1 ELECTRONIC SUPPLEMENTARY MATERIAL

2

3 The radiation of cynodonts and the ground plan of

4 mammalian morphological diversity

5 Marcello Ruta1,*, Jennifer Botha-Brink2, Stephen A. Mitchell3 and Michael J. Benton3

6 1 School of Life Sciences, University of Lincoln, Lincoln LN6 7TS, UK

7 2 Karoo Palaeontology, National Museum, P. O. Box 266, Bloemfontein 9300, South Africa,

8 and Department of Zoology and Entomology, University of the Free State, Bloemfontein

9 9300, South Africa

10 3 School of Earth Sciences, University of Bristol, Bristol BS8 1RJ, UK

11

* Author for correspondence ([email protected]).

1

11 SUPPLEMENTARY MATERIAL AND METHODS

12 (a) Taxon-character dataset

13 Two cladistic matrices [1,2] provided the foundations for a new, revised, and expanded taxon-

14 character data set that includes all major cynodont clades from Late Permian to Early Jurassic.

15 After checking these matrices for instances of character duplications and conflicting codings,

16 we merged them and consulted additional works [2–15] for further character inclusion and/or

17 coding refinements (Datasets S2, S3, S9, S10). If different authors gave conflicting codings of

18 a character, then the most recent codings were scrutinized and either endorsed or changed as

19 appropriate in light of available data from specimens and/or illustrations. J. B. B. checked the

20 majority of characters against original specimens, where possible. After all relevant data had

21 been scrutinised, taxon descriptions were surveyed to glean additional data: Van Heerden [16]

22 for Nanictosaurus; Crompton [17] for Aleodon; Crompton [18], Savage and Waldman [19],

23 Sues [20] and Luo and Sun [21] for Oligokyphus; Brink [22] for Cynosaurus; Crompton [23]

24 for both Scalenodon angustifrons and ‘Scalenodon’ hirschoni; Abdala and Ribeiro [24] for

25 Santacruzodon; Bonaparte and Barberena [25] for Therioherpeton; Bonaparte [26] and

26 Martinelli and Rougier [9] for Chaliminia; Barberena [27] for Traversodon; Hopson [28] for

27 Gomphodontosuchus; Flynn et al. [29] and Kammerer et al. [10] for Menadon; Bonaparte et

28 al. [3] and Soares et al. [30] for Riograndia; Abdala and Teixeira [31] and Abdala and Smith

29 [32] for Luangwa and Aleodon); Sidor and Hancox [7] for Elliotherium; Liu and Powell [33]

30 for Andescynodon; Reichel et al. [11] for Protuberum; Gow [34] for Diarthrognathus; Sues

31 and Jenkins [35] for Kayentatherium; Gao et al. [12] for Beishanodon; Oliveira et al. [14] for

32 Trucidocynodon.

33 Some taxa require comments. Relative to the data matrices in [1,2], Charassognathus

34 adds to Late Permian and basal cynodonts. Nanictosaurus augments Late Permian taxa and

35 also adds to the sample of epicynodonts in general. Beishanodon, Sinognathus, Cricodon and

2

36 Langbergia add to the diversity of Trirachodontidae. Traversodon, Andescynodon, Dadadon,

37 Santacruzodon, Scalenodontoides, Scalenodon attridgei, Arctotraversodon, Boreogomphodon

38 and Nanogomphodon add to Traversodontidae. These were diverse and successful tetrapods

39 in the Triassic, but were poorly represented in the cladistic matrices in [1,2]. Traversodon is a

40 Ladinian-Carnian traversodontid. Andescynodon is possibly transitional between Olenekian–

41 Anisian and Ladinian–Carnian traversodontids. Scalenodontoides is Rhaetian, and represents

42 the only known record of a South African traversodontid. Menadon and Protuberum are both

43 known from fairly complete specimens; Protuberum displays an unusual morphology relative

44 to other traversodontids. Trucidocynodon was included in our matrix as it is a close relative of

45 Ecteninion. Despite the incompleteness of Therioherpeton, this genus has diagnostic cranial,

46 dental and postcranial (a humerus) features, and belongs to a group not represented in either

47 of the data matrices in [1,2]. Tritylodon and Bienotherium add to the Tritylodontidae. Finally,

48 Riograndia, Chaliminia, Diarthrognathus and Elliotherium are fairly complete members of

49 Tritheledontidae, and cover the geographical range of this clade: Riograndia and Chaliminia

50 are from South America, whilst Diarthrognathus and Elliotherium are from South Africa.

51

52 (b) Stratigraphic assignments

53 The time scale of the Triassic is poorly resolved with very few radiometric dates to calibrate

54 against [3,36–38]. We endeavoured to bin the species as precisely as possible within a time

55 bin (whether that was the lower, middle or upper part of a stage or the stage in total) and date

56 the age of the taxa as being the midpoint of that time bin. The duration and age boundaries of

57 stages were based on the timescale from [40], though modified in agreement with recent work

58 [37] suggesting a longer Norian and shorter Carnian durations [38] than formerly thought. All

59 stratigraphic data can be found in Datasets S1, S11.

60

3

61 (c) Phylogenetic analyses

62 We used identical settings for all maximum parsimony analyses with PAUP* [39] and TNT

63 [40], as follows: heuristic searches with 5000 random stepwise addition sequences, holding a

64 single tree in memory during each step, using a tree bisection-reconnection branch swapping

65 algorithm, and collapsing all tree branches that have minimum length of zero. After this initial

66 run, we applied a new search to all the trees in memory, but with the option of saving multiple

67 trees. These settings were employed in three analyses: 1) analysis with unordered and equally

68 weighted characters; 2) analysis with all characters reweighted using the maximum values of

69 their respective rescaled consistency indices (from the first analysis); 3) analysis with implied

70 weights [41]. We ran implied weights analyses several times, each time increasing the integer

71 value for Goloboff’s K constant of concavity [41], until tree shape became stable (for K = 3).

72 Branch support for the implied weights tree was assessed via 1000 bootstrapping replicates in

73 TNT, with a 50% threshold value for bootstrap support.

74

75 (d) Time-calibrated cynodont phylogeny

76 The branch durations for the tree (i.e. branch lengths in millions of years; Myr) were obtained

77 with methods developed in [42,43]. Below, we supply the tree in a format (i.e. object of class

78 ‘phylo’) that is readable by the ‘R’ ape package [44]. The time-calibrated tree is reproduced in

79 figure S3a.

