Supplemental Material For: Inferring the Total-Evidence Timescale of Marattialean Fern Evolution in the Face of Extreme Model Sensitivity

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Supplemental Material for: Inferring the Total-Evidence Timescale of Marattialean Fern Evolution in the Face of Extreme Model Sensitivity

Contents

S§1Morphological Data S6

S§2Accessions S9

S§3Graphical Models S15 S§3.1Substitution Model ...... S15 S§3.2Molecular Clock Model ...... S16 S§3.3Morphological Transition Models ...... S17 S§3.4Morphological Clock Models ...... S20 S§3.5Tree Models ...... S22

S§4MCMC Analyses S27 S§4.1MCMC Diagnosis ...... S27

S§5Posterior-Predictive Simulation S28

S§6Empirical Considerations: Taxon Sample and Rooting Strategies S29 S§6.1Ancient plants ...... S29 S§6.2Polarized rooting ...... S29 S§6.3Ingroup-only ...... S30 S§6.4Results ...... S30

S§7Extended Results S32 S§7.1Ingroup Sampling Fraction ...... S32 S§7.2Overall Sampling Fraction ...... S42 S§7.3Ingroup vs. Overall Sampling Fraction ...... S53 S§7.4Uniform Tree Model ...... S54 S§7.5Polarized Analysis ...... S59 S§7.6Ancient Plants Analysis ...... S61 S§7.7Ingroup Analysis ...... S63 S§7.8Comparing Empirical Considerations ...... S65

S1 Contents S2

S§7.9Extant Phylogenies ...... S69 S§7.10StochasticMaps ...... S71 S§7.11Unrooted vs. Rooted Topologies ...... S86

S§8Model Adequacy for Relaxed Clocks S90 List of Figures

S1 The GTR+I+Γ substitution model ...... S15 S2 The uncorrelated lognormal (UCLN) relaxed molecular clock model ...... S16 S3 The Mk morphological model ...... S17 S4 The Mk+Γ morphological model ...... S17 S5 The F81 morphological model ...... S18 S6 The F81+Γ morphological model ...... S19 S7 The “linked” relaxed morphological model ...... S20 S8 The “unlinked” relaxed morphological model ...... S21 S9 The uniform tree model ...... S22 S10 The CRFBD tree model ...... S23 S11 The EFBDψ tree model ...... S24 S12 The EFBDλ,µ tree model ...... S25 S13 The EFBDλ,µ,ψ tree model ...... S26 S14 Comparing distributions of molecular trees among model combinations ...... S32 S15 Comparing distributions of extinct trees among model combinations ...... S33 S16 Comparing lineage-through-time curves among model combinations ...... S34 S17 Comparing lineage-through-time curves of extant taxa among model combinations . . . S34 S18 Comparing divergence-time estimates for each clade by morphological transition model S35 S19 Comparing divergence-time estimates for each clade by morphological clock model . . S36 S20 Comparing divergence-time estimates for each clade by tree model ...... S37 S21 The maximum clade credibility tree under the preferred model ...... S38 S22 The 20%-rule consensus tree under the preferred model ...... S39 S23 Diversification over time under the EFBDλ,µ,ψ model ...... S40 S24 Diversity through time under each fossilized birth-death model ...... S41 S25 Comparing distributions of trees among model combinations using the overall sampling fraction ...... S42 S26 Comparing distributions of molecular trees among model combinations using the overall sampling fraction ...... S43 S27 Comparing distributions of extinct trees among model combinations using the overall sampling fraction ...... S44 S28 Average lineage-through-time curves among model combinations using the overall sampling fraction ...... S45 S29 Comparing lineage-through-time curves among model combinations using the overall sampling fraction ...... S45 S30 Comparing lineage-through-time curves of extant taxa among model combinations using the overall sampling fraction ...... S46 S31 Comparing divergence-time estimates for each clade by morphological transition model using the overall sampling fraction ...... S47 S32 Comparing divergence-time estimates for each clade by morphological clock model using the overall sampling fraction ...... S48 S33 Comparing divergence-time estimates for each clade by tree model using the overall sampling fraction ...... S49 S34 Comparing model adequacy among model combinations using the overall sampling fraction ...... S50 S35 The maximum clade credibility tree under the preferred model with overall sampling fraction ...... S51 S36 The 20%-rule consensus tree under the preferred model with overall sampling fraction . S52 S37 Comparing divergence-time estimates for each clade by assumed sampling fraction . . S53 S38 The uniform tree model is an informative prior on node ages ...... S54 S39 The uniform tree model is an informative prior on lineage-through-time curves . . . . . S55 S40 The fossilized birth-death model is an informative prior on node ages when hyperparameters are fixed ...... S56 S41 The maximum clade credibility tree under the uniform tree model ...... S57 S42 The 20%-rule consensus tree under the uniform tree model ...... S58 S43 The maximum clade credibility tree under the preferred model with polarized root . . . S59 S44 The 20%-rule consensus tree under the preferred model with polarized root ...... S60 S45 The maximum clade credibility tree under the preferred model with ancient plant fossils S61 S46 The 20%-rule consensus tree under the preferred model with ancient plant fossils . . . . S62 S47 The maximum clade credibility tree under the preferred model and just ingroup taxa . . S63 S48 The 20%-rule consensus tree under the preferred model and just ingroup taxa ...... S64 S49 The impact of empirical considerations on phylogenetic estimates. We compute the RF distances and KF distances between chronograms among our “empirical considerations” analyses and the “standard” dataset under the preferred models (left and middle, respectively). We only compare samples where the ingroup is inferred to be monophyletic, and pruned outgroup taxa before computing pairwise distances. We also computed the LTT curves for the ingroup taxa for the same sets of analyses, again conditioning on the monophyly of the ingroup and pruning outgroup taxa (right). We compare the ages of particular clades in Fig. S51...... S65 S50 The impact of modeling and empirical considerations on divergence-time estimates of major clades. We plot the marginal posterior distribution of the age of each node (in rows) as a function of the morphological-transition model (column 1), the morphological clock model (column 2), the tree model (column 3), and the empirical considerations (column 4). White dots are the posterior median ages, and black bars correspond to the 50% (thick) and 95% (narrow) credible intervals. We report means, medians, and 95% CIs in the Supplemental Material (Tables S.3 and S.4) ...... S65 S51 Comparing divergence-time estimates for each clade with different empirical considerations ...... S67 S52 The maximum clade credibility trees for extant taxa among tree models ...... S69 S53 The maximum clade credibility trees for extant taxa among empirical datasets ...... S70 S54 Stochastic map for character 23: degree of pinnation ...... S72 S55 Stochastic map for character 28: foliar abaxial idioblasts ...... S73 S56 Stochastic map for character 52: synangial suture between valves ...... S74 S57 Stochastic map for character 54: number of sporangia per synangium ...... S75 S58 Stochastic map for character 55: synangium symmetry in x.s...... S76 S59 Stochastic map for character 57: synangium shape in long section pre-dehiscence . . . . S77 S60 Stochastic map for character 58: sporangium or synangium pedicel or receptacle histologyS78 S61 Stochastic map for character 59: sporangium tip extension ...... S79 S62 Stochastic map for character 62: bilateral synangium dehiscence ...... S80 S63 Stochastic map for character 70: spore ornamentation location ...... S81 S64 Stochastic map for character 75: eusporangium cavity shape ...... S82 S65 Stochastic map for character 77: synangium sporangia spread out from center on dehiscence ...... S83 S66 Stochastic map for character 78: synangium location on pinnule ...... S84 S67 Stochastic map for character 87: annulus of thick-walled cells ...... S85 S68 The maximum clade credibility tree under the unrooted (non-clock) model ...... S87 S69 Topological conflict beween rooted and unrooted MCC trees ...... S88 S70 Topological conflict beween rooted and unrooted MRC trees ...... S89 S71 Comparing distributions of morphograms with different taxon sets ...... S90 S72 Widths of posterior-predictive distributions between linked and unlinked morphological clock models ...... S91 S§1. Morphological Data S6

S§1 Morphological Data

Our morphological dataset was largely derived from Rothwell et al.(2018b), which itself relied heavily on Hill and Camus(1986) and Murdock(2008), and amended as necessary (see S §1). We based character and character-state circumscriptions, as well as the character coding itself, on specimens ex- amined at VT and on additional literature (Holttum 1978; Rolleri 1993; Rolleri et al. 2003; Christenhusz 2010a,b; He et al. 2013; Senterre et al. 2014). In a departure from Rothwell et al.(2018b)—which sim- plified stomata and pulvinus characters, and altered coding to avoid nested states—we instead used contingent character coding (Forey and Kitching 2000; Brazeau 2011). Our coding for the outgroup taxa was based on literature and our examination of specimens. Our new characters were primarily focused on the leptosporangiate ferns (our outgroup), e.g., the presence of linear aerophores (S§1 character 27) and morphology and variation within leptosporangia (S§1 characters 93 − 98). Our final morphological matrix comprised 98 discrete characters describing anatomy and gross morphology; in total, there were 79 binary characters, 10 three-state characters, four four-state characters, three five-state characters, one six-state character, and one seven-state character. Twenty-two percent of the matrix was unscored due to contingent character coding (i.e., inapplicable characters for a specific taxon), and an additional eight percent of the data were missing because they are unknown. Here we provide our final list of characters and character states. Except where noted, characters and states are from Rothwell et al.(2018b), which incorporated characters and states from Hill and Camus(1986) and Murdock(2008). Character coding primarily follows Rothwell et al.(2018b) with some corrections.

1. Leaf-bearing stems : erect (0); creeping (1). 2. Erect adult stem : squat (0); elongate (1). 3. Stipule (aphlebia) pairs at leaf base : absent (0); present (1). 4. Root mantle around stem : absent (0); present (1). 5. Scleriﬁed pith in root stele : absent (0); present (1). 6. Root cortex with continuous sclerenchyma band : absent (0); present (1). 7. Polyarch root stele : absent (0); present (1). 8. Multicellular root hairs : absent (0); present (1). 9. Mucilage canals in root : absent (0); present (1). 10. Stem symmetry (external morphology) 2 : radial (0); dorsiventral (1). 11. Basal pinnae more elaborated : absent (0); present (1). 12. Stem stele : protostele (0); solenostele (1); dictyostele (2); equisetostele (3). 13. Protoxylem development : exarch (0); mesarch (1); endarch (2). 14. Stem hypodermis of sclerenchyma : absent (0); present (1). 15. Stem/pinna internal sclerenchyma strand : absent (0); present (1). 16. Lysigenous lacunae in stem/pinnae : absent (0); present (1). 17. Mucilage canals in axial components of frond : absent (0); present (1). 18. Tannin cells in stem or pinnae cortex : absent (0); present (1). 19. Gum sacs in stems or petioles : absent or sparse (0); present (1). 20. Petiole or pinna vascular strand : continuous (0); discontinuous (1). 21. Phloem maturation : exarch (0); endarch (1). 22. Circinnate vernation : absent (0); present (1). New character 23. Number of fronds (megaphylls) : multiple fronds produced (0); one frond produced at a time (1). 24. Petiole trace : single undifferentiated trace (0); C-shaped (1); Omega-shaped (2); dissected Omega (3); multiple concentric rings of dissected traces (4); 3-shaped (5); elongate (6). New character. S§1. Morphological Data S7

25. Pulvinuloids at base of segments : absent (0); present (1). New character. A simplification of Rothwell et al.(2018b) characters 109–113. 26. Polycylic dictyostele : absent (0); present (1). New character. Coding contingent on dictyostele being present (character 12, state 2). 27. Aerating tissue upon petiole : lateral linear aerophores (0); scattered and lenticel-like (1). New character based upon ???. 28. Degree of pinnation : once (0); twice (1); three or more (2). 29. Ultimate segments articulated with sutures : absent (0); present (1). 30. Pinnule pinna base : margins parallel (0); narrowly confluent/cordate (1). 31. Pinnule pinna tips : acute (0); obtuse (1). 32. Epidermal cell walls thickened : absent (0); present (1). 33. Epidermal cell wall thickening : even (0); uneven (1). 34. Foliar abaxial idioblasts : absent (0); present (1). 35. Laminar idioblast groupings : solitary or small groupings (0); dense areas of idioblasts (1). 36. Idioblast chains on lateral veins : absent (0); present (1). 37. Idioblasts on synangium walls : absent (0); present (occasional) (1). 38. Scale cell shape : isodiametric (0); elongate (1). 39. Peltate scales : absent (0); present (1). 40. Peltate laminar scale morphology : with centrally attached stalks (0); with strongly asymmetrical stalk attachment (1). 41. Pinna/pinnule epidermal trichomes : absent (0); present (1). 42. Glandular trichomes : absent (0); present (1). 43. Scale margins : entire (0); lobed or fimbriate (1). 44. Sporangia individually vascularized : absent (0); present (1). 45. Sporangium/synangium base trichomes : absent (0); present (1). 46. Pinnule venation : simple (0); open dichotomous (1); reticulate (2). 47. Awns on veins : absent (0); present (1). 48. Fertile veins : all potentially fertile (0); preference towards distal vein branches (1). 49. Frond dimorphism : absent or slight (0); strongly dimorphic (1). 50. Synangia (sori) separated by surface foliar partitions : absent (0); present (1). 51. Lamina thickness : chartaceous to coriaceous (0); membranaceous (1). New character 52. Leaf cuticle (adaxial) : thin (0); thick (1). 53. Mesophyll cells with microscopic projections on exterior walls : absent (0); present (1). 54. Fertile pinnule margin morphology : flat (0); downturned (1); thin inrolled (2); thick inrolled (3). 55. Sporangia enclosed by pinnule margin : absent (0); present (1). 56. Functional sporangium annulus : absent (0); present (1). 57. Sporangia developmentally attached (synangium) : absent (0); present (1). 58. Extent of lateral sporangium fusion before dehiscence : none (0); partial (1); complete-almost complete (2). 59. Synangial suture between valves : deeply cut without central tissue pad (0); shallowly cut with central tissue pad (1). 60. Sporangia of sorus around central cellular area at base : present (0); absent (1). 61. Number of sporangia per synangium : 2–5 (0); 6–11 (1); 12–22 (2); more than 22 (3). 62. Synangium symmetry in x.s. : radial (0); radial and bilateral (1); bilateral (2). 63. Synangium receptacle morphology : flat or raised mound (0); radial stalk or pedicel (1). 64. Synangium shape in longitudinal section pre-dehiscence : cordate (0); fusiform (1); oval (2); two crescents (3). 65. Sporangium/synangium pedicel/receptacle histology : vascular (0); vascular + parenchyma (1); S§1. Morphological Data S8

+ (2); fiber + parenchyma (3); fiber (4); transfusion tissue (5). 66. Sporangium tip extension : present (0); absent (1). 67. Sporangium tip extension length : long, obvious (0); short, inconspicuous (1). 68. Initial synangium dehiscence : sporangia separate distally (0); sporangia do not separate distally (1); two rows of fused sporangia (valves) separate (2). 69. Bilateral synangium dehiscence : sporangial rows fused but not opening as two valves (0); sporangial rows opening as two valves (1). 70. Eusporangium aperture shape : pore (0); slit (1). 71. Eusporangium dehiscence position : inner/side facing wall (0); terminal (1). 72. Eusporangium aperture labiate : simple (0); labiate (1). 73. Eusporangium dehiscence area wall uniseriate : absent (0); present (1). 74. Spore suture : trilete (0); monolete (1); alete (2). 75. Spore morphology : spherical (0); ovoid (1); reniform (2); tetrahedral (3). Altered from Rothwell et al.(2018b), 2018 character 93 to include state 3. 76. Perine (perispore) : present (0); absent (1). 77. Spore ornamentation location : perine (perispore) (0); exine (1); perine and exine (2). 78. Perine (perispore) ornamentation units : smooth (0); spines (1); papillae (2); warts (3); rods (4). Altered from Rothwell et al.(2018b) character 96 to include state 4. 79. Exine ornamentation units : smooth (0); spines (1); papillae (2); warts (3); ridges (4). 80. Spore ornamentation units joined : absent (0); present (1). 81. Spore lasurae raised/thickened : absent (0); present (1). 82. Eusporangium cavity shape : cylinder tapering near tip (0); ovate wider in basal half (1); obovate wider in distal half (2). should the first one be “ovate”? 83. Eusporangium cavity length (mm) : greater than 1.0 (0); less than 1.0 (1). 84. Synangium sporangia spread out from center on dehiscence : absent (0); present (1). 85. Synangium location on pinnule : marginal (0); between margin and midvein (1). 86. Stipe pulvini : absent (0); present (at least in juvenile) (1). 87. Stomata of lamina cell arrangement : anomocytic to weakly cyclocytic (0); mostly cyclocytic (1); paracytic (2). 88. Stomata of lamina function : guard cells functional (0); guard cells permanently open (1). 89. Stomatal shape : elliptical (0); circular (1). 90. Stomatal complex : surficial or slightly sunken (0); raised (1). 91. Stomatal density : low (0); high (1). 92. Sporangium cavity base immersed in parenchyma : absent (0); present (1). 93. Number of sporangial initials : multiple (0); one (1). New character. 94. Annulus of thick-walled cells : absent (0); present (1). New character. 95. Position of annulus : lateral (0); oblique (1); transverse (2); apical (3); vertical (4). New character. 96. Sporangium wall thickness : thick walled (0); thin walled (1). New character. 97. Number of spores per sporangium : hundreds (0); 64 (1). New character. 98. Sorus protected by funnelform involucre : absent (0); present (1). New character. S§2. Accessions S9

