteus (Hook, 1983), Crassigyrinus (Panchen, 1985), 14319 Neldasaurus (Chase, 1965), Broiliellus (Carroll, 1964), Eoherpeton (Smithson, 1985), 14320 Pholiderpeton scutigerum (Clack, 1987b), Gephyrostegus (Carroll, 1970; Godfrey & Reisz, 14321 1991), Solenodonsaurus (Laurin & Reisz, 1999), Stegotretus (Berman, Eberth & Brinkman, 14322 1988) and Ariekanerpeton (Klembara & Ruta, 2005b). Similarly, no hemal arches are 14323 preserved in Triadobatrachus (Roček & Rage, 2000; Ascarrunz et al., 2016). 14324 Doleserpeton has state 0 as scored, but one wonders how this was done before 14325 Sigurdsen & Bolt (2010) described (any part of) the tail for the first time in a publication; 14326 Ruta, Coates & Quicke (2003) did not claim to have seen specimens and did not cite Bolt’s 14327 unpublished thesis (which dates to 1964). 14328 14329 259. TRU VER 7: Ossified pleurocentra: absent (0); present (1). Under the assumption that 14330 loss of ossification does not equal loss of the element, we have not treated this character or 14331 TRU VER 13-14 (see below) as irreversible in Analyses R7–R12. 14332 Like RC07, we have scored this and the next two characters as unknown in all taxa 14333 where the vertebrae are monospondylous, because in them there is no way – other than 14334 phylogenetic reconstruction – to tell whether the single centrum is the inter- or the 14335 pleurocentrum (i.e. the fused pair of left and right inter- or pleurocentra); see TRU VER 4 14336 (above) on the homology of hemal arches. We have correspondingly scored TRU VER 13-14 14337 as state 0 (intercentrum forms complete ring) or 2 (trunk intercentra absent), an option that 14338 was not available before we merged those two characters. The only cases RC07 overlooked 14339 are Batropetes (Carroll, 1991; Glienke, 2013, 2015), Microbrachis (CG78; Olori, 2015) and 14340 Scincosaurus (Bossy & Milner 1998; Milner & Ruta 2009) and, in the case of TRU VER 13 14341 but not TRU VER 7, 8 and 9, Triadobatrachus (Ascarrunz et al., 2016). The only exceptions, 14342 for which we have scored state 1, are Albanerpetidae (already so scored by RC07 for unclear 14343 reasons), which may have axis intercentra (Material and methods: Modifications to individual 14344 cells: The albanerpetid neck), and *Utaherpeton: the tail of the immature specimen of 14345 *Utaherpeton of demonstrates that the only ossified centra are pleurocentra because the last

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14346 few are broad dorsally but narrow to a point ventrally (Carroll & Chorn, 1995) – the opposite 14347 would be expected for intercentra. 14348 There is evidence from **extant frogs that their centra are pleurocentra: the tadpoles 14349 of certain megophryids ossify caudal centra that begin as paired ossifications dorsolateral to 14350 the notochord, with the distalmost centra not progressing beyond this stage before they are 14351 osteoclastically destroyed during metamorphosis (Handrigan & Wassersug, 2007). However, 14352 there are no megophryids, indeed no clear crown-group frogs at all, in this matrix; we have 14353 kept Notobatrachus, Vieraella and *Liaobatrachus as unknown. 14354 In the adelogyrinids, it is likewise difficult or impossible to determine the homology of 14355 the monospondylous, fully ossified centra; the fact that the neural arches are positioned dorsal 14356 to the cranial halves of the centra and even articulate with two successive centra in part of the 14357 trunk of **Palaeomolgophis (Andrews & Carroll, 1991: 243) rather strongly suggests that the 14358 centra are intercentra and all adelogyrinids are fully stereospondylous, but in order to avoid 14359 potential bias against the traditional hypothesis that the adelogyrinids are “lepospondyls”, we 14360 have scored them as unknown like the abovementioned other taxa with monospondylous 14361 centra. 14362 State 1 is found in Cochleosaurus (Sequeira, 2009), Cardiocephalus (CG78: fig. 31) 14363 and Utegenia (Klembara & Ruta, 2004b). Pierce et al. (2013) have confirmed it in 14364 Ichthyostega (contra Ahlberg, Friedman & Blom, 2005; though note that Jarvik, 1996, was 14365 right for the wrong reasons). 14366 Clear occurrences of state 0 are thus limited to Panderichthys and Crassigyrinus, and 14367 certainly not homologous between the two. State 0 in Crassigyrinus, at least, may be 14368 correlated to its generally very low degree of ossification in the endochondral skeleton; 14369 scoring Crassigyrinus as unknown would render this character parsimony-uninformative. 14370 14371 260. TRU VER 8: Trunk pleurocentra fused midventrally: no (0); yes (1). 14372 Cochleosaurus apparently has state 0 (Sequeira, 2009). 14373 Cardiocephalus (CG78: fig. 31) and Orobates (Berman et al., 2004: fig. 11; Nyakatura 14374 et al., 2015: digital model) have state 1. 14375 The vertebrae of *Casineria are preserved in strict lateral view. We have scored state 14376 1 because the pleurocentra reach the ventral side of the vertebral column and have a flat 14377 surface rather than a point there (Fig. 5). The following character remains unknown for 14378 *Casineria. 14379 14380 261. TRU VER 9: Trunk pleurocentra fused middorsally: no (0); yes (1). 14381 Cochleosaurus apparently has state 0 (Sequeira, 2009), as does Trimerorhachis 14382 (Pawley, 2007). 14383 Cardiocephalus (CG78: fig. 31) and Orobates (Berman et al., 2004: fig. 10B; 14384 Nyakatura et al., 2015: digital model) have state 1. 14385 In Proterogyrinus, the pleurocentra “are tightly appressed dorsally” (Sigurdsen & 14386 Green, 2011: 18), but not fused or apparently even sutured; we have therefore kept state 0. 14387 State 0 is observed in the tail and possibly the last presacral vertebra of the immature 14388 specimen of *Utaherpeton, but the condition is unknown in the other vertebrae (which should 14389 be more advanced ontogenetically) of that specimen and entirely unknown in the adult 14390 specimen (Carroll & Chorn, 1995). We have therefore scored *Utaherpeton as unknown for 14391 this character. 14392 Ariekanerpeton and Utegenia were scored as polymorphic. Given the ontogenetic 14393 progression from 0 to 1 in better-known seymouriamorphs, we have scored Ariekanerpeton as 14394 unknown following Klembara & Ruta (2005b: 80) and have kept only state 1 for Utegenia,

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14395 for which state 1 was mentioned to exist by Klembara & Ruta (2004b: 79), but not illustrated 14396 in their fig. 3C which is cited there. 14397 14398 262. TRU VER 10: Neural arches without (0) or with (1) distinct convex lateral surfaces. 14399 Chenoprosopus (D. M., pers. obs. of USNM 437646), Cochleosaurus (Sequeira, 2009) 14400 and Isodectes (D. M., pers. obs. of CM 81512) have state 0; apparently, so do Batropetes 14401 (Glienke, 2013) and Cardiocephalus (CG78: fig. 31, 33). 14402 Petrolacosaurus was scored as polymorphic in RC07, presumably because “[t]he 14403 neural arches are slightly swollen above the postzygapophyses, but only in the dorsal 14404 vertebrae” (Reisz, 1981: 34). We think, however, that this character should be considered 14405 inapplicable to the greatly elongate cervical vertebrae and have therefore scored state 1 alone. 14406 Similarly, we have kept state 1 for Limnoscelis and Orobates, which have swollen neural 14407 arches in the trunk but not the tail vertebrae (Kennedy, 2010; Nyakatura et al., 2015: digital 14408 model). – In principle, presence of different states in different parts of the vertebral column 14409 should be considered an intermediate state; polymorphism implies that different individuals or 14410 indeed subclades have different states, or that the left and right sides of the same individual 14411 do. 14412 State 1 makes a surprise appearance in Diplocaulus (Williston, 1909: pl. 3). 14413 We have scored Utegenia as unknown because the observed state 0 is also found in 14414 larvae but not “postmetamorphic” individuals of Discosauriscus, in which the appearance of 14415 state 1 is interpreted as part of the transition to terrestrial life (Klembara & Bartík, 2000; 14416 Klembara, 2009). 14417 14418 263. TRU VER 11: Neural arches of trunk vertebrae fused to centra: no (0); yes (1). 14419 According to RC07, this character “does not appear to be simply related to […] inferred 14420 degree of specimen maturity”, yet there is evidence that Batropetes and Microbrachis (see 14421 below) changed from state 0 to state 1 in ontogeny, and in amniotes this is a very widely used 14422 marker for skeletal maturity (Irmis, 2007); among OTUs with more or less holospondylous 14423 vertebrae, it seems to us that only the most paedomorphic ones keep state 0 throughout life, 14424 and the same may hold for seymouriamorphs (Laurin, 2000). 14425 Centra are altogether unknown in Leptorophus (Boy, 1987; Werneburg, 2007b); they 14426 probably only ossified during metamorphosis (if metamorphosis ever occurred in 14427 Leptorophus). We have accordingly scored it as unknown. 14428 State 0 is found in Cochleosaurus (Sequeira, 2009), Platyrhinops (Hook & Baird, 14429 1984), Saxonerpeton, Hapsidopareion and Micraroter (CG78) and Hyloplesion (Olori, 2015: 14430 46, apparently contradicting 57). 14431 State 1 is documented in Albanerpetidae (Estes & Hoffstetter, 1976; Fox & Naylor, 14432 1982; McGowan, 1996), Eocaecilia (Jenkins, Walsh & Carroll, 2007), Cardiocephalus (there 14433 is only “a trace of suture”; CG78: p. 60) and Batrachiderpeton (Bossy & Milner, 1998: fig. 14434 63A–D). 14435 Discosauriscus, Ariekanerpeton and Utegenia were scored as having state 0. This is 14436 probably ontogenetic (Laurin, 2000); we have changed their scores to unknown. 14437 Following the skeletally most mature specimens (Carroll, 1991; Glienke, 2013; Olori, 14438 2015), we have scored Batropetes and Microbrachis as possessing state 1. 14439 14440 264. TRU VER 12: Bicipital rib-bearers on trunk centra: absent (0); present (1). 14441 Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 437646), Cochleosaurus 14442 (Sequeira, 2009), Isodectes (D. M., pers. obs. of CM 81512), Broiliellus (Carroll, 1964: 198), 14443 Cardiocephalus (CG78) and apparently Batrachiderpeton (Bossy & Milner, 1998: fig. 63A) 14444 have state 0.

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14445 Centra are altogether unknown in Leptorophus (Boy, 1987; Werneburg, 2007b); they 14446 probably only ossified during metamorphosis (if metamorphosis ever occurred in 14447 Leptorophus). We have accordingly scored it as unknown. 14448 The rib-bearers of *Pangerpeton are not bicipital, because the ribs are single-headed 14449 (an autapomorphy of Cryptobranchoidea: Gao & Shubin, 2012), but because they are still rib- 14450 bearers as seen in salamanders and almost nowhere else, we have scored state 1 for 14451 *Pangerpeton. 14452 We have kept state 0 for all diadectomorphs for the time being, but should point out 14453 that the condition of at least Orobates (Nyakatura et al., 2015: digital model) is remarkably 14454 similar to state 1 and should likely be counted as such. 14455 14456 265. TRU VER 13-14: Trunk intercentra: fused middorsally (0), separate middorsally 14457 (1), absent (2) (ordered). Intercentra in state 1 have a wide range of sizes; usually they are 14458 crescent-shaped, and their dorsal tips do not touch. Evidently, this is a single continuous 14459 character, with the degree of intercentrum ossification gradually decreasing from state 0 to 14460 state 2 (though something in the middle of state 1 is the plesiomorphy). We assign state 0 or 2 14461 to taxa with single-piece centra throughout the column that cannot (without phylogenetic 14462 bracketing) be identified as pleuro- or intercentra (see TRU VER 7). 14463 Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 437646) and Cochleosaurus 14464 (Sequeira, 2009) have state 1, as does Cardiocephalus (CG78: fig. 31). 14465 Isodectes has state 0 or 1 (D. M., pers. obs. of CM 81430). 14466 Albanerpetidae seems to have axis intercentra (Material and methods: Modifications to 14467 individual cells: The albanerpetid neck), but lacks trunk intercentra, giving it state 2. 14468 Solenodonsaurus is known (Carroll, 1970: 294–295; Danto, Witzmann & Müller, 14469 2012) to have very small intercentra that are very far from reaching the dorsal edge of the 14470 pleurocentra (or rather the notochord) and thus cannot possibly have been fused middorsally; 14471 this means state 1. 14472 Orobates was scored as unknown by RC07. A photo of a specimen containing the first 14473 six vertebrae shows that only the first four, counted as “neck” rather than “trunk”, have 14474 intercentra (Berman et al., 2004: fig. 11); this suggests state 2. In the digital model of 14475 Nyakatura et al. (2015), all vertebrae behind the sixth have intercentra (state 1); they are, 14476 however, modeled after an isolated neural arch + pleurocentrum because the vertebrae in the 14477 articulated specimens were apparently too crushed to reconstruct. Given the presence of state 14478 1 in Diadectes (as already scored) and the presence of intercentra in caudal, but not cranial or 14479 middle, trunk vertebrae in Eocasea (*Caseasauria), which we have also counted as state 1, we 14480 have tentatively assigned state 1 to Orobates; John Nyakatura has not replied to D. M.’s e- 14481 mail about this matter. 14482 Unexpectedly, *Nigerpeton has state 0 (D. M., pers. obs. of MNN MOR 69). 14483 14484 266. TRU VER 15: Anteroposteriorly elongate, lateral and ventral carinae on trunk 14485 centra: absent (0); present (1). We have assigned state 0 in cases where ventral carinae 14486 occur but lateral ones do not (e.g. Westlothiana: Smithson et al., 1994: fig. 9B, C; 14487 *Archegosaurus: Witzmann & Schoch, 2006; *Lydekkerina: Pawley & Warren, 2005 – 14488 though see Hewison, 2008). 14489 Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 437646) and Cochleosaurus 14490 have state 0 (Sequeira, 2009), and so do Cardiocephalus (CG78: fig. 31) and Orobates 14491 (Berman et al., 2004: fig. 11). 14492 RC07 scored only Brachydectes and the adelogyrinids as having state 1, and all other 14493 OTUs with preserved centra except the above as having state 0. It is possible that they meant 14494 to restrict this character to taxa with monospondylous centra; but neither would that make

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14495 sense, nor did they score diplospondylous OTUs as unknown. We have ascribed state 1 to any 14496 inter- or pleurocentra that have the described carinae. Thus, weak but clear cases of state 1 – 14497 where the ventral carinae are not fully distinct from each other but more or less form a very 14498 wide median carina – are found in Colosteus (Hook, 1983), Greererpeton (only in caudal 14499 dorsals: Godfrey, 1989: 85, fig. 6d, f), Neldasaurus (Chase, 1965) and Trimerorhachis 14500 (Chase, 1965; Pawley, 2007). State 1 is also found in Eoherpeton (Smithson, 1985: fig. 16; 14501 “horizontal grooves” on p. 349), Proterogyrinus (Holmes, 1984), Archeria (Holmes, 1989), 14502 Pholiderpeton attheyi (Panchen, 1966), apparently Ph. scutigerum (Clack, 1987b: especially 14503 fig. 21f), and – a particularly striking case – Acherontiscus (Carroll, 1969b). Given the 14504 additional occurrence in *Pholidogaster (Romer, 1964), we strongly suspect that state 1 is 14505 universal in anguilliform swimmers; its strong phylogenetic signal (all colosteids, all 14506 anthracosaurs, all adelospondyls, Brachydectes, both dvinosaurs – scored as unknown for 14507 Isodectes, which D. M. forgot to check during his collection visits, and for *Erpetosaurus 14508 [Milner & Sequeira, 2011]; five steps, no reversals) may well be entirely ecological. All 14509 aïstopods seem to have state 0 as already scored for the three in the original sample, which 14510 may be additional evidence that some of them were terrestrial (Anderson, 2002, 2003a; 14511 Germain, 2008a, b); notably, we could not score *Coloraderpeton. 14512 Unclear in Bruktererpeton (Boy & Bandel, 1973). 14513 Centra are altogether unknown in Leptorophus (Boy, 1987; Werneburg, 2007b); they 14514 probably only ossified during metamorphosis (if metamorphosis ever occurred in 14515 Leptorophus). We have accordingly scored it as unknown. 14516 14517 267. TRU VER 16: Strong proximal emargination along anterior and posterior margins 14518 of haemal spines: absent (0); present (1). RC07 added “of tail vertebrae” at the end; that is 14519 redundant. 14520 The entire tail is unknown in Colosteus (Hook, 1983), Crassigyrinus (Panchen, 1985), 14521 Neldasaurus (Chase, 1965), Broiliellus (Carroll, 1964), Eoherpeton (Smithson, 1985), 14522 Pholiderpeton scutigerum (Clack, 1987b), Gephyrostegus (Carroll, 1970; Godfrey & Reisz, 14523 1991), Solenodonsaurus (Laurin & Reisz, 1999; Danto, Witzmann & Müller, 2012), 14524 Stegotretus (Berman, Eberth & Brinkman, 1988) and Ariekanerpeton (Klembara & Ruta, 14525 2005b). Similarly, no hemal arches are preserved in Triadobatrachus (Roček & Rage, 2000; 14526 Ascarrunz et al., 2016), and none have been described in Leptorophus. 14527 Doleserpeton has state 0 as scored, but one wonders how this was done before 14528 Sigurdsen & Bolt (2010) described (any part of) the tail for the first time in a publication; 14529 Ruta, Coates & Quicke (2003) did not claim to have seen specimens and did not cite Bolt’s 14530 unpublished thesis (which dates to 1964). 14531 Platyrhinops has state 0 (Hook & Baird, 1984; Werneburg, 2012b: fig. 9a); so do 14532 Hyloplesion (Olori, 2015), Orobates (Nyakatura et al., 2015: digital model) and Ossinodus 14533 (Warren, 2007). 14534 14535 268. TRU VER 18: Striated ornament on vertebral centra: absent (0); present (1). State 1 14536 does in fact exist and occurs where it was scored in RC07 (Williston, 1909; Bossy & Milner, 14537 1998). For this reason we have ignored the original description of this character (RC07: 109) 14538 which contradicts its name: “A ‘pleated’ or unevenly striated surface sculpture characterises 14539 the neural spines [!] of some of the more derived keraterpetontid [ = diplocaulid] 14540 nectrideans.” 14541 State 0 is found in Edops (D. M., pers. obs. of MCZ specimens), Chenoprosopus 14542 (Hook, 1993; D. M., pers. obs. of USNM 437646), Cochleosaurus (Sequeira, 2009), Isodectes 14543 (D. M., pers. obs. of CM 81430), Cardiocephalus (CG78: fig. 31), Euryodus (CG78), 14544 Hyloplesion (Olori, 2015) and Ossinodus (Warren, 2007).