80

81 #NEXUS 82 83 BEGIN TAXA; 84 DIMENSIONS NTAX = 54; 85 TAXLABELS 86 Charassognathus 87 Dvinia 88 Procynosuchus 89 Cynosaurus 90 Progalesaurus

4

91 Galesaurus 92 Nanictosaurus 93 Thrinaxodon 94 Platycraniellus 95 Lumkuia 96 Ecteninion 97 Aleodon 98 Chiniquodon 99 Probainognathus 100 Trucidocynodon 101 Therioherpeton 102 Riograndia 103 Diarthrognathus 104 Pachygenelus 105 Elliotherium 106 Chaliminia 107 Brasilitherium 108 Brasilodon 109 Morganucodon 110 Sinoconodon 111 Oligokyphus 112 Kayentatherium 113 Bienotherium 114 Tritylodon 115 Cynognathus 116 Diademodon 117 Beishanodon 118 Sinognathus 119 Trirachodon 120 Cricodon 121 Langbergia 122 Andescynodon 123 Pascualgnathus 124 Scalenodonangustifrons 125 Luangwa 126 Traversodon 127 Scalenodonattridgei 128 Scalenodonhirschoni 129 Nanogomphodon 130 Arctotraversodon 131 Boreogomphodon 132 Massetognathus 133 Dadadon 134 Santacruzodon 135 Menadon 136 Gomphodontosuchus 137 Protuberum 138 Scalenodontoides 139 Exaeretodon 140 ;

5

141 END; 142 BEGIN TREES; 143 TRANSLATE 144 1 Charassognathus, 145 2 Dvinia, 146 3 Procynosuchus, 147 4 Cynosaurus, 148 5 Progalesaurus, 149 6 Galesaurus, 150 7 Nanictosaurus, 151 8 Thrinaxodon, 152 9 Platycraniellus, 153 10 Lumkuia, 154 11 Ecteninion, 155 12 Aleodon, 156 13 Chiniquodon, 157 14 Probainognathus, 158 15 Trucidocynodon, 159 16 Therioherpeton, 160 17 Riograndia, 161 18 Diarthrognathus, 162 19 Pachygenelus, 163 20 Elliotherium, 164 21 Chaliminia, 165 22 Brasilitherium, 166 23 Brasilodon, 167 24 Morganucodon, 168 25 Sinoconodon, 169 26 Oligokyphus, 170 27 Kayentatherium, 171 28 Bienotherium, 172 29 Tritylodon, 173 30 Cynognathus, 174 31 Diademodon, 175 32 Beishanodon, 176 33 Sinognathus, 177 34 Trirachodon, 178 35 Cricodon, 179 36 Langbergia, 180 37 Andescynodon, 181 38 Pascualgnathus, 182 39 Scalenodonangustifrons, 183 40 Luangwa, 184 41 Traversodon, 185 42 Scalenodonattridgei, 186 43 Scalenodonhirschoni, 187 44 Nanogomphodon, 188 45 Arctotraversodon, 189 46 Boreogomphodon, 190 47 Massetognathus,

6

191 48 Dadadon, 192 49 Santacruzodon, 193 50 Menadon, 194 51 Gomphodontosuchus, 195 52 Protuberum, 196 53 Scalenodontoides, 197 54 Exaeretodon 198 ; 199 TREE * UNTITLED = [&R] 200 (1:1.0,((2:3.333333333,3:0.3333333333):0.3333333333,(4:1.833333333,((5:1.6,6:1):2.375,(( 201 7:0.4583333333,8:2.458333333):0.4583333333,(9:2.458333333,((10:2.8,(11:18.6,((12:0.2,13 202 :4.2):0.2,(14:4.2,(15:15.46666667,(16:4.733333333,((17:5.911111111,((18:20.5,19:5):10.940 203 74074,(20:9.97037037,21:2.97037037):2.97037037):2.97037037):5.911111111,((22:3.94074 204 0741,23:3.940740741):3.940740741,((24:4.960493827,25:15.96049383):4.960493827,(26:4. 205 960493827,(27:15.80699588,(28:3.653497942,29:3.653497942):3.653497942):3.653497942) 206 :4.960493827):4.960493827):3.940740741):5.911111111):4.733333333):4.733333333):4.2): 207 0.2):0.2):3.838888889,(30:1.819444444,(31:2.455555556,(((32:0.3638888889,33:1.36388888 208 9):0.3638888889,(34:0.3638888889,(35:5.181944444,36:0.1819444444):0.1819444444):0.36 209 38888889):0.3638888889,((37:2.5,38:2.5):3.31875,(39:5.545833333,(40:0.2729166667,(41:7 210 .9546875,((42:1.318229167,(43:0.6591145833,(44:2.329557292,(45:4.414778646,46:4.4147 211 78646):4.414778646):2.329557292):0.6591145833):1.318229167,((47:2.212152778,(48:4.35 212 6076389,49:4.356076389):4.356076389):2.212152778,(50:9.818229167,(51:18.21215278,(5 213 2:1.106076389,(53:25.55303819,54:5.553038194):5.553038194):1.106076389):1.106076389 214 ):1.106076389):2.212152778):1.318229167):1.318229167):0.2729166667):0.2729166667):0. 215 2729166667):0.3638888889):0.3638888889):1.819444444):1.819444444):2.458333333):0.45 216 83333333):0.4583333333):1.833333333):0.3333333333):1.0; 217 END; 218

219 (e) Cynodont phylogeny with branches expressed as number of changes under ACCTRAN

220 and DELTRAN and with correction for missing entries

221 Character-state changes (uncorrected for missing entries) under the accelerated transformation

222 (ACCTRAN) are provided below for the tree branches. To create an object of class phylo, the

223 final block in the previous file (parenthetical notations) should be replaced with the following:

224

225 TREE * UNTITLED = [&R] 226 (1:1.0,((2:12.0,3:3.0):9.0,(4:1.0,((5:3.0,6:2.0):3.0,((7:2.0,8:1.0):3.0,(9:6.0,((10:5.0,(11:10.0,(( 227 12:4.0,13:2.0):8.0,(14:5.0,(15:13.0,(16:1.0,((17:3.0,((18:1.0,19:3.0):5.0,(20:2.0,21:0.0):4.0):5. 228 0):9.0,((22:5.0,23:3.0):2.0,((24:8.0,25:4.0):7.0,(26:4.0,(27:3.0,(28:0.0,29:1.0):1.0):4.0):39.0): 229 7.0):14.0):8.0):21.0):10.0):7.0):3.0):3.0):9.0,(30:5.0,(31:2.0,(((32:3.0,33:2.0):11.0,(34:4.0,(35: 230 3.0,36:2.0):4.0):1.0):2.0,((37:3.0,38:3.0):7.0,(39:2.0,(40:1.0,(41:5.0,((42:1.0,(43:1.0,(44:0.0,( 231 45:1.0,46:1.0):0.0):5.0):1.0):5.0,((47:2.0,(48:2.0,49:3.0):5.0):7.0,(50:6.0,(51:1.0,(52:5.0,(53:5. 232 0,54:2.0):3.0):8.0):0.0):11.0):4.0):2.0):7.0):4.0):6.0):10.0):9.0):9.0):12.0):8.0):13.0):8.0):4.0): 233 10.0):2.0):0.0;