S§2 Accessions

Table S.1: Molecular Accessions

Taxon atpB rbcL rps4-trnS trnS-trnG+trnG Angiopteris caudata — — EU439172.1 — Angiopteris evecta EU439071.1 EU439092.1 EU439139.1 EU439228.1 Angiopteris henryi — DQ838062.1 — — Angiopteris itoi EU439073.1 EU439094.1 EU439170.1 EU439247.1 Angiopteris lygodiifolia X58429.1 X58429.1 EU439163.1 EU439241.1 Angiopteris smithii EU439072.1 EU439093.1 EU439169.1 EU439246.1 Angiopteris tonkinensis — DQ838058.1 — — Christensenia aesculifolia EU439057.1 EU439079.1 EU439102.1 EU439184.1 Cyathea multiflora EF463365.1 AM410197.1 FN667568.1 — Danaea elliptica EU439054.1 AF313578.1 EU439096.1 EU439178.1 Danaea grandifolia EU221704.1 EU221766.1 — — Danaea leprieurii — EU439077.1 EU439097.1 EU439179.1 Danaea nodosa — EU439078.1 EU439098.1 EU439180.1 Diplopterygium glaucum KU877749.1 KU936583.1 KU936648.1 — Dipteris conjugata AY612696.1 EF588692.1 AY612658.1 — Eupodium kaulfussii — — EU439105.1 EU439187.1 Eupodium laeve — EU439081.1 EU439104.1 EU439186.1 Hymenophyllum holochilum NC 039753.1 NC 039753.1 NC 039753.1 — Marattia alata — EU439082.1 EU439108.1 EU439190.1 Marattia douglasii EU439061.1 EU439083.1 EU439109.1 EU439191.1 Marattia laxa EU439062.1 EU439084.1 EU439111.1 EU439193.1 Matonia pectinata EU352280.1 EU352307.1 AY612666.1 — Osmunda regalis — EF588706.1 EF588771.1 — Osmundastrum cinnamomeum AF313539.1 EF588711.1 — — Ptisana attenuata — AF313581.1 EU439125.1 EU439206.1 Ptisana fraxinea EU439067.1 EU439088.1 EU439131.1 EU439212.1 Ptisana melanesica — EU439090.1 EU439134.1 EU439214.1 Ptisana mertensiana — — EU439120.1 EU439201.1 Ptisana oreades — EU439087.1 EU439130.1 EU439211.1 Ptisana pellucida — — EU439121.1 EU439202.1 Ptisana purpurascens — EU439089.1 EU439132.1 EU439213.1 Ptisana salicifolia — — EU439133.1 — Ptisana squamosa — — EU439119.1 EU439200.1 Ptisana sylvatica — — EU439117.1 EU439198.1 Saccoloma inaequale MK705756.1 MK705756.1 MK705756.1 — Schizaea elegans NC 035807.1 NC 035807.1 NC 035807.1 — S§2. Accessions S10 ´ ujo et al. Millay ( 1977 ); Jacobson ( 2006 ) — — — Millay ( 1982 ); Jacobson ( 2006 ) Tavares et al. ( 2014 ); ( 2016 ) Ara Naugolnykh ( 2013 ) Baxter and Baxendale ( 1976 ) — — — Halle ( 1921 ); seeet also al. ( 2012 ) Kustatscher 313.8 − — — — The Missourianstage North corresponds American tovian stage of the the ICC. Kasimo- Asselian to end of thethe Capitanian ICC. of Kungurian Stage of the ICC. — — — Rhaetian stage of the ICC. The Missourianstage North corresponds American tovian stage of the the ICC. Kasimo- Middle Pennsylvanian of the ICC. Rothwell and Good ( 2000 ) per FossilWorks,Middle Pennsylvanian approximately Asselian stage of the ICC. Shen ( 1995 ); Shen ( 1995 ) Desmoinesian Stage is 305.9 ıba Basin, in ´ ´ elfia region of Brasil. Either ı-Filad ´ Geologic andLiving Living Living Upper Pennsylvaniansourian Callhoun seriesMcLeansboro Coal; Group of Basis for Mis- the Matoon Formation, The reconstructed fossils comepart from the of middle the Balsasthe Group of Aragua the Par in the Motuca( 2014 ) Formation suggested (which toTavares be etthe early al. Pedro Permian de in Fogo age)2016). Formation or (see Occurrences in Araujarestricuted Germany et to and the al. Asselian-Sakmarian France (early are Per- mian). Based onfrom these the sources Early we toend use of Middle the a Permian Capitanian). range (Asselian to Lower Permian, Kungurian StageFore of Urals the middle Living Living Living Kustatscher et al. ( 2012 ) indicate that thisonly species occurs inis the distibuted Rhaetian in (late Europe,gentina. Triassic), Asia, but and possibly Ar- Upper Pennsylvaniansourian Callhoun seriesMcLeansboro Coal; Group of Mis- the Matoon Formation, LivingLivingLivingOccurs in coal ballscoal from swamp Upper deposits Carboniferous Germany from and the North America. Westphaliandescription of The whole-plant used herefrom the comes middle Pennsylvanian fromKansas. of southeastern coal balls — — —Living — Living — Living — Taiyuan Formation;Province; Longshou Northwest Mt.,Region, Chi Xizang Asselian, Chi earliest Autonomous Permian Floral — — — — — — Desmoinesian Stage of theCherokee Cabaniss Group Formation, ] ] ] ] ] ] ] ] 283.5 307 307 298.9 208.5 313.8 − 315.2 298.9 − − − − − ] ] ] ] ] ] ] ] ] ] ] ] 0 0 0 0 0 0 0 0 0 0 0 0 − − − − − − − − − − − − − − 303.7 0 0 0 303.7 259.1 272.95 0 0 0 201.3 0 0 0 307 0 305.9 0 0 295 [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ TaxonAcaulangium bulbaceum Angiopteris lygodiifolia Angiopteris itoi Angiopteris boninensis Age RangeAraiangium pygmaeum Stratigraphic InformationBuritiranopteris costata Numerical Age Determition References Convexocarpus distichus Cyathea multiiflora Daea grandifolia Daea nodosa Daeopsis fecunda Angiopteris evecta Angiopteris smithii Angiopteris tonkinensis Botryopteris tridentata Christensenia aesculifolia Corynepteris involucrata Daea elliptica Daea leprieurii Daeites rigida Table S.2: Fossil Accesions S§2. Accessions S11 ¨ ossler ´ ujo et al. ( 2016 ) ¨ oßler and Galtier ( 2002 ); R — Nadon et al. ( 1998 ); Millay ( 1978 ) Rothwell et al. ( 2018a ) — Baud et al. ( 2016 ); Duaiji ( 2001 ); SenalpStolle ( 2007 ); andWagner et Al- al. ( 1985 ) R Axsmith et al. ( 2001 ) Yang et al. ( 2008 ) Livera andKonijnenburg-Van Cittert ( 1975 ) Leeder ( 1981 ); Van and Noll ( 2002 ); Ara ( 1885 ); Weiss LesnikowskaGaltier ( 1992 ) and 303.7 per FossilWorks) − 305.9), Stephanian B upper − — Valanginian of the ICC. — Asselian to endstages of of the ICC. the Capitanian Carnian stage of the ICC. Lower Jurassic of the ICC. Aalenian to Bathonian stagesICC. of the The lower part ofgroup the Monongahela corresponds tostage the (295 Virgilian (see Nadon et al. 1998 ) Kazanian corresponds todian stage the of the Roa- ICCtotal range (FossilWorks), is Roadian to Changhsin- gian stages of the ICC. Lower Jurassic of the ICC. ( 1999 ) Wang Stephanian A isKhamovnichean, equivalent which tothe is the part Kasimovian of 304.8 (FossilWorks age boundary given by thevian, Dorogovilo- which is stillmovian part (FossilWorks). of the Kasi- ı- ´ ´ ujo Bu- 298.9). (see also − ) ´ elfia region of the Middle Permian (Rodian Living Longarm FormationEarly equivalent, Cretaceous, from Valanginian, Island) Apple Bay (Vancouver Living From the Pedro de Fogo Formation inhao the Basin, Maran- NE Brazil. Considered topart be the of upper the Pedra de Fogo Formation by Ara Late Triassic Pekin Formation of Northfrom Carolina; the middle portionBoren of the Clay formation Company in pitlate the Carnian near Gulf; said to be Lower Jurassic Daxigou FormationGansu, of Lanzhou, Chi.members, the plants The are collected from formation theone, upper but consists there is of no datingbers three to further constrain within the the mem- Lower (”Early”) Jurassic. Yorkshire Jurassic; theScalby formations span part Saltwick ofthe to Bathonian the ( Livera Aalenian and Leeder to1981 ) the end of Living —et al. ( 2016 ), from the exposuresFilad of the Aragua — through Capitanian). These depositsascibed have to been the Earlythus Permian a more by conservative otherto estimate authors, Middle ranges Permian Early (259.1 Late Pennsylvanian; From thethe lower Monongahela portion of Seriesseam equivalent in to Ohio, either theor from Pittsburgh Redstone (No. (No. a 8A) 8) Coals. coal Living —ritiranopteris costata Living — Living — — — — Description based onities: material from Gomaniimbrik two FormationChanghsingian local- (Capitanian stages; to Stolle 2016 )2007 ; of theBaud Hazro et inlierand in the al. southeastern Uyzah Turkey plantbia bed (Kazanian, of early central LateAl-Duaiji Permian; Saudi2001 ). Ara- Senalp and Described from theFormation in Lower Zigui, Hubei Jurassic Province, Chi. Hsiangchi From Poudingue Mosaiquethe at St. Grand Croix,imens Etienne in come Basin from of abase central conglomerate of France. that the is Stephaniancontains Spec- at material B, that the is but from is Stephanian A. reworked and ] ] ] ] ] ] ] ] ] 139.8 298.9 201.3 174.1 272.95 201.3 305.9 237 303.7 − − − − − − − ] ] ] ] ] ] 0 0 0 0 0 0 − − − − − − − − 0 0 132.9 0 259.1 227 174.1 166.1 295 0 251.9 0 0 174.1 303.4 [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ Diplopterygium glaucum Dipteris conjugata Escapia christensenioides Eupodium laeve Grammatopteris freitasii Hopetedia praetermissa Marattiopsis aganzhenensis Marattiopsis anglica Eoangiopteris goodii Eupodium kaulfussii Gemellitheca saudica Hymenophyllum holochilum Marattia alata Marattiopsis asiatica Grandeuryella reultii S§2. Accessions S12 ´ uneo et al. ´ esari ( 2016 ) ˇ cek ( 2014 ) — — Lundblad ( 1950 ) Escapa et al. ( 2015 ); C ( 2013 ) Kva Mapes and Schabilion ( 1979 ) — Delevoryas and Hope ( 1978 ) KasperGastaldo ( 2016 ); and Osberg et al. 1985 ( 1972 ); Andrews — — — — — Hill et al. ( 1985 ) Clements et al. ( 2019 ); ( 1967 ) Taylor Dittrich et al. ( 1983 ); ( 1976 ) Cornet et al. He et al. ( 2019 ) − 280 per GeoWhen. 370.6 per FossilWorks. − − — — Rhaetian stage of the ICC. Coniacian of the ICC. North American298.9 Wolfcampian is — Range provided isEifelian stages of the the ICC. Emsian to — — — — — The Westaphalian D is 306.95 Lopingian epoch of the ICC. 311.45 per FossilWorks. Aptian stage of the ICC. Ages constrained from U-Pbof dating ash layersLonco above Trapial andVera formation, and below C neo from the et Cu- al 2013. Late Triassic of the ICC. Hope and Patterson III ( 1970 ); Emsian stage of the ICC. Doran ( 1980 ) Kazanian corresponds todian stage the of the Roa- ICC (FossilWorks). Middle Famennian is part ofmennian the Fa- stage of364.7 the ICC, age is Living Living Triassic (Rhaetian) of Sweden Coniacian of the Hidden LakeRoss Formation, Island, James Antarctica Lower Permian (Wolfcampian) Bursumtion; Forma- clay shale pits in Tularosa, New Mexico. Living Described as being from the Trouttion Valley Forma- (Emsian?) andTomhegan revised formation as (Osberg a et member al.Geological of 1985, Survey). the Maine Gastaldo ( 2016 ) regardsTrout the Valley Formation as being between theEmsian late (Lower Devonian) to early Eifeliandle (Mid- Devonian) Living Living Living Living Living Middle Pennsylvanian, fromlocality,Francis the Creek Shale, Mazon Carbondale Creek Forma- tion of the Kewanee Group. From the Xuanweimining Formation district in ofsouthwest Chi; the western Lopingian epoch, Panxian Guizhou late Permian. Province, LivingSpecimens are synangia fromceous the (Aptian) Lower of Creta- Antarctica,mation, Byers Cerro Group. Negro For- Cerro Bayo Locality,Early Lonco Jurassic Trapial age (most Formation; likely Pliensbachian). LivingLiving —Pekin Formation of theNorth Carolina, Newark Upper Group, Triassic. central —Living — Living —LivingLiving — — — — — — — — — — Early Devonian (early to middlebly Esmian), the possi- Dalhousie Group Late Permian plant bed at UyzahArabia; in central Saudi Kazanian, earlyand Al-Duaiji Late2001 ). Permian ( Senalp Upper Devonian HampshireVirginia, which Formation, is West Cassadaganfordlan, to equivalent to earliest the Brad- uppernian middle (Fa2c). Famen- ] ] ] ] ] ] ] ] ] ] ] ] 311.45 189.036 208.5 407.6 259.1 237 407.6 272.95 370.6 89.8 − − 298.9 125 − − − − − − − ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] − 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 − − − − − − − − − − − − − − − − − 0 0 201.3 86.3 280 0 387.7 0 0 0 0 0 306.95 251.9 0 113 177.27 0 0 201.3 393.3 0 0 0 0 268.8 364.7 [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ Marattia douglasii Marattia laxa Marattiopsis crenulatus Marattiopsis vodrazkae Millaya tularosa Osmundastrum cinmomeum Pertica quadrifaria Ptisa attenuata Ptisa melanesica Ptisa oreades Ptisa purpurascens Ptisa sylvatica Radstockia kidstonii Rothwellopteris pecopteroides Marattia excavata Marattiaceae indet Vera 2016 Marattiopsis patagonica Matonia pectita Osmunda regalis Pekinopteris auriculata Psilophyton crenulatum Ptisa fraxinea Ptisa mertensia Ptisa pellucida Ptisa squamosa Qasimia schyfsmae Rhacophyton ceratangium S§2. Accessions S13 — ( 1906 ); Watson Millay ( 1982 ) Collinson et al. ( 2006 ); et al. ( 1992 ) Delevoryas Lesnikowska and Millay ( 1985 ) Lesnikowska and( 1997 ) Willard Millay ( 1979 ) Millay ( 1979 ) Mamay ( 1950 ) Millay ( 1979 ) Hoskins ( 1926 ) — Middle Triassic of the ICC. Upper Pennsylvanian of the ICC. Middle Pennsylvanian of the ICC. Upper Pennsylvanian of the ICC. Middle Pennsylvanian of the ICC. Middle Pennsylvanian of the ICC. Upper Pennsylvanian of the ICC. Middle Pennsylvanian of the ICC. Millay ( 1979 ) Bolsovian correspondswithin the to MoscovianICC. stage being of the Middle Pennsylvanian of the ICC. Mamay ( 1950 ) Upper Pennsylvanian of the ICC. Millay ( 1979 ) Middle Pennsylvanian of the ICC. Millay ( 1979 ) Upper Pennsylvanian of the ICC. Ewart ( 1961 ) Wesphalian A substage corresponds to the Bashkirian stage of the ICC. Changhsingian stage of the ICC. He et al. ( 2006 ) Living FremouwTransantarctic Peak Mountains;the locality base of fossils thewhich upper in part are is of the middlefossils Fremouw from and the Fm., Triassic palynology (see based also 2006 ). on central Collinson vertebrate et al. LateDuquesne Pennsylvanian Coal; Steubenville, Ohio. Conemaugh Group, Middle PennsylvanianMoines Cherokee Series; Group, “WhatIndia Cheer,” Des Keokuk County, Late Pennsylvanian coalFormation, balls McLeansboro of Group;Sumner, the Illinois “Berryville,” Mattoon Late Pennsylvanian coal balls of theMattoonmation, For- McLeansboro Group; “Berryville,” Sum- ner+D76:D77, Illinois Middle Pennsylvanian Carbondale Formation of the Kewanee Group, Sahara Mine,Illinois Carrier Mills, Late Pennsylvanian McLeansboro Group,the Danville from #7 coal, Heglernois mine, Danville, Illi- Living — — Middle PennsylvanianMoines Cherokee series; West Group, Mineral, Kansas. Des Early or Latefland Coal Bolsovian, Member; Schuler Pennsylvanian; Mine, India. Clif- Middle Pennsylvanian lower tokee Group, middle Des Chero- Moines Series,India Urbandale Mine, Late Pennsylvanian coalFormation, McLeansboro balls Group, of Calhoun Coal; Calhoun the coal mine, Mattoon Illinois Middle Pennsylvanian Lismanlegheny Series; Formation, Providence, Kentucky Al- Late Pennsylvanian coalFormation, balls McLeansboro of Group;Sumner, the Illinois “Berryville,” Mattoon Larkian Series; Shore, Lancashire,(Westaphalian England, A; UK Formation, Watson “Lewis1906 ) Creek,” andUSA Leslie Breathitt (lower County, KY, 1982 ) Middle Pennsylvanian; Millay Uppermost Permian Wangjiazhai FormationGuizhou in Province,sponding south-western to the Chi, Changhsingian stagemian. of corre- the Per- ] ] ] ] ] ] ] ] ] ] ] ] ] ] ] 307 307 307 323.2 254.14 307 307 247.2 315.2 315.2 315.2 315.2 315.2 315.2 315.2 − − − − − − − ] ] 0 0 − − − − − − − − − − 0 0 237 298.9 307 298.9 307 307 298.9 315.2 307 307 251.9 307 298.9 307 298.9 [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ [ Saccoloma iequale Schizaea elegans Scolecopteris antarctica L Scolecopteris charma O Scolecopteris fragilis L Scolecopteris illinoensis Scolecopteris iowensis O Scolecopteris majopsis O Scolecopteris minor M Scolecopteris alta A Scolecopteris calicifolia L Scolecopteris dispora Scolecopteris guizhouensis Scolecopteris incisifolia L Scolecopteris latifolia L Scolecopteris mamayi L Scolecopteris monothrix L S§2. Accessions S14 Millay ( 1979 ) Scott ( 1932 ) Lesnikowska and( 1997 ) Willard Millay ( 1979 ) ( 1999 ) Wang Zhaoqi and( 1988 ) Taylor Middle Pennsylvanian of the ICC. Upper Pennsylvanian of the ICC. Middle Pennsylvanian of the ICC. Asselian to Sakmarian stagesICC. of the Guadalupian stage of the ICC. The Autunian correlatesmian with Asselian stage Per- ofFossilWorks. the ICC per Upper Pennsylvanian of the ICC. Millay ( 1979 ) Upper Pennsylvanian of the ICC. Stubblefield ( 1984 ) Middle Pennsylvanian of the ICC. Millay ( 1979 ) Middle Pennsylvanian Carbondale Formation of the Kewanee Group, Sahara Mine,Illinois Carrier Mills, Late Pennsyvlaniansourian Patoka Provincial Series; Formation,County, “St. IN Mis- Wendel,” Posey Middle Pennsylvanian Carbondale Formation of the Kewanee Group, Sahara Mine,Illinois Carrier Mills, Early Permian Taiyuan Formation, Taiyuan City, Shanxi Province, Chi.Huebei province is said TaiyuanAsselian-early Sakmarian to Formation stages be of the in equivalent Early Per- mian. to the From the late Early Permianto near njing be Chi, approximately said equivalentGaudalupian to age sediments of inmarine inverts. North America based on From the Permian (UpperMillery Autunian) Formation, Autun Assise Basin, de Autun,France Central Late Pennsylvanian coalFormation, balls McLeansboro of Group;Sumner, the Illinois “Berryville,” Mattoon Late Pennsylvanian,nellsville Sandstone, Shade, from Ohio above the Con- Middle Pennsylvanian Carbondale Formation of the Kewanee Group, Sahara Mine,Illinois Carrier Mills, ] ] ] ] ] ] ] ] ] 307 298.9 272.95 307 307 315.2 315.2 298.9 315.2 − − − − − − − − − 307 298.9 307 290.1 259.1 295 298.9 298.9 307 [ [ [ [ [ [ [ [ [ Scolecopteris nigra A Scolecopteris parkerensis L Scolecopteris saharaensis M Scolecopteris shanxiensis Szea sinensis Scolecopteris oliveri O Scolecopteris parvifolia Scolecopteris shadensis Scolecopteris vallumii L S§3. Graphical Models S15

S§3 Graphical Models

The Bayesian total-evidence model includes five separate components: 1) the substitution model; 2) the molecular clock model; 3) the morphological transition model; 4) the morphological clock model, and; 5) the tree model. For each of the first two components, we use only one model. For the remaining components, we perform analyses under several different possible models. We provide graphical model representations for each component in the following sections. We represent our models as directed factor graphs using the TikZ library BayesNet (Dietz and Luttinen 2012). In this representation, free parameters (stochastic nodes) are represented as unfilled circles, data (“clamped” stochastic nodes) are represented as filled circles, and deterministic parameters (deterministic nodes) are represented as dashed circles. Edges represent dependencies between nodes. Black squares are “factors” that express either the probability distribution from which the descending random variable is drawn, or the functional relationship between the input nodes and the descending deterministic node. In each of the following figures, we focus on the parameters that are specific to a particular model component. When a parameter depends on a value from another model component, we include a placeholder node from that model component that is meant to represent the entire module. These placeholder nodes are indicated with labels connected by dashed lines.