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14545 Centra are altogether unknown in Leptorophus (Boy, 1987; Werneburg, 2007b); they 14546 probably only ossified during metamorphosis (if metamorphosis ever occurred in 14547 Leptorophus). We have accordingly scored it as unknown. 14548 14549 269. TRU VER 19: Tallest ossified part of neural arch in posterior trunk vertebrae 14550 situated above (aligned vertically with) posterior half of vertebral centrum: no (0); yes 14551 (1). State 1 is much more widespread than RC07 scored it, at least if we assume that the 14552 neural spine counts as part of the neural arch, and if “entirely behind the centrum” still counts 14553 as “above […] posterior half” as opposed to the middle or the anterior half. In the absence of 14554 evidence for variation among the dorsal vertebrae, we have resorted to middle or anterior ones 14555 if no posterior ones are preserved. 14556 Specifically, state 1 is present in Eusthenopteron and Acanthostega (Coates, 1996; 14557 Pierce et al., 2013), Greererpeton (Godfrey, 1989), Whatcheeria (Lombard & Bolt, 1995), 14558 Cochleosaurus (Sequeira, 2009), Isodectes (D. M., pers. obs. of CM 81430), Neldasaurus 14559 (Chase, 1965), Trimerorhachis (Pawley, 2007), Balanerpeton (Milner & Sequeira, 1994: fig. 14560 9), Dendrerpetidae (Holmes, Carroll & Reisz, 1998), Eryops (Moulton, 1974), Ecolsonia 14561 (Berman, Reisz & Eberth, 1985), Amphibamus (Daly, 1994: fig. 22), Eoscopus (Daly, 1994: 14562 fig. 6, 7), Platyrhinops (Hook & Baird, 1984), Micromelerpeton (Boy, 1995), Albanerpetidae 14563 (Estes & Hoffstetter, 1976), Eocaecilia (Jenkins, Walsh & Carroll, 2007: fig. 37A), Karaurus 14564 (Ivachnenko, 1978), Triadobatrachus (Roček & Rage, 2000; Ascarrunz et al., 2016: fig. 9, 3D 14565 model 1), Valdotriton (Evans & Milner, 1996), Caerorhachis (Ruta, Milner & Coates, 2002), 14566 Proterogyrinus (Holmes, 1984), Archeria (somewhat borderline: Holmes, 1989), 14567 Bruktererpeton (Boy & Bandel, 1973), Gephyrostegus (Godfrey & Reisz, 1991), 14568 Solenodonsaurus (Danto, Witzmann & Müller, 2012), Discosauriscus (Klembara & Bartík, 14569 2000: fig. 4h), Diadectes (Berman, Sumida & Martens, 1998: fig. 13C), Cardiocephalus 14570 (CG78: fig. 31, 33), Scincosaurus (Bossy & Milner, 1998: fig. 63L), Lethiscus (Wellstead, 14571 1982), Ariekanerpeton (Klembara & Ruta, 2005b), apparently Vieraella (Báez & Basso, 14572 1996: fig. 6), Ossinodus (Warren & Turner, 2004) and Pederpes (Clack & Finney, 2008; 14573 Pierce et al., 2013). In *Australerpeton, Dias & Schultz (2003: fig. 8) reconstructed state 0, 14574 but their photo and drawing of an articulated specimen (fig. 2, 3) clearly show state 1, which 14575 we have therefore scored. 14576 We have retained state 0 for the unusual lumbar vertebrae of Ichthyostega (Pierce et 14577 al., 2013: fig. 1d); for Batrachiderpeton and Diploceraspis (Bossy & Milner, 1998: fig. 63) as 14578 well as, somewhat tentatively, Diplocaulus (Williston, 1909: pl. 3); for Eoherpeton, where the 14579 highest point of the neural spine is between the inter- and the pleurocentrum, in the middle of 14580 the centrum as a whole (Smithson, 1985: fig. 19); for Pholiderpeton attheyi, where the highest 14581 point is at least that far cranial in middle trunk vertebrae (more caudal trunk vertebrae are 14582 insufficiently preserved; Panchen, 1966); very tentatively for Ph. scutigerum, where at least 14583 some neural arches show state 0 even though it is less clear where in the column they come 14584 from (Clack, 1987b); and for neural spines with a horizontal flat top where the entire dorsal 14585 edge is the tallest “point” and covers at least part of the cranial half of the centrum 14586 (Keraterpeton, Diceratosaurus, Ptyonius, Sauropleura, Urocordylus: Bossy & Milner, 1998: 14587 fig. 61, 63, 76; *Karpinskiosaurus: Bystrow, 1944: fig. 22). State 0 further occurs in 14588 *Nigerpeton (D. M., pers. obs. of MNN MOR 83) and *NSM 994 GF 1.1 (Holmes & Carroll, 14589 2010). 14590 Unknown in Colosteus (Hook, 1983), Kotlassia (Bystrow, 1944: 409) and Utegenia 14591 (Klembara & Ruta, 2004b). *Llistrofus has state 1 in cranial to midtrunk vertebrae, but the 14592 preservation makes the condition of caudal trunk vertebrae unclear (CG78). 14593

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14594 270. TRU VER 20-21-22-23-24-25: Zygapophyses absent throughout, or nearly so (0), 14595 present only on trunk and proximal tail vertebrae (1), or present throughout (2) 14596 (ordered). These originally six characters concerned the presence of prezygapophyses (TRU 14597 VER 20, 22 and 24) and postzygaphopyses (TRU VER 21, 23 and 25) in the trunk (TRU 14598 VER 20 and 21) and the proximal (TRU VER 22 and 23) and distal tail (TRU VER 24 and 14599 25). 14600 One would at first think (as Pawley [2006: 205] did) that pre- and postzygapophyses 14601 only occur together because they articulate with each other. The reason given by RC07 for 14602 keeping them as separate characters was that Crassigyrinus and Trimerorhachis had been 14603 reported to possess pre- but lack postzygapophyses. 14604 In Trimerorhachis, however, the postzygapophyses merely happen not to be visible in 14605 lateral view in tail and caudal trunk vertebrae because the neural spine is continuous with 14606 them (much like in *Acanthostomatops: Witzmann & Schoch, 2006a); they are 14607 unambiguously present throughout the trunk and tail, like the prezygapophyses (Pawley, 14608 2007), so we have assigned state 2 to Trimerorhachis. 14609 In Crassigyrinus, the situation is less clear. Panchen (1985: 534) described two neural 14610 arch pairs as showing “no sign” of a postzygapophysis and then stated: “Postzygapophyses, 14611 formerly thought of (with prezygapophyses) as an autapomorphous feature of tetrapods, 14612 appear to be absent.” Two pages earlier, however, we find the statement: “The neural arches 14613 of Crassigyrinus are remarkable for their primitive or degenerate condition. All those visible 14614 occur as separate bilateral halves with no sign of suture or fusion in the middle. They lack 14615 clear zygapophyses of tetrapod type and they are very small for the size of the animal. None 14616 has been found in natural articulation with a centrum and in the absence of clearly defined 14617 matching articular facets on each it is not clear precisely what their mutual orientation was.” 14618 This implies quite strongly that prezygapophyses are also absent – yet, prezygapophyses 14619 (though unusually small ones) are illustrated and described as present. In the light of this, it 14620 must be wondered if postzygapophyses were likewise present – not necessarily as processes 14621 visible in lateral view, but at least as articular facets. Indeed, fig. 17(e), which shows the 14622 presumed left atlas arch in left lateral and cranial views, shows a convex surface that would fit 14623 into the concave craniodorsal margin of the prezygapophysis of the same arch. This convex 14624 surface is overhung by the craniocaudally very broad neural spine. We consider it likely that 14625 Crassigyrinus simply has a less well ossified version of the condition seen in Trimerorhachis. 14626 (The vertebrae of Crassigyrinus are indeed as poorly ossified as the quote above implies; fig. 14627 17(a)–(c) shows three pairs of incompletely fused left and right intercentra, the broadest pair 14628 measuring more than 2 cm from side to side.) At least, this interpretation is more probable 14629 than the occurrence of prezygapophyses that have nothing to articulate with. The tail of 14630 Crassigyrinus being unknown, we have scored Crassigyrinus as showing state 1 or 2. 14631 The reason given for keeping the zygapophyses of the trunk, the proximal tail and the 14632 distal tail as three separate pairs of characters was “to account for the possibility that 14633 acquisition of fully developed and ossified zygapophyses occurred in a ‘stepwise’ fashion 14634 along the backbone (e.g. tail of certain Devonian taxa, notably Acanthostega and 14635 Ichthyostega; trunk of Crassigyrinus and Trimerorhachis)” (RC07: 110). First, to the best of 14636 our knowledge, it is never observed, and would be unexpected from functional considerations, 14637 that prezygapophyses occur in the distal but not the proximal part of the tail. This confirms 14638 the suspicion of the “‘stepwise’ fashion” by RC07. Second, stepwise evolution can only be 14639 represented by an ordered multistate character (a meristic character, more precisely). Thus, 14640 TRU VER 22/23 and 24/25 should have been merged already by Ruta, Coates & Quicke 14641 (2003). Third, to the best of our knowledge, no animal is known that has zygapophyses in the 14642 trunk but nowhere in the tail (the urostyle of frogs perhaps excepted); the distinction between

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14643 TRU VER 20/21 and 22/23 is therefore useless in this matrix. For these reasons we feel 14644 obliged to perform this megamerger of six characters into one. 14645 Chenoprosopus (Hook, 1993; D. M., pers. obs. of USNM 437646), Cochleosaurus 14646 (Sequeira, 2009), Isodectes (D. M., pers. obs. of CM 81512 and CM 81430) and 14647 Cardiocephalus (CG78) have state 1 or 2. 14648 Doleserpeton has state 2 as already scored for TRU VER 22 through 25, but one 14649 wonders how this was done before Sigurdsen & Bolt (2010) described (any part of) the tail for 14650 the first time in a publication; Ruta, Coates & Quicke (2003) did not claim to have seen 14651 specimens and did not cite Bolt’s unpublished thesis (which dates to 1964). 14652 Triadobatrachus has state 1 or 2: the distalmost tail vertebrae are poorly preserved and 14653 poorly ossified (Ascarrunz et al., 2016). 14654 We have scored Bruktererpeton (Boy & Bandel, 1973) as possessing state 1 or 2 14655 because the distal tail is not described and only visible in one illustration (the plate), the 14656 resolution of which is insufficient to determine whether zygapophyses are present. About the 14657 same holds for Leptorophus (Werneburg, 2007b: fig. 2, 3). 14658 We have assigned the same score to Westlothiana, the distal part of whose tail is 14659 entirely unknown (Smithson et al., 1994). Similar things hold for Albanerpetidae (McGowan, 14660 2002) and for Microphon (only an axis is known: Bulanov, 2014), so we have scored them the 14661 same way. 14662 14663 271. TRU VER 26: Capitular facets situated on posterior rim of vertebral midtrunk 14664 centra: absent (0); present (1). State 0 will need to be divided; the capitular facet often sits 14665 on the intercentrum when inter- and pleurocentra are both present, but it can sit in the center 14666 of a pleurocentrum in gastrocentral vertebrae. State 1 includes cases where the facet straddles 14667 two successive centra. 14668 Gephyrostegus has state 0 (Godfrey & Reisz, 1991), as do Cardiocephalus (CG78) 14669 and Orobates (Nyakatura et al., 2015: digital model). 14670 State 1 is found in Scincosaurus (Milner & Ruta, 2009). We have also assigned it to 14671 Eocaecilia, where the facets commonly straddle two neighboring centra (Jenkins, Walsh & 14672 Carroll, 2007). 14673 State 1 was scored for Batropetes in RC07; however, capitular facets are altogether 14674 absent in Batropetes (Glienke, 2015), so we have changed the score to unknown. 14675 14676 272. TRU VER 27: Height of the ossified portion of the neural arch in midtrunk 14677 vertebrae greater (0) or smaller (1) than the distance between pre- and 14678 postzygapophyses. 14679 Chenoprosopus has state 0 (D. M., pers. obs. of USNM 437646). So does *Nigerpeton 14680 (D. M., pers. obs. of MNN MOR 83). 14681 State 1 is found, at least, in Cochleosaurus (Sequeira, 2009: fig. 12), Trimerorhachis 14682 (Pawley, 2007: fig. 5.1), Amphibamus (Daly, 1994: fig. 22), Doleserpeton (Sigurdsen & Bolt, 14683 2010), Eoscopus (Daly, 1994: fig. 6, 7), Albanerpetidae (Estes & Hoffstetter, 1976), 14684 Eocaecilia (Jenkins, Walsh & Carroll, 2007), Karaurus (M. L., pers. obs. of unnumbered 14685 MNHN cast of PIN 2585/2), Valdotriton (judging from cranial dorsals and proximal caudals: 14686 Evans & Milner, 1996: fig. 9a, 10), Cardiocephalus (CG78: fig. 31, 33), Scincosaurus (Bossy 14687 & Milner, 1998: fig. 63; Milner & Ruta, 2009), Diplocaulus, Diploceraspis and Ptyonius 14688 (Williston, 1909: pl. 3; Bossy & Milner, 1998: fig. 61, 63), Urocordylus (borderline: Bossy, 14689 1976), all aïstopods (Wellstead, 1982; Anderson, 2002, 2003a) and Orobates (Nyakatura et 14690 al., 2015: digital model). 14691 Tseajaia is given state 0 because that state is found in the vertebrae with the 14692 dorsoventrally longest neural spines (Moss, 1972).

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14693 Unknown in Kotlassia (Bystrow, 1944: 409); borderline and probably not completely 14694 prepared in the photo of *Chroniosaurus (Clack & Klembara, 2009: fig. 8). 14695 We have scored state 0 for *Coloraderpeton because the neural spines are described as 14696 “tall” or “high” in two of the three accessible sources (Carroll, 1998b; Anderson, 2003a). The 14697 third, however, scored them as “low” as opposed to “high” without quantifying these states 14698 (Anderson, Carroll & Rowe, 2003: table A1). 14699 14700 273. TRU VER 28: Crenulations or fimbriate sculpture along dorsal margin of ossified 14701 portion of neural spines: absent (0); present (1). 14702 Edops (D. M., pers. obs. of MCZ 7136) has state 0, as do Cochleosaurus (Sequeira, 14703 2009), Isodectes (D. M., pers. obs. of CM 81430), Triadobatrachus (Roček & Rage, 2000), 14704 Cardiocephalus and Euryodus (CG78), Hyloplesion (pers. obs. of NHMW specimens; Olori, 14705 2015) and Ossinodus (Warren & Turner, 2004). 14706 Inapplicable to Diplocaulus, the neural spines of which are too small to be ornamented 14707 (Williston, 1909; Douthitt, 1917). 14708 14709 274. TRU VER 29: Intravertebral foramina for spinal nerves in at least some trunk 14710 vertebrae: absent (0); present (1). 14711 Cardiocephalus has state 0 (CG78: fig. 31). 14712 Sauropleura is polymorphic (Bossy & Milner, 1998; Milner & Ruta, 2009: matrix). 14713 We have scored state 1 for *Pseudophlegethontia following the matrix of Anderson, 14714 Carroll & Rowe (2003). 14715 14716 275. TRU VER 30: Transverse processes stout and abbreviated, the length of which is 14717 less than 30% of neural arch height: absent (0); present (1). State 0, which D. M. has 14718 observed in Isodectes (CM 81512), probably hides some phylogenetically informative 14719 diversity. For instance, Carroll & Chorn (1995: 49f.) mentioned that adelogyrinids (scored 1 14720 in RC07) “are unique among lepospondyls in having very long transverse processes […] as in 14721 primitive labyrinthodonts” (emphasis ours), implying that the other “lepospondyls” have an 14722 intermediate condition (in terms of length) between those seen in “primitive labyrinthodonts” 14723 and adelogyrinids on the one hand and seymouriamorphs and diadectomorphs (which were 14724 scored as having state 0) on the other hand. 14725 Anyway, Adelospondylus and Adelogyrinus have state 0 (Andrews & Carroll, 1991), 14726 and the condition in Acherontiscus is unknown (Carroll, 1969b). State 0 further seems to be 14727 known in Cardiocephalus (CG78: fig. 31). This leaves state 1 exclusively to Colosteus and 14728 Greererpeton. 14729 14730 276. DIG 1-2-3-4: “Independent radials” (0); polydactyly (1); pentadactyly (2); 14731 tetradactyl forelimb (3); tridactyl forelimb (4) (ordered). RC07 treated the 14732 presence/absence of digits (DIG 1), the presence/absence of four or fewer fingers per hand 14733 (DIG 2), the presence/absence of five or fewer fingers per hand (DIG 3), and the 14734 presence/absence of three or fewer fingers per hand (DIG 4) as completely independent 14735 characters. It goes without saying that, if a taxon has three or fewer fingers per hand, it also 14736 has fewer than four and fewer than five, yet RC07 did not even provide for these cases by 14737 scoring inapplicability. We have therefore merged all these characters, except for splitting 14738 DIG 1 to differentiate the mere absence of digits (state 0 of the present character) from the 14739 wholesale absence of limbs (state HUM 18/DIG 1(0), see character 219). 14740 The present character differs from DIG 5 of Germain (2008a) by being ordered, 14741 containing partial uncertainty, and defining state 0 of this character and of character 219 (his 14742 states DIG 5(0) and DIG 5(5)) morphologically where Germain (2008a) had called them