7

234 END; 235

236 In order to obtain a phylo object with branch changes corrected through patristic dissimilarity

237 [45] (i.e. taking into account missing data), the following ACCTRAN block should be used:

238

239 TREE * UNTITLED = [&R] 240 (1:0.02380952381,((2:0.09448818898,3:0.02040816327):0.06,(4:0.009009009009,((5:0.0272 241 7272727,6:0.01379310345):0.02,((7:0.0243902439,8:0.006896551724):0.02,(9:0.057142857 242 14,((10:0.03937007874,(11:0.08196721311,((12:0.05128205128,13:0.01428571429):0.05333 243 333333,(14:0.03676470588,(15:0.1074380165,(16:0.01818181818,((17:0.0306122449,((18:0. 244 01754385965,19:0.02189781022):0.03333333333,(20:0.0487804878,21:0):0.02666666667):0 245 .03333333333):0.06,((22:0.06097560976,23:0.0303030303):0.01333333333,((24:0.05797101 246 449,25:0.0380952381):0.04666666667,(26:0.03773584906,(27:0.025,(28:0,29:0.0090090090 247 09):0.006666666667):0.02666666667):0.26):0.04666666667):0.09333333333):0.0533333333 248 3):0.14):0.06666666667):0.04666666667):0.02):0.02):0.06,(30:0.03448275862,(31:0.013698 249 63014,(((32:0.05263157895,33:0.02702702703):0.07333333333,(34:0.02797202797,(35:0.06 250 ,36:0.02127659574):0.02666666667):0.006666666667):0.01333333333,((37:0.05882352941, 251 38:0.025):0.04666666667,(39:0.01886792453,(40:0.007692307692,(41:0.1,((42:0.058823529 252 41,(43:0.01149425287,(44:0,(45:0.07692307692,46:0.04761904762):0):0.03333333333):0.00 253 6666666667):0.03333333333,((47:0.01360544218,(48:0.05882352941,49:0.09375):0.033333 254 33333):0.04666666667,(50:0.12,(51:0.01315789474,(52:0.1086956522,(53:0.05813953488,5 255 4:0.01379310345):0.02):0.05333333333):0):0.07333333333):0.02666666667):0.0133333333 256 3):0.04666666667):0.02666666667):0.04):0.06666666667):0.06):0.06):0.08):0.05333333333) 257 :0.08666666667):0.05333333333):0.02666666667):0.06666666667):0.01333333333):0.0; 258 END; 259

260 The tree block with the branches expressed as uncorrected number of character-state changes

261 under a delayed transformation (DELTRAN) is as follows:

262

263 TREE * UNTITLED = [&R] 264 (1:1.0,((2:13.0,3:6.0):5.0,(4:1.0,((5:3.0,6:2.0):4.0,((7:2.0,8:4.0):3.0,(9:7.0,((10:7.0,(11:9.0,((1 265 2:4.0,13:7.0):4.0,(14:9.0,(15:11.0,(16:3.0,((17:5.0,((18:3.0,19:7.0):4.0,(20:2.0,21:3.0):1.0):4.0 266 ):6.0,((22:8.0,23:2.0):6.0,((24:11.0,25:1.0):9.0,(26:6.0,(27:4.0,(28:0.0,29:6.0):1.0):9.0):30.0): 267 6.0):7.0):19.0):8.0):6.0):4.0):4.0):4.0):5.0,(30:5.0,(31:2.0,(((32:3.0,33:8.0):5.0,(34:4.0,(35:3.0, 268 36:3.0):3.0):3.0):4.0,((37:4.0,38:5.0):5.0,(39:1.0,(40:4.0,(41:5.0,((42:1.0,(43:2.0,(44:0.0,(45:1 269 .0,46:3.0):2.0):2.0):2.0):1.0,((47:6.0,(48:5.0,49:3.0):3.0):4.0,(50:5.0,(51:2.0,(52:5.0,(53:6.0,54 270 :7.0):4.0):4.0):2.0):6.0):6.0):4.0):4.0):3.0):4.0):9.0):7.0):7.0):14.0):13.0):1.0):6.0):8.0):6.0):1. 271 0):0.0; 272 END; 273

8

274 When patristic dissimilarity is introduced, the modified branch lengths yield the following

275 DELTRAN tree block:

276

277 TREE * UNTITLED = [&R] 278 (1:0.02380952381,((2:0.1023622047,3:0.04081632653):0.03333333333,(4:0.009009009009,( 279 (5:0.02727272727,6:0.01379310345):0.02666666667,((7:0.0243902439,8:0.0275862069):0.0 280 2,(9:0.06666666667,((10:0.05511811024,(11:0.0737704918,((12:0.05128205128,13:0.05):0.0 281 2666666667,(14:0.06617647059,(15:0.09090909091,(16:0.05454545455,((17:0.0510204081 282 6,((18:0.05263157895,19:0.05109489051):0.02666666667,(20:0.0487804878,21:0.06122448 283 98):0.006666666667):0.02666666667):0.04,((22:0.09756097561,23:0.0202020202):0.04,((24 284 :0.07971014493,25:0.009523809524):0.06,(26:0.05660377358,(27:0.03333333333,(28:0,29: 285 0.05405405405):0.006666666667):0.06):0.2):0.04):0.04666666667):0.1266666667):0.05333 286 333333):0.04):0.02666666667):0.02666666667):0.02666666667):0.03333333333,(30:0.0344 287 8275862,(31:0.01369863014,(((32:0.05263157895,33:0.1081081081):0.03333333333,(34:0.0 288 2797202797,(35:0.06,36:0.03191489362):0.02):0.02):0.02666666667,((37:0.07843137255,38 289 :0.04166666667):0.03333333333,(39:0.009433962264,(40:0.03076923077,(41:0.1,((42:0.058 290 82352941,(43:0.02298850575,(44:0,(45:0.07692307692,46:0.1428571429):0.01333333333): 291 0.01333333333):0.01333333333):0.006666666667,((47:0.04081632653,(48:0.1470588235,4 292 9:0.09375):0.02):0.02666666667,(50:0.1,(51:0.02631578947,(52:0.1086956522,(53:0.069767 293 44186,54:0.04827586207):0.02666666667):0.02666666667):0.01333333333):0.04):0.04):0.0 294 2666666667):0.02666666667):0.02):0.02666666667):0.06):0.04666666667):0.04666666667) 295 :0.09333333333):0.08666666667):0.006666666667):0.04):0.05333333333):0.04):0.00666666 296 6667):0.0; 297 END; 298