S§3.1 Substitution Model S§3.1.1 GTR + I + Γ We assume that each molecular data subset evolves under a GTR+I+Γ model, and that rates vary among the k molecular data partitions according to the vector of relative-rate multipliers, s.

απ αe αp βp min max αs

Dir Dir Beta Unif Dir

π e p αΓ s

Q r molecular clock model

tree Ψ PhyloCTMC model

Si molecular subset i i 1 : k ∈

Figure S1: The GTR+I+Γ substitution model. The parameters are: 1) the stationary frequency, π; 2) the relative exchange- ability rates, e; 3) the proportion of invariable sites, p; 4) the degree of among-site rate variation, αΓ, and; 5) the subset-speciﬁc rate multipliers, s. S§3.2. Molecular Clock Model S16

S§3.2 Molecular Clock Model S§3.2.1 Uncorrelated Lognormal Relaxed Clock We assume the (2n − 2) lineage-speciﬁc rates of molecular evolution are drawn from a lognormal prior. We estimate the hyperparameters of the lognormal distribution from the data.

minr maxr λσ

LogUnif Exp

substitution µr σr Q model

LogNorm tree ri Ψ model i 1 : 2n 2 ∈ − PhyloCTMC

S molecular data

Figure S2: The uncorrelated lognormal (UCLN) relaxed molecular clock model. The parameters are: 1) the average rate of molecular evolution, µr; 2) the degree of variation in rates of molecular evolution, σr, and; 3) the lineage-speciﬁc rates of evolution, ri. S§3.3. Morphological Transition Models S17

S§3.3 Morphological Transition Models S§3.3.1 Mk The Mk model assumes that transitions among states occur at equal rates for the m morphological partitions. We assume that rates vary among morphological data partitions according to the vector of relative-rate multipliers, d. Additionally, we assume that invariant characters are excluded from the dataset (not represented in the graphical model; Lewis 2001).

αd

Dir

Qi d

m morphological PhyloCTMC clock model

morphological tree Di Ψ subset model i 1 : m ∈

Figure S3: The Mk morphological model. The parameters are: 1) the partition-speciﬁc rate of evolution, d.

S§3.3.2 Mk+Γ The Mk+Γ model assumes that transitions among states occur at equal rates for the m morphological partitions. Additionally, we allow relative rates to vary among characters within a given data partition according to a mean-one Gamma distribution. We assume that rates vary among morphological data partitions according to the vector of relative-rate multipliers, d. Additionally, we assume that invariant characters are excluded from the dataset (not represented in the graphical model; Lewis 2001).

lα uα αd

Unif Dir

Qi αi d

m morphological PhyloCTMC clock model

morphological tree Di Ψ subset model i 1 : m ∈

Figure S4: The Mk+Γ morphological model. The parameters are: 1) the partition-speciﬁc rate of evolution, d, and; 2) the degree of rate variation among characters, αi. S§3.3. Morphological Transition Models S18

S§3.3.3 F81 The F81 model assumes that the morphological characters evolve toward a non-uniform stationary distribution, π. We allow the stationary distribution to vary among characters according to a discrete mixture model with k categories. For binary characters, the k categories are deﬁned by a discrete Beta distribution with k bins of equal probability mass. For multistate characters, the k categories are drawn from a shared Dirichlet prior distribution and mixture weights, ω. We assume that rates vary among morphological data partitions according to the vector of relative-rate multipliers, d. Additionally, we assume that invariant characters are excluded from the dataset (not represented in the graphical model; Lewis 2001).

ηm αω

InvExp Dir

π0j γm πij ωi DiscBeta Dir

Q0j Qij αd j 1 : k j 1 : k PhyloCTMC ∈ Dir ∈ PhyloCTMC

D0 d Di binary subset multistate subset i i 1 : m ∈ m Ψ

morphological tree clock model model

Figure S5: The F81 morphological model. The parameters are: 1) the partition-speciﬁc rate of evolution, d; 2) the degree of variation among stationary frequencies, γm; 3) the partition-speciﬁc stationary frequencies, πij, and; 4) the mixture weight of multistate stationary frequencies, ωi. S§3.3. Morphological Transition Models S19

S§3.3.4 F81+Γ The F81 model assumes that the morphological characters evolve toward a non-uniform stationary distribution, π. We allow the stationary distribution to vary among characters according to a discrete mixture model with k categories. For binary characters, the k categories are deﬁned by a discrete Beta distribution with k bins of equal probability mass. For multistate characters, the k categories are drawn from a shared Dirichlet prior distribution and mixture weights, ω. Additionally, we allow relative rates to vary among characters within a given data partition according to a mean-one Gamma distribution. We assume that rates vary among morphological data partitions according to the vector of relative-rate multipliers, d. Additionally, we assume that invariant characters are excluded from the dataset (not represented in the graphical model; Lewis 2001).

lα uα ηm αω lα uα

Unif InvExp Dir Unif

α0 π0j γm πij ωi αi DiscBeta Dir

Q0j Qij αd j 1 : k j 1 : k PhyloCTMC ∈ Dir ∈ PhyloCTMC

D0 d Di binary subset multistate subset i i 1 : m ∈ m Ψ

morphological tree clock model model

Figure S6: The F81+Γ morphological model. The parameters are: 1) the partition-speciﬁc rate of evolution, d; 2) the degree of variation among stationary frequencies, γm; 3) the partition-speciﬁc stationary frequencies, πij; 4) the mixture weight of multistate stationary frequencies, ωi, and; 5) the degree of rate variation among characters, αi. S§3.4. Morphological Clock Models S20

S§3.4 Morphological Clock Models S§3.4.1 Linked The linked morphological clock model assumes that lineage-speciﬁc rates of morphological evolution, m, are proportional to lineage-speciﬁc rates of molecular evolution. The parameter βm describes the relative rate of morphological to molecular evolution.

αm βm

BetaPrime molecular β r m clock model

morphological M βm r transition model × i tree mi Ψ model i 1 : 2n 2 ∈ − PhyloCTMC

D morphological data

Figure S7: The “linked” relaxed morphological model. The parameters are: 1) the relative rate of morphological to molecular evolution, βm, and; 2) the lineage-speciﬁc rate of morphological evolution, mi. S§3.4. Morphological Clock Models S21

S§3.4.2 Unlinked The unlinked morphological clock model assumes that lineage-speciﬁc rates of morphological evolution are drawn from a lognormal prior distribution. The parameter βm describes the relative mean rate of morphological evolution to the mean rate of molecular evolution; the parameter σm describes how much rates of morphological evolution vary among branches.

αm βm

BetaPrime molecular βm µr λm clock model

Exp βm µr ×

σm µm

morphological M LogNorm transition model tree mi Ψ model i 1 : 2n 2 ∈ − PhyloCTMC

D morphological data

Figure S8: The “unlinked” relaxed morphological model. The parameters are: 1) the relative mean rate of morphological to molecular evolution, βm; 2) the degree of variation in lineage-speciﬁc rates of morphological evolution, σm, and; 3) the lineage-speciﬁc rate of morphological evolution, mi. S§3.5. Tree Models S22

S§3.5 Tree Models In all of the following tree models, we assume the process begins with the stem lineage with age o. Additionally, we accommodate uncertainty in the ages of fossil tips by requiring that the age of fossil tip i in the tree Ψ falls within the interval of uncertainty associated with the fossil. This is represented as an indicator function, 1, which has value 1 if the fossil tip is within the boundaries and 0 otherwise.

S§3.5.1 Uniform The uniform tree prior model assumes that the ages of nodes are uniformly distributed sensu Ronquist et al.(2012).

lo uo

Unif

li ui 1

i 1 : n ∈

Figure S9: The uniform tree model. The parameters are: 1) the origin time (stem age) of the tree, o, 2) the phylogeny, Ψ, and; 3) the ages of the tips, ti. S§3.5. Tree Models S23

S§3.5.2 Constant-rate fossilized birth-death The constant-rate fossilized birth-death model assumes that rates of fossilization, speciation, and extinction are constant through time and among lineages, and that extant species are sampled with probability ρ.

lo uo ηλ ηµ ηψ

Unif Exp Exp Exp

o ρ λ µ ψ

CRFBD

li ui 1

i 1 : n ∈

Figure S10: The CRFBD tree model. The parameters are: 1) the origin time (stem age) of the tree, o, 2) the fraction on extant species included in the dataset, ρ; 3) the rate of speciation, λ; 4) the rate of extinction, µ; 5) the rate of fossilization, ψ; 6) the phylogeny, Ψ, and; 7) the ages of the tips, ti. S§3.5. Tree Models S24

S§3.5.3 Episodic fossilized birth-death with variable fossilization rates This episodic fossilized birth-death model assumes that rates of speciation, and extinction are constant through time and among lineages, and that extant species are sampled with probability ρ. However, the fossilization rate is drawn from a mixture distribution with m = 3 categories. The rates and mixture weights of each category are free parameters.

ηψ αψ

Exp Dir Mix sk ωψ lo uo ηλ ηµ k 1 : l Unif Exp Exp ∈

o ρ λ µ ψj

j 1 : m ∈

EFBDψ

li ui 1

i 1 : n ∈

Figure S11: The EFBDψ tree model. The parameters are: 1) the origin time (stem age) of the tree, o, 2) the fraction on extant species included in the dataset, ρ; 3) the rate of speciation, λ; 4) the rate of extinction, µ; 5) the rates of the fossilization-rate mixture model, sk; 6) the weights of the fossilization-rate mixture model, ωψ; 7) the epoch-speciﬁc rates of fossilization, ψi; 8) the phylogeny, Ψ, and; 9) the ages of the tips, ti. S§3.5. Tree Models S25

S§3.5.4 Episodic fossilized birth-death with variable diversiﬁcation rates This episodic fossilized birth-death model assumes that rates of fossilization are constant through time and among lineages, and that extant species are sampled with probability ρ. However, the speciation and extinction rates are drawn from separate mixture distributions with m = 3 categories. The rates and mixture weights of each category are free parameters.

ηλ αλ ηµ αµ

Exp Dir Exp Dir Mix Mix lk ωλ mk ωµ lo uo ηψ k 1 : l k 1 : l Unif Exp ∈ ∈

o ρ ψ λj µj

j 1 : m j 1 : m ∈ ∈

EFBDλ,µ

li ui 1

i 1 : n ∈

Figure S12: The EFBDλ,µ tree model. The parameters are: 1) the origin time (stem age) of the tree, o, 2) the fraction on extant species included in the dataset, ρ; 3) the rates of the speciation-rate mixture model, lk; 4) the weights of the speciation-rate mixture model, ωλ; 5) the epoch-speciﬁc rates of speciation, λi; 6) the rates of the extinction-rate mixture model, mk; 7) the weights of the extinction-rate mixture model, ωµ; 8) the epoch-speciﬁc rates of extinction, µi; 9) the rate of fossilization, ψ; 10) the phylogeny, Ψ, and; 11) the ages of the tips, ti. S§3.5. Tree Models S26

S§3.5.5 Episodic fossilized birth-death with variable diversiﬁcation and fossilization rates This episodic fossilized birth-death model assumes that extant species are sampled with probability ρ. The fossilization, speciation and extinction rates are drawn from separate mixture distributions with m = 3 categories. The rates and mixture weights of each category are free parameters.

ηψ αψ ηλ αλ ηµ αµ

Exp Dir Exp Dir Exp Dir Mix Mix Mix sk ωψ lk ωλ mk ωµ lo uo k 1 : l k 1 : l k 1 : l Unif ∈ ∈ ∈

o ρ ψj λj µj

j 1 : m j 1 : m j 1 : m ∈ ∈ ∈

EFBDλ,µ,ψ

li ui 1

i 1 : n ∈

Figure S13: The EFBDλ,µ,ψ tree model. The parameters are: 1) the origin time (stem age) of the tree, o, 2) the fraction on extant species included in the dataset, ρ; 3) the rates of the speciation-rate mixture model, lk; 4) the weights of the speciation-rate mixture model, ωλ; 5) the epoch-specific rates of speciation, λi; 6) the rates of the extinction-rate mixture model, mk; 7) the weights of the extinction-rate mixture model, ωµ; 8) the epoch-specific rates of extinction, µi; 9) the rates of the fossilization-rate mixture model, sk; 10) the weights of the fossilization-rate mixture model, ωψ; 11) the epoch-specific rates of fossilization, ψi; 12) the phylogeny, Ψ, and; 13) the ages of the tips, ti. S§4. MCMC Analyses S27

S§4 MCMC Analyses

We performed all analyses in RevBayes, compiled from branch ssbdp fix (commit ff39b2). In particular, we modified the episodic fossilized birth-death model (alias dnSSBDP) to use a starting tree, which significantly improves the initialization and convergence of the chain. However, the starting tree may also bias chains toward particular parts of the posterior distribution of trees, which could be an issue if the posterior distribution is rugged and mixing among trees is poor. To overcome this issue, we generated a marginal posterior distribution of trees under the uniform tree model (which does not require a starting tree), then initialized each independent chain under the FBD with a starting tree drawn randomly from the marginal posterior under the uniform model. We refer readers to our Supplemental Archive URL needed for specific details about chain lengths, proposal schemes, and prior specification.

S§4.1 MCMC Diagnosis We diagnosed the convergence and mixing of each MCMC analysis, and ensured that each replicate analysis converged to the same joint posterior distribution. Owing to the large number of analyses, and the complexity of our models, we developed a semi-automated pipeline using custom R scripts (R Core Team 2019). This pipeline is available in our Supplementary Archive URL needed. First, we determined the optimal burnin for each chain according to an ESS criterion. We computed the ESS for each continuous parameter using the R package coda (Plummer et al. 2006). To compute the ESS of the sampled phylogeny, we first computed the Robinson-Foulds and Kuhner-¨ Felsenstein distance from each sampled tree to the maximum clade-credibility (MCC) and maximum a posterior (MAP) tree for the analysis using the R package phangorn (Schliep et al. 2017). We then computed the ESS of these distance scores, as suggested by Warren et al.(2017); these ESS values reflect how well the chain mixes over tree topologies (the RF distance), and the tree topologies and branch lengths (the KF distance). To determine the optimal burnin fraction, we computed the ESS as described above at each burnin fraction from 1% to 95% in increments of 0.1%. For each increment, we computed the harmonic mean ESS among continuous parameters, and chose the burnin that yielded the highest harmonic mean ESS. (We used the harmonic mean as it is more sensitive to low values than the arithimetic mean, and therefore is a better reflection of the worst-behaving parameters in the chain.) Likewise, we found the burnin fraction that yields the highest ESS for the tree distance metrics by computing their harmonic mean. We then used the larger of these two burnin fractions to discard pre-burnin samples (for both the continuous-parameter and tree samples). Note: Unsurprisingly, in all cases the burnin fraction for the tree samples was much larger than for the continuous parameters. We therefore focused our assessment of multichain convergence on the tree samples. Next, we assessed whether replicate chains converged to the same posterior distribution of trees. We used multidimensional scaling (MDS) to create plots of sampled tree space among the post-burnin samples from replicate chains (Hillis et al. 2005; Warren et al. 2017). We computed MDS plots of pairwise Robinson-Foulds and Kuhner-Felsenstein¨ distances within and among chains using the R package smacof (de Leeuw and Mair 2009). We visually assessed whether each chain sampled from the same part of tree space for each metric. If a chain failed to achieve a harmonic-mean average ESS of at least 200, or if MDS plots indicated that some or all of the runs failed to converge, we deemed the run(s) failed and re-ran the analysis (or analyses). We repeated this procedure until we had at least four replicate chains that had sufficient ESS and that demonstrated multichain convergence. We then combined the samples from the four replicate chains for all downstream analyses. S§5. Posterior-Predictive Simulation S28

S§5 Posterior-Predictive Simulation

We used posterior-predictive simulation to assess the adequacy of different models. Owing to the complexity of the morphological mixture model, patterns of missing morphological data, and acqui- sition bias (only sampling variable characters), we could not use existing simulators to perform these analyses. We therefore developed our own simulation protocol, which we provide in our Supplemen- tary Archive. These scripts depend heavily on the R packages ape and phytools (Paradis and Schliep 2018; Revell 2012) for computing conditional likelihoods and simulating characters. A given MCMC sample, i, includes a phylogeny Ψi, a vector of morphological branch rates, mi, and a vector of morphological model parameters, θi. To simulate a new dataset for sample i, we simulate each of the c morphological characters. To simulate character j, we first determine the character- specific rate multiplier (if there is among-character rate variation) and character-specific rate matrix (if there is among-character matrix variation). We denote the conditional probability of character Dj, given that it has character-specific rate rk and character-specific matrix Ql, as P(Dj | rk, Ql, Ψi, θi). We sample a character-specific rate and character-specific matrix from their joint posterior distribution:

P(rk, Ql | Ψ,θi, Dj) ∝ P(Dj | rk, Ql, Ψi, θi)P(rk)P(Ql),

where P(rk) and P(Ql) are the prior probabilities of the character-specific rates and the character- specific matrices. In the among-character rate-variation models that we use (i.e., discretized Gamma models), P(rk) is uniform among rate categories, as each category has equal cumulative probability under the Gamma distribution. The prior probability of the character-specific matrices are determined by the appropriate mixture-weight parameter, ω (as depicted in S5). After sampling the character-specific rate and matrix, we simulate a new character on the tree Ψi with branch-specific rate multipliers mi. We then remove simulated data according to the pattern of missing data for character Dj. If the remaining characters are invariant, we simulate a new character until the character is not invariant. We repeat the above procedure for each character in the morphological matrix. We then compute sim obs the parsimony score for each simulated character, pi,j , and for each observed character, pi,j , given the tree Ψi. We compute the discrepency statistics Si and Vi as:

sim obs Si = ∑ pi,j − pi,j , j and

  2   2 1 2 1 1 2 1  sim − sim  −  obs − obs  Vi =  ∑ pi,j  ∑ pi,j    ∑ pi,j  ∑ pi,j   j j j j j j j j

The statistic Si, the sum of the difference in parsimony score among characters, is intended to capture the ability of the model to describe overall rates of evolution. The statistic Vi, the variance in the difference in parsimony scores among characters, is intended to capture whether the model adequately describes how rates vary among characters. We repeat this procedure for each of r samples from the posterior distribution. For a given posterior distribution, this generates a posterior-predictive distribution of S and V. If these posterior- predictive distributions do not include 0 in their 95% predictive interval, we consider the model to the inadequate (it is unable to describe overall rates of evolution or how rates vary among characters, or both). S§6. Empirical Considerations: Taxon Sample and Rooting Strategies S29

S§6 Empirical Considerations: Taxon Sample and Rooting Strategies

The goal of our study is to estimate the divergence times within our ingroup (the extant and extinct Marattiales). Presumably, this inference depends critically on our ability to identify the position and age of fossil lineages, and especially the position and age of the root (i.e., the node separating the Marattiales and leptosporangiate ferns, assuming that they are inferred to be reciprocally monophyletic). However, our fossil dataset is dominated by a cluster of late Carboniferous taxa whose relationships to each other and to surviving lineages are apt to be highly uncertain, which may limit our ability to infer ancient divergences. Additionally, the inclusion of a sparsely sampled outgroup makes it difﬁcult to specify an appropriate taxon-sampling fraction for the fossilized birth-death models. A speciﬁc set of analyses, described here, were designed to understand the robustness of divergence- time estimates within the Marattiales to these empirical considerations. In all of the analyses that follow, we assume the best-performing morphological transition model, morphological clock model, and tree model, as determined in the main set of analyses.