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14743 “primary absence of digits” and “secondary absence of digits”, which should be an inference 14744 from the analysis and not an assumption of coding. It differs from DIG 1 of Ruta & Bolt 14745 (2006) in not splitting polydactyly into two states (eight and six fingers per hand, each only 14746 present in a single OTU), in providing for OTUs with three fingers per hand (which do not 14747 occur in the matrix of Ruta & Bolt, 2006), and again in being ordered. 14748 We have not counted the prepollex/-hallux, where identifiable as such, as a digit, 14749 because it is not homologous to an “independent radial” (Johanson et al., 2007) and because it 14750 is so common in otherwise four-fingered lissamphibians (if only, in most cases, as something 14751 like a distal carpal). The postminimus of Tulerpeton does count, but the possibly homologous 14752 pisiform bone does not, because its homology is unclear, because it is only a carpal without a 14753 digit, and because it is common in less-than-pentadactyl hands. 14754 In relation to a pentadactyl limb, a tetradactyl one can have digits I–IV or II–V. We 14755 have ignored this issue, treating all tetradactyl hands as primarily homologous, but see 14756 Marjanović & Laurin (2013a) for discussion. 14757 Greererpeton has often been thought to have tetradactyl hands, but Coates (1996: 415) 14758 mentioned and illustrated a well preserved hand with five fingers and mentioned another that 14759 preserves four, one of which is the distinctively small fifth. Accordingly, we have scored 14760 Greererpeton as having state 2, even though the closely related Colosteus really does seem to 14761 have only four fingers per hand as scored by RC07 (the third is the longest, as common in 14762 tetradactyl limbs, not the fourth as would usually be expected in a pentadactyl one; Hook, 14763 1983). – D. M. has not been able to find the fourth finger in the articulated hand of AMNH 14764 6917 (pers. obs.), but there is sufficient space for it. 14765 Only state 0 can be ruled out for Crassigyrinus (Panchen, 1985; Panchen & Smithson, 14766 1990), Baphetes (Milner & Lindsay, 1998), Edops (D. M., pers. obs. of MCZ 7126 and MCZ 14767 7274), Ecolsonia (Berman, Reisz & Eberth, 1985 – inferred from the hindlimb), Eocaecilia 14768 (Jenkins, Walsh & Carroll, 2007), Pholiderpeton scutigerum (Clack, 1987b), Kotlassia 14769 (Bystrow, 1944 – inferred from the hindlimb), Stegotretus (Berman, Eberth & Brinkman, 14770 1988), Saxonerpeton (CG78: 38), Asaphestera, Pelodosotis, Cardiocephalus, Euryodus 14771 (CG78), Ossinodus (Warren, 2007) and Pederpes (Clack & Finney, 2005); we have thus 14772 scored them all, and several OTUs which we added, as having state 1, 2, 3, or 4. 14773 The same appears to hold for Whatcheeria (Lombard & Bolt, 1995: 483; Bolt & 14774 Lombard, 2000: 1049), even though the latter source makes state 4 appear unlikely. 14775 In Eucritta, the same holds. The hindlimb does appear to be pentadactyl, which would 14776 strongly suggest five or fewer fingers in the forelimb, but we do not think polydactyly – 14777 especially a small postminimus like in the hand of Tulerpeton – can be ruled out. 14778 Cochleosaurus has state 3 (Sequeira, 2009). So does Isodectes (D. M., pers. obs. of 14779 USNM 4471, USNM 4555, and CM 81430). 14780 Trimerorhachis has state 2 or 3 (Case, 1935; Pawley, 2007). 14781 Dendrysekos (Dendrerpetidae) preserves four distal carpals (Holmes, Carroll & Reisz, 14782 1998). That most likely means four or five fingers (state 2 or 3). 14783 No metacarpals or fingers are preserved in Acheloma cumminsi, but there appear to 14784 have been five distal carpals (Olson, 1941), of which the tiny preaxialmost one could belong 14785 to a prepollex; this means four or five fingers and thus state 2 or 3. Dilkes (2015a) described 14786 only four distal carpals (all set in a plaster sculpture), but did not explicitly exclude (or 14787 mention) the possibility of a fifth beyond the absence of an articulation facet for one on distal 14788 carpal 4. – A. dunni only preserves two fragments of pedal phalanges (Polley & Reisz, 2011). 14789 Doleserpeton has state 3 (Sigurdsen & Bolt, 2009, 2010), as do Platyrhinops (Carroll, 14790 1964) and Leptorophus (judging from the drawings in Werneburg, 2007b). 14791 Bruktererpeton can safely be given state 2 (Boy & Bandel, 1973: 63 and fig. 14).

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14792 Solenodonsaurus has at least four metacarpals (Carroll, 1970; Danto, Witzmann & 14793 Müller, 2012), giving it state 1, 2, or 3. 14794 Westlothiana preserves parts of four fingers (Smithson et al., 1994) and may have had 14795 more, meaning state 1, 2, or 3. 14796 Keraterpeton has state 3 (A. C. Milner, pers. comm., September 2009) as scored by 14797 RC07. This agrees with Bossy & Milner (1998), contradicting Bossy (1976) and possibly 14798 Jaekel (1903: fig. 2), probably agreeing with pl. XIX of Huxley & Wright (1867), and 14799 contradicting the text of Huxley & Wright (1867) which mentions five metacarpals and 14800 fingers. 14801 Diceratosaurus, however, has state 2 (A. C. Milner, pers. comm., September 2009; D. 14802 M., pers. obs. of MB.Am.776, “Dicey 2-hands” = CM 34617, CM 81504, CM 81508, CM 14803 25468, and AMNH 6933, the type specimen), agreeing with Jaekel (1903: three times 14804 explicitly, and pl. IV-6, which shows MB.Am.776) and with Bossy (1976) but contradicting 14805 Bossy & Milner (1998). 14806 Diplocaulus has state 2 or 3 (Douthitt, 1917). 14807 In *Erpetosaurus, four incomplete fingers are preserved next to a break (Milner & 14808 Sequeira, 2011: fig. 8). We have scored state 1, 2 or 3. 14809 14810 deleted DOR FIN 1: Ossified lepidotrichia in : present (0); absent (1). As RC07 14811 pointed out, this character is parsimony-uninformative, so we have deleted it. 14812 14813 277. CAU FIN 1: Ossified lepidotrichia in caudal fin: present (0); absent (1). 14814 State 0 is probably present in Ventastega (Ahlberg et al., 2008); we have tentatively 14815 scored it accordingly. 14816 State 1 is found in Isodectes (D. M., pers. obs. of MCZ 6044, a cast of USNM 4481) 14817 and seems to be a safe inference for Platyrhinops (Clack & Milner, 2010; Werneburg, 2012b: 14818 fig. 9a). 14819 Although there is no evidence for lepidotrichia or endoskeletal radials around the 34 14820 preserved tail vertebrae of Bruktererpeton, in all but the first few very little is known beyond 14821 the centra, and what is known does not seem to preclude a tail fin skeleton (Boy & Bandel, 14822 1973); we have kept the score as unknown. 14823 Complete tails of Hyloplesion, preserving state 1, are known (CG78). 14824 We have scored both Proterogyrinus and Archeria as unknown, because at least the 20 14825 distalmost tail vertebrae in the latter (Holmes, 1989) and more in the former (Holmes, 1984) 14826 are unknown. Some discussion is provided by Clack (2011a). 14827 Further unknown in Broiliellus (the entire tail is unknown; Carroll, 1964), 14828 Doleserpeton (as already scored; although Sigurdsen & Green [2011: appendix 2] reported 14829 state 1, and although a tail fin is of course unexpected in this terrestrial or at most amphibious 14830 animal, the middle and distal parts of the tail are unknown: Sigurdsen & Bolt, 2010), 14831 Gephyrostegus (the entire tail is unknown: Carroll, 1970), Acherontiscus (the tail tip, and 14832 possibly the entire tail, is unknown: Carroll, 1969b), apparently Silvanerpeton (the known 14833 tails are very poorly preserved: Clack, 1994c: 375, fig. 1, 2; Ruta & Clack, 2006: fig. 9C) and 14834 Tseajaia (almost the entire tail is unknown; Moss, 1972). 14835 We have also scored Caerorhachis as unknown: only the first 16 or so caudal 14836 vertebrae are preserved (Holmes & Carroll, 1977; Ruta, Milner & Coates, 2002), and the first 14837 caudal with a supraneural radial in **CM 34638 appears to be around number 17 (Clack, 14838 2011a). 14839 14840 deleted BAS SCU 1: Basal scutes: present (0); absent (1). As RC07 pointed out, this 14841 character is parsimony-uninformative, so we have deleted it.

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14842 Appendix 2: Human-readable version of the revised data matrix (the computer-readable version is contained in Data S1). Polymorphism 14843 in parentheses, partial uncertainty in curly braces. The order of the original OTUs (Eusthenopteron through Utegenia) is unchanged from one 14844 version of the matrix of RC07. The deleted characters and the changes to them are not shown, but are documented and justified in Appendix 1. 14845 Note that the added OTU *Caseasauria is exclusively scored after Eothyris, Oedaleops and Eocasea. Abbreviations: micro., microsaur; Ph., 14846 Pholiderpeton; Pseudophleg., Pseudophlegethontia. 14847 Scores unchanged from RC07 are black; state numbers that have changed as a result of mergers or changes in the order of states remain 14848 black. Green font marks new scores when a state is new, redefined or possibly redefined (in cases where we are not sure of the meaning intended 14849 by RC07) and is used to mark all but the most trivial newly recognized cases of inapplicability as well as the scores changed to unknown 14850 following the removal of all postcranial material from Rhynchonkos (Material and methods: Treatment of OTUs: Rhynchonkos). Blue: score 14851 changed in order to account for ontogeny (Material and methods: Treatment of characters: “Ontogeny discombobulates phylogeny”); red: score 14852 changed at face value. The distinction between green and red should not be mistaken for different degrees of certainty; those are instead 14853 discussed in Appendix 1. Only green is shown when red and green apply, only blue is shown when red or green and blue apply; blue font is also 14854 used for the added OTUs where appropriate (their other scores are all black). 14855 5 10 15 20 25 30 35 40 45 Eusthenopteron 00300 00??? ?0000 00000 00000 ?000? 00000 00000 000?0 Panderichthys 00110 00?0? 10000 00000 00000 1000? 00000 00100 000?0 Ventastega 00000 0?10? ?0000 0001? 00000 1{12}000 ?010? 00?00 10000 Acanthostega 00200 0210? 00101 0001? 00000 12001 02111 0?100 00(01)00 Ichthyostega 00111 0010? 00010 0101? 00000 12000 02101 100(01)0 00100 Tulerpeton 2???? ????? ????? ????? ????? ????? ????? ????? ????? Colosteus 1020? ??11? 10000 ??00(01) 00000 12001 02210 01(01)00 00010 Greererpeton 10101 ??11? 10100 {02}1000 00000 12001 02210 01100 00010 Crassigyrinus 20001 11101 00000 200(01)0 00000 1{12}000 00211 0??00 00000 Whatcheeria 00?0? ??101 00000 000?0 00000 12001 00111 00000 10000 Baphetes 00(01)00 10101 00(01)?1 0?0?? 00000 12000 00211 01100 (01)0100 Megalocephalus 00200 10101 00101 1?0?? 00000 12000 (01)1211 00000 00(01)00 Eucritta 0010? 1?101 000(01)0 000?? 0000? 11000 00211 00000 00000 Edops ?11?0 11100 00000 0001? 00000 12000 002?1 01100 00100 Chenoprosopus 01100 10101 00100 1001? 00000 12000 00211 00000 00000 Cochleosaurus 01000 10100 00000 0001? 00001 12000 00201 00000 00000 Isodectes 10200 10101 10000 200?0 02000 10000 00210 00100 00000

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5 10 15 20 25 30 35 40 45 Neldasaurus 00300 1?100 00100 10000 0000{01} 10000 00210 00000 00000 Trimerorhachis 10100 10101 10000 0000(01) 00000 11(01)00 00210 01100 00100 Balanerpeton 10100 1?101 00010 00000 00000 1(12)000 00211 01100 10000 Dendrerpetidae 10000 11101 00000 00000 00000 10000 002(01)1 11100 10100 Eryops 10000 11101 00000 0001? 10000 12000 01111 00000 00(01)00 Acheloma 10200 11100 00000 21000 00000 12100 01211 00000 00100 Phonerpeton 30200 10100 00010 21000 0(02)001 12100 01211 00000 00000 Ecolsonia 1020? 11100 00000 20000 02000 11100 01201 01000 00000 Broiliellus brevis ?020? 1?101 00010 01000 00010 10100 01201 00000 00000 Amphibamus 10100 1?101 10010 00000 0200{01} 12000 01201 00001 00000 Doleserpeton 10100 11101 00010 01000 02012 12100 01211 00001 00000 Eoscopus 30100 1{12}101 00010 0?000 01000 11100 01211 00001 00100 Platyrhinops 10100 1{12}101 00010 00000 01000 1(12)000 01201 00000 10000 Micromelerpeton 10200 11101 00000 0?0?? 02000 11100 (01)1201 00000 00000 Apateon 10100 1?101 10010 0(01)000 02002 12100 01201 01000 00000 Leptorophus ?0300 1?101 10010 0?000 0{12}002 1{12}100 01211 01?00 00000 Schoenfelderpeton ?0200 1?101 10010 00000 {01}??02 1?100 01211 01100 00000 Albanerpetidae 20100 1?101 10100 01001 {01}0002 0(01)?01 ?{34}211 00?2? ????1 Eocaecilia 20200 10101 10100 {02}01?? 01000 11000 ?3201 10000 10000 Karaurus 10000 1?101 10011 2001? {01}?101 11?00 ?{34}{12}01 10?2? ????1 Triadobatrachus ????? ??1?? ?00?0 ????? 0{01}?0? ???1? ?{34}??? ???2? 0?0?1 Valdotriton 30200 1?100 100?0 {02}???? {01}?10{12} 10?00 ?{34}?11 ?0?2? ????1 Caerorhachis 0?0?? ??101 0???? ????? 0?000 1??00 00211 01100 00000 Eoherpeton 00200 1?101 00000 0001? 10000 12000 10211 00000 00000 Proterogyrinus 00300 1?10? 00100 010?0 00000 12000 10211 00000 10000 Archeria 00300 1?101 00100 0001? 10000 12000 10211 00100 10000 Ph. attheyi 20300 1?101 00000 1001? 00000 12000 10211 00000 10000 Anthracosaurus 20200 1?101 00100 00000 {01}0000 12000 10211 00000 10000 Ph. scutigerum 20300 1?101 00000 {01}?01? 10?00 1??0? 10?11 0??00 10000 Bruktererpeton 2?30? 1?101 00?0? 0?0?? 0?000 12100 10211 000{01}0 00000

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5 10 15 20 25 30 35 40 45 Gephyrostegus 20200 10101 00100 00000 00000 12000 10201 01001 00000 Solenodonsaurus ??2?? 1?101 00100 00000 10000 12000 11211 01100 00000 Kotlassia ??3?? ??101 10010 00000 ??0?0 10000 10211 00000 ?00?0 Discosauriscus 00300 10101 (01)0010 00000 10000 11000 10211 00000 00100 Seymouria 20200 10100 00000 00000 10000 12000 10211 00000 00100 Diadectes 30200 10101 00000 00000 10000 12000 12211 0111(01) 1(01)100 Limnoscelis 30310 11101 00000 00000 10000 12000 12211 01111 01100 Captorhinus 20310 10101 00000 00000 10000 12100 ?2211 00002 00100 Paleothyris ?0200 10101 00000 00000 10000 12100 12211 01002 00000 Petrolacosaurus 20300 1?101 00000 00000 10000 12100 12211 10002 00000 Westlothiana 20200 1011? (01)0??? ?1??? {01}??00 1200(01) 12211 00000 0?000 Batropetes 20310 ?0101 10100 (02)0000 10000 1(01)100 ?32(01)1 0(01)?2? 1?1?0 Tuditanus 2?3?? 1?10? 00000 ?0001 {12}?000 12000 ?4201 0000? ???00 Pantylus 20410 10111 10000 00000 10012 10000 ?4211 01100 00000 Stegotretus 20310 10101 ?0000 00000 00010 11000 ?4211 00000 01000 Asaphestera 20200 1?101 10000 00000 10000 12000 ?4211 00000 10000 Saxonerpeton 20200 1?101 10000 00000 1?000 12?00 ?4201 00001 00000 Hapsidopareion 20100 11101 00000 00000 10000 12000 ?4201 01?00 01000 Micraroter 20210 11101 00000 0100(01) 1?000 11000 ?4211 00000 11000 Pelodosotis 20210 1?101 00000 00001 10000 12000 ?4211 00000 11000 Rhynchonkos 20210 11101 00000 00000 11000 12000 ?4201 00000 01000 Cardiocephalus 20310 10101 10100 00001 11000 10000 ?4211 00000 01000 Euryodus (02)0210 10101 10000 00001 00000 10000 ?4211 00000 01000 Microbrachis 20300 12101 10000 00001 10000 10000 ?3211 10000 00000 Hyloplesion 20300 1?101 10000 01000 1?000 10000 ?3211 11102 00000 Odonterpeton 20400 1?111 10000 00000 00000 11?00 ?{34}211 10?2? 0?0?0 Brachydectes {12}0000 1?101 10100 20000 1{01}100 10?00 ?{34}21(01) 01100 11111 Acherontiscus ????? 1?111 ?0100 ?0000 {01}0000 1?00? ?{34}??? ????? ????? Adelospondylus ????? ??1?? ?0100 ?00?? 0?00? 11000 ?{34}210 ?1100 00010 Adelogyrinus 20?0? 1?1?1 ?0000 ?00?? {01}100? 10?00 ?{34}?10 ?11?{01} 00010