299 (f) Cynodont phylogeny with branches expressed as rates

300 With information on branch durations and on character-state changes under ACCTRAN and

301 DELTRAN optimizations (both corrected through the patristic dissimilarity), we obtain the

302 following tree blocks in which the tree branches are expressed as rates (figure S3b, c):

303

304 For ACCTRAN:

305

306 TREE * UNTITLED = [&R] 307 (1:0.02380952381,((2:0.0283464566968346,3:0.0612244898161224):0.180000000018,(4:0.0 308 049140049148935,((5:0.01704545454375,6:0.01379310345):0.0084210526315789,((7:0.053 309 2150776038702,8:0.002805376972855):0.0436363636395372,(9:0.023244552060101,((10:0. 310 0140607424071429,(11:0.0044068394145161,((12:0.2564102564,13:0.0034013605452381): 311 0.26666666665,(14:0.0087535014,(15:0.0069464234791064,(16:0.0038412291932283,((17: 312 0.0051787632350598,((18:0.0008557980317073,19:0.004379562044):0.0030467163167601,

9

313 (20:0.0048925452104343,21:0.0):0.0089775561119673):0.0112219451374342):0.010150375 314 9400404,((22:0.0154731340546211,23:0.0076896787410355):0.0033834586455481,((24:0.0 315 116865410001043,25:0.0023868458273136):0.0094076655062028,(26:0.0076072766897932 316 ,(27:0.0015815781942242,(28:0.0,29:0.0024658585147767):0.0018247353010278):0.007298 317 9412046588):0.0524141363879577):0.0094076655062028):0.0236842105239118):0.009022 318 5563905831):0.0295774647908153):0.0140845070439496):0.0111111111119048):0.1):0.1): 319 0.0156295224308067,(30:0.0189523558873777,(31:0.0055786276578138,(((32:0.144636400 320 1635226,33:0.0198161501629478):0.2015267175419381,(34:0.0768696951823857,(35:0.01 321 15786652381949,36:0.1169400682178785):0.1465648855503059):0.0183206106873795):0. 322 0366412213637667,((37:0.023529411764,38:0.01):0.0140615191472693,(39:0.00340218023 323 10084,(40:0.0281855548985422,(41:0.0125712040856413,((42:0.04462314359488,(43:0.01 324 74389296811664,(44:0.0,(45:0.0174239940635973,46:0.0107862820400169):0.0):0.0143088 325 703782779):0.0101145792187178):0.0252864480353286,((47:0.0061503176070419,(48:0.0 326 135037873896201,49:0.0215216611528527):0.0076521461869157):0.0210955893888085,(5 327 0:0.0122221632800476,(51:0.0007224788249333,(52:0.0982713791569779,(53:0.00227524 328 94027404,54:0.0024838841311957):0.0036016319897835):0.0482184900251044):0.0):0.066 329 3004237856487):0.0120546225085363):0.0101145792126143):0.0354010272555288):0.097 330 7099236644018):0.1465648854782822):0.244274809142684):0.1648854961781714):0.1648 331 854961781714):0.0439694656595956):0.029312977104565):0.0352542372942718):0.11636 332 36363648264):0.0581818181933223):0.0363636363720661):0.039999999994):0.0; 333 END; 334

335 For DELTRAN:

336

337 TREE * UNTITLED = [&R] 338 (1:0.02380952381,((2:0.0307086614130709,3:0.1224489796022449):0.1,(4:0.004914004914 339 8935,((5:0.01704545454375,6:0.01379310345):0.0112280701768421,((7:0.05321507760387 340 02,8:0.011221507893047):0.0436363636395372,(9:0.0271186440728296,((10:0.0196850393 341 714286,(11:0.0039661554731183,((12:0.2564102564,13:0.0119047619047619):0.133333333 342 35,(14:0.0157563025214286,(15:0.0058777429455005,(16:0.0115236875817974,((17:0.008 343 6312720573051,((18:0.002567394095122,19:0.010218978102):0.0024373730539565,(20:0.0 344 048925452104343,21:0.0206117359701511):0.0022443890278235):0.0089775561119673):0 345 .0067669172933603,((22:0.0247570144858712,23:0.0051264524940236):0.0101503759391 346 818,((24:0.0160689938764034,25:0.0005967114567657):0.0120955699356825,(26:0.011410 347 9150326738,(27:0.0021087709254214,(28:0,29:0.0147951510875656):0.0018247353010278 348 ):0.0164226177084295):0.0403185664522751):0.008063713290455):0.0118421052632247): 349 0.0214285714346133):0.0112676056338921):0.0084507042259472):0.00634920635):0.1333 350 3333335):0.13333333335):0.0086830680162465,(30:0.0189523558873777,(31:0.005578627 351 6578138,(((32:0.1446364001635226,33:0.0792646006371271):0.0916030534231572,(34:0.0 352 768696951823857,(35:0.0115786652381949,36:0.1754101023817796):0.109923664148989) 353 :0.0549618320593905):0.0732824427550143,((37:0.03137254902,38:0.016666666668):0.01 354 00439422463277,(39:0.0017010901153239,(40:0.1127422196014971,(41:0.0125712040856 355 413,((42:0.04462314359488,(43:0.0348778593775047,(44:0,(45:0.0174239940635973,46:0. 356 0323588461291112):0.0030201589703893):0.0057235481504526):0.0202291584313668):0. 357 0050572896078243,((47:0.0184509528166051,(48:0.0337594684683111,49:0.02152166115 358 28527):0.0045912877126086):0.0120546225085363,(50:0.0101851360667064,(51:0.001444 359 9576493175,(52:0.0982713791569779,(53:0.002730299283445,54:0.0086935944582844):0.