S§6.1 Ancient plants Our standard dataset includes only our focal taxon (the Marattiales) and its sister group (the leptosporangiate ferns). Consequently, there may only be minimal information available about the age of the root, and whether the ingroup and outgroup are reciprocally monophyletic. In most applications of phylogenetic inference, the monophyly of the ingroup is enforced by the rooting procedure, which is not the case here; instead, inference of the root position comes from the clock and tree models, and small differences in root position can result in fossils switching from one side of the tree to the other. Therefore, including older fossils that are outside of the Marattiales + leptosporangiate clade might have a strong effect on divergence-time estimates, both by imposing stronger constraints on the maximum age, and by helping to inform the position of the ﬁrst split within the Marattiales + leptosporangiates clade (the root in the standard analysis). To investigate this possibility, we conducted analyses with three additional ancient land-plant fossils: 1) Psilophyton crenulatum from the early De- vonian (Doran 1980); 2) Pertica quadrifaria from the early Devonian (Kasper and Andrews 1972), and; 3) Rhacophyton ceratangium from the late Devonian (Cornet et al. 1976; Dittrich et al. 1983.

S§6.2 Polarized rooting A common alternative to using a more inclusive taxon set to identify the root is to specify hard topological constraints: effectively, placing a prior probability of 0 on trees where the ingroup is not monophyletic. However, given potential uncertainty about the topological positions of our fossils, hard topological constraints could be overly informative. We explored a novel strategy to place the root, without adding taxa outside of the Marattiales + leptosporangiates clade, by imposing a priori assumptions about the states of some morphological characters at the root of the tree (effectively “polarizing” the state of the character). For characters that evolve relatively slowly, imposing an assumption on the root state effectively constrains the branches on which the root may be placed. However, this constraint is weaker than a hard topological constraint, as the probabilities of alternative rootings depend on the implied amount of morphological evolution, and no root position is ruled out a priori. In this experiment, we polarized four binary characters based on external information about the state at the root. Speciﬁcally, we polarized three binary characters for which there is good reason to believe the ingroup has a derived state (char. 7: polyarch root stele, absent at the root; char. 21: S§6.3. Ingroup-only S30 phloem maturation, exarch at the root, and; char. 50: sporangia developmentally attached forming synangium, absent at the root), and one binary character that is derived in the outgroup (char. 89: sporangium wall thickness, thick at the root; Rothwell et al. 2018a). We achieved polarization by setting the prior probability of the appropriate state at the root to 1 and the remaining states to 0 (as opposed to using the stationary frequency as the prior probability).

S§6.3 Ingroup-only The fossilized birth-death models require specifying a single taxon-sampling fraction (ρ) that applies across the full tree. However, our standard dataset includes a well-sampled ingroup (the Marat- tiales) and a very sparsely sampled outgroup (the leptosporangiate ferns); the assumption that an extant sample from each lineage has an equal chance of being included in the dataset will be incorrect whether we assume the ingroup sampling fraction (ρ = 27 ÷ 111) or the overall sampling fraction (ρ = 36 ÷ 12000). To understand the impact of the assumed taxon-sampling fraction on estimates of divergence times, we conducted analyses with only ingroup taxa (extant and extinct Marattiaceae). In this case, the ingroup sampling fraction is a realistic representation of the actual extant-taxon sampling scheme, and may provide more reliable estimates of divergence times.

S§6.4 Results The broad pattern and timing of divergences are similar among these experimental analyses. Nev- ertheless, there are some notable trends in the effect of the different approaches on inferred ages of speciﬁc clades. The divergence estimates for older splits are consistently similar in the ancient plants analysis (i.e., adding both character and age data) and the standard analysis (Figs. S49, S50). Con- versely, polarizing characters at the root (i.e., adding character data but not age data directly) resulted in older divergence estimates than all other analyses, for both the deeper divergences and for the crown group (Figs. S49, S50), although the effect was increasingly pronounced for older clades (Fig. S51). The ingroup-only analysis resulted in similar divergence-time estimates to the standard taxon set and to the ancient plants analysis (Fig. S51), even though the ingroup-only analyses were topolog- ically the most distinct (Fig. S49), and support values for the deeper nodes were particularly low. Including an extra set of ancient plant fossils or rooting the tree by polarizing a few characters each resulted in increased support for the ingroup-outgroup split (0.43 and 0.85 posterior probability, respectively, compared to 0.33 with the standard dataset). In other words, as expected, these approaches improved our ability to estimate the location of the root. The polarized analysis also resulted in markedly improved MCMC mixing, but, surprisingly, inferred noticeably older ages for the crown group (Figs. S49, S51), possibly because polarized characters require fewer state changes near the root, leading to lower rates of evolution and therefore older ages near the present. By contrast, the ancient plants dataset resulted in ages that were very consistent with the standard dataset (Fig. S51), suggesting that, in our case at least, the addition of both rooting and age information (via the inclusion of an additional outgroup “layer”) was more effective than adding rooting information alone (via polarizing some characters). The similarity between the age inferences from our ingroup-only analyses and those under the standard dataset (with the ingroup sampling fraction) was encouraging, and suggests that ages estimated from the full dataset under the ingroup sampling fraction are reliable, whereas those under the overall sampling fraction are probably overestimates. However, using only ingroup taxa also lead to increased topological uncertainty near the root of the tree (Fig. S47, S48). More generally, using alternative sampling fractions and taxon sets proved to be an effective means of validating divergence- time estimates, and may be useful for rooting other TED analyses and for evaluating the impact of S§6.4. Results S31 violations to the assumptions of existing incomplete-sampling models. S§7. Extended Results S32

S§7 Extended Results

S§7.1 Ingroup Sampling Fraction

Figure S14: Comparing distributions of molecular trees among model combinations. We compute the Robinson-Foulds distance (RF, a measure of topological distance, top row), the Kuhner-Felsenstein¨ distance (KF, a distance metric that incorporates both topology and branch lengths) between morphological phylograms (“morphograms”, middle row) and chronograms (bottom row). We removed taxa without molecular data before computing distances. We then plot the (square-root transformed) distances in two-dimensional space using multi-dimensional scaling (MDS); each point represents the location of a given sampled tree in tree space according to the distance metric. We color points according to the morpological transition model (column 1), the morphological clock model (column 2), or the tree model (column 3). S§7.1. Ingroup Sampling Fraction S33

Figure S15: Comparing distributions of extinct trees among model combinations. We compute the Robinson-Foulds distance (RF, a measure of topological distance, top row), the Kuhner-Felsenstein¨ distance (KF, a distance metric that incorporates both topology and branch lengths) between morphological phylograms (“morphograms”, middle row) and chronograms (bottom row). We removed extant taxa before computing distances. We then plot the (square-root transformed) distances in two-dimensional space using multi-dimensional scaling (MDS); each point represents the location of a given sampled tree in tree space according to the distance metric. We color points according to the morpological transition model (column 1), the morphological clock model (column 2), or the tree model (column 3). S§7.1. Ingroup Sampling Fraction S34

morphological transition model morphological clock model tree model 100 Mk F81 unlinked linked uniform EFBDλ,µ Mk + Γ F81 + Γ CRFBD EFBDλ,µ,ψ 50 EFBDψ

number of lineaeges number 2

500 400 300 200 100 0 500 400 300 200 100 0 500 400 300 200 100 0 age (Ma) age (Ma) age (Ma)

Figure S16: Comparing lineage-through-time curves among model combinations. Each curve corresponds to the lineage- through-time (LTT) curve for a given model, averaged over the posterior distribution of trees from that model. The curves in each panel are color coded by morphological-transition model (left), morphological-clock model (middle), and tree model (right), respectively. We removed outgroup taxa to emphasize the inﬂuence of model speciﬁcation on age estimates within our ingroup.

morphological transition model morphological clock model tree model Mk unlinked uniform Mk + Γ linked CRFBD 20 F81 EFBDψ F81 + Γ EFBDλ,µ EFBDλ,µ,ψ 10

2 number of lineaeges number

500 400 300 200 100 0 500 400 300 200 100 0 500 400 300 200 100 0 age (Ma) age (Ma) age (Ma)

Figure S17: Comparing lineage-through-time curves of extant taxa among model combinations. Each curve corresponds to the lineage-through-time (LTT) curve of the extant Marattiaceae for a given model, averaged over the posterior distribution of trees from that model. The curves in each panel are color coded by morphological-transition model (left), morphological-clock model (middle), and tree model (right), respectively. We removed outgroup taxa to emphasize the inﬂuence of model speciﬁcation on age estimates within our ingroup. S§7.1. Ingroup Sampling Fraction S35 500

1 400 0.75 Γ +

300 0.5

Mk 0.25 200 posterior probability 0 100 0 500 400 300 F81 200 100 0 500 400 Γ + 300 F81 200 100 0

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Mk Mk + Γ F81

Figure S18: Comparing divergence-time estimates for each clade by morphological transition model. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the transition model on the x-axis against the transition model on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological clock and tree models (linked and EFBDλ,µ, respectively). S§7.1. Ingroup Sampling Fraction S36

0.75 400

0.5 linked 0.25 200 posterior probability 0 0

0 200 400 unlinked

Figure S19: Comparing divergence-time estimates for each clade by morphological clock model. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the clock model on the x-axis against the clock model on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological transition and tree models (F81+Γ and EFBDλ,µ, respectively). S§7.1. Ingroup Sampling Fraction S37 500

1 400 0.75

300 0.5

CRFBD 0.25 200 posterior probability 0 100 0 500 400 ψ 300 EFBD 200 100 0 500 400 µ , λ 300 EFBD 200 100 0 500 400 ψ , µ , λ 300 EFBD 200 100 0

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 uniform CRFBD EFBDψ EFBDλ,µ

Figure S20: Comparing divergence-time estimates for each clade by tree model. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the tree model on the x-axis against the tree model on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological transition and clock models (F81+Γ and linked, respectively). S§7.1. Ingroup Sampling Fraction S38

● Botryopteris tridentata ● Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis ● Grammatopteris freitasii Hymenophyllum holochilum ● Hopetedia praetermissa ● Pekinopteris auriculata 3● Matonia pectinata Dipteris conjugata Diplopterygium glaucum Schizaea elegans Saccoloma inaequale Cyathea multiflora ● Floratheca apokalyptica ● Scolecopteris shadensis ● Araiangium pygmaeum ● Convexocarpus distichus ● Scolecopteris iowensis ● Scolecopteris charma ● Scolecopteris vallumii ● Scolecopteris incisifolia ● Scolecopteris saharaensis ● Scolecopteris minor ● Scolecopteris dispora ● Scolecopteris oliveri ● Scolecopteris alta ● Grandeuryella renaultii ● Scolecopteris parvifolia ● Scolecopteris nigra ● Scolecopteris illinoensis ● Acaulangium bulbaceum ● Scolecopteris parkerensis ● Scolecopteris fragilis ● Scolecopteris mamayi ● Scolecopteris majopsis ● Scolecopteris calicifolia ● Scolecopteris monothrix ● Scolecopteris antarctica ● Scolecopteris shanxiensis ● Scolecopteris latifolia ● Scolecopteris guizhouensis ● Gemellitheca saudica ● Buritiranopteris costata ● Millaya tularosana ● Eoangiopteris goodii 1 ● Danaeopsis fecunda ● Danaeites rigida ● Radstockia kidstonii ● Rothwellopteris pecopteroides 0.75 ● Escapia christensenioides ● Marattiopsis crenulatus ● Marattiopsis asiatica ● Marattiopsis vodrazkae 0.5 ● Marattiopsis anglica 1 ● Marattiopsis patagonica ● ● Marattiaceae indet Vera 2016 Danaea nodosa 0.25 Danaea grandifolia Danaea leprieurii posterior probability Danaea elliptica Marattia douglasii 0 Marattia alata 2 Marattia laxa ● Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea 1: Qasimia schyfsmae Ptisana oreades Ptisana attenuata 2: Marattiopsis aganzhenensis Ptisana mertensiana Ptisana sylvatica 3: Szea sinensis Ptisana pellucida Ptisana squamosa Ptisana melanesica Mi Pe Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Eocene Miocene Cisuralian Furongian Oligocene Paleocene Llandovery

Cm O S Devonian Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S21: The maximum clade credibility tree under the preferred model. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on branches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.1. Ingroup Sampling Fraction S39

● Grammatopteris freitasii ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum 1 Osmunda regalis ● Hymenophyllum holochilum ● Szea sinensis ● Pekinopteris auriculata Matonia pectinata Dipteris conjugata Diplopterygium glaucum Schizaea elegans Cyathea multiflora Saccoloma inaequale ● Danaeopsis fecunda ● Floratheca apokalyptica ● Radstockia kidstonii ● Scolecopteris shanxiensis ● Scolecopteris guizhouensis ● Scolecopteris alta ● Escapia christensenioides ● Danaeites rigida ● Scolecopteris majopsis ● Scolecopteris mamayi ● Scolecopteris calicifolia ● Scolecopteris antarctica ● Araiangium pygmaeum ● Convexocarpus distichus ● Scolecopteris shadensis ● Scolecopteris nigra ● Scolecopteris parvifolia ● Scolecopteris fragilis ● Scolecopteris parkerensis ● Acaulangium bulbaceum ● Scolecopteris illinoensis ● Grandeuryella renaultii ● Scolecopteris oliveri ● Scolecopteris latifolia ● Scolecopteris monothrix ● Scolecopteris iowensis ● Scolecopteris charma ● Eoangiopteris goodii ● Millaya tularosana ● Buritiranopteris costata ● Gemellitheca saudica ● Scolecopteris vallumii ● Scolecopteris incisifolia 1 ● Scolecopteris dispora ● Scolecopteris minor ● Scolecopteris saharaensis ● Qasimia schyfsmae 0.75 ● Rothwellopteris pecopteroides ● Marattiopsis asiatica ● Marattiopsis crenulatus ● Marattiopsis patagonica 0.5 ● Marattiopsis anglica ● Marattiopsis vodrazkae ● Marattiaceae indet Vera 2016 Danaea elliptica 0.25 Danaea leprieurii

posterior probability Danaea nodosa Danaea grandifolia Marattia douglasii 0 Marattia alata 2 Marattia excavata ● Marattia laxa Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium kaulfussii Eupodium laeve Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata 1: Hopetedia praetermissa Ptisana mertensiana Ptisana sylvatica 2: Marattiopsis aganzhenensis Ptisana pellucida Ptisana melanesica Ptisana squamosa Mi Pe Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Eocene Miocene Cisuralian Furongian Oligocene Paleocene Llandovery

Cm O S Devonian Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S22: The 20%-rule consensus tree under the preferred model. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.1. Ingroup Sampling Fraction S40

1200 1000 10000 800 1000 600 100 400

of lineages 200 10 implied number 0 1 0.6 0.4 0.2 0.0

diversification −0.2 0.7 0.6 0.5 0.4 0.3 0.2 sample_times speciation 0.1 0.0 0.35 0.30 0.25 0.20 0.15 0.10 extinction sample_times 0.05 0.00 0.008

0.006

0.004

0.002 sample_times fossilization

0.000 Mi Pe Terr Guad Lower Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Ludlow Eocene Series2 Series3 Miocene Wenlock Lopingian Cisuralian Furongian Oligocene Paleocene Llandovery

Ed Cambrian Ordovician Silurian Devonian Carboniferous Permian Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S23: Diversification through time under the EFBDλ,µ,ψ model. The top panel shows the implied total number of lineages over time (before pruning unsampled lineages). The next four panels correspond to the posterior distribution of epoch-specific net-diversification rates, speciation rates, extinction rates, and fossilization rates, respectively. In the top panel, the dark line represents the posterior median estimate, in the remaining panels it represents the posterior mean estimate. In all cases, and the shaded region corresponds to the 95% credible interval. S§7.1. Ingroup Sampling Fraction S41