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5 10 15 20 25 30 35 40 45 Dolichopareias 10?0? 1?1?1 ?0100 200?? {01}?000 1?000 ??210 ?11?{01} 0?010 Scincosaurus 20300 1?100 10000 20000 20000 10000 ?4211 01?2? ????0 Keraterpeton 0020? 1?100 10000 20000 {12}0000 10000 ?3211 11100 00010 Batrachiderpeton 00400 1?101 10000 00000 11000 10000 ?3211 11000 00110 Diceratosaurus 2030? 1?101 10100 20000 {12}1000 10000 ?3211 11000 00110 Diplocaulus 20400 1?0?? ?0000 0(01)01? 20000 0010? ?3211 10000 001?0 Diploceraspis 20400 1?0?? ????0 {02}11?? 2000? 0010? ?3211 10001 001?0 Ptyonius 00100 1?100 00000 20001 00000 10001 12210 01100 10000 Sauropleura 00200 1?1(01)0 (01)0100 20001 01000 02001 12210 01100 (01)0000 Urocordylus ?030? 1???? ????? ?0001 {01}0000 ????? ????? ????? ????? Lethiscus 30100 1210? 10?10 2?000 01000 12100 12200 011{01}0 ?0011 Oestocephalus {23}0200 1?101 10100 20000 0{12}000 10000 12210 01100 11111 Phlegethontia {23}1000 12100 ?0000 {02}01?? {12}{12}000 0?101 ?{34}2?? ???2? ????1 Ariekanerpeton 00300 10101 00010 00000 10000 11000 10211 00000 00100 Leptoropha ????? ??1?? 00000 ?0??? ?0001 11000 10211 00000 00?00 Microphon ?0200 10101 00000 (01)0000 10001 10000 10211 00000 00100 Capetus 10100 1?101 00000 01000 00000 12000 00201 01100 10100 Notobatrachus 00300 121?1 ?1??? ??1?? 0?002 ???1? ?{34}??? 0??2? ????1 Vieraella 00100 1?1?? ?1??? ??1?? 1??0{01} ???1? ?{34}??? ???2? ????1 Orobates 30110 10101 00000 00000 10000 12000 12211 0101(12) 11100 Ossinodus ??201 ????? ?0000 ??000 00001 1??0? 0{02}210 00000 ?01?0 Pederpes ?030? 1?1?1 ?0000 01000 00000 1?0?0 00??? ??100 00000 Silvanerpeton 2020? ??101 00000 00000 00000 12000 10211 00000 00000 Tseajaia 2030? 1?101 000?0 0000? 10000 12000 02211 01002 11?00 Utegenia 00300 10101 00000 00000 10000 1200(01) 10211 00001 00000 Gerobatrachus ?0200 11101 000?0 0000? ??0?0 12100 0{012}201 ?11{01}{01} ??000 Chroniosaurus 3020? 1?101 00000 0001? 00000 12100 11211 00000 10000 Micropholis 30100 11101 00010 00000 02000 11100 01201 01100 (01)0100 Nigerpeton 01100 10100 0010? 1?01? 00000 12?00 00200 01100 ?0100 Saharastega ??{123}00 ??101 00000 1001? 00000 10000 00100 01100 00000

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5 10 15 20 25 30 35 40 45 Iberospondylus 10100 ?0100 00000 00000 00001 12000 0{01}2?1 0??00 10100 Tungussogyrinus 30200 ??101 00010 00000 ???02 10000 01211 01100 00000 Utaherpeton 1030? ??11? 10100 21001 010?? 11000 ??1?? 01??? ????0 Caseasauria 3031? 1?10? 00100 00000 0(01)00(12) 12100 12210 011(01)(12) 11000 Goreville microsaur ???0? ??1?? ?00?? ?0??? ????? 1?1?? ????? ????? ????? Sparodus ??4?0 ????? ????? ????? ????? ????? ?4??? 0?100 000?0 Liaobatrachus 00200 121?1 ?1??? ??1?? 0?002 ???1? ?{34}??? 0??2? 1???1 Acanthostomatops (12)0100 1(01)101 000(01)0 00000 10000 12000 012(01)1 11100 00(01)00 Deltaherpeton 2020? ??1?? ?01?0 ?1000 00000 1?00? 02211 01110 10000 Karpinskiosaurus 20300 10101 10000 00000 00000 10000 00211 00000 00100 Carrolla 20210 11101 10000 20001 {01}0000 1110? ?{34}211 ?0?2? 1???0 NSM 994 GF 1.1 ????? ????? ?0??? ????? 0?0?? 1?00? 10211 00100 101?0 Crinodon 00300 ?010? 00100 01001 10000 12000 ?4201 00000 00000 Sigournea ????? ????? ????? ????? ????? ????? ????? ????? ????? Doragnathus 00?00 ????? ????? ????? ????? ????? ????? ????? ????? Spathicephalus 00000 ??10? 0000(01) {01}10?? {01}0000 12100 0(12)211 01100 00000 Metaxygnathus ????? ????? ????? ????? ????? ????? ????? ????? ????? Sclerocephalus 10100 12101 00000 1001? 00000 12000 01211 01100 00100 Cheliderpeton 202?0 ?0101 00000 1001? 00001 12000 01210 01100 00(01)00 Archegosaurus 10300 10100 00100 1001? 00000 12000 01(12)00 01100 00100 Konzhukovia 20100 1{12}100 00000 1001? 00000 12(01)00 01210 00100 00100 Lydekkerina 00200 10101 00000 (01)001? 00000 11000 0121(01) 11100 00100 Beiyanerpeton 10?00 1110? 10(01)00 0?000 {01}{01}102 10?00 ?{34}?01 11?2? 1???1 Pangerpeton {13}?200 ????1 ????? ????? {01}??02 ????? ????? ????? ????? Ymeria 00?00 ?0??? ????? ????? 0?0?? ????? ????? ????? ????? Densignathus ????? ????? ????? ????? ????? ????? ????? ????? ????? Chelotriton 10301 12101 00000 {01}01?? 0?001 12?00 ?{34}201 10?2? ????1 Palatinerpeton ??200 ???01 ?00?? 000?? 0?000 ??000 ?{012}21? 0???? ????0 Glanochthon (13)0200 10101 00000 1001? 000(01)(012) 1200(01) 012(01)1 01100 00100 Archaeovenator 20{34}?? 11101 00?00 00000 10000 12100 12201 01002 01000

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5 10 15 20 25 30 35 40 45 Platyoposaurus 00400 1{12}100 00100 1001? 00011 12(01)00 01210 01100 00100 Trihecaton ????? ????? ????? ????? ????? ????? ????? ????? ????? Erpetosaurus 10001 10101 10000 20000 00010 10000 02210 00100 10110 Mordex 1010? 1?100 00010 20000 {01}2001 1(12)000 01211 01100 00000 Branchiosaurus 10?0? ??101 00000 00000 {01}{01}002 11000 01201 01000 00000 Pholidogaster 0010? ?110? ?0?00 {02}100? 10010 12001 02211 00100 00000 Palaeoherpeton {03}02?0 1?10? 00??0 ????? 00000 1200(01) 10211 01100 10100 Neopteroplax 20310 1{12}101 00000 {02}0??? 10010 11000 10(12)11 011{01}0 ?0?00 St. Louis tetrapod ?0?0? ?{01}1?? ?0??? ????? 0???? 1?0?? ??{12}?? ????? ????? Parrsboro jaw ????? ????? ????? ????? ????? ????? ????? ????? ????? Elginerpeton 00??? 0???? ????? ????? ????? ????? ????? ????? ????? Australerpeton 00300 12100 00(01)00 1001? 00000 12000 01210 01100 00(01)00 Quasicaecilia {012}???? ??101 00100 {01}0??? {12}???? 10100 ?{34}211 00?2? 0?0?0 Casineria ????? ????? ????? ????? ????? ????? ????? ????? ????? Llistrofus ??1?? ??10? 10000 ?0000 10000 10100 ?4201 01100 01000 Bystrowiella 2030? ???0? 00000 {01}1?1? ?000? 12100 1{012}211 00001 11000 Coloraderpeton ????? ????? ?010? 20000 0?0?0 1000? 12210 01100 100?1 Pseudophlegethontia 3030? ????? ????? ????? ????? ???0? 1{012}2?0 01100 100?? Perittodus ????0 ????? ????? ????? ????? ????? ????? ????? ????? Diploradus {02}0?0? ????? ?0??? ????? 0{02}000 ???0? ??{12}1? ?1100 000?0 Aytonerpeton 20?00 0?1?? ????? {02}?00? 00001 ????? ????? ????? ????? 14856 50 55 60 65 70 75 80 85 90 Eusthenopteron 10000 0000? 00000 000?1 00020 00000 00000 00?0? 00000 Panderichthys 0?0?0 0000? 00000 000?1 00020 00000 00000 00?0? 20000 Ventastega 00101 ?001? 10000 000?0 0002? 00?11 1000? 00010 22002 Acanthostega 0???? 00010 10000 000?1 10020 00000 10000 00010 20102 Ichthyostega 0???? 01011 00000 00(01)?1 10020 00001 00000 00021 21000 Tulerpeton ????? ????? ????? ????? ????? ????? ????? ????? ????? Colosteus 0???? 010{02}0 00000 010?1 00100 0{01}?00 0000? 100{12}? 10000

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50 55 60 65 70 75 80 85 90 Greererpeton 0???? 01021 00000 000?1 10000 00000 0000? 1001? 20000 Crassigyrinus 00101 0001? 00000 000?0 00120 00001 00000 1001? 22101 Whatcheeria 01101 0101? 00000 000?0 0012? 0{01}?11 ?000? 00022 22112 Baphetes 01011 0102? (01)0000 000?0 10120 0100? 10000 10020 21200 Megalocephalus 0???1 0102? (01)0000 001?0 10120 0010? 10000 1002(01) 21200 Eucritta 01011 010{02}? 00000 001?0 10120 0{01}??1 0000? 100?? 2?{12}02 Edops 01000 0102? 00000 001?1 10120 00?01 10000 100?? 20000 Chenoprosopus 01000 0101? 10000 001?0 00120 01100 10001 10022 10000 Cochleosaurus 01000 0100? 10000 (01)01?1 10120 01100 10000 10022 20000 Isodectes 0101? 00000 00000 001?0 00100 01110 ?000? 10122 20000 Neldasaurus 0100? 01001 00000 001?0 10110 01010 ?000? 10022 20000 Trimerorhachis 0101? 01020 10000 001?1 1(01)(01)20 00000 00000 101(12)2 21000 Balanerpeton 01010 010?? 10000 001?0 00120 00010 00000 101{12}2 22002 Dendrerpetidae 010(01)0 000?? 10000 001?0 001(12)0 00010 (01)0001 10(01)(12)2 (12)0(01)00 Eryops 0???0 0101? 10000 101?0 10120 00000 10000 10122 20000 Acheloma 0???0 0101? 10000 001?0 00120 00010 00001 12?12 22002 Phonerpeton 0???0 0102? 00000 000?0 00120 00010 00001 12?12 22002 Ecolsonia 0???? 0100? 00000 001?0 00110 00010 ?0001 12?22 21002 Broiliellus brevis 0???0 00010 11000 001?0 00110 02010 0000? 11122 21002 Amphibamus 0???0 000?? 11000 001?0 10110 00010 ?0001 10122 22002 Doleserpeton 0???0 0000? 01000 001?0 10110 00010 ?0001 10112 22002 Eoscopus 0???0 0101? 11000 001?0 10110 00010 ?0001 10112 22002 Platyrhinops 0???0 0101? (01)1000 (01)00?0 10110 00010 ?0001 10122 20002 Micromelerpeton 0???0 0100? (01)0000 001?0 00120 00010 ?000? 10112 22002 Apateon 0???0 0101? 11000 001?0 10120 00010 ?000? 101(12)2 22002 Leptorophus 1???0 0101? 10000 001?0 00120 00010 ?000? 10112 22002 Schoenfelderpeton 0???0 0?0?? 00000 001?0 00110 0?010 ?000? 10112 22002 Albanerpetidae ????? ??1?? ????1 ????? ??10? 01?1? 0???? 10122 2?0?? Eocaecilia 0???? ??000 00?01 ????? ??100 00010 ?001? 10122 00100 Karaurus ????? ??1?? ?1??1 ????? ??000 1???? ?011? 10112 2?0??

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50 55 60 65 70 75 80 85 90 Triadobatrachus ????? ??1?? ?1??1 ????? ???10 ????? ????? 1???? 22??? Valdotriton ????? ??1?? ????1 ????? ??100 1???? ?1??? 10122 2?0?? Caerorhachis ?1?00 0?01? 00000 001?0 00120 ??0?? ?000? 1?122 ????? Eoherpeton 00100 0001? 10000 00??0 00?20 00010 1000? 10022 10?00 Proterogyrinus 00000 0001? 10000 001?0 00120 01110 ?0000 10022 22001 Archeria 00000 0001? 10000 001?0 00120 01110 10000 10022 22002 Ph. attheyi 01000 0001? 10000 001?0 00120 01011 10000 10022 22000 Anthracosaurus 01000 0101? 11000 000?0 00120 00011 10000 10022 22001 Ph. scutigerum 00?00 0001? 1?000 00??0 00?20 00100 00000 10022 22000 Bruktererpeton ?0?00 0000? 1000? ????? ????? ????? ????? ?0022 2???? Gephyrostegus 00100 0000? 11000 001?0 00110 01010 00000 10122 22002 Solenodonsaurus 0???0 0100? 00000 001?0 0011? 01?10 00000 100?? 20000 Kotlassia 01100 0103? 00000 000?0 101{12}0 0{01}?10 00000 10022 10000 Discosauriscus 00100 0003? 11000 001?0 00110 01010 00000 10022 22001 Seymouria 01100 0103? 11000 000?0 00120 01010 10000 10022 10100 Diadectes 0???(01) 0000? 01(01)10 001?0 00110 01010 00000 10122 (01)0002 Limnoscelis 0???? 0002? 01000 001?0 00100 01010 1000? 10122 00000 Captorhinus 0???? 001?? ?0??0 000?0 00100 01110 1000? 10022 22000 Paleothyris 1???? 0000? 01010 001?0 00100 01010 0000? 10?22 22002 Petrolacosaurus 1???? 0000? 01010 001?0 00100 01010 0000? 10122 22002 Westlothiana 0???? 1001? 11?00 ?01?0 01000 0{01}?1? ?000? 10?22 1??0{01} Batropetes 0???? ??00(01) 01000 00(01)10 00110 0??(01)0 01??? ?0122 (01)1102 Tuditanus ????? ??0?0 01?00 00010 01000 01?10 0000? 10?22 10000 Pantylus 0???? ??001 00000 00011 01100 02010 1000? 10022 00000 Stegotretus 0???? ??00? 00100 00010 01?00 02010 0000? 10022 00000 Asaphestera 0???? ??0?0 01000 00010 01000 01010 0000? 10122 00001 Saxonerpeton 0???? ??000 01000 00010 0?000 01010 0011? 10?22 00000 Hapsidopareion 0???? ??000 0?100 00??0 010?0 0?010 0???? 10122 ?000{01} Micraroter 1???? ??001 01100 00010 00000 0??10 0011? 10122 00000 Pelodosotis 1???? ??001 01100 00010 00000 0??10 0011? 10122 00000

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50 55 60 65 70 75 80 85 90 Rhynchonkos 1???? ??000 00000 10110 01000 0??10 0???? 10122 00000 Cardiocephalus 1???? ??000 00100 00010 011?0 01010 ????? 10122 00000 Euryodus 1???? ??000 00100 00010 01000 00010 0011? 10122 00000 Microbrachis 0???? ??000 01000 00010 01100 01010 0000? 10122 10000 Hyloplesion 0???? ??000 01000 00?00 01100 01010 0000? 10122 10000 Odonterpeton 0???? ??1?? ?0??0 000?0 0?100 01010 0011? 10?22 00000 Brachydectes ????? ??0?1 ?0?01 ????? ??100 1???? ?1??? 1{01}122 00000 Acherontiscus ????? ????? ????0 0?0?1 10?0? 0??10 0???? 1?0?? ??000 Adelospondylus 0???? ??11? 10??? ????? ??110 01010 00000 1???? ?1000 Adelogyrinus 0???? ??1?? 10??0 010?0 ?011? 0{01}?10 ?0000 1?0?? 21000 Dolichopareias 0???? ??1?? ?0??0 010?1 10??? 0{01}?10 0???? 10022 ??000 Scincosaurus 0???? ??000 01000 00011 10101 01010 10?0? 10022 10000 Keraterpeton 0???? ??000 10000 00000 10101 01?10 0000? 10022 10000 Batrachiderpeton 0???? ??000 11000 00001 10101 01010 ?000? 10022 00000 Diceratosaurus ????? ??000 10000 00001 10101 01?10 ?000? 10022 10000 Diplocaulus 1???? ??000 11000 01001 10101 01000 1000? 10?22 21000 Diploceraspis 0???? ??000 11000 01000 10101 01010 1000? 10?22 21000 Ptyonius 0???? 1000? 00000 100?1 10100 01010 0000? 10022 22000 Sauropleura 0???? 10000 10000 100?1 10100 00010 ?000? 10022 22000 Urocordylus ????? ??000 ???00 100?1 10?00 0001? 0000? 1???? ??0?0 Lethiscus ????? 0?00? 10000 00??? ??020 01010 0000? ?0112 22000 Oestocephalus ????? 10000 00100 00??? ??0{02}0 00010 ?000? 100?? 12000 Phlegethontia ????? ??1?? ?0??0 00??0 ????0 01010 ?0??? 12022 22000 Ariekanerpeton 00100 0003? 01000 001?0 00110 01010 0000? 10022 10001 Leptoropha 10000 000?? 01000 001?0 10110 0??10 ?000? 1???? 10?01 Microphon 10100 0003? 01000 001?0 (01)0120 01010 (01)0000 10122 00001 Capetus 00000 000?? 10000 001?0 10120 00000 10000 10122 00000 Notobatrachus ????? ??1?? ?1??1 ????? ???10 1???? ?(01)1?? 10022 2?0?? Vieraella ????? ??1?? ?1??1 ????? ????0 1???? ????? 101?? 2???? Orobates 1???0 1000? 01110 001?0 00110 01?10 00000 10122 00002