10

360 0048021759869783):0.0241092450170727):0.0120546225040159):0.0361638675210885):0. 361 0180819337605443):0.0202291584328144):0.0202291584328144):0.0732824427391411):0. 362 0977099236644018):0.2198473282174232):0.1282442748144048):0.1282442748144048):0. 363 0512977099343628):0.0476335877997273):0.002711864407283):0.0872727272790744):0.1 364 163636363648264):0.0218181818221488):0.020000000003):0.0; 365 END;

366

367 (g) Correlations between diversity and disparity

368 For each of the 11 time intervals discussed in the main text, we selected the mid point of the

369 interval duration (Dataset S1). For diversity, we used both taxa that appear in the phylogeny

370 and the total number of known taxa from Permian to Lower Jurassic. For disparity, we used

371 un-rarefied mean values of each of the four indices. We performed correlations (Spearman’s

372 correlation coefficient) with and without generalized differencing of the time series [46]. The

373 generalised differencing method removes trends in time series, eliminates autocorrelation by

374 calculating differences between the values in any two adjacent intervals, but accounting for

375 the strength of autocorrelation in adjacent intervals [47]. We show plots of un-rarefied mean

376 disparity values and total cynodont diversity from Permian to Early Jurassic in figure S4.

377

378 (h) An explanatory note on Ripley’s K function

379 Let us consider n data points in a sample. Let A be the area (e.g. optimal observation window)

380 where the n points are. Let λ be the average density of the points, that is, λ = n/A. Let dij be

381 the Euclidean distance between the ith and jth points. Let s be the radius of a circle such that,

382 for a completely random distribution of the n points, K(s) = πs2. The left term of the equation

383 is the Ripley’s K function for spatial randomness, increasing in proportion to the square of s,

384 where s can take increasing values depending on the distance scale (small to large distances

385 between taxa). For the n data points, the pattern of distribution is expressed by the following

386 formula:

387 K(s) = 1/λn ∑i ∑j I (dij ≤ s), with 1 ≤ i ≤ n and for j ≠ i

11

388 The function I (dij ≤ s) is 1 if the argument (dij ≤ s) holds true, and 0 otherwise. Technicalities

389 aside, the distances along which the K function is calculated are dimension-less. In figure 2d,

390 the distance values on the horizontal axis of the K plot are the dij values. The above summary

391 of the K function relates to a two-dimensional pattern, but the function can also be calculated

392 for several dimensions.

393

394 (i) An explanatory note on Mantel test and phylogenetic signal

395 As explained in the main text, we employed the Mantel tests to correlate pair-wise generalised

396 Euclidean distances with phylogenetic distances. We recall that the former are the inter-taxon

397 distances generated from the cladistic data matrix, whereas the phylogenetic distances are the

398 inter-taxon distances calculated in millions of years using branch durations (the phylogenetic

399 distances were further transformed by taking their square-root values [48]). We further recall

400 that the Mantel test was introduced solely as a test of the association between the two distance

401 matrices, and not as a test of phylogenetic signal. A seminal paper on the performance of this

402 test [49] has questioned its power when used in analyses of phylogenetic signal. In that same

403 paper, explicit recommendations are offered for the use of the Mantel test exclusively in those

404 cases in which species data can only be expressed as pair-wise distances. This is certainly the

405 case for the morphological distances built from the data matrix. Also, we should bear in mind

406 that signal refers solely to the statistical dependence among traits in taxa that results from the

407 phylogenetic proximity of those taxa [49,50].

408 Here, we adapted two widely employed methods for testing phylogenetic signal in our

409 data, but we urge caution in their application and interpretation. The first method relies on the

410 K-statistic of Blomberg et al. [51]. The K-statistic is the variance of independent contrasts for

411 a trait divided by the expected variance under a Brownian model of trait evolution [51,52]. A

412 comparison is then made between the K value for the trait and a null distribution of K values

12

413 built from re-shuffling the trait at random across the tips of a tree. The K-statistic and p value

414 were obtained for each of the 20 PCo axes used in disparity analyses. Each axis represents a

415 ‘trait’, and the PCo scores are the trait values across our 54-taxon sample. Calculations were

416 performed in the ‘R’ phytools package [53]. The second method, devised by Klingenberg and

417 Gidaszewski [54], is implemented in the morphometric package MorphoJ [55]. In the original

418 formulation, a test of phylogenetic signal is devised through permutation of shape data across

419 the tips of the tree (the statistic is the sum over all tree branches of the total amount of squared

420 change), e.g. [56]. Here, we apply the test to the PCo scores. MorphoJ requires the phylogeny

421 with branch lengths and the set of PCo scores imported as a tabulation of co-variates, after the

422 specification of a taxon grouping (a classifier) identical to the 54-taxon set.

423 The reason for urging caution in the application of these methods is that in our case, the

424 tree topology and the PCo scores hinge upon the same data matrix. However, although some

425 elements of circularity might be involved, we note that both approaches are not conceptually

426 different from analyses of characters relative to a tree built from those very characters.

427

428 SUPPLEMENTARY RESULTS

429 (a) Cynodont phylogeny

430 A maximum parsimony search with all characters unordered and of equal unit weight yielded

431 486 trees, 526 steps long, with ensemble consistency index (C.I.) of 0.3525 (excluding all the

432 uninformative characters), ensemble retention index (R.I.) of 0.7188, and ensemble rescaled

433 consistency index (R.C.) of 0.2569. The base of the cynodont radiation is fully resolved in the

434 strict consensus (figure S1a), except for a trichotomy formed by Platycraniellus, a clade with

435 Nanictosaurus and Thrinaxodon as sister taxa, and the eucynodonts. Loss of resolution affects

436 the base of the probainognathians and, more apically, the tritheledonts. Mammals are placed

437 in a clade with Brasilitherium and Brasilodon (as successive outgroups). This wider clade, in

13

438 turn, forms the sister-group to a clade of tritheledonts plus tritylodonts. In the cynognathians,

439 loss of resolution affects for the most part trirachodontids. The agreement subtree includes 45

440 of the 54 taxa, with the following taxa deleted: Platycraniellus, Ecteninion, Trucidocynodon,

441 Riograndia, Pachygenelus, Diarthrognathus, Andescynodon, Nanogomphodon and Menadon

442 (figure S1b). Character reweighting by the maximum value of the rescaled consistency index

443 results in nine trees, the strict consensus of which is reported in figure S1c. The nine trees are

444 141.99613 steps long (C.I. = 0.5469; R.I. = 0.8328; R.C. = 0.4661. Two trichotomies within

445 cynognathians affect Arctotraversodon, Boreogomphodon and Nanogomphodon, as well as

446 Gomphodontosuchus, Menadon and a clade of immediately more apical taxa. The single tree

447 from the implied weights (figures 1, S3a) is 532-step long, with a C.I. of 0.3485 (excluding

448 uninformative characters), a R.I. of 0.7138 and a R.C. of 0.2522. The most salient difference

449 in taxon arrangement relative to the trees from previous analyses is the position of mammals

450 as sister-group to tritylodonts. Bootstrap support above the 50% threshold value occurs in

451 very few clades, as follows: tritylodonts (95%), mammals (81%), a clade including

452 Nanictosaurus and Thrinaxodon (63%), a clade including Dvinia and Procynosuchus (60%)

453 and eucynodonts (53%).