3000 CRFBD 2500 10000 2000 1500 100

lineages 1000 number of number 500 0 1 3000 EFBDψ 2500 10000 2000 1500 100

lineages 1000 number of number 500 0 1 3000 EFBDλ,µ 2500 10000 2000 1500 100

lineages 1000 number of number 500 0 1 3000 EFBDλ,µ,ψ 2500 10000 2000 1500 100

lineages 1000 number of number 500 0 1 Mi Pe Fur Terr Cisu Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Eocene Series2 Series3 Miocene

Ed Cm O S D Ca P T J C P N 2.58 66.00 23.03 541.00 485.40 443.80 419.20 358.90 298.90 252.17 201.30 145.00 age (Ma)

Figure S24: Diversity-over-time under each fossilized birth-death model. For each tree model, we draw samples from the posterior distribution and simulate lineages given those parameter values. We plot the median number of lineages at each time point on the absolute scale (orange, left axis) and the log10 scale (orange, right axis). Here, we assume the best morphological transition and clock models (F81+Γ and linked, respectively). S§7.2. Overall Sampling Fraction S42

S§7.2 Overall Sampling Fraction

Figure S25: Comparing distributions of trees among model combinations using the overall sampling fraction. We compute the Robison-Foulds distance (RF, a measure of topological distance, top row), the Kuhner-Felsenstein¨ distance (KF, a distance metric that incorporates both topology and branch lengths between morphological phylograms (“morphograms”, middle row) and chromograms (bottom row). We then plot the (square-root transformed) distances in two-dimensional space using multi-dimensional scaling (MDS); each point represents the location of a given sampled tree in tree space according to the distance metric. We color points according to the tree model (column 1), the morphological matrix model (column 2), or the morphological clock model (column 3). These results assume the ingroup sampling fraction for all of the fossilized birth-death models. S§7.2. Overall Sampling Fraction S43

Figure S26: Comparing distributions of molecular trees among model combinations using the overall sampling fraction. We compute the Robinson-Foulds distance (RF, a measure of topological distance, top row), the Kuhner-Felsenstein¨ distance (KF, a distance metric that incorporates both topology and branch lengths) between morphological phylograms (“morphograms”, middle row) and chronograms (bottom row). We removed taxa without molecular data before computing distances. We then plot the (square-root transformed) distances in two-dimensional space using multi-dimensional scaling (MDS); each point represents the location of a given sampled tree in tree space according to the distance metric. We color points according to the morpological transition model (column 1), the morphological clock model (column 2), or the tree model (column 3). S§7.2. Overall Sampling Fraction S44

Figure S27: Comparing distributions of extinct trees among model combinations using the overall sampling fraction. We compute the Robinson-Foulds distance (RF, a measure of topological distance, top row), the Kuhner-Felsenstein¨ distance (KF, a distance metric that incorporates both topology and branch lengths) between morphological phylograms (“morphograms”, middle row) and chronograms (bottom row). We removed extant taxa before computing distances. We then plot the (square-root transformed) distances in two-dimensional space using multi-dimensional scaling (MDS); each point represents the location of a given sampled tree in tree space according to the distance metric. We color points according to the morpological transition model (column 1), the morphological clock model (column 2), or the tree model (column 3). S§7.2. Overall Sampling Fraction S45

morphological transition model morphological clock model tree model 100 Mk F81 unlinked uniform EFBDλ,µ Mk + Γ F81 + Γ linked CRFBD EFBDλ,µ,ψ 50 EFBDψ

number of lineages number 2

500 400 300 200 100 0 500 400 300 200 100 0 500 400 300 200 100 0 age (Ma) age (Ma) age (Ma)

Figure S28: Average lineage-through-time curves among model combinations using the overall sampling fraction. For each focal model component (morphological transition model, and morphological clock model, and the the tree model, respectively), we compute the LTT curve averaged over the remaining model components, i.e., the average number of branches in the phylogeny at a given time, averaged over all model combinations that share the focal model component. We removed outgroup taxa to emphasize the inﬂuence of model speciﬁcation on age estimates within our ingroup. Left) We compute the average LTT for each of the 40 models (from 2000 sampled trees for each model), then compute the mean of the resulting average LTT among models with the same morphological-transition model. Middle) As in left, but we compute the mean of the average LTT among models with the same morphological clock model. Right) As in left, but we compute the mean of the average LTT among models with the same tree model.

morphological transition model morphological clock model tree model 100 Mk F81 unlinked linked uniform EFBDλ,µ Mk + Γ F81 + Γ CRFBD EFBDλ,µ,ψ 50 EFBDψ

number of lineaeges number 2

500 400 300 200 100 0 500 400 300 200 100 0 500 400 300 200 100 0 age (Ma) age (Ma) age (Ma)

Figure S29: Comparing lineage-through-time curves among model combinations using the overall sampling fraction. Each curve corresponds to the lineage-through-time (LTT) curve of the extant Marattiacaea for a given model, averaged over the posterior distribution of trees from that model. The curves in each panel are color coded by morphological- transition model (left), morphological-clock model (middle), and tree model (right), respectively. We removed outgroup taxa to emphasize the inﬂuence of model speciﬁcation on age estimates within our ingroup. S§7.2. Overall Sampling Fraction S46

morphological transition model morphological clock model tree model Mk unlinked uniform Mk + Γ linked CRFBD 20 F81 EFBDψ F81 + Γ EFBDλ,µ EFBDλ,µ,ψ 10

2 number of lineaeges number

500 400 300 200 100 0 500 400 300 200 100 0 500 400 300 200 100 0 age (Ma) age (Ma) age (Ma)

Figure S30: Comparing lineage-through-time curves of extant taxa among model combinations using the overall sampling fraction. Each curve corresponds to the lineage-through-time (LTT) curve of the extant Marattiacaea for a given model, averaged over the posterior distribution of trees from that model. The curves in each panel are color coded by morphological-transition model (left), morphological-clock model (middle), and tree model (right), respectively. We removed outgroup taxa to emphasize the inﬂuence of model speciﬁcation on age estimates within our ingroup. S§7.2. Overall Sampling Fraction S47 500

1 400 0.75 Γ +

300 0.5

Mk 0.25 200 posterior probability 0 100 0 500 400 300 F81 200 100 0 500 400 Γ + 300 F81 200 100 0

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 Mk Mk + Γ F81

Figure S31: Comparing divergence-time estimates for each clade by morphological transition model using the overall sampling fraction. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the transition model on the x-axis against the transition model on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological clock and tree models (linked and EFBDλ,µ, respectively). S§7.2. Overall Sampling Fraction S48

0.75 400

0.5 linked 0.25 200 posterior probability 0 0

0 200 400 unlinked

Figure S32: Comparing divergence-time estimates for each clade by morphological clock model using the overall sampling fraction. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the clock model on the x-axis against the clock model on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological transition and tree models (F81+Γ and EFBDλ,µ, respectively). S§7.2. Overall Sampling Fraction S49 500

1 400 0.75

300 0.5

CRFBD 0.25 200 posterior probability 0 100 0 500 400 ψ 300 EFBD 200 100 0 500 400 µ , λ 300 EFBD 200 100 0 500 400 ψ , µ , λ 300 EFBD 200 100 0

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 uniform CRFBD EFBDψ EFBDλ,µ

Figure S33: Comparing divergence-time estimates for each clade by tree model using the overall sampling fraction. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the tree model on the x-axis against the tree model on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological transition and clock models (F81+Γ and linked, respectively). S§7.2. Overall Sampling Fraction S50

tree model

uniform CRFBD EFBDψ EFBDλ,µ EFBDλ,µ,ψ 100

S 0

−50

−100 20 transition model clock model Mk F81 linked unlinked + Γ + Γ 10 Mk F81

V 0 * * * *

−10

−20

Figure S34: Comparing model adequacy among model combinations using the overall sampling fraction. Each boxplot represents the posterior-predictive distribution for a given model for a given statistic. The top row of panels correspond to the posterior-predictive distributions of the total parsimony score statistic, S; the bottom row of panels are for the variance in parsimony score statistic, V. Each column of panels corresponds to analyses under a given tree model. Within each panel, boxplots are colored by the morphological matrix model, and regions of the panel are colored according to the morphological clock model. Models that are inadequate at the α = 0.05 level are indicated with an asterisk. S§7.2. Overall Sampling Fraction S51

● Grammatopteris freitasii ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum Osmunda regalis ● Szea sinensis Diplopterygium glaucum ● Pekinopteris auriculata Matonia pectinata 1 Dipteris conjugata ● Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora ● Millaya tularosana ● Eoangiopteris goodii ● Danaeites rigida ● Scolecopteris shanxiensis ● Scolecopteris guizhouensis ● Floratheca apokalyptica ● Convexocarpus distichus ● Scolecopteris nigra ● Scolecopteris parvifolia ● Grandeuryella renaultii ● Escapia christensenioides ● Scolecopteris illinoensis ● Acaulangium bulbaceum ● Scolecopteris alta ● Scolecopteris saharaensis ● Scolecopteris oliveri ● Scolecopteris minor ● Scolecopteris vallumii ● Scolecopteris incisifolia ● Scolecopteris dispora ● Araiangium pygmaeum ● Scolecopteris shadensis ● Scolecopteris charma ● Scolecopteris iowensis ● Danaeopsis fecunda ● Scolecopteris fragilis ● Scolecopteris majopsis ● Scolecopteris mamayi ● Gemellitheca saudica ● Buritiranopteris costata ● Scolecopteris parkerensis ● Scolecopteris antarctica ● Scolecopteris calicifolia ● Scolecopteris monothrix 1 ● Scolecopteris latifolia ● Radstockia kidstonii ● Qasimia schyfsmae ● Rothwellopteris pecopteroides 0.75 ● Marattiopsis patagonica ● Marattiopsis crenulatus ● Marattiopsis asiatica ● Marattiopsis vodrazkae 0.5 ● Marattiopsis anglica ● Marattiopsis aganzhenensis ● Marattiaceae indet Vera 2016 Danaea nodosa 0.25 Danaea grandifolia

posterior probability Danaea leprieurii Danaea elliptica Marattia douglasii 0 Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris tonkinensis Angiopteris boninensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana sylvatica Ptisana mertensiana 1: Hopetedia praetermissa Ptisana pellucida Ptisana squamosa Ptisana melanesica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Eocene Series2 Series3 Miocene Cisuralian Furongian Oligocene Llandovery

Cm O S Devonian Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S35: The maximum clade credibility tree under the preferred model with overall sampling fraction. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.2. Overall Sampling Fraction S52

● Grammatopteris freitasii ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum 1 Osmunda regalis ● Hymenophyllum holochilum ● Szea sinensis ● Pekinopteris auriculata Diplopterygium glaucum Dipteris conjugata Matonia pectinata Schizaea elegans Saccoloma inaequale Cyathea multiflora ● Danaeopsis fecunda ● Escapia christensenioides ● Danaeites rigida ● Radstockia kidstonii ● Scolecopteris guizhouensis ● Scolecopteris majopsis ● Floratheca apokalyptica ● Scolecopteris alta ● Scolecopteris shanxiensis ● Scolecopteris mamayi ● Scolecopteris calicifolia ● Scolecopteris antarctica ● Scolecopteris parvifolia ● Scolecopteris nigra ● Araiangium pygmaeum ● Convexocarpus distichus ● Scolecopteris shadensis ● Scolecopteris oliveri ● Grandeuryella renaultii ● Acaulangium bulbaceum ● Scolecopteris illinoensis ● Scolecopteris parkerensis ● Scolecopteris fragilis ● Scolecopteris latifolia ● Scolecopteris monothrix ● Millaya tularosana ● Eoangiopteris goodii ● Scolecopteris iowensis ● Scolecopteris charma ● Buritiranopteris costata ● Gemellitheca saudica ● Scolecopteris incisifolia ● Scolecopteris vallumii ● Scolecopteris dispora 1 ● Scolecopteris saharaensis ● Scolecopteris minor ● Qasimia schyfsmae ● Rothwellopteris pecopteroides 0.75 ● Marattiopsis asiatica ● Marattiopsis anglica ● Marattiopsis crenulatus ● Marattiopsis patagonica 0.5 ● Marattiaceae indet Vera 2016 ● Marattiopsis vodrazkae ● Marattiopsis aganzhenensis Danaea elliptica 0.25 Danaea leprieurii

posterior probability Danaea nodosa Danaea grandifolia Marattia douglasii 0 Marattia alata Marattia excavata Marattia laxa Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris evecta Angiopteris smithii Eupodium kaulfussii Eupodium laeve Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana melanesica 1: Hopetedia praetermissa Ptisana squamosa Ptisana mertensiana Ptisana pellucida Ptisana sylvatica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Eocene Series2 Series3 Miocene Cisuralian Furongian Oligocene Llandovery

Cm O S Devonian Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S36: The 20%-rule consensus tree under the preferred model with overall sampling fraction. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.3. Ingroup vs. Overall Sampling Fraction S53

S§7.3 Ingroup vs. Overall Sampling Fraction

0.75 400

0.5 outgroup 0.25 200 posterior probability 0 0

0 200 400 ingroup

Figure S37: Comparing divergence-time estimates for each clade by assumed sampling fraction. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the sampling fraction on the x-axis against the sampling fraction on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological transition and clock models and tree model (F81+Γ, linked, EFBDλ,µ respectively). S§7.4. Uniform Tree Model S54

S§7.4 Uniform Tree Model

youngest middle oldest 1.0 0.8 0.6 0.4

relative age relative 0.2 0.0

0 20 40 60 80 100

number of nodes

Figure S38: The uniform tree model is an informative prior on node ages. Here we consider a tree with all extant species for the sake of simplicity, but the logic applies equally to trees with extinct tips. Under the uniform tree model, node ages are drawn from an ordered uniform distribution. Because the ages are ordered, the age of the ith node in a tree with n internal nodes is the ith order statistic a uniform distribution. Assuming the age of the tree is 1 arbitrary time unit, the ith node age is a Beta random variable with α = i and β = n + 1 − i. We show the resulting prior mean (solid lines) and 95% marginal prior interval (dashed lines) for the youngest node, the oldest node, and the middle node as a function of the total number of internal nodes. As the number of nodes increases, the ﬁrst and last nodes are pushed toward the boundaries and have highly constrained (informative) priors. Likewise, the middle node is halfway between the present and the root (/stem) age with increasing prior probability as the number of nodes increases. S§7.4. Uniform Tree Model S55

500

200 100 50

20 10 5 number of lineages number 2 1

1.0 0.8 0.6 0.4 0.2 0.0

relative age

Figure S39: The uniform model is an informative prior on lineage-through-time curves. We simulated trees of extant species under the uniform tree model, and computed the distribution of resulting LTT curves as a function of the number of extant species (lines are prior mean number of lineages, shaded regions are the 95% prior interval). As the number of species grows, the distribution of ages becomes increasingly narrow. S§7.4. Uniform Tree Model S56

uniform EFBDλ,µ fixed FBD (high) CRFBD fixed FBD (low)

5 number of lineages number 2

500 400 300 200 100 0

age (Ma)

Figure S40: The fossilized birth-death model is an informative prior on node ages when hyperparameters are fixed. We estimated the posterior distribution of trees under two constant-rate fossilized birth-death models with fixed hyperparameters: the “low” fixed FBD (λ = 0.001, µ = 0.0009, ψ = 0.0001, yellow LTT curve) and the “high” fixed FBD (λ = 0.5, µ = 0.45, ψ = 0.01, green LTT curve). These parameter values were selected to be arbitrarily high or low to demonstrate the potential informativeness of the FBD with fixed hyperparameters. LTT curves under both models are significantly different from each other and every other model, whereas the LTT curves under both FBD models with estimated hyper- pameters (blue and pink curves) are relatively similar, indicating that with fixed hyperparameters the fossilized birth-death model strongly informs node ages. S§7.4. Uniform Tree Model S57

● Scolecopteris nigra ● Scolecopteris illinoensis ● Scolecopteris parvifolia ● Scolecopteris alta ● Grandeuryella renaultii ● Acaulangium bulbaceum ● Qasimia schyfsmae ● Marattiaceae indet Vera 2016 ● Escapia christensenioides ● Scolecopteris oliveri ● Scolecopteris saharaensis ● Scolecopteris minor ● Scolecopteris dispora ● Scolecopteris vallumii ● Scolecopteris incisifolia ● Scolecopteris antarctica ● Scolecopteris parkerensis ● Scolecopteris fragilis ● Scolecopteris calicifolia ● Scolecopteris monothrix ● Scolecopteris latifolia ● Scolecopteris majopsis ● Scolecopteris mamayi ● Gemellitheca saudica ● Buritiranopteris costata ● Scolecopteris shadensis ● Convexocarpus distichus ● Araiangium pygmaeum ● Scolecopteris iowensis ● Scolecopteris charma ● Floratheca apokalyptica ● Scolecopteris shanxiensis ● Scolecopteris guizhouensis ● Millaya tularosana ● Eoangiopteris goodii ● Radstockia kidstonii ● Danaeites rigida ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum Osmunda regalis ● Grammatopteris freitasii Diplopterygium glaucum ● Szea sinensis Matonia pectinata ● Pekinopteris auriculata Dipteris conjugata Hymenophyllum holochilum 1 ● Hopetedia praetermissa Schizaea elegans Saccoloma inaequale Cyathea multiflora 0.75 ● Danaeopsis fecunda Christensenia aesculifolia ● Marattiopsis aganzhenensis Marattia douglasii 0.5 Marattia alata Marattia laxa Marattia excavata Angiopteris boninensis Angiopteris evecta 0.25 Angiopteris smithii posterior probability Angiopteris lygodiifolia Angiopteris tonkinensis 0 Angiopteris itoi ● Rothwellopteris pecopteroides Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Eupodium laeve Eupodium kaulfussii ● Marattiopsis patagonica ● Marattiopsis crenulatus ● Marattiopsis asiatica ● Marattiopsis anglica ● Marattiopsis vodrazkae Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana sylvatica Ptisana mertensiana Ptisana attenuata Ptisana pellucida Ptisana squamosa Ptisana melanesica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Eocene Series2 Series3 Miocene Cisuralian Furongian

Ed Cm O S D Ca P T Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S41: The maximum clade credibility tree under the uniform tree model. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). Here, we assume the “best” morphological transition and clock models (F81+Γ and linked, respectively). S§7.4. Uniform Tree Model S58