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50 55 60 65 70 75 80 85 90 Ossinodus 01100 0000? 00000 000?0 01120 00010 10000 0???? 1?00? Pederpes 01101 0102? 01000 000?0 00?2? 0{01}010 0000? 000?? 12012 Silvanerpeton 00001 00010 10000 001?0 00110 01?10 0000? 10022 12002 Tseajaia 0???0 0000? 01110 000?0 00110 01?10 0000? 10122 21002 Utegenia 00000 0001? 01000 001?0 00110 01010 0000? 10022 12002 Gerobatrachus ????1 0100? ???00 00??0 10110 00010 00??? ?01?? 22002 Chroniosaurus 0???0 0000? 10000 001?0 1011? 00011 1000? 10112 22010 Micropholis 0???? 01001 (01)0000 00(01)?0 10110 00010 00001 10122 2200(012) Nigerpeton ?1101 0101? ?1000 001?? 0?120 0?000 1???? ?0022 20000 Saharastega ?1?0? 0?0?? ?1000 001?1 00?0? 0{01}110 1000? ?{01}112 00000 Iberospondylus 0???0 0100? 10000 ?01?0 10110 00?10 10001 10022 22002 Tungussogyrinus 1???0 0000? 01000 101?0 00110 0?01? ????? 10112 22??? Utaherpeton ????? ????? ????0 ?0??? ?0??? 01?10 ?0??0 ?0?22 2200{12} Caseasauria 0???? 0000? 01110 001?0 00000 00?10 0001? 10122 12101 Goreville microsaur ????? ????? ????0 100?? 1???? 0???0 ????? ????? ????? Sparodus ????? ??0{023}? 00000 10010 11100 0??10 ?0??? ????? 0??0? Liaobatrachus ????? ??1?? ????1 ????? ???10 1???? ?0110 10112 220?? Acanthostomatops 1???0 0(01)00? 11000 (01)01?0 (01)0110 00000 10000 10(01)12 20001 Deltaherpeton 0???? 0002? 00000 100?1 10100 01?00 0000? 10011 20000 Karpinskiosaurus 01101 010{12}? 11000 001?0 00120 00010 00000 10112 10000 Carrolla 0???? ????? ?1??0 ?01?0 01100 0{01}?10 0???? ?0122 21000 NSM 994 GF 1.1 01?0? 0001? 1?00? ????? ??020 0??1? ?0000 1???? 22??{12} Crinodon 1???? ??001 01000 10010 01000 01010 0000? 1??{12}? 20002 Sigournea ????? ????? ????? ????? ????? ????? ????? ????? ????? Doragnathus ????? ????? ????? ????? ????? ????? ????? ????? ????? Spathicephalus 0???1 0102? 11000 000?? 10120 0000? 10010 10?22 2{12}2?{01} Metaxygnathus ????? ????? ????? ????? ????? ????? ????? ????? ????? Sclerocephalus 0???0 000(01)? 10000 000?0 10120 0000(01) 10000 10122 20000 Cheliderpeton 1???0 000?? (01)0000 000?0 1012? 00?00 1000? 10022 20000 Archegosaurus 0???0 0101? 10000 001?0 10120 00010 10000 10022 21000

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50 55 60 65 70 75 80 85 90 Konzhukovia 0???1 0100? 10000 000?0 10?20 01100 10000 10022 22000 Lydekkerina 0???? 01011 10000 00(01)?? 10120 0(01)100 10001 10122 22000 Beiyanerpeton ????? ??1?? ?1??1 ????? ??10? 1???? ?1??? 10?12 2?0?? Pangerpeton ????? ????? ????? ????? ????? ????? ????? ??1?? 2???? Ymeria ????? ????? ????? ????? ????? ?0??? ?0??? ????{01} ????? Densignathus ????? ????? ????? ????? ????? ????? ????? ????? ????? Chelotriton ????? ??1?? ????1 ????? ??100 1???? ?001? 10022 10100 Palatinerpeton 0???0 ?00?? ??000 00??0 ?0120 0101? ?000? 10??? 22?00 Glanochthon (01)???? 0(01)010 10000 001?0 (01)0120 000(01)0 10000 10022 2(12)000 Archaeovenator 0???? 1000? 11?10 101?0 ?0000 01010 0011? 11122 ?2002 Platyoposaurus 0???1 0100? 10000 00(01)?0 10120 01010 10000 10022 20000 Trihecaton ????? ????? ????? ????? ????? ????? ????? ????? ????? Erpetosaurus 0???? 0100? 10000 000?0 10(01)20 00110 00000 10122 22000 Mordex 1???0 0000? 10000 001?0 10110 0??10 00001 12??? 21002 Branchiosaurus ????0 0?01? 11?00 001?0 10010 00?10 0000? 101{12}2 22002 Pholidogaster 0???? 01020 00000 000?? 1?0{12}? 01?00 1000? ?00?? 2{01}000 Palaeoherpeton 01000 0001? 11000 001?0 01120 01?11 ?0000 10?{12}? 22000 Neopteroplax 01101 010{13}? 1?000 001?0 10120 01?01 10000 10122 22100 St. Louis tetrapod ????? ????? ????? ????? ????? ????? ????? ????? 20??? Parrsboro jaw ????? ????? ????? ????? ????? ????? ????? ????? ????? Elginerpeton ????? ????? ????0 ?0??? ?0??? ????? ????? ????1 ????? Australerpeton (01)???(01) 0101? 10000 000?0 1(01)121 00010 10001 10022 22000 Quasicaecilia 1???? ??1?? ?1??? ????? ??1?0 0?010 ????? ?0122 20?02 Casineria ????? ????? ????? ????? ????? ????? ????? ????? ????? Llistrofus 0???? ??00? 00100 00110 01020 0??10 0011? 1???? 10000 Bystrowiella 0???0 ??02? 11100 001?0 0?110 00?10 10??? ???2? 22002 Coloraderpeton ????0 110{12}? 10000 ?0??? ??020 00?10 00?10 000?? {01}{01}{01}00 Pseudophlegethontia ????? ?10{01}? 1000? ????? ??0?0 ????? ?000? ?0?{02}? 22?00 Perittodus ????? ????? ????? ????? ????? 0??1? ????? ????? ????? Diploradus ????? ????? ????? ????? ????? 00?10 ?000? ????? ?????

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50 55 60 65 70 75 80 85 90 Aytonerpeton ????? ????? ????? ????? ????? 00?10 0???? ?002{02} ??0?? 14857 95 100 105 110 115 120 125 130 135 Eusthenopteron 02001 00000 01002 00000 00100 00000 0?0?0 00000 00?02 Panderichthys 00001 00000 01002 00000 0010{01} 000?0 0?0?0 00000 00?0? Ventastega 0?000 00001 00000 10000 0010? ???00 ??000 0???? ?{01}??? Acanthostega 02001 00001 11001 10010 00200 00000 01000 00000 01001 Ichthyostega 0(01)032 00000 {01}1001 10100 00100 (01)0000 0?000 00000 00?02 Tulerpeton 0???? ????? 3?01? ?01?? ????? ????? ????? ????? ?0??? Colosteus 000?0 00002 20??1 ????0 ?010{01} 0?0?0 0?010 00000 11??? Greererpeton 00011 00002 21001 01100 00101 00000 0?010 00000 01011 Crassigyrinus 000?1 00001 3100{01} 10000 00100 00000 ??000 0???0 11?0? Whatcheeria 00012 00002 1?001 00??0 00?0{01} 010?0 ????? 00??? 0???1 Baphetes 00011 00002 {23}1010 01100 11100 01100 0?100 0???0 020?1 Megalocephalus 00011 00002 31010 01100 11100 01100 0?000 0???0 0(01)?11 Eucritta 000?1 0000? ??01{01} 011?0 11101 0?0?0 ??100 0???? ????? Edops 00001 0000{04} 41001 01?00 ?1100 011?0 ?100? 00000 1?010 Chenoprosopus 00111 00003 3?012 01100 ?1100 0?110 000?0 01101 12?10 Cochleosaurus 111?1 0000{04} 4?012 01100 11100 01110 010?0 01101 12?{13}? Isodectes 010?1 0000{23} {23}1004 01100 ??10{123} ???{01}0 001?0 01100 01010 Neldasaurus 02010 0000{23} {23}?0?2 11100 ?0100 0?010 010?0 01100 01010 Trimerorhachis 00011 00003 {123}100(23) 0(01)000 00101 00010 010?0 01100 11010 Balanerpeton 020?1 00004 41012 11100 11100 01110 010?0 01110 12?1? Dendrerpetidae 020?1 00004 ?1012 11100 11100 01110 010?0 01101 12010 Eryops 00013 0000{04} 41012 01100 11101 01110 010?0 01100 120(145)0 Acheloma 02013 00004 4?012 01100 11100 01110 010?0 01101 10050 Phonerpeton 02012 00004 41012 (01)1100 11100 01110 000?0 01100 12?50 Ecolsonia 01013 00004 41012 ?1100 1110{01} 00110 010?0 01111 1?050 Broiliellus brevis 020?3 00004 41?15 01100 1?101 ???20 010?0 01110 12??? Amphibamus 020?2 00004 ?0014 01110 11?01 001{12}0 010?0 01111 12???

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95 100 105 110 115 120 125 130 135 Doleserpeton 02013 00004 40114 01011 0020{23} ???10 ?10?0 01111 1205{02} Eoscopus 020?3 00004 ?0013 11110 ?1101 0?110 010?0 01110 12??? Platyrhinops 020?3 00004 40014 ?1110 11101 01110 011?0 01110 02?{45}? Micromelerpeton 020?1 00004 {234}1003 00100 00101 10010 010?0 01110 10??? Apateon 02014 00004 ?1003 01110 00101 10010 010?0 01110 02??? Leptorophus 020?3 00004 41103 01101 00101 10010 010?0 01110 02??? Schoenfelderpeton 020?3 00004 41103 01111 00102 10000 010?0 01110 02??? Albanerpetidae 1?0?1 01014 4???{123} ????? ????? ????? ????? ?1010 1??42 Eocaecilia 1?030 00004 41105 11001 0010{23} ???10 000?0 01?00 02042 Karaurus 1?0?3 01?14 ?0105 ?101? ???13 ???01 011?0 11110 10?4? Triadobatrachus ??0{13}4 01?1? ????5 ????1 0120{23} ???00 ?10?0 0111? ???4? Valdotriton 1?0?2 01?14 ?0105 1100? ???13 ???01 100?0 1111? 12042 Caerorhachis 0{12}0?1 0000? ?1011 ?1100 11100 01100 10100 00100 12??? Eoherpeton 02032 00004 4{12}??{123} ????0 0?000 0?000 ?01?0 00?0? 1???1 Proterogyrinus 02031 00003 4{12}??1 ????0 01100 01000 0?000 0000? 1?01? Archeria 02032 00003 ????1 ????? ????{01} ?0000 0?000 0000? ??011 Ph. attheyi 020?1 00003 3(12)101 01100 01101 00000 0?100 00000 ?2??? Anthracosaurus 02033 00003 32101 01100 01100 00000 0??00 00000 02011 Ph. scutigerum 00?31 00003 32101 01100 0?100 00000 ??100 00000 12011 Bruktererpeton 02??1 0?0?? ?1012 ?1100 1100{12} ?1?{123}? 0???? 00000 00??? Gephyrostegus 020?2 00004 42011 01?00 11001 01120 0?000 00000 1???? Solenodonsaurus 020?2 00004 ????? ????? ????? ????? ????? ????? ????? Kotlassia 01012 0000? ????{01} 0??01 ?010{01} 1?020 ??000 0???0 1?010 Discosauriscus 02012 00004 {34}2010 01100 11100 11120 0?000 0???0 12?1? Seymouria 02012 00004 42010 01100 1110(01) 11120 0?000 0???0 12010 Diadectes 0(12)024 00004 4210(01) 01101 01101 10120 0?000 00000 02?21 Limnoscelis 01023 00004 42111 01111 11101 10130 0?000 00001 121{1235}1 Captorhinus 02020 00004 42101 01101 01103 ???20 0?000 00000 02121 Paleothyris 00021 00004 42101 01101 1110? ???30 0?000 00000 02121 Petrolacosaurus 02023 01004 42111 01101 11101 10130 0?000 00000 02121

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95 100 105 110 115 120 125 130 135 Westlothiana 020?1 0000? ????{12} ????? 11101 11100 ??0?0 0000? ????? Batropetes 02023 00104 41102 01111 0110{123} ????2 01??0 01000 12141 Tuditanus ??0?4 0000? 4???1 ????? ????? ???00 ??0?0 0010? ???3? Pantylus 1?011 00004 42101 01100 11003 ???00 0?000 00(01)01 12130 Stegotretus 010?2 00004 ?2101 01100 11003 ???00 ??000 00101 12030 Asaphestera 00013 00004 41??{12} ????? 1?10? ????0 0?1?0 0011? ??140 Saxonerpeton 020?3 0000{34} 4211{12} 01101 1?101 ???10 0?0?0 0000? ?2?{1345}? Hapsidopareion ??0?{012} 0?114 4111{12} ?110? ?0101 10110 0?0?? 0000? 0?13? Micraroter (01)2013 00104 41{01}1{12} 01101 10101 11000 1?1?1 0000? ?2130 Pelodosotis 1?0?2 00104 4???2 ????1 ?010? ???00 ?10?1 0000? ?2130 Rhynchonkos 1?0{23}2 00004 4110{12} 00101 00100 10010 010?1 00000 12130 Cardiocephalus (01)20?1 00104 4{12}101 00101 00101 10000 0?101 0000? ?2030 Euryodus (01)20?1 00004 4{12}01{12} 0?101 10101 11010 0?(01)?1 0000? ?2030 Microbrachis 020?2 00003 3{01}111 01101 11101 11110 0?000 00000 02?30 Hyloplesion 020?2 00003 42111 0??01 1110{12} 11120 01000 00010 02??0 Odonterpeton 020?0 00004 42111 01101 10101 101{12}0 0??00 00000 02?{13}{02} Brachydectes 1?031 01?14 42102 0??01 01{12}03 ???02 0???0 01?00 12131 Acherontiscus ??0?? 00003 ????? ????? ????? ????? ????? ????? ????? Adelospondylus 01?10 0000{34} 3???{0123} ????? 1?101 11100 0???0 0???? ????? Adelogyrinus 00??0 0000? 3???? ????? ????? ????? ????? ????? ???1? Dolichopareias 000?? 00003 ????? ????? ???0? ????? ????? ????? ????? Scincosaurus 020?3 0000(34) ?1102 ?11?1 11103 ???{01}2 0?1?0 0000? ???4? Keraterpeton 020?2 00003 ????? ????? ????? ????? ????? ????? ????? Batrachiderpeton 020?3 00003 31100 ?1001 00103 ???01 0?100 0???0 02?40 Diceratosaurus 020?3 00003 ?11(01)1 11(01)01 11{12}0? ???01 011?0 0000? 12?4? Diplocaulus 010?4 0000? 31103 01001 00103 ???01 011?0 01110 1204{02} Diploceraspis 01014 00003 31105 01001 0010{23} ???01 011?0 01110 12040 Ptyonius 020?1 00004 41101 ?1001 0010? ???00 01000 01100 02?{13}{01} Sauropleura 02010 00004 4210{12} 01101 00103 ???00 0?0?0 00000 02?{13}? Urocordylus ????0 0000? ????1 ????1 ?010? ????0 ??0?? 0010? ???{13}?

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95 100 105 110 115 120 125 130 135 Lethiscus 02?{13}0 01104 421?{12} 10000 ??101 1?110 000?0 01000 10?12 Oestocephalus 00010 01?14 4???{012} ????? 00103 ???10 0???0 0???? ??012 Phlegethontia 020?0 01114 4???{12} ????? ???13 ????? ????? ?0?0? ???12 Ariekanerpeton 02012 0000{34} {234}001{01} 01100 01100 11120 0?000 0???0 02?10 Leptoropha 0201? 00?0{234} ????{01} ????? ????? ???{23}0 ??0?0 0???? ????? Microphon 02013 0000{34} {234}211{01} 00100 10100 11020 0?000 0???0 02??? Capetus ?00?1 00004 4101{12} ?110? ??10? ???10 011?0 0111? ?2??? Notobatrachus 1?0?0 11014 4010{34} 0100? ???13 ???10 111?0 01110 1?042 Vieraella 1?0?2 110?? ?01?{34} ?10?? ????3 ???10 111?0 01111 10??? Orobates 00033 00004 421?2 ?11?1 01101 10120 ??0?0 00000 12121 Ossinodus 001?2 0000{12} {12}{01}11 10000 ?0100 10000 0?000 0???0 0???? {01} Pederpes ????2 ?0001 ?1011 ????? 00100 010?? 0??0? 0000? ?0??? Silvanerpeton 010?1 00004 ?101{01} 01100 0110? ???10 ??100 0???0 1??{01}? Tseajaia 000?4 00004 ?2?0{12} ?1?01 01100 10120 0?0?0 00000 0??21 Utegenia 02014 0000{34} {234}101{01} 01100 00101 11020 0?000 0???0 02?1? Gerobatrachus 02??4 000?? ?0115 ?11?? ?1202 10110 010?0 ?111? 1??{1345}? Chroniosaurus 020?1 0000{04} ?2011 01100 1010{01} 01120 0?010 00000 02?1? Micropholis 02012 00004 4100(34) 01100 0(01)20(01) 001(12)0 0(01)0?0 01111 1(02)040 Nigerpeton 1?113 00?02 {23}?002 11100 11100 0?110 010?0 01111 01010 Saharastega 1?0{13}3 0000{34} ?{12}?12 ?100? 11{01}00 ?1110 011?0 01110 11?1? Iberospondylus 020?2 00003 41012 01100 11100 01110 ?1??0 01110 12010 Tungussogyrinus 02??4 00?0? ?1??3 0??0? ??100 ???10 010?? 01110 1???? Utaherpeton 0{12}0?1 0?004 4???{0123} ????? 1?10? ????? ????? ????? ???{13}? Caseasauria 0(01)013 01004 4???{012} ????? ????? ???30 ??0?0 0000? ???{1235}1 Goreville micro. ????? 0000? ?1?1{012} ???00 1?10? ????0 ????0 ????? ???3? Sparodus 02030 00004 4???? ????0 1000? ????? ????? ????? ???{34}0 Liaobatrachus ????4 11014 40104 0101? ???13 ???10 110?1 0111? 1?042 Acanthostomatops 020?3 00004 41012 11100 11101 01110 010?0 01111 10?{345}? Deltaherpeton 000?1 00002 2?0?? ????0 ????? 0???? ????? ????? ?????