454

455 (b) Phylogenetic signal

456 The K-statistic values for the first 20 PCo axes, and associated signifcance, are as follows: 457 458 PCo1: K = 1.036851, p = 0.001; 459 PCo2: K = 2.128994, p = 0.001; 460 PCo3: K = 0.5637574, p = 0.009; 461 PCo4: K = 0.430949, p = 0.016; 462 PCo5: K = 0.3757458, p = 0.022; 463 PCo6: K = 0.269345, p = 0.077; 464 PCo7: K = 0.837169, p = 0.001; 465 PCo8: K = 0.2731058, p = 0.095; 466 PCo9: K = 0.2061463, p = 0.19; 467 PCo10: K = 0.175391, p = 0.35; 468 PCo11: K = 0.1311685, p = 0.665; 469 PCo12: K = 0.4668876, p = 0.013;

14

470 PCo13: K = 0.2739074, p = 0.097; 471 PCo14: K = 0.1336754, p = 0.644; 472 PCo15: K = 0.1151144, p = 0.78; 473 PCo16: K = 0.139438, p = 0.573; 474 PCo17: K = 0.1506301, p = 0.496; 475 PCo18: K = 0.1105352, p = 0.823; 476 PCo19: K = 0.08680619, p = 0.941; 477 PCo20: K = 0.08075433, p = 0.958. 478

479 Thus, signal is detected in axes PCo1–5 and PCo7. For the first three axes, the K values show

480 that the PCo scores are more similar than we would expect under the Brownian model of trait

481 evolution (particularly on PCo2), and less similar on PCo3. However, it is difficult to provide

482 a satisfactory interpretation for this result. The higher-than-expected similarity in PCo2 scores

483 might be related to the separation of derived cynognathians and probainognathians from most

484 basal members of each of these clades and from epicynodonts. A similar reasoning might be

485 applied to PCo1, where tritylodonts and tritheledonts are distinctly set aside from other taxa.

486 With the application of the test proposed by Klingenberg and Gidaszewski, permutation

487 tests for the distribution of PCo scores allow us to reject a null hypothesis of no phylogenetic

488 signal for axes PCo1–13 (p << 0.05).

489

15

489

490 SUPPLEMENTARY DATASETS

491 Dataset S1. Temporal data on cynodonts and mammaliamorphs from Permian through to

492 Early Jurassic, with information on first and last appearance data (FAD, LAD) in Myr and

493 taxonomic assignments.

494 Dataset S2. Data matrix. Symbols are as follows: & = polymorphic condition; - =

495 inapplicable state; ? = unknown state.

496 Dataset S3. List of characters used in phylogenetic, disparity and rate analyses. For each

497 character, we provide ‘keys’ indicating the original literature sources were the character was

498 used and its position in the relevant data sets. For example, character 1 in our list is identified

499 by two keys, A21 and R22, to signify that it corresponds to character 21 in Abdala et al. 2006

500 and to character 22 in Reichel et al. 2009. Abbreviations: A, Abdala et al. 2006; AB, Abdala

501 2007; B, Bonaparte et al. 2001; BO, Botha et al. 2007; G, Gao et al. 2010; HK, Hopson &

502 Kitching 2001; K, Kammerer et al. 2008; KA, Kammerer et al. 2012; L, Liu & Olsen 2010;

503 M, Martinelli et al. 2005; MR, Martinelli & Rougier 2007; O, Oliveira 2006; OS, Oliveira et

504 al. 2010; R, Reichel et al. 2009; SH, Sidor & Hancox 2006.

505 Dataset S4. Pair-wise inter-taxon distances.

506 Dataset S5. PCo scores (coordinates) of taxa on the 54 PCo axes.

507 Dataset S6. Complete rarefaction profiles of four disparity indices for the three major

508 cynodont groups.

509 Dataset S7. Complete rarefaction profiles of four disparity indices for the 11 time intervals.

510 Dataset S8. Distribution of ACCTRAN and DELTRAN rates by groups and through time.

511 Dataset S9. Distribution of missing data (both unknown and inapplicable states) in the data

512 matrix.

513 Dataset S10. Nature and preservation of excluded taxa.

16

514 Dataset S11. Geographic, stratigraphic and geological data.

515 Dataset S12. Correlations between diversity and mean un-rarefied disparity, with and without

516 generalised differencing of time series, using both all recorded taxa and taxa that appear only

517 in the phylogeny.

518

519 SUPPLEMENTARY REFERENCES

520 1 Hopson, J. A. & Kitching, J. W. 2001 A probainognathian cynodont from South Africa

521 and the phylogeny of non-mammalian cynodonts. Bull. Mus. Comp. Zool. 156, 5–35.

522 2 Abdala, F. 2007 Redescription of Platycraniellus elegans (Therapsida, Cynodontia)

523 from the Lower Triassic of South Africa, and the cladistic relationships of

524 eutheriodonts. Palaeontology 50, 591–618.

525 3 Bonaparte, J. F., Ferigolo, J. F. & Ribeiro, A. M. 2001 A primitive Late Triassic

526 “ictidosaur” from Rio Grande do Sul, Brazil. Palaeontology 49, 931–936.

527 4 Martinelli, A. G., Bonaparte, J. F., Schultz, C. L. & Rubert, R. 2005 A new

528 trithelodontid (Therapsida, Eucynodontia) from the Late Triassic of Rio Grande do Sul

529 (Brazil) and its phylogentic relationships among carnivorous non-mammalian

530 eucynodonts. Ameghiniana 42, 191–208.

531 5 Abdala, F., Neveling, J. & Welman, J. 2006 A new trirachodontid cynodont from the

532 lower levels of the Burgersdorp Formation (Lower Triassic) of the Beaufort Group,

533 South Africa and the cladistic relationships of Gondwanan gomphodonts. Zool. J. Linn.

534 Soc. 147, 383–413.

535 6 Oliveira, E. V. 2006 Reevaluation of Therioherpeton cargnini Bonaparte & Barberena,

536 1975 (Probainognathia, Therioherpetidae) from the Upper Triassic of Brazil.