● Araiangium pygmaeum ● Scolecopteris shadensis ● Scolecopteris parvifolia ● Acaulangium bulbaceum ● Qasimia schyfsmae ● Radstockia kidstonii ● Floratheca apokalyptica ● Scolecopteris incisifolia ● Scolecopteris vallumii ● Scolecopteris shanxiensis ● Scolecopteris guizhouensis ● Scolecopteris calicifolia ● Scolecopteris antarctica ● Danaeites rigida ● Convexocarpus distichus ● Scolecopteris fragilis ● Scolecopteris parkerensis ● Scolecopteris illinoensis ● Scolecopteris nigra ● Scolecopteris majopsis ● Scolecopteris mamayi ● Grandeuryella renaultii ● Scolecopteris oliveri ● Millaya tularosana ● Eoangiopteris goodii ● Scolecopteris iowensis ● Scolecopteris charma ● Escapia christensenioides ● Scolecopteris alta ● Scolecopteris monothrix ● Scolecopteris latifolia ● Buritiranopteris costata ● Gemellitheca saudica ● Scolecopteris dispora ● Scolecopteris minor ● Scolecopteris saharaensis ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum Osmunda regalis ● Grammatopteris freitasii Diplopterygium glaucum ● Szea sinensis ● Pekinopteris auriculata Matonia pectinata Dipteris conjugata ● Hopetedia praetermissa Hymenophyllum holochilum 1 Schizaea elegans Saccoloma inaequale Cyathea multiflora ● Marattiaceae indet Vera 2016 0.75 ● Rothwellopteris pecopteroides Danaea nodosa Danaea grandifolia Danaea leprieurii 0.5 Danaea elliptica ● Marattiopsis patagonica ● Marattiopsis crenulatus ● Marattiopsis asiatica 0.25 ● Marattiopsis vodrazkae ● Marattiopsis anglica posterior probability ● Marattiopsis aganzhenensis Marattia douglasii 0 Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia ● Danaeopsis fecunda Angiopteris boninensis Angiopteris smithii Angiopteris evecta Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana melanesica Ptisana squamosa Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Eocene Series2 Series3 Miocene Cisuralian Furongian

Ed Cm O S D Ca P T Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S42: The 20%-rule consensus tree under the uniform tree model. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). Here, we assume the “best” morphological transition and clock models (F81+Γ and linked, respectively). S§7.5. Polarized Analysis S59

S§7.5 Polarized Analysis

● Grammatopteris freitasii ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum Osmunda regalis Matonia pectinata Dipteris conjugata 5 ● Pekinopteris auriculata ● 4 Diplopterygium glaucum ● Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora ● Scolecopteris parvifolia ● Scolecopteris nigra ● Scolecopteris illinoensis ● Acaulangium bulbaceum ● Convexocarpus distichus ● Scolecopteris charma ● Scolecopteris iowensis ● Scolecopteris shadensis ● Araiangium pygmaeum ● Scolecopteris majopsis ● Scolecopteris dispora ● Scolecopteris saharaensis ● Scolecopteris vallumii ● Scolecopteris minor ● Scolecopteris incisifolia ● Scolecopteris fragilis ● Gemellitheca saudica ● Buritiranopteris costata ● Scolecopteris mamayi ● Scolecopteris antarctica ● Scolecopteris calicifolia ● Scolecopteris parkerensis ● Scolecopteris monothrix ● Scolecopteris latifolia ● Scolecopteris oliveri ● Grandeuryella renaultii ● Scolecopteris alta ● Escapia christensenioides ● Scolecopteris shanxiensis ● Millaya tularosana ● Eoangiopteris goodii ● Scolecopteris guizhouensis 1 ● Floratheca apokalyptica ● Danaeites rigida ● Danaeopsis fecunda ● Radstockia kidstonii 0.75 ● Qasimia schyfsmae ● Rothwellopteris3 pecopteroides ● ● Marattiopsis patagonica ● Marattiopsis anglica 0.5 2 ● Marattiaceae indet Vera 2016 ● ● Marattiopsis vodrazkae Danaea nodosa Danaea grandifolia 0.25 Danaea leprieurii

posterior probability Danaea elliptica Marattia douglasii Marattia alata 0 1 Marattia laxa ● Marattia excavata Christensenia aesculifolia Angiopteris tonkinensis Angiopteris boninensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii 1: Marattiopsis aganzhenensis Ptisana purpurascens 2: Marattiopsis asiatica Ptisana fraxinea 3: Marattiopsis crenulatus Ptisana oreades Ptisana attenuata 4: Hopetedia praetermissa Ptisana sylvatica Ptisana pellucida 5: Szea sinensis Ptisana mertensiana Ptisana squamosa Ptisana melanesica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Eocene Series2 Series3 Miocene Cisuralian Furongian Oligocene

Ed Cm O S D Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S43: The maximum clade credibility tree under the preferred model with polarized root. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.5. Polarized Analysis S60

● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum Osmunda regalis ● Grammatopteris freitasii Diplopterygium glaucum ● Szea sinensis ● Pekinopteris auriculata Matonia pectinata 2 Dipteris conjugata ● Hymenophyllum holochilum Schizaea elegans Cyathea multiflora Saccoloma inaequale ● Scolecopteris mamayi ● Scolecopteris antarctica ● Scolecopteris calicifolia ● Scolecopteris majopsis ● Scolecopteris parvifolia ● Escapia christensenioides ● Scolecopteris nigra ● Scolecopteris shadensis ● Scolecopteris alta ● Convexocarpus distichus ● Araiangium pygmaeum ● Danaeopsis fecunda ● Scolecopteris shanxiensis ● Radstockia kidstonii ● Danaeites rigida ● Floratheca apokalyptica ● Scolecopteris guizhouensis ● Scolecopteris fragilis ● Scolecopteris parkerensis ● Acaulangium bulbaceum ● Scolecopteris illinoensis ● Grandeuryella renaultii ● Scolecopteris oliveri ● Scolecopteris latifolia ● Scolecopteris monothrix ● Eoangiopteris goodii ● Millaya tularosana ● Scolecopteris charma ● Scolecopteris iowensis ● Gemellitheca saudica ● Buritiranopteris costata ● Scolecopteris incisifolia ● Scolecopteris vallumii 1 ● Scolecopteris dispora ● Scolecopteris minor ● Scolecopteris saharaensis ● Qasimia schyfsmae 0.75 ● Rothwellopteris pecopteroides ● Marattiopsis anglica ● Marattiopsis crenulatus ● Marattiopsis patagonica 0.5 ● Marattiopsis asiatica ● Marattiaceae indet Vera 2016 ● Marattiopsis vodrazkae Danaea elliptica 0.25 Danaea leprieurii

posterior probability Danaea nodosa Danaea grandifolia Marattia douglasii 0 Marattia alata 1 Marattia laxa ● Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris itoi Angiopteris lygodiifolia Angiopteris evecta Angiopteris smithii Eupodium kaulfussii Eupodium laeve Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata 1: Marattiopsis aganzhenensis Ptisana melanesica 2: Hopetedia praetermissa Ptisana squamosa Ptisana mertensiana Ptisana pellucida Ptisana sylvatica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Eocene Series2 Series3 Miocene Cisuralian Furongian Oligocene

Ed Cm O S D Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S44: The 20%-rule consensus tree under the preferred model with polarized root. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.6. Ancient Plants Analysis S61

S§7.6 Ancient Plants Analysis

● Rhacophyton ceratangium ● Psilophyton crenulatum ● Pertica quadrifaria ● Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis ● Botryopteris tridentata ● 5 Grammatopteris6 freitasii ● ● Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata 4 Schizaea elegans ● Saccoloma inaequale Cyathea multiflora ● Scolecopteris illinoensis ● Acaulangium bulbaceum ● Scolecopteris parvifolia ● Scolecopteris nigra ● Convexocarpus distichus ● Araiangium pygmaeum ● Scolecopteris shadensis ● Scolecopteris iowensis ● Scolecopteris charma ● Scolecopteris saharaensis ● Scolecopteris minor ● Scolecopteris vallumii ● Scolecopteris dispora ● Scolecopteris incisifolia ● Scolecopteris fragilis ● Scolecopteris parkerensis ● Scolecopteris antarctica ● Scolecopteris calicifolia ● Scolecopteris monothrix ● Scolecopteris latifolia ● Scolecopteris mamayi ● Gemellitheca saudica ● Buritiranopteris costata ● Scolecopteris oliveri ● Grandeuryella renaultii ● Scolecopteris alta ● Floratheca apokalyptica ● Scolecopteris majopsis ● Scolecopteris shanxiensis ● Scolecopteris guizhouensis ● Danaeites rigida 1 ● Millaya tularosana ● Eoangiopteris goodii ● Radstockia kidstonii ● Escapia christensenioides 0.75 ● Danaeopsis fecunda ● Marattiopsis crenulatus ● Marattiopsis patagonica ● Marattiopsis vodrazkae ● 0.5 1● 2● Marattiopsis asiatica ● Marattiopsis anglica ● Marattiaceae indet Vera 2016 Danaea nodosa 0.25 Danaea grandifolia Danaea leprieurii

posterior probability 3 ● Danaea elliptica Marattia douglasii 0 Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta 1: Qasimia schyfsmae Eupodium laeve 2: Rothwellopteris pecopteroides Eupodium kaulfussii Ptisana purpurascens 3: Marattiopsis aganzhenensis Ptisana fraxinea 4: Pekinopteris auriculata Ptisana oreades Ptisana mertensiana 5: Szea sinensis Ptisana attenuata Ptisana sylvatica 6: Hopetedia praetermissa Ptisana pellucida Ptisana squamosa Ptisana melanesica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Eocene Series2 Series3 Miocene Cisuralian Furongian Oligocene Llandovery

Ed Cm O S D Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S45: The maximum clade credibility tree under the preferred model with ancient plant fossils. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.6. Ancient Plants Analysis S62

● Rhacophyton ceratangium ● Pertica quadrifaria ● Psilophyton crenulatum ● Grammatopteris freitasii ● Corynepteris involucrata ● Botryopteris tridentata Osmundastrum cinnamomeum 1 Osmunda regalis ● Hymenophyllum holochilum ● Szea sinensis ● Pekinopteris auriculata Matonia pectinata Dipteris conjugata Diplopterygium glaucum Schizaea elegans Saccoloma inaequale Cyathea multiflora ● Scolecopteris nigra ● Araiangium pygmaeum ● Scolecopteris shadensis ● Floratheca apokalyptica ● Scolecopteris shanxiensis ● Radstockia kidstonii ● Escapia christensenioides ● Danaeites rigida ● Convexocarpus distichus ● Danaeopsis fecunda ● Scolecopteris guizhouensis ● Scolecopteris majopsis ● Scolecopteris mamayi ● Scolecopteris parvifolia ● Scolecopteris alta ● Scolecopteris calicifolia ● Scolecopteris antarctica ● Scolecopteris illinoensis ● Acaulangium bulbaceum ● Scolecopteris parkerensis ● Scolecopteris fragilis ● Grandeuryella renaultii ● Scolecopteris oliveri ● Scolecopteris iowensis ● Scolecopteris charma ● Scolecopteris monothrix ● Scolecopteris latifolia ● Millaya tularosana ● Eoangiopteris goodii ● Gemellitheca saudica ● Buritiranopteris costata 1 ● Scolecopteris incisifolia ● Scolecopteris vallumii ● Scolecopteris dispora ● Scolecopteris minor 0.75 ● Scolecopteris saharaensis ● Qasimia schyfsmae ● Rothwellopteris3 pecopteroides ● ● Marattiopsis patagonica 0.5 ● Marattiopsis asiatica ● Marattiopsis anglica ● Marattiaceae indet Vera 2016 ● Marattiopsis vodrazkae 0.25 Danaea leprieurii Danaea elliptica posterior probability Danaea grandifolia Danaea nodosa 0 Marattia douglasii Marattia alata 2 Marattia laxa ● Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea 1: Hopetedia praetermissa Ptisana oreades Ptisana attenuata 2: Marattiopsis aganzhenensis Ptisana melanesica 3: Marattiopsis crenulatus Ptisana squamosa Ptisana mertensiana Ptisana pellucida Ptisana sylvatica Mi Pe Terr Guad Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Eocene Series2 Series3 Miocene Cisuralian Furongian Oligocene Llandovery

Ed Cm O S D Ca P Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S46: The 20%-rule consensus tree under the preferred model with ancient land plant fossils. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.7. Ingroup Analysis S63

S§7.7 Ingroup Analysis

● Scolecopteris alta ● Floratheca apokalyptica ● Scolecopteris charma ● Araiangium pygmaeum ● Scolecopteris iowensis ● Convexocarpus distichus ● Scolecopteris parvifolia ● Scolecopteris nigra ● Scolecopteris illinoensis ● Scolecopteris shadensis ● Acaulangium bulbaceum ● Scolecopteris vallumii ● Scolecopteris incisifolia ● Scolecopteris dispora ● Scolecopteris saharaensis ● Scolecopteris minor ● Scolecopteris parkerensis ● Scolecopteris fragilis ● Scolecopteris antarctica ● Gemellitheca saudica ● Buritiranopteris costata ● Scolecopteris mamayi ● Scolecopteris monothrix ● Scolecopteris latifolia ● Scolecopteris calicifolia ● Scolecopteris shanxiensis ● Scolecopteris majopsis ● Scolecopteris oliveri ● Scolecopteris guizhouensis ● Grandeuryella renaultii ● Radstockia kidstonii ● Danaeites rigida ● Millaya tularosana ● Eoangiopteris3 goodii ● 2 ● Escapia christensenioides ● ● Marattiopsis asiatica ● Marattiopsis patagonica ● Marattiopsis vodrazkae 1 ● 1 ● Marattiaceae indet Vera 2016 ● Marattiopsis anglica ● Danaeopsis fecunda 0.75 ● Marattiopsis aganzhenensis Danaea nodosa Danaea grandifolia 0.5 Danaea leprieurii Danaea elliptica Marattia douglasii 0.25 Marattia alata Marattia laxa posterior probability Marattia excavata Christensenia aesculifolia 0 Angiopteris tonkinensis Angiopteris boninensis Angiopteris evecta Angiopteris lygodiifolia Angiopteris smithii Angiopteris itoi Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades 1: Rothwellopteris pecopteroides Ptisana attenuata Ptisana mertensiana 2: Marattiopsis crenulatus Ptisana sylvatica 3: Qasimia schyfsmae Ptisana pellucida Ptisana squamosa Ptisana melanesica Mi Pe Guad Lower Lower Lower Upper Upper Upper Upper Middle Middle Middle Eocene Miocene Lopingian Cisuralian Oligocene Paleocene

S Devonian Ca Permian Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S47: The maximum clade credibility tree under the preferred model and just ingroup taxa. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on branches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.7. Ingroup Analysis S64

● Floratheca apokalyptica ● Convexocarpus distichus ● Scolecopteris alta ● Radstockia kidstonii ● Qasimia schyfsmae ● Danaeites rigida ● Scolecopteris shanxiensis ● Scolecopteris majopsis ● Scolecopteris guizhouensis ● Araiangium pygmaeum ● Scolecopteris parvifolia ● Rothwellopteris pecopteroides ● Scolecopteris illinoensis ● Scolecopteris nigra ● Scolecopteris charma ● Scolecopteris iowensis ● Grandeuryella renaultii ● Scolecopteris oliveri ● Acaulangium bulbaceum ● Scolecopteris shadensis ● Eoangiopteris goodii ● Millaya tularosana ● Scolecopteris calicifolia ● Scolecopteris antarctica ● Scolecopteris mamayi ● Scolecopteris monothrix ● Scolecopteris latifolia ● Scolecopteris parkerensis ● Scolecopteris fragilis ● Buritiranopteris costata ● Gemellitheca saudica ● Scolecopteris incisifolia ● Scolecopteris vallumii ● Scolecopteris dispora ● Scolecopteris saharaensis ● Scolecopteris minor ● Danaeopsis fecunda ● Escapia christensenioides ● Marattiopsis patagonica 1 ● Marattiopsis asiatica ● Marattiopsis anglica ● Marattiopsis crenulatus 0.75 ● Marattiaceae indet Vera 2016 ● Marattiopsis vodrazkae Danaea leprieurii Danaea elliptica 0.5 Danaea nodosa Danaea grandifolia Christensenia aesculifolia 0.25 1 Marattia douglasii posterior probability ● Marattia alata Marattia laxa 0 Marattia excavata Angiopteris boninensis Angiopteris tonkinensis Angiopteris smithii Angiopteris itoi Angiopteris evecta Angiopteris lygodiifolia Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica 1: Marattiopsis aganzhenensis Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Mi Pe Guad Lower Lower Lower Upper Upper Upper Upper Middle Middle Middle Eocene Miocene Lopingian Cisuralian Oligocene Paleocene

S Devonian Ca Permian Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S48: The 20%-rule consensus tree under the preferred model and just ingroup taxa. Bars correspond to the 95% credible interval of clade ages (for internal nodes) and tip ages (for fossils). Numbers on braches and associated age bars correspond to sampled ancestors (key bottom left). Bars are colored in proportion to the posterior probability of the clade for internal nodes, by the probability that the specimen is not a sampled ancestor for tips, and by the probability that the specimen is a sampled ancestor for sampled ancestors (legend, left). S§7.8. Comparing Empirical Considerations S65

S§7.8 Comparing Empirical Considerations

Figure S49: The impact of empirical considerations on phylogenetic estimates. We compute the RF distances and KF distances between chronograms among our “empirical considerations” analyses and the “standard” dataset under the preferred models (left and middle, respectively). We only compare samples where the ingroup is inferred to be monophyletic, and pruned outgroup taxa before computing pairwise distances. We also computed the LTT curves for the ingroup taxa for the same sets of analyses, again conditioning on the monophyly of the ingroup and pruning outgroup taxa (right). We compare the ages of particular clades in Fig. S51.

morphological transition model morphological clock model tree model empirical considerations 550

● 500

450

● ● ● ● 400 ● ● ● ● ● ● ● ● Marattiales stem Marattiales ●

350 ●

300 250

200

150

● ● ● 100 ● ● ● ● ● ● ● ● ● ● Marattiales crown Marattiales 50

0 JC JC + Γ linked unlinked uniform CRFBD ancient polarized ingroup F81 F81 + Γ EFBDψ EFBDλ,µ EFBDλ,µ,ψ

Figure S50: The impact of modeling and empirical considerations on divergence-time estimates of major clades. We plot the marginal posterior distribution of the age of each node (in rows) as a function of the morphological-transition model (column 1), the morphological clock model (column 2), the tree model (column 3), and the empirical considerations (column 4). White dots are the posterior median ages, and black bars correspond to the 50% (thick) and 95% (narrow) credible intervals. We report means, medians, and 95% CIs in the Supplemental Material (Tables S.3 and S.4) S§7.8. Comparing Empirical Considerations S66

Table S.3: Age of stem Marattiales under various models and empirical consideration.