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95 100 105 110 115 120 125 130 135 Karpinskiosaurus 020{13}3 00004 4{12}010 00100 11100 01120 00000 0???1 10?{134}1 Carrolla 02?34 0??14 42102 01101 01101 10101 011?0 0000? ??0{45}2 NSM 994 GF 1.1 02032 000?3 ????? ????? ????? 0???0 ??0?? ????? ??0{123}1 Crinodon 000{23}4 00004 {34}1011 11100 11100 01100 0??00 00001 1???? Sigournea ????? ????? 2???? ????? ????? ????? ????? ????? ????? Doragnathus ????? ????{12} {12}???? ????? ????? ????? ????? ????? ?2??? Spathicephalus 02034 0000? 20100 010?? ????{01} 10100 0?100 0???0 02?11 Metaxygnathus ????? ????? {12}???? ????? ????? ????? ????? ????? ????? Sclerocephalus 01011 0000(34) 41012 01100 1(01)100 010(12)0 0(01)0?0 00(01)0 (01)20{34} (01) {02} Cheliderpeton 000?1 00003 ????? 0???? ????? ????? ????? ????? ????? Archegosaurus 00011 00003 3?012 10100 00201 10010 000?0 01100 02040 Konzhukovia 02011 00003 ?1002 11000 00101 00010 010?0 01100 11050 Lydekkerina 02012 00003 31014 10000 00100 (01)0010 010?0 01110 10040 Beiyanerpeton 1???? 11?13 ?0104 ?1011 ?0203 ???11 011?0 1111? ?00{1345}{01} Pangerpeton ????? ?1?1? 41105 ?10?? ???1? ???11 000?0 1111? ?0?4{01} Ymeria ????? ??0?{12} 200?{012} 10?00 ?0100 0?000 0???? 0???0 0{01}??? Densignathus ????? ????? 1???? ????? ????? ????? ????? ????? ????? Chelotriton 1?0?4 01014 40104 1100? ???13 ???1{01} 111?0 0111? 10042 Palatinerpeton ????1 ?000? ?1012 11100 11100 01110 010?0 01110 12??? Glanochthon 0(012)0?1 00003 ??0?2 10100 00100 (01)0010 010?0 01100 02?{34}? Archaeovenator 000{23}4 01004 42??1 0??01 11102 10130 010?0 00?01 1?1?1 Platyoposaurus 00011 00003 3?012 11100 10101 01010 000?0 00101 01050 Trihecaton ????? ????? 4???? ????? ????? ????? ????? ????? ????? Erpetosaurus 0(12)0?0 0000 {04}1012 01100 01100 00110 110?0 01100 11?10 {123} Mordex 020?2 00?04 ?1?13 ???0? 1??0? ???10 ?1??0 01110 12??? Branchiosaurus 020?? 00004 ????3 ???0? ????{012} ????? ????? ?11?? 1???? Pholidogaster 00??1 00001 2???? ????? ????? ????? ????? ????? ?1??? Palaeoherpeton 02031 00003 ????{12} ????? ????? ???10 ?01?0 00?0? ??01{01}

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95 100 105 110 115 120 125 130 135 Neopteroplax ?{01}0?1 00004 3211{12} 01100 01100 000{01}0 ????0 00?00 02??? St. Louis tetrapod ????? 0???{123} 2??11 ??1?0 ???0{01} 0???0 ?1??? ??00? ????? Parrsboro jaw ????? ????? 3???? ????? ????? ????? ????? ????? ????? Elginerpeton ????? ????1 0???? ????? ????? ????? ????? ????? ????? Australerpeton 01011 00003 {23}?014 10100 00200 10000 010?0 01000 0104{02} Quasicaecilia 020{03}4 00?14 ????3 ????? ??{01}0 ???01 011?? 00??? ???32 {23} Casineria ????? ????? ????? ????? ????? ????? ????? ????? ????? Llistrofus 01010 01114 42112 ?1100 1110? ???10 010?0 00000 0?131 Bystrowiella 020?3 00?04 4???? 0???? ????? ????? ????? ????? ????? Coloraderpeton 000?0 01?0? {01}?10{12} ?0??? 00?00 10010 000?0 0??0? ?0?12 Pseudophleg. 02??0 01?0? ????{123} ????? ????? ???{01}0 000?0 0000? ????? Perittodus ????? ????{123} ????? ????? ????? ????? ????? ????? ????? Diploradus 02??? 00?0? ????{01} ????? ????? ???00 ??0?? 0???? ????? Aytonerpeton ????? ????{12} {12}{01}011 01100 11101 01100 ?1?10 0?000 01??? 14858 140 145 150 155 160 165 170 175 180 185 Eusthenopteron 00??0 0000? 10000 20000 00000 10000 00010 00100 0?0?? 00000 Panderichthys 00??0 00001 00000 00000 000?0 00000 00010 00100 01000 00000 Ventastega 00??? ?100? 00011 01000 10000 00000 00010 00100 01000 00010 Acanthostega 00??? ?100? 00110 01000 10010 10010 00110 01100 11000 00010 Ichthyostega 00??0 0100? 00101 11000 10000 00010 00110 01100 11000 00010 Tulerpeton ????? ????? ????? 0000? ????0 {01}0??? ????? ????? ????? ?00?? Colosteus 1???? ?2??? 0???? 1010? ????? ????? ?0?10 01?00 1??00 ?0001 Greererpeton 10110 12000 00101 10101 10010 20010 00010 01000 10000 10001 Crassigyrinus 00101 01000 00101 00001 00010 20010 00101 01010 ????? 00001 Whatcheeria ????? ?2??0 00011 00001 10010 10010 00110 01100 11021 00010 Baphetes 00000 12000 00101 0000? ?0?10 ?0010 ????? 0?0?0 ?0??0 10000 Megalocephalus 000?0 12000 00001 00001 20110 20010 00111 01110 11100 10000 Eucritta 00101 02000 0???? ?000? ????? ????? ????? ????? ????? ?00?0

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140 145 150 155 160 165 170 175 180 185 Edops 10010 02011 01??? 00000 10110 20010 10101 01010 10110 10000 Chenoprosopus 10000 ?2001 0???? ?000? ?0110 20010 ?0??? 0???0 ????? ?0010 Cochleosaurus 12010 02001 11??? 00000 20110 20011 ?0101 01010 10110 10010 Isodectes 10000 02010 2???? 0000? ?0110 21010 ????? ????0 10121 10001 Neldasaurus 10000 02010 0???? 0000? ?0110 20010 ????? ????? ????? 10001 Trimerorhachis 12000 02011 11??? 00000 ?0110 20010 ?0111 0(01)010 00100 10001 Balanerpeton 12010 0201{12} 01??? 00000 10110 20010 10101 01010 101?? 10001 Dendrerpetidae 12010 020(01) (12) 0???? ?000? ?0110 20010 ????? ????0 ?0??? 10001 Eryops 10010 02001 01??? 00000 10110 20010 101(01)1 01(01)10 10121 10010 Acheloma 10110 0201{01} 01??? 0000? {12}???0 ?1010 ?0101 ????? ????? 10010 Phonerpeton 10000 02001 01??? 00000 20110 21010 10101 01010 10121 10010 Ecolsonia 100?0 02011 01??? 00000 10110 21010 10101 01010 10121 10000 Broiliellus brevis 10011 02011 0???? ?000? ????0 ?1??? ????? ????? ????? 10000 Amphibamus 11000 02111 0???? ?000? ?0??0 ??010 ?0??? 0???0 ????? 1?200 Doleserpeton 02000 02111 01??? 2000? ?0110 21010 1???? 01??0 11121 11200 Eoscopus 12??? ??0?? 01??? 0000? ?0110 2???? ????? ????0 ?0??? ?0000 Platyrhinops 10000 02102 01??? 00000 10110 20010 10101 01010 101{12}? 10201 Micromelerpeton 10000 02011 01??? 00000 10110 21010 10??? 01010 10121 100?0 Apateon 10000 02111 0???? ?000? ?0??0 ??010 ????? ????? ????? 10000 Leptorophus 00000 02011 01??? ???00 10110 21010 10001 01010 10121 10000 Schoenfelderpeton 10000 02011 {012}1??? 00000 ?0110 21010 ????? ????0 0??21 10000 Albanerpetidae ??0?0 0?01{12} 31??? 2000? ?1??1 ??1?? ?1??? 1???1 ????? 00000 Eocaecilia 000?0 02??? 21??? 2000? ?1??1 ??1?? ?1??? 1???1 ????? 11200 Karaurus 10000 02112 3???? 2?00? ?1??0 2?1?? ?1??? 1???1 ????? ????? Triadobatrachus 100?0 02?11 0???? 2??1? ?1??? ??1?? ?1??? 1???1 ????? ????? Valdotriton 10000 02012 31??? 2000? ?1??1 ??1?? ?1??? 1???1 ????? ?1?00 Caerorhachis ?1001 02000 00100 00001 101?0 20010 00101 01010 10110 10001 Eoherpeton ?0101 020?1 1???? ?0001 20110 20010 00101 01010 101?0 10000 Proterogyrinus 0{12}101 02001 0???? 00001 {12}0?10 20010 ?0?0? 01010 1010? 10010 Archeria 0{12}101 02001 00001 (02)0001 20110 20010 00101 01010 10111 10000

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140 145 150 155 160 165 170 175 180 185 Ph. attheyi 01101 02001 0???? 20000 10110 20010 10101 01010 10100 10010 Anthracosaurus 0?101 02000 0???? (12)000? 10110 2?010 101?? 01010 10100 ?0010 Ph. scutigerum 0{12}101 02000 00001 00001 20110 20010 00101 01010 10111 10000 Bruktererpeton ????? ????? 0???? ????? ????? ????? ????? ????? ????? ?0010 Gephyrostegus 01111 0?000 01??? 00001 20110 20010 00001 00010 101{12}1 10000 Solenodonsaurus 00??0 0???? 0???? 2000? ????0 ??010 ????? ????? ????? ?0000 Kotlassia 00121 02002 11??? 20001 20110 20010 00111 01110 11121 000?0 Discosauriscus 02120 02000 11??? 20001 20110 21010 00101 01010 10121 10010 Seymouria 00121 02000 11??? 20001 20110 21010 00101 01010 10121 10010 Diadectes 00121 0(12)000 11??? 10001 ?1??0 21010 01??? 1???0 11121 10210 Limnoscelis 0{12}101 0{12}000 11??? 10001 21??0 21010 01??? 01010 10110 10010 Captorhinus 00111 02000 11??? 1000? ?1??0 21010 01??? 1???0 11121 10010 Paleothyris 00111 02000 1???? 20001 ?1??0 21010 0???? ????0 11121 10010 Petrolacosaurus 00111 02000 11??? 20001 ?0110 21010 01??? 1???0 11111 10010 Westlothiana 000?1 02000 0???? 2000? ????0 ??0?0 ????? ????? ????? ?0000 Batropetes 00000 02112 41??? 20001 ?1??0 21010 11??? 1???1 ????? 00000 Tuditanus 00010 02010 0???? ?000? ????0 ?1010 ????? ????? ????? ?0010 Pantylus 00020 02010 11??? 10001 ?0110 21010 01??? 1???0 00021 00010 Stegotretus 00020 02000 2???? 1000? ????0 ?1010 ????? ????0 0???? ?0010 Asaphestera ??0?? ?2??? 1???? 2000? ????0 ?1010 ????? ????? ????? ?0000 Saxonerpeton 00010 02000 1???? 2000? ????0 ?1??? ????? ????? ????? ?0010 Hapsidopareion ?00?0 0211? {12}???? 20001 ?1??0 21011 0???? ????? ????? 00010 Micraroter 00010 12(01)01 2???? 20001 ?0110 21010 0???? ????? ????? 00001 Pelodosotis 02020 12010 2???? ?000? ????0 ?1010 ????? ????? ????? ?0000 Rhynchonkos 02010 02011 21??? 2000? ????0 21010 ????? ????0 11110 00000 Cardiocephalus 00020 02(01)00 2???? 20001 ?0110 21011 ????? ????? ????? 00100 Euryodus 00010 0200(02) 2???? 20001 ?1??0 21011 0???? ????? ????? 000(01)0 Microbrachis 00020 02102 11??? 20001 10110 21010 00101 01010 10120 10000 Hyloplesion 100?0 02011 1???? 2000? ?0?10 ?1??? ????? ????? ????? ?0010 Odonterpeton 000?0 02001 2???? 2000? ?0??0 ????? ????? ????? ????? ?0000

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140 145 150 155 160 165 170 175 180 185 Brachydectes 00000 02?01 41??? 2000? ?1??0 21010 ?1??? 1???0 11121 00000 Acherontiscus ????? ????? 1???? 2000? ????0 ?1??? ????? ????? ????? ?00?? Adelospondylus 00?0? 0???? 1???? 2000? ?0??0 ?1010 ????? ????? ????? ?00?0 Adelogyrinus ????? ?{12}??? 1???? 2000? ?0010 ?1010 ????? ????? ????? ?0000 Dolichopareias ????? ????? ????? ????? ????? ????? ????? ????? ????? ?000? Scincosaurus 00000 02?11 3???? 20?0? ????? ????? ????? ????? ????? ?00?0 Keraterpeton ????? ????? 2???? 2000? ????0 ?1010 ????? ????? ????? ?000? Batrachiderpeton 000?0 0200? {23}1??? 20001 ?1??0 21010 01??? 1???0 10000 00000 Diceratosaurus 00??? ????? {34}???? 2000? ????0 ?10?? ????? ????0 1?0?? ?00?0 Diplocaulus 00000 02002 {23}???? 20001 ?0110 21110 0???? ????? ????? 00000 Diploceraspis 00000 02002 {23}1??? 20001 ?1??0 21111 01??? 1???0 11010 10000 Ptyonius 10010 02000 1???? 2000? ????0 ?1010 ????? ????? ????? ?0000 Sauropleura 00000 02001 01??? 20001 ?1??0 ?1010 0???? ????1 ????? 10000 Urocordylus ????? ????? {012}???? 2000? ????0 ?1010 ????? ????? ????? ?000? Lethiscus 00??0 0100? 1000? 20001 21??0 01010 001?1 ????? ????? 10000 Oestocephalus 00000 02012 0???? ?000? ?1??0 21010 0???? ????? ????? 1?000 Phlegethontia 00??0 ??0?? {23}1??? 2?00? ?1??1 ??1?? ?1??? 1???1 ????? ??000 Ariekanerpeton 01120 02000 11??? 2000? 20110 21010 ?0101 01010 10120 10010 Leptoropha ????? ????0 ????? ?000? ????? ????? ????? ????? ????? ?0000 Microphon 00??0 02000 ????? 2000? ?0?10 ?1010 ????? ????? ????? ?0000 Capetus 1???? ?200? 0???? ??00? ?0?10 2?010 ????? ????0 ????? ?0011 Notobatrachus 10000 02111 21??? 2001? ?1??1 ??1?? ?1??? 1???1 ????? ?020? Vieraella ????? ???1{12} 2???? 2001? ?1??1 ??1?? ?1??? 1???1 ????? ?1?0? Orobates 001{12}1 02000 2???? 10001 ?1??0 21010 0???? 1???0 11121 10210 Ossinodus ????? ??00? 0???? 0??0? ?00?? ??01? ????? ????? ????? ?001? Pederpes 00100 0{01}000 0???? ???0? ??0?? 10??? ????? ?0??? ????? ?0?10 Silvanerpeton 00101 02000 0???? ?0001 ?0110 ?0010 ????? 0???0 10100 10000 Tseajaia 00?20 01000 1???? 20001 21??0 21010 0???? 01010 10120 10010 Utegenia 02120 02000 01??? 2000? ?0110 21010 ?0101 01010 10110 10010 Gerobatrachus ????? ???1? {01}???? ????? ????0 2?0?? ????? ????? ????? ??00?

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140 145 150 155 160 165 170 175 180 185 Chroniosaurus 1{12}101 02000 0???? 2000? {12}0110 2001? 00111 01010 111?? 10000 Micropholis 10000 02111 0???? ?0000 ?0110 21010 ????? ????0 11121 10000 Nigerpeton 10110 02010 01??? 0000? 101?0 ????? 101?1 01?1? ???21 ?0000 Saharastega 10100 02011 1???? ???0? 101?? ????? 10101 0101? ????? ?0000 Iberospondylus ?0?10 0?0?? 0???? 20001 {12}0110 21010 ?0101 01010 10111 10000 Tungussogyrinus 10000 0??12 {012}???? ???0? ????? ????? ?0100 ????? ????? ?0000 Utaherpeton ????? ????? {012}???? ??00? ????? ????? ????? ????? ????? ??000 Caseasauria ????? ??000 1???? 20001 ?1??0 21010 ????? ????0 ???21 ?0010 Goreville micro. ?0000 02002 1???? ?0?0? ????? ????? ????? ????? ?0??? ?0?0? Sparodus ????? ????? 3???? ???0? ????? ????? ????? ????0 0???? ?0010 Liaobatrachus 00100 12(01)11 11??? 2?01? ?1??1 ??1?? ?1??? 1???1 ????? ?0?0? Acanthostomatops 02000 02012 1???? ????? ????? ????? ????? ????? ????? ?00?? Deltaherpeton ????? ????? 00??? 1010? 100?0 ?00?0 ?00?1 01010 101?? ?00?1 Karpinskiosaurus 02121 02000 11??? 20000 {01}0110 21010 0???? ????0 1??21 10010 Carrolla 10000 02111 4???? 2?00? ????0 210?0 0???? ????? ????? 0?{02}00 NSM 994 GF 1.1 0???? ??0?? 0???? ????? ????? ????? ????? ????? ????? ??0?? Crinodon 00010 02002 1???? ?000? ????0 ?10?0 ????? ????0 0???? ??00? Sigournea ????? ????? ?0??? 0000? 20110 21010 00110 01100 11010 100?? Doragnathus ????? ????? ?1??? 20001 {12}0110 20010 00110 01100 11000 10000 Spathicephalus 0001? ?2011 00011 2000? {12}0??0 ????? ?0111 ????? ????? ?0000 Metaxygnathus ????? ????? ?011? 01000 000?0 10000 000?0 00?00 0?0{01}0 000?? Sclerocephalus 10000 0201(12) 01??? 00000 00110 20011 00101 01010 10121 10010 Cheliderpeton ????? ????? ????? ??00? ????0 ?0??? ????? ????? ????? ?00?1 Archegosaurus 10101 02002 01??? 00000 10110 20010 00101 01010 10111 10010 Konzhukovia 101{01}0 02001 0???? ????? ????? ????? ????? ????? ????? ?000? Lydekkerina 10100 02002 11??? 00000 {12}0010 20010 1000(01) 00010 10(01)21 000(01)0 Beiyanerpeton 10?00 020?? 31??? 2?00? ?1??1 ??1?? ?1??? 1???1 ????? ?0?00 Pangerpeton 10001 02011 1???? ?000? ?1??1 ????? ????? ????1 ????? ????? Ymeria ????? ????? ?01(01)1 0100? ?00?0 100?0 00010 00100 01000 ?0010 Densignathus ????? ????? ?0100 01001 100?0 10010 00001 00010 01000 000??