537 Geodiversitas 28, 447–465.

538 7 Sidor, C. A. & Hancox, P. J. 2006 Elliotherium kersteni, a new tritheledontid from the

17

539 Lower Elliot Formation (Upper Triassic) of South Africa. J. Paleontol. 80, 333–342.

540 8 Botha, J., Abdala, F. & Smith, R. M. H. 2007 The oldest cynodont: new clues on the

541 origin and early diversification of the Cynodontia. Zool. J. Linn. Soc. 149, 477–492.

542 9 Martinelli, A. G. & Rougier, G. W. 2007 On Chaliminia musteloides (Eucynodontia:

543 Tritheledontidae) from the Late Triassic of Argentina, and a phylogeny of Ictidosauria.

544 J. Vert. Paleontol. 27, 442–460.

545 10 Kammerer, C. F., Flynn, J. J., Fanivoharimanana, L. & Wyss, R. R. 2008 New material

546 of Menadon besairiei (Cynodontia: Traversodontidae) from the Triassic of Madagascar.

547 J. Vert. Paleontol. 28, 445–462.

548 11 Reichel, M., Schultz, C. & Soares, M. B. 2009 A new traversodontid cynodont

549 (Therapsida, Eucynodontia) from the Middle Triassic Santa Maria formation of Rio

550 Grande do Sul, Brazil. Palaeontology 52, 229–250.

551 12 Gao, K.-Q., Fox, R. C., Zhou, C.-F. & Li, D.-Q. 2010 A new nonmammalian

552 eucynodont (Synapsida: Therapsida) from the Triassic of Northern Gansu Province,

553 China, and its biostratigraphic and biogeographic implications. Am. Mus. Novit. 3685,

554 1–25.

555 13 Liu, J. & Olsen, P. 2010 The phylogenetic relationships of Eucynodontia (Amniota:

556 Synapsida). J. Mammal Evol. 17, 151–176.

557 14 Oliveira, T. V. D., Soares, M. B. & Schultz, C. L. 2010 Trucidocynodon riograndensis

558 gen. nov. et sp. nov. (Eucynodontia), a new cynodont from the Brazilian Upper Triassic

559 (Santa Maria Formation). Zootaxa 2832, 1–71.

560 15 Kammerer, C. F., Flynn, J. J., Ranivoharimanana, L. & Wyss, R. R. 2012 Ontogeny in

561 the Malagasy traversodontid Dadadon isaloi and a reconsideration of its phylogenetic

562 relationships Fieldiana: Life Earth Sci. 5, 112–125.

563 16 Van Heerden, J. 1976 The cranial anatomy of Nanictosaurus rubidgei and the

18

564 classification of the Cynodontia (Reptilia: Therapsida). Navors. Nas. Mus.,

565 Bloemfontein 3, 141–164.

566 17 Crompton, A. W. 1955 On some Triassic cynodonts from Tanganyika. Proc. Zool. Soc.

567 London 125, 617–669.

568 18 Crompton, A. W. 1964 On the skull of Oligokyphus. Bull. Br. Mus. Nat. Hist. (Geol.

569 Ser.) 9, 69–82.

570 19 Savage, R. J. G. & Waldman, N. F. 1966 Oligokyphus from Holwell Quarry, Somerset.

571 Proc. Bristol. Nat. Soc. 31, 185-192.

572 20 Sues, H. D. 1985 First record of the tritylodontid Oligokyphus (Synapsida) from the

573 Lower Jurassic of Western North America. J. Vert. Paleontol. 5, 328-335.

574 21 Luo, Z. & Sun, A. 1993 Oligokyphus (Cynodontia: Tritylodontidae) from the Lower

575 Lufeng Formation (Lower Jurassic) of Yunnan, China. J. Vert. Paleontol. 13, 477–482.

576 22 Brink, A. S. 1965 On two new specimens of Lystrosaurus-zone cynodonts. Palaeontol.

577 Afr. 9, 107–122.

578 23 Crompton, A. W. 1972 Postcanine occlusion in cynodonts and tritylodontids. Bull. Br.

579 Mus. Nat. Hist. (Geol. Ser.) 21, 27–71.

580 24 Abdala, F. & Ribeiro, A. M. 2003 A new traversodontid cynodont from the Santa Maria

581 Formation (Ladinian-Carnian) of southern Brazil, with a phylogenetic analysis of

582 Gondwanan traversodontids. Zool. J. Linn. Soc. 139, 529–545.

583 25 Bonaparte, J. F. & Barberena, M. C. 1975 A possible mammalian ancestor from the

584 Middle Triassic of Brazil (herapsida-Cynodontia). J. Paleontol. 49, 931–936.

585 26 Bonaparte, J. F. 1980 The first ictidosaur (Reptila-Therapsida) of South America,

586 Chaliminia musteloides, from the Upper Triassic of the Fioja, Argentina (Spanish).

587 Actas II Congreso Argentino de Paleontología y Biostratigrafía y I Congreso

588 Lainoamericano de Paleontología 1, 123–133.

19

589 27 Barberena, M. C. 1981 Noves materiais de Traversodon stahleckeri da Formação Santa

590 Maria (Triássico do Rio Grande do Sul). Pesquisas 14, 149–162.

591 28 Hopson, J. A. 1985 Morphology and relationships of Gomphodontosuchus brasiliensis

592 von Huene (Synapsida, Cynodontia, Tritylodontidae) from the Triassic of Brazil. N.

593 Jahr. Geol. Paläontol. Abt. 1985, 285–299.

594 29 Flynn, J. J., Parrish, J. M., Rakotosamimanana, B., Ranivoharimanana, L., Simpson, W.

595 F. & Wyss, A. R. 2000 New traversodontids (Synapsida: Eucynodontia) from the

596 Triassic of Madagascar. J. Vert. Paleontol. 20, 422–427.

597 30 Soares, M. B., Schultz, C. L. & Horn, B. L. D. 2011 New information on Riograndia

598 quaibensis Bonaparte, Ferigolo & Ribeiro, 2001 (Eucynodontia, Tritheledontidae) from

599 the Late Triassic of southern Brazil: anatomical and biostratigraphic implications. An.

600 Acad. Bras. Cienc. 83, 329–354.

601 31 Abdala, F. & Teixira, A. M. S. 2004 A traversodontid cynodont of African affinity in

602 the South American Triassic. Palaeontol. Afr. 40, 11–22.

603 32 Abdala, F. & Smith, R. M. H. 2009 A Middle Triassic cynodont fauna from Namibia

604 and its implications for the biogeography of Gondwana. J. Vert. Paleontol. 29, 837–851.

605 33 Liu, J. & Powell, J. 2009 Osteology of Andescynodon (Cynodontia: Traversodontidae)

606 from the Middle Triassic of Argentina. Am. Mus. Novit. 3674, 1–19.