Dataset Transition model Clock model Tree model Mean Median 95% CI

standard Mk linked EFBDλ,µ 455.79 452.88 [392.17 − 520.74] standard Mk+Γ linked EFBDλ,µ 470.22 470.38 [399.28 − 533.04] standard F81 linked EFBDλ,µ 465.34 465.23 [392.78 − 529.96] standard F81+Γ linked EFBDλ,µ 428.87 427.26 [366.98 − 506.83] standard F81+Γ unlinked EFBDλ,µ 409.14 406.43 [355.79 − 483.87] standard F81+Γ linked uniform 520.74 527.45 [460.15 − 547.77] standard F81+Γ linked CRFBD 441.42 439.69 [391.07 − 505.03] standard F81+Γ linked EFBDψ 457.70 457.03 [395.20 − 523.94] standard F81+Γ linked EFBDλ,µ,ψ 443.84 439.29 [381.55 − 523.05] ancient F81+Γ linked EFBDλ,µ 414.84 413.80 [350.90 − 505.74] polarized F81+Γ linked EFBDλ,µ 455.02 453.48 [383.54 − 530.10]

Table S.4: Age of crown Marattiales under various models and empirical consideration.

Dataset Transition model Clock model Tree model Mean Median 95% CI

standard Mk linked EFBDλ,µ 93.80 85.15 [46.99 − 179.36] standard Mk+Γ linked EFBDλ,µ 110.99 104.39 [54.06 − 186.06] standard F81 linked EFBDλ,µ 107.68 99.48 [54.78 − 181.12] standard F81+Γ linked EFBDλ,µ 83.92 74.74 [46.32 − 169.07] standard F81+Γ unlinked EFBDλ,µ 74.85 69.84 [44.76 − 139.55] standard F81+Γ linked EFBDλ,µ 83.92 74.74 [46.32 − 169.07] standard F81+Γ linked uniform 322.65 313.39 [214.69 − 426.96] standard F81+Γ linked CRFBD 80.95 75.38 [42.91 − 151.43] standard F81+Γ linked EFBDψ 95.91 89.73 [49.67 − 173.27] standard F81+Γ linked EFBDλ,µ,ψ 95.79 84.85 [45.51 − 185.14] ancient F81+Γ linked EFBDλ,µ 85.50 76.21 [37.44 − 173.74] polarized F81+Γ linked EFBDλ,µ 107.97 100.00 [52.31 − 188.56] ingroup F81+Γ linked EFBDλ,µ 79.87 66.51 [45.11 − 168.21] S§7.8. Comparing Empirical Considerations S67 500

1 400 0.75

300 0.5

ancient 0.25 200 posterior probability 0 100 0 500 400 300 ingroup 200 100 0 500 400 300 polarized 200 100 0

0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 standard ancient ingroup

Figure S51: Comparing divergence-time estimates for each clade with different empirical considerations. For each pair of models, we compare the posterior-mean age of each clade with posterior probability > 0.05 under the analysis on the x-axis against the analysis on the y-axis. Each point is divided in half, with the top-left semicircle colored by the posterior probability under the model on the y-axis and the bottom-right semicircle colored by the posterior probability under the model on the x-axis. In these comparisons, we assume the preferred morphological transition and clock models and tree model (F81+Γ, linked, EFBDλ,µ respectively). S§7.8. Comparing Empirical Considerations S68

Table S.5: Delay before appearance of crown Marattiales under various models and empirical considerations. Speciﬁ- cally, we calculate the difference between the age of the MRCA of extant Marattiales (conditional on it being monophyletic, i.e.,, it does not include extinct taxa) and the age of the node from which it descends (the most recent common ancestor with another sample). We do not report this difference under the uniform model because the crown Marattiales never exclude fossils.

Dataset Transition model Clock model Tree model Mean Median 95% CI

standard Mk linked EFBDλ,µ 100.36 106.44 [12.66 − 162.64] standard Mk+Γ linked EFBDλ,µ 81.35 85.14 [5.75 − 148.87] standard F81 linked EFBDλ,µ 86.72 91.56 [10.17 − 151.81] standard F81+Γ linked EFBDλ,µ 111.12 116.35 [18.29 − 169.06] standard F81+Γ unlinked EFBDλ,µ 130.47 134.53 [45.82 − 187.93] standard F81+Γ unlinked EFBDλ,µ 130.47 134.53 [45.82 − 187.93] standard F81+Γ linked EFBDψ 92.81 96.99 [13.93 − 156.50] standard F81+Γ linked CRFBD 105.22 110.37 [27.89 − 159.10] standard F81+Γ linked EFBDλ,µ,ψ 98.02 106.45 [7.38 − 165.26] ancient F81+Γ linked EFBDλ,µ 107.42 114.57 [12.54 − 172.42] polarized F81+Γ linked EFBDλ,µ 87.77 91.49 [8.04 − 157.08] S§7.9. Extant Phylogenies S69

S§7.9 Extant Phylogenies

Osmundastrum cinnamomeum Osmunda regalis Diplopterygium glaucum Matonia pectinata Dipteris conjugata Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora Marattia douglasii Marattia laxa Marattia alata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Eupodium laeve uniform Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Osmundastrum cinnamomeum Osmunda regalis Diplopterygium glaucum Matonia pectinata Dipteris conjugata Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia laxa Marattia alata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve CRFBD Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Osmundastrum cinnamomeum Osmunda regalis Diplopterygium glaucum Matonia pectinata Dipteris conjugata Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora Danaea nodosa Danaea grandifolia

ψ Danaea leprieurii Danaea elliptica Marattia douglasii Marattia laxa Marattia alata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta

EFBD Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Osmundastrum cinnamomeum Osmunda regalis Hymenophyllum holochilum Matonia pectinata Dipteris conjugata Diplopterygium glaucum Schizaea elegans Saccoloma inaequale Cyathea multiflora Danaea nodosa

µ Danaea grandifolia , Danaea leprieurii Danaea elliptica λ Marattia douglasii Marattia laxa Marattia alata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve

EFBD Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Osmundastrum cinnamomeum Osmunda regalis Hymenophyllum holochilum Matonia pectinata Dipteris conjugata Diplopterygium glaucum Schizaea elegans Saccoloma inaequale Cyathea multiflora ψ Danaea nodosa , Danaea grandifolia Danaea leprieurii µ

, Danaea elliptica Marattia douglasii λ 1 Marattia laxa Marattia alata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis 0.75 Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta 0.5 Eupodium laeve Eupodium kaulfussii Ptisana purpurascens EFBD Ptisana fraxinea 0.25 Ptisana oreades Ptisana attenuata posterior probability Ptisana squamosa Ptisana melanesica Ptisana mertensiana 0 Ptisana sylvatica Ptisana pellucida Mi Pe Fur Terr Llan Cisu Oligo Guad Paleo Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Eocene Series2 Series3 Miocene

Ed Cambrian O S Devonian Ca Permian Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S52: The maximum clade credibility trees for extant taxa among tree models. Bars correspond to the 95% credible interval of clade ages. Bars are colored in proportion to the posterior probability of the clade (legend, bottom left). In these comparisons, we assume the preferred morphological transition and clock models (F81+Γ and linked, respectively). S§7.9. Extant Phylogenies S70

Osmundastrum cinnamomeum Osmunda regalis Hymenophyllum holochilum Matonia pectinata Dipteris conjugata Diplopterygium glaucum Schizaea elegans Saccoloma inaequale Cyathea multiflora

µ Danaea nodosa

, Danaea grandifolia Danaea leprieurii λ Danaea elliptica Marattia douglasii Marattia laxa Marattia alata AngiopterisChristensenia boninensis aesculifolia Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii

EFBD Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Osmundastrum cinnamomeum Osmunda regalis Diplopterygium glaucum Matonia pectinata Dipteris conjugata Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia laxa Marattia alata AngiopterisChristensenia boninensis aesculifolia Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve

ancient Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Osmundastrum cinnamomeum Osmunda regalis Diplopterygium glaucum Matonia pectinata Dipteris conjugata Hymenophyllum holochilum Schizaea elegans Saccoloma inaequale Cyathea multiflora Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia laxa Marattia alata AngiopterisChristensenia boninensis aesculifolia Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens

polarized Ptisana fraxinea Ptisana oreades Ptisana attenuata Ptisana squamosa Ptisana melanesica Ptisana mertensiana Ptisana sylvatica Ptisana pellucida Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Christensenia aesculifolia Marattia douglasii Marattia laxa Marattia alata Angiopteris boninensis 1 Angiopteris tonkinensis Angiopteris smithii Angiopteris itoi 0.75 Angiopteris lygodiifolia Angiopteris evecta Eupodium laeve Eupodium kaulfussii 0.5 Ptisana purpurascens Ptisana fraxinea ingroup Ptisana oreades 0.25 Ptisana attenuata Ptisana squamosa posterior probability Ptisana melanesica Ptisana mertensiana 0 Ptisana sylvatica Ptisana pellucida Mi Pe Fur Terr Llan Cisu Oligo Guad Paleo Lower Lower Lower Lower Upper Upper Upper Upper Upper Middle Middle Middle Middle Eocene Series2 Series3 Miocene

Ed Cambrian O S Devonian Ca Permian Triassic Jurassic Cretaceous Pg N 66.0 23.0 2.58 541.0 485.4 443.8 419.2 358.9 298.9 251.9 201.3 145.0 age (Ma)

Figure S53: The maximum clade credibility trees for extant taxa among empirical datasets. Bars correspond to the 95% credible interval of clade ages. Bars are colored in proportion to the posterior probability of the clade (legend, bottom left). In these comparisons, we assume the preferred morphological transition and clock models and tree model (F81+Γ, linked, EFBDλ,µ respectively). S§7.10. Stochastic Maps S71

S§7.10 Stochastic Maps We simulated stochastic maps on maximum clade credibility trees using posterior-mean estimates for all relevant parameters under the preferred models (the F81+Γ morphological-transition model, the linked morphological-clock model, and the EFBDλ,µ tree model). Here, we report stochastic maps for characters of interest (i.e., those that we interpret biologically in the main text) under the ancient plants analyses. We provide the stochastic maps for the remaining characters and for the standard dataset under the preferred model in the Supplemental Archive (DRYAD XXXX). In each of the following stochastic maps, we assign a unique color to each character state. The color at a given time on a given branch is the weighted average of the state-speciﬁc colors, weighted by the posterior probability that the character is in each state. Pie charts at the tips of the tree represent the raw data, not the posterior estimate of the state under the model (i.e., as implied by the stochastic map); pies with multiple colors therefore reﬂect partial or complete missing data. The legend indicates the labels for each state and their associated color, and the axis is the age in millions of years (Ma). S§7.10. Stochastic Maps S72

degree of pinnation

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana once Ptisana attenuata Ptisana sylvatica Ptisana pellucida twice Ptisana squamosa three or more Ptisana melanesica

400 300 200 100 0

Figure S54: Stochastic map for character 23: degree of pinnation. S§7.10. Stochastic Maps S73

foliar abaxial idioblasts

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida absent Ptisana squamosa present Ptisana melanesica

400 300 200 100 0

Figure S55: Stochastic map for character 28: foliar abaxial idioblasts. S§7.10. Stochastic Maps S74

synangial suture between valves

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida deeply cut without central tissue Ptisana squamosa shallow with central tissue Ptisana melanesica

400 300 200 100 0

Figure S56: Stochastic map for character 52: synangial suture between valves. S§7.10. Stochastic Maps S75

number of sporangia per synangium

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens 2 to 5 Ptisana fraxinea Ptisana oreades Ptisana mertensiana 6 to 11 Ptisana attenuata Ptisana sylvatica Ptisana pellucida 12 to 22 Ptisana squamosa more than 22 Ptisana melanesica

400 300 200 100 0

Figure S57: Stochastic map for character 54: number of sporangia per synangium. S§7.10. Stochastic Maps S76

synangium symmetry in x.s.

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana radial Ptisana attenuata Ptisana sylvatica Ptisana pellucida radial and bilateral Ptisana squamosa bilateral Ptisana melanesica

400 300 200 100 0

Figure S58: Stochastic map for character 55: synangium symmetry in x.s. S§7.10. Stochastic Maps S77

'synangium shape in long section pre−dehiscence'

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens cordate Ptisana fraxinea Ptisana oreades Ptisana mertensiana fusiform Ptisana attenuata Ptisana sylvatica Ptisana pellucida oval Ptisana squamosa two crescents Ptisana melanesica

400 300 200 100 0

Figure S59: Stochastic map for character 57: synangium shape in long section pre-dehiscence. S§7.10. Stochastic Maps S78

sporangium or synangium pedicel or receptacle histology

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi vascular Angiopteris smithii Angiopteris evecta vascular and parenchyma Eupodium laeve Eupodium kaulfussii Ptisana purpurascens fiber and parenchyma Ptisana fraxinea Ptisana oreades Ptisana mertensiana parenchyma Ptisana attenuata Ptisana sylvatica Ptisana pellucida fiber Ptisana squamosa transfusion tissue Ptisana melanesica

400 300 200 100 0

Figure S60: Stochastic map for character 58: sporangium or synangium pedicel or receptacle histology. S§7.10. Stochastic Maps S79

sporangium tip extension

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida present Ptisana squamosa absent Ptisana melanesica

400 300 200 100 0

Figure S61: Stochastic map for character 59: sporangium tip extension. S§7.10. Stochastic Maps S80

bilateral synangium dehiscence

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida sporangial rows fused but not opening as two valves Ptisana squamosa sporangial rows opening as two valves Ptisana melanesica

400 300 200 100 0

Figure S62: Stochastic map for character 62: bilateral synangium dehiscence. S§7.10. Stochastic Maps S81

spore ornamentation location

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida perine or perispore Ptisana squamosa exine Ptisana melanesica

400 300 200 100 0

Figure S63: Stochastic map for character 70: spore ornamentation location. S§7.10. Stochastic Maps S82

eusporangium cavity shape

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana cylinder tapering near tip Ptisana attenuata Ptisana sylvatica Ptisana pellucida ovate wider in basal half Ptisana squamosa obovate wider in distal half Ptisana melanesica

400 300 200 100 0

Figure S64: Stochastic map for character 75: eusporangium cavity shape. S§7.10. Stochastic Maps S83

synangium sporangia spread out from center on dehiscence

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida absent Ptisana squamosa present Ptisana melanesica

400 300 200 100 0

Figure S65: Stochastic map for character 77: synangium sporangia spread out from center on dehiscence. S§7.10. Stochastic Maps S84

synangium location on pinnule

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida marginal Ptisana squamosa between margin and midvein Ptisana melanesica

400 300 200 100 0

Figure S66: Stochastic map for character 78: synangium location on pinnule. S§7.10. Stochastic Maps S85

'annulus of thick−walled cells'

Rhacophyton ceratangium Psilophyton crenulatum Pertica quadrifaria Corynepteris involucrata Osmundastrum cinnamomeum Osmunda regalis Botryopteris tridentata Grammatopteris freitasii Hymenophyllum holochilum Diplopterygium glaucum Matonia pectinata Dipteris conjugata Schizaea elegans Saccoloma inaequale Cyathea multiflora Scolecopteris illinoensis Acaulangium bulbaceum Scolecopteris parvifolia Scolecopteris nigra Convexocarpus distichus Araiangium pygmaeum Scolecopteris shadensis Scolecopteris iowensis Scolecopteris charma Scolecopteris saharaensis Scolecopteris minor Scolecopteris vallumii Scolecopteris dispora Scolecopteris incisifolia Scolecopteris fragilis Scolecopteris parkerensis Scolecopteris antarctica Scolecopteris calicifolia Scolecopteris monothrix Scolecopteris latifolia Scolecopteris mamayi Gemellitheca saudica Buritiranopteris costata Scolecopteris oliveri Grandeuryella renaultii Scolecopteris alta Floratheca apokalyptica Scolecopteris majopsis Scolecopteris shanxiensis Scolecopteris guizhouensis Danaeites rigida Millaya tularosana Eoangiopteris goodii Radstockia kidstonii Escapia christensenioides Danaeopsis fecunda Marattiopsis crenulatus Marattiopsis patagonica Marattiopsis vodrazkae Marattiopsis asiatica Marattiopsis anglica Marattiaceae indet Vera 2016 Danaea nodosa Danaea grandifolia Danaea leprieurii Danaea elliptica Marattia douglasii Marattia alata Marattia laxa Marattia excavata Christensenia aesculifolia Angiopteris boninensis Angiopteris tonkinensis Angiopteris lygodiifolia Angiopteris itoi Angiopteris smithii Angiopteris evecta Eupodium laeve Eupodium kaulfussii Ptisana purpurascens Ptisana fraxinea Ptisana oreades Ptisana mertensiana Ptisana attenuata Ptisana sylvatica Ptisana pellucida absent Ptisana squamosa present Ptisana melanesica

400 300 200 100 0

Figure S67: Stochastic map for character 87: annulus of thick-walled cells. S§7.11. Unrooted vs. Rooted Topologies S86

S§7.11 Unrooted vs. Rooted Topologies To understand the discrepancies between the topology we inferred compared to those from previous work, we performed an unrooted phylogenetic analysis using the ancient plants dataset. For these analyses, we assumed the F81+Γ morphological transition model, but used an unrooted tree where where the tree topology was drawn from a uniform prior distribution and molecular branch lengths were drawn from an exponential distribution. To mimic the assumption that rates of morphological and molecular evolution are proportional (as in the ancient plants analysis), we included an additional rate multiplier, βm, that scaled the morphological branch lengths relative to the molecular branch lengths. We then compared the phylogeny tree estimated under the ancient plant analysis to that estimated under this unrooted analysis (Figs. S69, S70) using cophylo from the R package phytools (Revell 2012). S§7.11. Unrooted vs. Rooted Topologies S87