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140 145 150 155 160 165 170 175 180 185 Chelotriton 000?0 02??{12} 01??? 2000? ?1??0 211?? ?1??? 1???1 ????? 0??00 Palatinerpeton ????? ????? 11??? 00000 20110 21010 10101 01110 11121 1001? Glanochthon 12100 02012 01??? 00000 101?0 200?0 10??? ????0 10(01)21 10011 Archaeovenator ?0101 0?000 11??? 20001 ?1??0 21010 01??? ????0 11121 10000 Platyoposaurus 12111 02011 01??? (01)0001 201?0 210?1 10101 01010 1012? 10000 Trihecaton ????? ????? ????? ??00? ????? ??0?? ????? ????0 ???21 ?0?00 Erpetosaurus 10120 0{12}002 0???? 0010? ?0??0 ?00?0 ????? ????? ????? ?000? Mordex 11010 0?011 {01}???? 0??0? ????0 ??0?? ?0101 01010 101?? ?0010 Branchiosaurus 10010 0?012 {012}???? ?000? ????0 ??0?0 ????? ????? ????? ?0000 Pholidogaster ????? ????? {01}???? {01}010? ?0?10 ?00?? ????? ????? ????? 100?1 Palaeoherpeton ??101 02100 0???? ????? ????? ????? ????? ????? ????? ?00?? Neopteroplax ??1?1 02?00 0???? ?0001 ?0110 20010 ????? ????0 1?12? 10?10 St. Louis tetrapod ????? ????? {0123}0??? ?0101 ?0010 ????? 00?0? ????? ????? ?00?0 Parrsboro jaw ????? ????? ?0100 0??00 001?? ????? 00101 01010 1011? 100?? Elginerpeton ????? ????? ?0111 0000? 00000 10000 00010 00100 0?0?? 000?? Australerpeton 10110 02011 01??? (01)0001 {12}0110 ?10?0 00111 01110 111{12}1 10000 Quasicaecilia ?00?0 0211{12} 4???? ????? ????? ????? ????? ????? ????? ????? Casineria ????? ????? ????? ????? ????? ????? ????? ????? ????? ????? Llistrofus 10000 02112 21??? 2?00? ?1??0 21011 0???? ????? ????? 00010 Bystrowiella ????? ????? 1???? ????? ????0 ??0?? ????? ????? ????? ?00?? Coloraderpeton 001{01}1 01000 0000? 20000 01??0 {01}1010 001?1 01?10 1?100 000?0 Pseudophleg. 001{01}? 01000 3???? ?000? ?1??0 {01}10?0 ????? ????? ????? ?00?? Perittodus ????? ????? ?011? ?0000 {12}00?0 ?00?0 000?0 00?00 1?000 ?00?0 Diploradus 00?10 02011 ?000? 1??00 {12}00?0 ????? 00110 01100 110?0 0??00 Aytonerpeton ????? ????? ?010? 1000? 00010 ????? 00011 01110 111?? ?0001 14859 190 195 200 205 210 215 220 225 230 235 Eusthenopteron 00000 00000 00000 000?0 00000 00010 01011 00000 0000? 00000 Panderichthys 00000 00000 00000 00000 01000 00011 01011 0000? ????? ???00 Ventastega 00000 00011 00000 100?? ????? ????? ????? ????1 ??00? ?????

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190 195 200 205 210 215 220 225 230 235 Acanthostega 00000 00011 00000 10000 00001 00000 10021 10011 00000 11020 Ichthyostega 00020 00012 10001 01??0 0?001 00100 10021 12011 01100 01000 Tulerpeton 000?0 0?10{12} 00001 01011 00011 10001 101?1 1101? ????? 11020 Colosteus 000{01}0 ???00 010?? ????? ????? ????? ???1? 1???? ????? ????? Greererpeton 00000 00100 01000 01110 01011 10000 10110 12010 01001 11120 Crassigyrinus 00010 0?1?1 000?? ???10 01001 {12}000? 10011 100?1 0?00? 11120 Whatcheeria 00020 00(01)02 10?1? 01100 01011 10000 10121 ??011 01000 0?0?1 Baphetes 00010 0011{12} ????? ???00 01011 2000? 1112? 1?0?1 0100? ????0 Megalocephalus 00010 ????? ????? ????? ????? ????? ????? ????? ????? ????? Eucritta 00020 0?11(01) 0000? ??1?0 ??011 200{01}? 1?12? 11011 0??0? ???20 Edops 00020 ????? ????? ????1 1?111 21110 1112? 12011 ??101 0?1?0 Chenoprosopus 00010 ???0? ??0?? ????? ????? ????? ????? ????1 0?10? ??1?? Cochleosaurus 00020 01110 010?0 ??1?? ????? ?1?1? 1?12? 12011 0100? 1?120 Isodectes 000{12}0 0?111 000?? ???1? 11??{01} 2111? ?1120 12011 0??0? ???20 Neldasaurus 00000 ???00 0100? 0?111 ?1111 21?1? 11120 12011 0?00? {12}?1?? Trimerorhachis 00000 ???10 010?? ???11 11111 21?10 11120 12011 0?10? 11120 Balanerpeton 00000 01110 0000? ??1?? 1?012 ?111? 11120 11010 0100? 1?020 Dendrerpetidae 00000 01110 00000 011?? 1?011 2111? 11120 11011 01101 2?120 Eryops 00000 01(01)10 11101 01111 11111 21110 11120 12011 0(01)101 21120 Acheloma 000{12}0 011?? ???01 01111 11111 21110 01120 ??011 11101 20110 Phonerpeton 00020 011?? ????? 01?11 11?11 2111? ???2? ??01? ????1 ?01?? Ecolsonia 00020 01110 10001 01111 11111 211{12}0 1?120 ??010 ?1001 2?1?? Broiliellus brevis 00000 011?? ???0? ??1?? ??112 ?1?11 11120 ????1 01001 {12}???? Amphibamus 00000 01110 000?? ?11?? 1?112 ?1?21 11120 1?0?? 0100? {12}??20 Doleserpeton 00000 01110 ?1000 011?0 1?112 ?1121 11120 11011 01001 20120 Eoscopus 00000 ??110 00000 0???? ??11? ?1?2? 11120 12011 01001 101?0 Platyrhinops 00000 01110 0000? ????0 1?111 21?21 11120 12011 01?0{12} 20120 Micromelerpeton 00010 ???10 0000? ????1 ??112 ?1??? ??120 110?0 0??0? ???2? Apateon 00000 01110 10000 011?? 1???2 ?1?2? 11120 11011 0?00? ???20 Leptorophus 000(01)0 ???10 000?? ????? ??112 ?1?2? ??120 110?1 0??0? ???2?

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190 195 200 205 210 215 220 225 230 235 Schoenfelderpeton 00000 ????0 ?00?? ????? ??112 ?1?1? ??1{12}0 110?? ????? ????? Albanerpetidae 0002(12) ????? ???11 ??1?0 1?112 ?1121 11120 11011 ????? ???20 Eocaecilia 00000 ????? ???11 011?0 1?112 ?1121 11110 1101? ????? 20110 Karaurus ????? ????? ???0? ??110 1?112 ?1?21 11120 11010 0??0? ???20 Triadobatrachus ????? 011?? ???1? 011?0 1?112 ?112? ?1120 12011 ?001? 00?20 Valdotriton 0002? ????? ???01 011?0 1?112 ?1?21 11120 1201? ????? 2?120 Caerorhachis 0000? ????? ????? ????? ????? ????? ????? ??011 0110? 1?1?0 Eoherpeton 00020 ??1?? ???01 01?10 01011 10?00 11121 ????1 01101 ??1?0 Proterogyrinus 10000 0?111 00000 01110 01011 20100 1?121 11011 01100 {12}1120 Archeria 10000 00112 01000 01111 01011 20110 11121 12011 11101 21120 Ph. attheyi 10000 ????? ????? ????? ????? ????? ????? ????? ????? 111?? Anthracosaurus 00020 ????? ????? ????? ????? ????? ????? ????? ????? ????? Ph. scutigerum 10000 0?1?{12} ???00 010?? 0?0?1 {12}??10 1112? 1201? ????? ????? Bruktererpeton 000{01}0 ??1?? 0???? 01?10 11011 20111 11120 1201? ????? {12}0120 Gephyrostegus 00000 01112 00001 01110 11011 20111 11120 12011 01101 10120 Solenodonsaurus 00010 011?2 100?? ????1 1?011 21?10 11120 1?00? ????? ????? Kotlassia 00010 0?1?2 11000 011?1 ??111 21110 11120 ??011 01101 21120 Discosauriscus 00021 01102 10010 0100? 11011 21?1? 10120 110?1 1?101 ?0020 Seymouria 00020 01102 ?1011 01111 11011 21110 10120 12011 11101 21020 Diadectes 00020 01102 10011 01101 11011 21110 10120 12011 11101 21120 Limnoscelis 00020 011?2 10001 01?01 11011 21100 10120 12011 11101 11010 Captorhinus 00020 ???12 10001 01111 11011 21110 11120 12010 01?01 11120 Paleothyris 00010 01112 10001 01?11 11011 21121 11120 12010 01001 10120 Petrolacosaurus 00010 01112 10001 01111 11011 21121 11120 12010 11001 {12}0120 Westlothiana 0001{01} ??1?? ???0? ?1?11 11011 21111 11110 12011 11001 10120 Batropetes 00032 0?111 1000(01) 011?0 1?012 ?1111 11120 12011 (01)?001 20100 Tuditanus 00020 01112 000?? ????1 ??01? ?1?11 11120 1{12}0?1 01101 {12}01?0 Pantylus 001?0 01102 00000 01100 11011 21111 11120 12010 0100? 101?0 Stegotretus 001?0 ????{12} 10000 ?11?? ??1?? ?1?1? ???20 12011 0??01 10110 Asaphestera 00020 ???11 10001 11??1 ??011 21?1? ??120 ??0?1 0?00? ???{12}?

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190 195 200 205 210 215 220 225 230 235 Saxonerpeton 00020 01112 10001 ??1?0 1?012 ?1111 11120 12011 0100? 001{12}0 Hapsidopareion 00020 ????? ????? ????? ????? ????? ????? ????1 ????? ????? Micraroter 00020 01102 1001? ?11?? ????? ????? ????? ????1 01001 {12}01?? Pelodosotis 00020 01112 1000? 1?1?0 1?011 21111 11120 12011 0??01 {12}0120 Rhynchonkos 00020 ????? ????? ????? ????? ????? ????? ????? ????? ????? Cardiocephalus 001?? ????? ????? ????? ????? ?1?{12}? ?1?2? 1101? ???01 ????? Euryodus 001?0 ??1?2 10001 ?1?10 11111 21111 11120 ??011 01?01 {12}0120 Microbrachis 0002? 01112 100?? ????0 1?012 ?1111 11110 12011 01001 {12}0120 Hyloplesion 00020 011?{12} 1??01 ????0 1?012 ?1111 11110 12011 0100? 10120 Odonterpeton 00020 011?? ????? ??1?0 ????? ?1?11 11110 110?? ????? ????? Brachydectes 00030 01110 100?? ??1?0 ??112 ?1?1? 11110 11000 0?00? {12}0120 Acherontiscus 001?0 ????0 010?? ????? ????? ????? ????? ????? ????? ????? Adelospondylus 110{012}0 ????0 ????? ????? ????? ????? ????? ????? ????? ????? Adelogyrinus 11010 0?1?0 010?? ??1?? ????? ????? ???0? ????? ????? ????? Dolichopareias 11000 ????? ????? ????? ????? ????? ????? ????? ????? ????? Scincosaurus 00031 01100 10001 ?11?1 1?01? ?1111 1?110 12011 0?002 {12}0120 Keraterpeton 00030 11100 010?? ??1?0 ??11? ?0?01 10110 0101? 0?00? ???20 Batrachiderpeton 00030 11100 010?? ????? ????? ????? ????? ????? ????? ????? Diceratosaurus 00030 11100 010?? ??1?0 ??11? ???01 10110 01011 0?00? ???20 Diplocaulus 00020 11100 01010 111?? 1?011 21?1? 11110 1201? ????? 20020 Diploceraspis 00030 ???00 010?? ??1?? ????? ????? ????? ????? ????? ????? Ptyonius 00020 01110 0100? ?11?0 ??11? ?011? 11110 11011 0?002 ???20 Sauropleura 00020 01110 0100? ?11?1 ??11? ?0110 11110 11011 1?002 ???20 Urocordylus 00020 01110 0100? ??1?0 ??01? ?011? 10110 11011 0?0?2 {02}1120 Lethiscus 0?020 ????? ????? ??1?? ????? ????? ???0? ????? ????? ????? Oestocephalus (01)0020 01??? ????? ??1?? ????? ????? ???0? ????? ????? ????? Phlegethontia 00020 01??? ????? ??1?? ????? ????? ???0? ????? ????? ????? Ariekanerpeton 00020 01102 1001? 0???1 11011 21?1? 10120 11011 1?10? ???20 Leptoropha 00023 ????? ????? ????? ????? ????? ????? ????? ????? ????? Microphon 00023 ????? ????? ????? ????? ????? ????? ????? ????? 201??

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190 195 200 205 210 215 220 225 230 235 Capetus 000{01}0 ????0 000?? ????? ????? ????? ????? ????? ????? ????? Notobatrachus 00000 011?? ???10 011?0 1?112 ?1?21 11120 12111 0?01? 00?2? Vieraella 0002? 011?? ???1? ??1?0 ??112 ?1?21 11120 1211? ???1? ???2? Orobates 00020 0110? 10?11 01111 11011 21100 11120 12011 10101 20120 Ossinodus 00010 00112 ?11?1 ?1?0? 0101? 0000? ?01{12}1 ??0?1 0?10? 200?0 Pederpes 0002? 0111{12} 1011? 0??1? 01011 1000? 1012? 110?1 0?00? 00021 Silvanerpeton 00010 0?111 0000? ????0 ??011 20?1? 11121 120?1 0??0? ???2? Tseajaia 00020 01102 1?011 011?1 1?011 2111? 10120 12011 11101 21120 Utegenia 00020 011?2 1001? ????? ??01? ???1? 1?120 110?1 1?10? ???20 Gerobatrachus 00000 011?? ????? ????? ????? ?1?2? ?1?2? ???11 0??0? ????? Chroniosaurus 00010 ????2 000?? ????? 1?011 211{12}? 1?12? ????1 0110? ????0 Micropholis 000(01)0 01110 0?010 ??1?? ??1?? ?1?1? ?112? 12011 01001 10110 Nigerpeton 00000 ????? ????? ????? ????? ????? ????? ????? ????? ?1??? Saharastega 00000 ????? ????? ????? ????? ????? ????? ????? ????? ????? Iberospondylus 00010 ????? ????? ????? ????? ????? ????? ????? ????? ????? Tungussogyrinus 00022 ????? ????? ????? ????? ?1?2? ?1?2? 100?1 0101? ???20 Utaherpeton 00020 ????0 100?? ????? 1?01? ?111? ?1110 12011 ????? ???20 Caseasauria 00020 ??1?2 11001 0???1 1?011 21?11 11120 ???11 ??101 {12}1120 Goreville microsaur 0?02? ????? 10??? ????? ??0?? ?1?1? 111?? ????? ????? {12}01{12}? Sparodus 00020 01112 1??01 ????0 1?11? ?1111 11120 12011 01001 2???? Liaobatrachus 00000 0110? ???10 011?0 1?112 ?1121 11120 12111 ?101? 00?2? Acanthostomatops 00010 01110 1?0?? ??1?1 1???? ?1?1? ?1?2? 120?? 01?0? ???00 Deltaherpeton 00000 ????? ????? ????? ????? ????? ????? ????? ????? ????? Karpinskiosaurus 000(12)0 ????? ????? ????? ????? ????? ????? ????? ????? ????? Carrolla 0003{02} ????? ????? ????? ????? ????? ????? ????? ????? ????? NSM 994 GF 1.1 000{12}0 0?11? ????? ????0 0?0?? ?0100 1112? 1201? ????? ????? Crinodon 00020 ????? ????? ????? ????? ????? ????? ????? ????? ????? Sigournea 00000 ????? ????? ????? ????? ????? ????? ????? ????? ????? Doragnathus 00000 ????? ????? ????? ????? ????? ????? ????? ????? ????? Spathicephalus 10000 ????? ????? ????? ????? ????? ????? ????? ????? ?????

