Supplemental Material for: Inferring the Total-Evidence Timescale of Marattialean Fern Evolution in the Face of Extreme Model Sensitivity Contents Sx1Morphological Data S6 Sx2Accessions S9 Sx3Graphical Models S15 Sx3.1Substitution Model . S15 Sx3.2Molecular Clock Model . S16 Sx3.3Morphological Transition Models . S17 Sx3.4Morphological Clock Models . S20 Sx3.5Tree Models . S22 Sx4MCMC Analyses S27 Sx4.1MCMC Diagnosis . S27 Sx5Posterior-Predictive Simulation S28 Sx6Empirical Considerations: Taxon Sample and Rooting Strategies S29 Sx6.1Ancient plants . S29 Sx6.2Polarized rooting . S29 Sx6.3Ingroup-only . S30 Sx6.4Results . S30 Sx7Extended Results S32 Sx7.1Ingroup Sampling Fraction . S32 Sx7.2Overall Sampling Fraction . S42 Sx7.3Ingroup vs. Overall Sampling Fraction . S53 Sx7.4Uniform Tree Model . S54 Sx7.5Polarized Analysis . S59 Sx7.6Ancient Plants Analysis . S61 Sx7.7Ingroup Analysis . S63 Sx7.8Comparing Empirical Considerations . S65 S1 Contents S2 Sx7.9Extant Phylogenies . S69 Sx7.10StochasticMaps . S71 Sx7.11Unrooted vs. Rooted Topologies . S86 Sx8Model Adequacy for Relaxed Clocks S90 List of Figures S1 The GTR+I+G substitution model . S15 S2 The uncorrelated lognormal (UCLN) relaxed molecular clock model . S16 S3 The Mk morphological model . S17 S4 The Mk+G morphological model . S17 S5 The F81 morphological model . S18 S6 The F81+G 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 EFBDy tree model . S24 S12 The EFBDl,m tree model . S25 S13 The EFBDl,m,y 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 EFBDl,m,y model . S40 S24 Diversity through time under each fossilized birth-death model . S41 S25 Comparing distributions of trees among model combinations using the overall sam- pling fraction . S42 S26 Comparing distributions of molecular trees among model combinations using the over- all 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 us- ing 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 hyperpa- rameters 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 consid- erations” 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 morphologi- cal 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 consider- ations . 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 de- hiscence . 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 morpholog- ical clock models . S91 Sx1. Morphological Data S6 Sx1 Morphological Data Our morphological dataset was largely derived from Rothwell et al.(2018b), which itself relied heav- ily on Hill and Camus(1986) and Murdock(2008), and amended as necessary (see S x1). 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 primar- ily focused on the leptosporangiate ferns (our outgroup), e.g., the presence of linear aerophores (Sx1 character 27) and morphology and variation within leptosporangia (Sx1 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.