Psilophyton crenulatum Rhacophyton ceratangium ● Pertica quadrifaria Corynepteris involucrata ● Osmundastrum cinnamomeum ● Osmunda regalis ● Botryopteris tridentata ● Diplopterygium glaucum Dipteris conjugata ● ● Pekinopteris auriculata ● Matonia pectinata ● Hymenophyllum holochilum ● Hopetedia praetermissa ● Szea sinensis ● Schizaea elegans ● Grammatopteris freitasii ● Saccoloma inaequale ● Cyathea multiflora Radstockia kidstonii ● Marattiaceae indet Vera 2016 ● Qasimia schyfsmae ● Marattiopsis vodrazkae Marattiopsis anglica ● Marattiopsis crenulatus ● ● Marattiopsis asiatica Marattiopsis patagonica ● Rothwellopteris pecopteroides ● Marattiopsis aganzhenensis ● ● ●Marattia douglasii ●Marattia alata ●Marattia laxa Marattia excavata ● Angiopteris boninensis ● Angiopteris evecta ● ● Angiopteris smithii ● Angiopteris itoi ●Angiopteris tonkinensis ● ● Angiopteris lygodiifolia ● Danaeopsis fecunda Christensenia aesculifolia Danaea nodosa ● ● Danaea grandifolia ● Danaea leprieurii ●Danaea elliptica ● Eupodium laeve ●Eupodium kaulfussii ● Ptisana purpurascens ● ● Ptisana fraxinea ● Ptisana oreades ●Ptisana attenuata ●Ptisana squamosa ●Ptisana pellucida ●Ptisana melanesica ● Ptisana sylvatica Ptisana mertensiana Danaeites rigida ● Eoangiopteris goodii 1 Millaya tularosana ● Scolecopteris guizhouensis ● Floratheca apokalyptica ● Scolecopteris shanxiensis ● ● Scolecopteris alta 0.75 ● Escapia christensenioides ● Scolecopteris majopsis Scolecopteris oliveri ● Grandeuryella renaultii Scolecopteris saharaensis 0.5 ● ● Scolecopteris minor ● Scolecopteris dispora ● Scolecopteris vallumii ● ● Scolecopteris incisifolia Scolecopteris parkerensis 0.25 ● ● Scolecopteris fragilis posterior probability ● ● Scolecopteris calicifolia ● Scolecopteris monothrix ● Scolecopteris antarctica 0 ● Scolecopteris latifolia ● Scolecopteris mamayi ● Gemellitheca saudica ● Buritiranopteris costata Scolecopteris parvifolia ● Scolecopteris nigra ● Scolecopteris shadensis ● Araiangium pygmaeum ● ● Scolecopteris charma ● Scolecopteris iowensis ● Convexocarpus distichus Scolecopteris illinoensis 0.05 ● Acaulangium bulbaceum

Figure S68: The maximum clade credibility tree under the unrooted (non-clock) model. Nodes are colored in proportion to their posterior probability (legend, left). S§7.11. Unrooted vs. Rooted Topologies S88

● Rhacophyton ceratangium Psilophyton crenulatum ● ● Psilophyton crenulatum Rhacophyton ceratangium ● ● Pertica quadrifaria Pertica quadrifaria ● ● Corynepteris involucrata Corynepteris involucrata ● ● Osmundastrum cinnamomeum Osmundastrum cinnamomeum ● ● Osmunda regalis Osmunda regalis ● ● Botryopteris tridentata Botryopteris tridentata ● ● Diplopterygium glaucum Diplopterygium glaucum ● ● Dipteris conjugata Dipteris conjugata ● ● Matonia pectinata Matonia pectinata ● ● Pekinopteris auriculata Pekinopteris auriculata ● ● Saccoloma inaequale Saccoloma inaequale ● ● Cyathea multiflora Cyathea multiflora ● ● Schizaea elegans Schizaea elegans ● ● Szea sinensis Grammatopteris freitasii ● ● Hymenophyllum holochilum Szea sinensis ● ● Hopetedia praetermissa Hymenophyllum holochilum ● ● Grammatopteris freitasii Hopetedia praetermissa ● ● Radstockia kidstonii Radstockia kidstonii ● ● Qasimia schyfsmae Marattiaceae indet Vera 2016 ● ● Rothwellopteris pecopteroides Qasimia schyfsmae ● ● Marattiopsis crenulatus Marattiopsis vodrazkae ● ● Marattiopsis vodrazkae Marattiopsis anglica ● ● Marattiopsis asiatica Marattiopsis crenulatus ● ● Marattiopsis patagonica Marattiopsis asiatica ● ● Marattiopsis anglica Marattiopsis patagonica ● ● Marattiopsis aganzhenensis Rothwellopteris pecopteroides ● ● Marattiaceae indet Vera 2016 Marattiopsis aganzhenensis ● ● Marattia douglasii Marattia douglasii ● ● Marattia alata Marattia alata ● ● Marattia laxa Marattia laxa ● ● Marattia excavata Marattia excavata ● ● Angiopteris boninensis Angiopteris boninensis ● ● Angiopteris evecta Angiopteris evecta ● ● Angiopteris smithii Angiopteris smithii ● ● Angiopteris itoi Angiopteris itoi ● ● Angiopteris lygodiifolia Angiopteris lygodiifolia ● ● Angiopteris tonkinensis Angiopteris tonkinensis ● ● Christensenia aesculifolia Christensenia aesculifolia ● ● Eupodium laeve Danaeopsis fecunda ● ● Eupodium kaulfussii Eupodium laeve ● ● Ptisana purpurascens Eupodium kaulfussii ● ● Ptisana fraxinea Ptisana purpurascens ● ● Ptisana oreades Ptisana fraxinea ● ● Ptisana attenuata Ptisana oreades ● ● Ptisana squamosa Ptisana attenuata ● ● Ptisana melanesica Ptisana squamosa ● ● Ptisana pellucida Ptisana pellucida ● ● Ptisana sylvatica Ptisana melanesica ● ● Ptisana mertensiana Ptisana sylvatica ● ● Danaea nodosa Ptisana mertensiana ● ● Danaea grandifolia Danaea nodosa ● ● Danaea leprieurii Danaea grandifolia ● ● Danaea elliptica Danaea leprieurii ● ● Danaeopsis fecunda Danaea elliptica ● ● Escapia christensenioides Danaeites rigida ● ● Danaeites rigida Eoangiopteris goodii ● ● Eoangiopteris goodii Millaya tularosana ● ● Millaya tularosana Scolecopteris guizhouensis ● ● Scolecopteris guizhouensis Escapia christensenioides ● ● Scolecopteris shanxiensis Scolecopteris alta ● ● Scolecopteris majopsis Scolecopteris shanxiensis ● ● Scolecopteris alta Floratheca apokalyptica ● ● Floratheca apokalyptica Scolecopteris majopsis ● ● Scolecopteris oliveri Scolecopteris oliveri ● ● Grandeuryella renaultii Grandeuryella renaultii ● ● Scolecopteris saharaensis Scolecopteris saharaensis ● ● Scolecopteris minor Scolecopteris minor ● ● Scolecopteris dispora Scolecopteris dispora ● ● Scolecopteris vallumii Scolecopteris vallumii ● ● Scolecopteris incisifolia Scolecopteris incisifolia ● ● Scolecopteris fragilis Scolecopteris fragilis ● ● Scolecopteris parkerensis Scolecopteris parkerensis ● ● Scolecopteris antarctica Scolecopteris calicifolia ● ● Scolecopteris calicifolia Scolecopteris antarctica ● ● Scolecopteris monothrix Scolecopteris monothrix ● ● Scolecopteris latifolia Scolecopteris latifolia ● ● Scolecopteris mamayi Scolecopteris mamayi ● ● Gemellitheca saudica Gemellitheca saudica ● ● Buritiranopteris costata Buritiranopteris costata ● ● Scolecopteris parvifolia Scolecopteris parvifolia ● ● Scolecopteris nigra Scolecopteris nigra ● ● Scolecopteris shadensis Scolecopteris shadensis ● ● Scolecopteris charma Scolecopteris charma ● ● Scolecopteris iowensis Scolecopteris iowensis ● ● Convexocarpus distichus Convexocarpus distichus ● ● Araiangium pygmaeum Araiangium pygmaeum ● ● Acaulangium bulbaceum Acaulangium bulbaceum ● ● Scolecopteris illinoensis Scolecopteris illinoensis ●

Figure S69: Topological conﬂict beween rooted and unrooted MCC trees. We compared the maximum-clade-credibility (MCC) tree under the ancient plant analysis (left) against the MCC tree from the unrooted analysis (right), with branch lengths set arbitrarily to 1. Blue and orange links correspond to extinct and extant taxa, respectively. S§7.11. Unrooted vs. Rooted Topologies S89

● Rhacophyton ceratangium Rhacophyton ceratangium ● ● Psilophyton crenulatum Psilophyton crenulatum ● ● Pertica quadrifaria Pertica quadrifaria ● ● Scolecopteris vallumii Scolecopteris guizhouensis ● ● Scolecopteris parkerensis Convexocarpus distichus ● ● Scolecopteris guizhouensis Danaeites rigida ● ● Scolecopteris shanxiensis Millaya tularosana ● ● Scolecopteris majopsis Eoangiopteris goodii ● ● Scolecopteris oliveri Scolecopteris dispora ● ● Scolecopteris incisifolia Scolecopteris incisifolia ● ● Scolecopteris latifolia Scolecopteris vallumii ● ● Scolecopteris monothrix Scolecopteris mamayi ● ● Scolecopteris calicifolia Scolecopteris antarctica ● ● Scolecopteris fragilis Scolecopteris monothrix ● ● Scolecopteris mamayi Scolecopteris latifolia ● ● Scolecopteris antarctica Scolecopteris calicifolia ● ● Scolecopteris illinoensis Scolecopteris parkerensis ● ● Acaulangium bulbaceum Acaulangium bulbaceum ● ● Scolecopteris shadensis Scolecopteris illinoensis ● ● Scolecopteris charma Scolecopteris parvifolia ● ● Scolecopteris iowensis Scolecopteris nigra ● ● Scolecopteris nigra Scolecopteris iowensis ● ● Danaeites rigida Scolecopteris shadensis ● ● Araiangium pygmaeum Araiangium pygmaeum ● ● Scolecopteris parvifolia Scolecopteris charma ● ● Scolecopteris dispora Scolecopteris fragilis ● ● Scolecopteris alta Scolecopteris oliveri ● ● Floratheca apokalyptica Grandeuryella renaultii ● ● Convexocarpus distichus Floratheca apokalyptica ● ● Grandeuryella renaultii Scolecopteris shanxiensis ● ● Millaya tularosana Radstockia kidstonii ● ● Eoangiopteris goodii Scolecopteris majopsis ● ● Escapia christensenioides Scolecopteris alta ● ● Danaeopsis fecunda Escapia christensenioides ● ● Rothwellopteris pecopteroides Scolecopteris minor ● ● Qasimia schyfsmae Scolecopteris saharaensis ● ● Radstockia kidstonii Gemellitheca saudica ● ● Gemellitheca saudica Buritiranopteris costata ● ● Buritiranopteris costata Qasimia schyfsmae ● ● Scolecopteris minor Rothwellopteris pecopteroides ● ● Scolecopteris saharaensis Marattiopsis aganzhenensis ● ● Marattiaceae indet Vera 2016 Marattiopsis anglica ● ● Marattiopsis patagonica Marattiopsis asiatica ● ● Marattiopsis crenulatus Marattiopsis vodrazkae ● ● Marattiopsis anglica Marattiopsis crenulatus ● ● Marattiopsis asiatica Marattiopsis patagonica ● ● Marattiopsis vodrazkae Marattiaceae indet Vera 2016 ● ● Marattiopsis aganzhenensis Eupodium kaulfussii ● ● Danaea leprieurii Eupodium laeve ● ● Danaea elliptica Danaea leprieurii ● ● Danaea nodosa Danaea elliptica ● ● Danaea grandifolia Danaea nodosa ● ● Marattia douglasii Danaea grandifolia ● ● Marattia alata Marattia douglasii ● ● Marattia excavata Marattia alata ● ● Marattia laxa Marattia excavata ● ● Christensenia aesculifolia Marattia laxa ● ● Angiopteris boninensis Danaeopsis fecunda ● ● Angiopteris lygodiifolia Christensenia aesculifolia ● ● Angiopteris itoi Angiopteris boninensis ● ● Angiopteris tonkinensis Angiopteris lygodiifolia ● ● Angiopteris smithii Angiopteris itoi ● ● Angiopteris evecta Angiopteris smithii ● ● Eupodium kaulfussii Angiopteris tonkinensis ● ● Eupodium laeve Angiopteris evecta ● ● Ptisana purpurascens Ptisana purpurascens ● ● Ptisana fraxinea Ptisana fraxinea ● ● Ptisana oreades Ptisana oreades ● ● Ptisana attenuata Ptisana attenuata ● ● Ptisana pellucida Ptisana sylvatica ● ● Ptisana sylvatica Ptisana pellucida ● ● Ptisana mertensiana Ptisana mertensiana ● ● Ptisana melanesica Ptisana melanesica ● ● Ptisana squamosa Ptisana squamosa ● ● Corynepteris involucrata Corynepteris involucrata ● ● Osmundastrum cinnamomeum Osmundastrum cinnamomeum ● ● Osmunda regalis Osmunda regalis ● ● Botryopteris tridentata Botryopteris tridentata ● ● Diplopterygium glaucum Diplopterygium glaucum ● ● Pekinopteris auriculata Szea sinensis ● ● Szea sinensis Matonia pectinata ● ● Hopetedia praetermissa Dipteris conjugata ● ● Hymenophyllum holochilum Hopetedia praetermissa ● ● Matonia pectinata Hymenophyllum holochilum ● ● Dipteris conjugata Pekinopteris auriculata ● ● Schizaea elegans Schizaea elegans ● ● Saccoloma inaequale Grammatopteris freitasii ● ● Cyathea multiflora Saccoloma inaequale ● ● Grammatopteris freitasii Cyathea multiflora ●

Figure S70: Topological conﬂict beween rooted and unrooted MRC trees. We compared the majority-rule consensus (MRC) tree under the ancient plant analysis (left) against the MRC tree from the unrooted analysis (right), with branch lengths set arbitrarily to 1. Blue and orange links correspond to extinct and extant taxa, respectively. S§8. Model Adequacy for Relaxed Clocks S90

S§8 Model Adequacy for Relaxed Clocks

In the main text, we propose that the discrepancy between morphograms under the linked and unlinked morphological clocks, combined with the similar posterior-predictive simulations under these models, indicates that the unlinked model is overparameterized. Here, we elaborate on this argument. We identify three possible explanations for the discrepancy between morphograms that we ob- serve between the linked and unlinked clocks. One possibility is that the linked model is better, but there is not enough information in the morphological data to estimate the rates under the unlinked model. As a result, the morphograms under the unlinked model do not collapse to those under the linked model. We refer to this as the “prior sensitivity” hypothesis: the morphological data are unable to update the prior morphological branch rates under the unlinked model sufficiently to match the branch rates under the linked model. Another possibility is that the unlinked model is better, and there is sufficient information for the unlinked morphograms to diverge from the linked morphograms. A final possibility is that the linked model is correct, but the unlinked model is fitting noise in the rates of morphological evolution. Under the unlinked model, branches with evidence for implied morphological transition events may be inferred to have a high rate and those without evidence for such events will be inferred to have a low rate, even if the true rates of those events are proportional to rates of molecular evolution. We refer to this as the “overfitting” hypothesis, because the patterns of molecular and morphological transitions only appear different because of stochastic noise.

Figure S71: Comparing distributions of morphograms with different taxon sets. We compute the Kuhner-Felsenstein¨ distance on the morphograms with absolute branch lengths (top row) and relative branch lengths (morphograms scaled to have a mean branch length of 1, bottom row). We show the KF distances for full trees (left column), for trees after pruning taxa without molecular data (all extant taxa, and Marattia excavata), and for trees after pruning extant taxa (right column). We color points according to the morphological morphological clock model, though we include models with all combinations of morphological transition and tree models (as in our other MDS plots). S§8. Model Adequacy for Relaxed Clocks S91

Each of these hypotheses makes predictions about distributions of morphograms as demonstrated by MDS plots, and also about posterior-predictive distributions. The prior sensitivity hypothesis predicts that differences in morphograms between the two models should be similar for fossil and extant groups and that PPS distributions would be wider for the unlinked model. However, while the disparity among morphograms is unchanged when we prune taxa without molecular data (extinct taxa and the extant Marattia excavata) from the posterior distribution of trees (Fig. S71, column 2), the disparity changes when we prune extant taxa (Fig. S71, column 3). In particular, there is much less separation between morphogram distributions for extinct taxa: distributions of trees measured by absolute KF distance (with branch lengths unchanged) are broadly overlapping, while those measured by relative KF distance (with branch lengths rescaled to have a mean of 1) indicate that the linked morphograms are more clustered than the unlinked morphograms. These contrasting patterns indicate that the overall rate of evolution on the extinct tree is not sensitive to the morphological clock prior (presumably because the molecular data do not provide information about the rates of evolution in this part of the tree), but that inferred patterns of variation in lineage-specific rates of morphological evolution are prior sensitive (i.e., under the linked model, because the molecular data in other parts of the tree inform global patterns of rate variation). Nonetheless, the stark difference in KF distributions for extant and extinct taxa suggests that prior sensitivty is not the the main factor driving differences in morphogram distributions. Additionally, the posterior-predictive distributions for the unlinked model are not apparently wider than for the linked model; while the widths of these distributions are relatively noisy (owing to the fact that we simulated 1000 posterior-predictive replicates), there is no apparent pattern that these distributions are wider under unlinked model. We conclude that discrepencies among morphograms under the clock models are not a result of prior sensitivity. Both the improved fit and overfit hypotheses would predict strong departures in the morphograms for clades with both molecular and morphological data, because that is where differences in molecular and morphological rates would be most evident (whether or not the differences are statistically

S statistic width V statistic width

125 uniform 14.5 CRFBD 120 EFBDψ 14.0 EFBDλ,µ EFBDλ µ ψ 115 , , 13.5

110 13.0

105 12.5 ● ● unlinked model unlinked 100 12.0 ● ● ● Mk ● ● 95 ● Mk + Γ 11.5 F81 ● ● 90 F81 + Γ 11.0 ●

90 95 100 110 120 11.0 12.0 13.0 14.0 linked model linked model

Figure S72: Widths of posterior-predictive distributions between linked and unlinked morphological clock models. We compute the width of the 95% predictive interval of the posterior-predictive distribution for each model combination for the S and V statistics. We plot the width between models that differ by the morphological clock model; the color and shape of points are determined by the tree model and morphological transition model, respectively. S§8. Model Adequacy for Relaxed Clocks S92 real). Indeed, this appears to be the case: as described above, the discrepency between morphograms are markedly different for trees with extinct and extant taxa pruned out (Fig. S71, middle and right columns, respectively). This phenomenon is also apparent from LLT plots, which demonstrate that ages are most different for young clades, presumably because they include taxa with both molecular and sequence data (Fig. S16). However, the improved fit hypothesis predicts that the linked model would be unable to simulate realistic datasets. This does not appear to be the case: the posterior- predictive distributions of models with the linked morphological clock are nearly the same as those with the unlinked model. This suggests the unlinked model is overfitting—that whatever (implied) events are making the morphograms depart under the unlinked model can still be adequately accom- modated by the linked model. We therefore prefer the linked model to the unlinked model. We note that the morphological clock models we used—linked and unlinked—result in different likelihood functions and therefore can, in principle, be distinguished from each other by model adequacy. However, the linked and unlinked models are both individually un- or semi-identifiable. As with the tree models, two different linked models that differ by their prior distributions may be indis- tinguishable by model adequacy (and likewise for two different unlinked models). We therefore do not advocate comparing two different morphological clock models of the same type but with different priors using posterior-predictive simulation (though see Ducheneˆ et al. 2015 for a solution when the tree is fixed). References

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