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190 195 200 205 210 215 220 225 230 235 Metaxygnathus 000?0 ????? ????? ????? ????? ????? ????? ????? ????? ????? Sclerocephalus 00010 01110 01001 00111 11112 ?111? ??120 12011 0?10? ?1120 Cheliderpeton 000{12}0 0111{01} 010?? ??1?? ????? ?1?1? ???2? 12011 ???0? ?1??0 Archegosaurus 00000 01110 010?? ??1?? ????? ?1?1? ???2? 12011 1?10? ??120 Konzhukovia 00010 ????? ????? ????? ????? ????? ????? ????? ????? ????? Lydekkerina 00010 011(01)1 01000 00111 11111 21111 11120 12011 0?101 21110 Beiyanerpeton 000{012}0 ????? ???0? ??1?0 1?11? ?1?21 11120 11011 01?1? 2?010 Pangerpeton 000{01}0 ????? ???01 ????0 1???? ?1?2? ?1120 11011 0??0? ???20 Ymeria 00020 ????? ????? ????? ????? ????? ????? ????? ????? ????? Densignathus 000{012}0 ????? ????? ????? ????? ????? ????? ????? ????? ????? Chelotriton ??00? ????? ???0? ??1?0 ?111? ?1?21 11110 1201? ???0? ?1?20 Palatinerpeton 000{12}0 011?? ????? ????? ????? ????? ???{12}? ????1 0??0? ??1?0 Glanochthon 000(12)0 01110 000?? ????? ????? ?1?1? ?1?2? 1{12}0?1 0??0? ???2? Archaeovenator 000{12}0 ????2 10?01 0???? ????? ?1??? ?1?2? ????1 ?1?01 00??0 Platyoposaurus 00000 0?1?0 0?00? ??1?? ????? ????? ???{12}? ?1011 0??0? 211?? Trihecaton 00020 ????2 11?11 11?10 11?11 21111 ?1120 12011 0??0? 1?12? Erpetosaurus 00000 0?1?0 010?? ????? ??1?1 {12}0?1? ?1?2? 1{12}011 0?0?? ??1?? Mordex 00000 ???1? 01??? ?1??? 0???? ?1?1? 01120 1{12}011 11?0? ??120 Branchiosaurus 00010 ???10 1?0?? ????? ????? ?1?1? ?112? 1{12}011 ???0? ???20 Pholidogaster 00020 ??110 000?? ????? ????? ???{01}? ???2? 1?0?? ???0? {12}??20 Palaeoherpeton 000{12}0 ????? ????? ????? ????? ????? ????? ????? ????? ????? Neopteroplax ??01? ????? ????? ????? ????? ????? ????? ????? ????? ????? St. Louis tetrapod 000{012}0 ????? ????? ????? ????? ????? ????? ????? ????? ????? Parrsboro jaw 000{012}0 ????? ????? ????? ????? ????? ????? ????? ????? ????? Elginerpeton 00000 ??1?? ????? ????? ????? ????? ????? ????1 0?00? ??0?0 Australerpeton 00000 0?110 01001 0???1 1?1?? ?1?1? ?1120 12010 1?101 2?120 Quasicaecilia ????? ????? ????? ????? ????? ????? ????? ????? ????? ????? Casineria ????? 001?? ???11 ??1?? ??01? ?1?1? 11?20 1?0?1 0??0? ???2? Llistrofus 00020 ????? ????? ????? ????? ????? ???{12}? ?201? ????? ????? Bystrowiella 000?0 011?1 000?? ????1 1?011 21110 ?1120 ????? ????? 1012?

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190 195 200 205 210 215 220 225 230 235 Coloraderpeton 000{12}0 ????? ????? ????? ????? ????? ???0? ????? ????? 000{12}0 Pseudophlegethontia 000?0 01??? ????? ????? ????? ????? ???0? ????? ????? 000?0 Perittodus 00020 ????? ????? ????? ????? ????? ???{12}? ?10?? ????? 00020 Diploradus ??01? ????? ????? ????? ????? ????? ????? ????? ????? ??01? Aytonerpeton 00000 ????? ????? ????? ????? ????? ????? ????0 0??0? ??0?0 14860 240 245 250 255 260 265 270 275 277 Eusthenopteron 0000? ???0? 00000 ?0?00 01010 00001 00010 00000 00 Panderichthys 00??? ???0? 00000 0??00 0000? ?0?01 000?0 00000 00 Ventastega ????? ????? ????? ????? ????? ????? ????? ????? ?0 Acanthostega 00100 00000 00000 00?00 01010 00001 00011 00000 10 Ichthyostega 00000 00001 11000 ???00 01010 00001 00001 00000 10 Tulerpeton 11010 111?? ????? ????? ???10 0??01 0???? ????0 1? Colosteus ????? ????? ????? ???00 ???10 000?1 1?0?{12} ??001 3? Greererpeton 01000 0?101 00110 00?00 01010 00001 1001{12} 00001 2? Crassigyrinus 1110? ???0? 10000 0??00 ???0? ?0?01 0?0?{12} 00000 {1234}? Whatcheeria 0101? ???01 11000 ???00 00010 10001 0001{12} 00000 {1234}? Baphetes 0110? ????? ??1?0 ???00 0?0?? ????1 ?00?? ??0?? {1234}? Megalocephalus ????? ????? ????? ????? ????? ????? ????? ????? ?? Eucritta 01??? ???00 00000 ????? ????? ????? ????? ????? {1234}? Edops 11??? ????? ????? 0??00 ?1?10 00001 0?0?{12} ?0000 {1234}? Chenoprosopus ????? ????? ????? ????0 ????? ?0?01 0?0?{12} ?0??? ?? Cochleosaurus 01??? ???00 00000 0??0? ???10 00001 0?01{12} ?10?? 3? Isodectes 01??? ???00 1???0 ???0? ????? ?0?0{01} ??01{12} ??0?0 31 Neldasaurus ????? ???0? 00000 ???00 ???10 00001 1?01{12} 00000 3? Trimerorhachis 0110? ???01 10000 00?00 01010 00001 10012 01000 {23}1 Balanerpeton 01000 01100 00001 00?00 01010 00001 0001{12} 00000 31 Dendrerpetidae 01??0 01100 00001 ???00 01010 00001 0001{12} 00000 {23}1 Eryops 01110 01100 01000 (01)0?00 01010 00001 00012 00000 31 Acheloma 01??0 0110? 00001 00000 01010 00001 0000{12} 00000 {23}?

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240 245 250 255 260 265 270 275 277 Phonerpeton ????? ???0? 0000? ???00 01010 00001 00002 ?0000 ?? Ecolsonia ?1000 0??0? 00000 ???00 01010 00001 00012 00000 {1234}? Broiliellus brevis ????? ???0? 00000 ???00 ????? ?0001 0?0?{12} ?0000 ?? Amphibamus 0100? ???00 00001 ?0?00 01010 00001 00012 01000 31 Doleserpeton 0110? ???00 00001 0??00 01011 ?0101 00012 01000 3? Eoscopus 01000 01100 00001 00?00 01010 ?0001 00012 01000 31 Platyrhinops ?1??0 ?1100 00001 ???00 01010 00001 00012 00000 31 Micromelerpeton ?1??? ???00 00000 ???00 ???10 00001 0??12 00?00 31 Apateon 01??? ???00 00001 ???00 ????? ?0?01 0?0?2 00000 31 Leptorophus ?1??? ????? ????? ???00 ????? ?0??? ????{12} ?0000 3? Schoenfelderpeton ????? ????? ????? ???00 ????? ????? 0???{12} ?0?00 3? Albanerpetidae ?1??0 01100 00001 11100 0?011 10102 0001{12} 01000 31 Eocaecilia 01??0 0??01 00001 11100 00011 10101 00012 11010 {1234}1 Karaurus 01??? ???00 00001 1??00 010?? ?011{02} 00012 010?0 31 Triadobatrachus 01000 0??00 00001 01100 ????? ?010{02} 0?01{12} ?1000 ?1 Valdotriton 01?0? ???00 00001 ?1100 010?? ?011{02} 00012 01010 31 Caerorhachis 01??0 11100 10000 ?0?00 01011 00001 00012 00000 {1234}? Eoherpeton 0110? ???0? 10000 0?000 ???11 00001 1?00{12} 00000 ?? Proterogyrinus 01100 11100 10000 00?00 01011 00001 10012 00000 2? Archeria 01100 11100 10000 00?00 01011 10000 10012 00000 2? Ph. attheyi ????? ???0? 10000 ???00 01011 10000 1000{12} ?0000 ?? Anthracosaurus ????? ????? ????? ????? ????? ????? ????? ????? ?? Ph. scutigerum ????? ???00 10000 0??00 ???11 10000 1?00{12} ?0000 {1234}? Bruktererpeton 01000 1??00 10000 ???00 01011 00001 ?001{12} 00000 2? Gephyrostegus 01101 11100 10100 00?00 ???11 00001 0?01{12} 00000 2? Solenodonsaurus ????? ???00 10000 ???00 ???11 10101 0?01{12} 00000 {123}? Kotlassia 01000 0?100 10100 01?00 01011 11101 000?2 0?000 {1234}1 Discosauriscus 0100? ???00 00000 00?00 01011 11?01 00012 00000 2? Seymouria 01100 01100 00000 00?00 01011 11101 00012 00000 21 Diadectes 01001 11?00 10000 01?00 01011 11101 00012 00000 21

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240 245 250 255 260 265 270 275 277 Limnoscelis 01100 0??00 10000 01?00 01011 11101 00012 00000 21 Captorhinus 01??1 11100 10000 01?00 01011 11101 00012 01000 21 Paleothyris 01001 11101 10000 01?00 0?011 10101 0001{12} 00000 21 Petrolacosaurus 01001 11100 10000 01?00 01011 11101 00012 00000 21 Westlothiana 11000 1110? 1000? ???00 01011 11101 0001{12} 01000 {123}1 Batropetes 01000 01100 10000 01100 0(01)0?? ?010{02} 00012 ?1000 31 Tuditanus 01001 11?01 10000 ???00 ????? ?010? 0??1{12} ?1?00 31 Pantylus 0???1 01100 10000 11?00 0?0?? ?000{02} 00012 11000 3? Stegotretus 0???? ????? ????? ???00 ????? ?000{02} 0?01{12} 11000 {1234}? Asaphestera ????? ???0? 10000 ???00 ????? ?010? 0??1{12} ?1?00 {1234}? Saxonerpeton 01000 01100 10000 ??100 ????? ?000? 0??1{12} 11?00 {1234}? Hapsidopareion ????? ????0 ????? 001?? ????? ??0?? ????? ????? ?? Micraroter ????? ???00 10000 01?00 01011 10001 00012 01000 ?? Pelodosotis 0100? ???00 10000 0??00 ???11 10001 0??1{12} ?1?00 {1234}? Rhynchonkos ????? ????? ????? ????? ????? ????? ????? ????? ?? Cardiocephalus ????? ???00 10001 ?1?00 ???11 10101 0?01{12} 01000 {1234}? Euryodus 0100? ????? ????? (01)1?00 ???11 10101 0?01{12} 01000 {1234}? Microbrachis 01000 0??00 10000 ?1?00 000?? ?010{02} 00012 11000 41 Hyloplesion 01000 01100 10000 ?1?00 000?? ?000{02} 0001{12} ?1000 41 Odonterpeton ????? ???00 10001 ??100 ????? ?000{02} 0???{12} 11?00 4? Brachydectes 01??? ???01 10010 00?00 000?? ?000{02} 1001{12} 11000 31 Acherontiscus ????? ????? 1???1 ???00 00011 10000 100?? ??00? ?? Adelospondylus ????? ???0? 10110 ???0? ????? ?000{02} 1???{12} 1??00 ?? Adelogyrinus ????? ???0? 10110 0??0? ????? ??00{02} 1???{12} 10?00 ?? Dolichopareias ????? ????? ????? ????? ????? ????? ????? ????? ?? Scincosaurus 01??0 0010? 10000 ?1011 111?? ?010{02} 00012 11100 31 Keraterpeton 01??? ???0? 10000 ?1011 110?? ?010{02} 01002 00100 31 Batrachiderpeton ????? ????? ????? ??011 110?? ?010{02} 00002 00100 ?? Diceratosaurus 01??? ???0? 10000 ?1011 110?? ?010{02} 01102 00100 21 Diplocaulus 01??? ???00 00000 11111 110?? ?111{02} 01112 01?00 {23}1

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240 245 250 255 260 265 270 275 277 Diploceraspis ????? ????? ????? 11111 110?? ?011{02} 01102 01100 ?1 Ptyonius 01??? ???00 10000 ?1?11 111?? ?010{02} 00002 01100 31 Sauropleura 01??? 0?10? 10000 01?11 111?? ?010{02} 00002 001(01)0 31 Urocordylus 01??? ???0? 10000 ?1?11 111?? ?010{02} 00002 01100 21 Lethiscus ????? ???11 00001 11100 ????? ?010{02} 0??12 01??0 ?1 Oestocephalus ????? ???21 00001 ?1?10 ????? ?010{02} 0?002 01110 ?1 Phlegethontia ????? ???21 00001 01100 ????? ?010{02} 0?002 01110 ?1 Ariekanerpeton ?1??? ???00 10000 ???00 ???11 ?1?01 0?01{12} 00000 21 Leptoropha ????? ????? ????? ????? ????? ????? ????? ????? ?? Microphon ????? ????? ????? ????? ????? ????? ????{12} ????? ?? Capetus ????? ????? ????? ????? ????? ????? ????? ????? ?? Notobatrachus ?1??? ???00 00101 11100 ????? ?010{02} 0?01{12} 01000 31 Vieraella ????? ???0? 00101 1??0? ????? ?010{02} 0?01{12} 01000 31 Orobates 01000 11000 10000 0??00 01011 11?01 00012 01000 21 Ossinodus 1???0 ???0? 00000 ???00 010?? ?000? ?001{12} ??0?0 {1234}? Pederpes 0110? ???00 01000 ?0?00 0??10 ?0001 0?01{12} 00000 {1234}? Silvanerpeton ?1??0 01100 10000 ???00 01011 00001 000?{12} ??000 2? Tseajaia ?1??0 01?0? 10000 01?0? ???11 11101 0?01{12} 00000 2? Utegenia ?1??? ???00 10000 ???00 01011 1??01 000?{12} 00000 21 Gerobatrachus ????? ???00 00001 1?1?? ???11 ??001 0?0?? 0???? {234}1 Chroniosaurus 01??0 0??0? 10?0? ?0?00 00011 10100 00012 0?000 {1234}? Micropholis ?1??0 ??101 ?0001 ?0?00 ???10 00001 0?0?{12} ??000 3? Nigerpeton ????? ????? ?1000 ????0 ????? ?00?0 ???0{12} ?0??0 ?? Saharastega ????? ????? ????? ????? ????? ????? ????? ????? ?? Iberospondylus ????? ???00 01000 00000 010?? ?0001 00012 ?00?0 ?? Tungussogyrinus 0100? ????? ????? ????? ????? ?0?0? ????{12} ????0 31 Utaherpeton 0100? ???00 10000 ???00 00011 ?0102 000?2 01000 31 Caseasauria 01??1 01101 00000 1??00 0?011 10?01 0001{12} ?1000 {234}? Goreville microsaur ????? ???0? 10000 00?00 01011 10001 00012 01000 {1234}? Sparodus ????? ???00 10000 ???0? ????? ?010{02} 0?01{12} 0?00? {1234}?

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240 245 250 255 260 265 270 275 277 Liaobatrachus ?1??? ?1100 00101 1110? ????? ?010{02} 0?01{12} 01000 31 Acanthostomatops ?1??? ???00 00001 ???00 00010 00001 00012 00000 31 Deltaherpeton ????? ????? ????? ????? ????? ????? ????? ????? ?? Karpinskiosaurus ????? ????? ????? 010?? ???11 11101 0?00{12} 01000 ?? Carrolla ????? ????? ????? ????? ????? ????? ????? ????? ?? NSM 994 GF 1.1 ????? ???00 1???0 00?00 ???1? 10001 ??00{12} ?00?0 ?? Crinodon ????? ????? ????? ????? ????? ????? ????? ????? ?? Sigournea ????? ????? ????? ????? ????? ????? ????? ????? ?? Doragnathus ????? ????? ????? ????? ????? ????? ????? ????? ?? Spathicephalus ????? ????? ????? ????? ????? ????? ????? ????? ?? Metaxygnathus ????? ????? ????? ????? ????? ????? ????? ????? ?? Sclerocephalus 01000 01100 11100 00?00 01010 00001 00012 00000 31 Cheliderpeton 01000 01100 1?100 ???0? ????? ?0001 ????{12} ????? {23}? Archegosaurus 11000 01100 10100 00?00 01010 00001 0001{12} 00000 31 Konzhukovia ????? ????? ????? ????? ????? ????? ????? ????? ?? Lydekkerina 0100? 0??00 10100 0000? ?0?10 00001 0?0?{12} 00000 {234}? Beiyanerpeton 0100? ???00 00001 ?1100 010?? ?011{02} 000?{12} 0?0?0 31 Pangerpeton 0100? ???01 ?000? ??1?? ????? ???1{02} 0?0?? ????? 3? Ymeria ????? ????? ????? ????? ????? ????? ????? ????? ?? Densignathus ????? ????? ????? ????? ????? ????? ????? ????? ?? Chelotriton ?1??0 01101 10000 11101 01??? ?011? 00012 011?0 31 Palatinerpeton 0100? ????? ????? ????? ????? ????? ????? ????? {1234}? Glanochthon ????? ???0? 1?1?? ????? ???10 00001 ????{12} ??000 {1234}? Archaeovenator 01001 11100 10000 01000 01011 10101 0001{12} 0?00? {234}? Platyoposaurus ????? ???01 11100 00?00 01010 00001 0001{12} 00000 3? Trihecaton ????? ???00 10000 01100 00011 10101 0001{12} 010?0 {1234}? Erpetosaurus ?1??? ???00 00100 ????? ???10 00001 ???1{12} ?00?? {123}? Mordex 01??? ???00 ????? ????0 0?01? ????1 ????2 ????? 31 Branchiosaurus ?1??? ???00 ????? ???00 ????? ????? ????{12} ????? 31 Pholidogaster ?1??0 ?11?? 1???0 ???00 01010 0?001 100?2 0?00? {1234}?

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240 245 250 255 260 265 270 275 277 Palaeoherpeton ????? ????? ????? ????? ????? ????? ????? ????? ?? Neopteroplax ????? ????? ????? ????? ????? ????? ????? ????? ?? St. Louis tetrapod ????? ????? ????? ????? ????? ????? ????? ????? ?? Parrsboro jaw ????? ????? ????? ????? ????? ????? ????? ????? ?? Elginerpeton ????? ????? ????? ????0 ????? ?00?? ???0{12} ??0?? ?? Australerpeton 0110? ???00 10100 ?0?00 01010 00001 0001{12} 00000 {1234}? Quasicaecilia ????? ????? ????? ????? ????? ????? ????? ????? ?? Casineria ????? ???00 10000 ???00 ???11 ?0001 0?01{12} 000?0 2? Llistrofus ????? ???00 10000 ???00 ????? ?000{02} 0?0?{12} 1100? {1234}? Bystrowiella ?110? ???0? 10100 ???00 ?1?11 10100 0?01{12} 00000 {1234}? Coloraderpeton ????? ???21 0???? 111?1 ????? ?010{02} ????? 00110 ?? Pseudophlegethontia ????? ???21 00001 ?110? ????? ?010{02} 0?0?2 01010 ?1 Perittodus ????? ????? ????? ????? ????? ????? ????? ????? {1234}? Diploradus ????? ????? ????? ????? ????? ????? ????? ????? ?? Aytonerpeton 01??? ????? 0???? ????? ????? ????? ????? ????? {1234}? 14861

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