607 34 Gow, C. 1994 New find of Diarthrognathus (Therapsida: Cynodontia) after seventy

608 years. Palaeont. Afr. 31, 51–54.

609 35 Sues, H.-D. & Jenkins Jr., F. A. 2006 The postcranial skeleton of Kayentatherium

610 wellesi from the Lower Jurassic Kayenta Formation of Arizona and the phylogenetic

611 significance of postcranial features in tritylodontid cynodonts. In Amniote

612 paleobiology: perspectives on the evolution of mammals, birds, and reptiles (eds. M. T.

613 Carrano, T. J. Gaudin, R. W. Blob & J. R. Wible), pp. 114–152. Chicago: The

20

614 University of Chicago Press.

615 36 Abdala, F., Hancox, P. J. & Neveling, J. 2005 Cynodonts from the uppermost

616 Burgersdorp Formation, South Africa, and their bearing on the biostratigraphy and

617 correlation of the Triassic Cynognathus Assemblage Zone. J. Vert. Paleontol. 25, 192–

618 199.

619 37 Walker, J. D. & Geissman, J. W. 2009 Geologic Time Scale. Geological Society of

620 America.

621 38 Furin, S. F. et al. 2006 High-precision U-Pb zircon age from the Triassic of Italy:

622 Implications for the Triassic time scale and the Carnian origin of calcareous

623 nannoplankton and dinosaurs. Geology 34, 1009–1012.

624 39 Swofford, D. L. 2002 PAUP*: phylogenetic analysis using parsimony (and other

625 methods) 4.0 beta. Sinauer Associates, Sunderland, Massachusetts.

626 40 Goloboff, P. A., Farris, J. S. & Nixon, K. C. 2008 TNT, a free program for phylogenetic

627 analysis. Cladistics 24, 774–786.

628 41 Goloboff, P. A. 1993 Estimating character weights during tree search. Cladistics 9, 83–

629 91.

630 42 Brusatte, S. L., Benton, M. J., Ruta, M. & Lloyd, G. T. 2008 The first 50 million years

631 of dinosaur evolution: macroevolutionary pattern and morphological disparity. Biol.

632 Lett. 4, 733–736.

633 43 Lloyd, G. T., Wang, S. C. & Brusatte, S. L. 2011 Identifying heterogeneity in rates of

634 morphological evolution: discrete character change in the evolution of lungfish

635 (Sarcopterygii; Dipnoi). Evolution 66, 330–348.

636 44 Paradis, E., Claude, J. & Strimmer, K. 2004 APE: analyses of phylogenetics and

637 evolution in R language. Bioinformatics 20, 289–290.

638 45 Wagner, P. J. 1997 Patterns of morphologic diversification among the Rostroconchia.

21

639 Paleobiology 23, 115–150.

640 46 McKinney, M. L., 1990. Classifying and analyzing evolutionary trends. In Evolutionary

641 trends (ed. K. J. McNamara), pp. 28–58. London: Belhaven.

642 47 Butler, R. J., Benson, R. B. J., Carrano, M. T., Mannion, P. D. & Upchurch, P. 2011

643 Sea-level, dinosaur diversity, and sampling biases: investigating the ‘common cause’

644 hypothesis in the terrestrial realm. Proc. R. Soc. London B 278, 1165-1170.

645 48 Vienne, D. M. de, Aguileta, G. & Ollier, S. 2011 Euclidean nature of phylogenetic

646 distance matrices. Syst. Biol. 60, 826–832.

647 49 Harmon, L. J. & Glor, R. E. 2010 Poor statistical performance of the Mantel test in

648 phylogenetic comparative analyses. Evolution 64, 2173–2178.

649 50 Revell, L. J., Harmon, L. J. & Collar, D. C. 2008. Phylogenetic signal, evolutionary

650 process, and rate. Syst. Biol. 57, 591–601.

651 51 Blomberg, S. P., Garland, T. & Ives, A. R. 2003. Testing for phylogenetic signal in

652 comparative data: behavioral traits are more labile. Evolution 57, 717–745.

653 52 Münkemüller, T. et al. 2013 How to measure and test phylogenetic signal. Methods

654 Ecol. Evol. 3, 743–756.

655 53 Revell, L. J. 2012 phytools: An R package for phylogenetic comparative biology (and

656 other things). Methods Ecol. Evol. 3, 217–223.

657 54 Klingenberg, C. P. & Gidaszewski, N. A. 2010 Testing and quantifying phylogenetic

658 signal in comparative data. Syst. Biol. 59, 245–261.

659 55 Klingenberg, C. P. 2011 MorphoJ: an integrated software package for geometric

660 morphometrics. Mol. Ecol. Resources 11, 353–357.

661 56 Foth, C., Brusatte, S. L. & Butler, R. J. 2012 Do different disparity proxies converge on

662 a common signal? Insights from the cranial morphometrics and evolutionary history of

663 Pterosauria (Diapsida: Archosauria). J. Evol. Biol. 25, 904–915.

22

664

665 SUPPLEMENTARY FIGURES

666 Figure S1. Results of phylogenetic analyses. (a) Strict consensus of 486 trees resulting from

667 analysis with all characters unordered and of equal unit weight. (b) Agreement subtree from

668 the same analysis. (c) Strict consensus of nine trees obtained from reweighting characters by

669 the maximum value of their rescaled consistency indices.

670

671 Figure S2. Plots of rarefied mean disparity values and 95% confidence intervals for four

672 metrics. (a–d) Group disparity (B = basal taxa plus epicynodonts; C = cynognathians; P =

673 probainognathians); (e–h) temporal disparity (for intervals t1–t9, see text).

674

675 Figure S3. Cynodont phylogeny. (a) Tree with time-calibrated branch lengths (see also figure

676 1 in the main text). (b) Tree with branches drawn in proportion to ACCTRAN rates. (c) Tree

677 with branches drawn in proportion to DELTRAN rates. Green and red circles mark branches

678 with significantly high and significantly low rates, respectively.

679

680 Figure S4. Plots of cynodont diparity and diversity through time. Mean un-rarefied disparity

681 values for four disparity indices are represented by white circles; the total cynodont diversity

682 (along right verical axis) is represented by grey squares (for intervals t1–t11, see main text).

683 (a) Sum of ranges vs. diversity. (b) Root-product of ranges vs. diversity. (c) Sum of variances

684 vs. diversity. (d) Root-product of variances vs. diversity.

685

23

685 686 figure S1 687

24

687 688 figure S2 689

25

689 690 figure S3 691

26

691 692 figure S4

27