1 Supplementary Appendix S1 2 Methods for estimating new time-calibrated phylogenies 3 i) Emydid turtles 4 To estimate a time-calibrated phylogeny for emydid turtles, we used the data set 5 of six combined nuclear genes (ETS, GAPD, NGFB, ODC, R35, Vimentin) from Wiens 6 et al. (2010). Although not all genes have data for all species, these combined data 7 nevertheless yield a generally well-supported phylogeny, with seemingly little impact of 8 missing data (Wiens et al. 2010; Wiens & Morrill 2011). We did not include the 9 mitochondrial genes, as they appear to seriously distort branch lengths in some emydid 10 11 groups (Wiens et al. 2010). The phylogeny was estimated using the Bayesian uncorrelated lognormal 12 approach (Drummond et al. 2006) in BEAST version 1.5.4 (Drummond & Rambaut 13 2007). We used substitution models with parameters estimated separately for each gene 14 but with a tree model and clock model shared among genes. We used the following 15 general substitution models for each gene, as estimated by Wiens et al. (2010): HKY+ 16 gamma (GAPD, NGFB, ODC, R35), and GTR + gamma (ETS, Vim). We used 17 estimated base frequencies and used four-rate categories for gamma. We used a relaxed, 18 uncorrelated, clock model with an estimated clock rate and randomly generated trees with 19 a Yule speciation tree prior. 20 We used two fossil calibration points. First, the oldest described emydid species 21 is Chrysemys antiqua (Hutchinson 1996), from the Chadronian (minimum age 33.9 22 million years ago, based on the Paleobiology Database). Joyce & Bell (2004) showed 23 that characters used to assign this species to Chrysemys are plesiomorphic for Emydidae 24 or Deirocheylinae. We therefore used this fossil to merely constrain the minimum age of 25 the emydid crown group (the age of the split between Emydinae and Deirocheylinae). 26 For this clade, we used a lognormal distribution with an offset of 33.9 Myr, a mean of 5.0 27 Myr, and a standard deviation of 1.0. The mean and standard deviation were selected to 28 reflect that emydids are at least as old as this fossil, are most likely similar in age to this 29 fossil, but might be considerably older. The 95% highest probability density limits were 30 34.49–49.61 Mya. 31 The second calibration point involves the minimum age of the split between Emys 32 and its sister group (Emydoidea). According to Lenk et al. (1999), the earliest appearance 33 of Emys in the fossil record is 12 Myr ago. We used this fossil to constrain the minimum 34 age of this split. We used a lognormal distribution with an offset of 12.0 Myr, a mean of 35 5.0 Myr, and a standard deviation of 1.0. The mean and standard deviation were selected 36 to reflect that the clade is at least as old as this fossil, but might also be considerably 37 older. The 95% highest probability density limits were 12.59–27.71 Mya. 38 We performed two replicate analyses of 20 million generations each, sampling 39 every 1,000 generations. These analyses yielded very similar likelihood values, identical 40 majority-rule topologies, and mean estimated dates for all clades within ~1 Myr of each 41 other. We therefore combined the results of these two analyses using LogCombiner in 42 the BEAST package. Using Tracer (also in the BEAST package), we identified the first 2 43 million generations as burnin. We then combined results from the subsequent 44 generations of each analysis. The combined results had an effective sample size (ESS) > 45 1,000 for all estimated dates and other parameters. The estimated tree was based on the 46 tree with the highest clade credibility and ages were estimated based on mean ages across 47 the postburnin trees. 48 The estimated phylogeny (including posterior probabilities of clades) is shown in 49 Fig. S1, and mean estimated divergence dates are shown in Fig. S2. In general, the 50 estimated tree is strongly supported and similar to other recent estimates (e.g. Wiens et 51 al. 2010). 52 53 54 ii) New World ranid frogs Wiens et al. (2009) estimated an extensive time-calibrated phylogeny for ranid 55 frogs, but this phylogeny lacked many New World species. However, a relatively 56 comprehensive phylogeny of New World species was provided by Pyron & Wiens 57 (2011). We therefore took the data from Pyron & Wiens (2011) and estimated a time- 58 calibrated phylogeny for the New World ranid species. 59 We first reduced the matrix of Pyron & Wiens (2011) to include only the 48 60 sampled New World species. These species do not form a monophyletic group, but 61 belong to two closely related clades (which can therefore serve as outgroups to each 62 other). The data set of Pyron & Wiens (2011) includes 12 nuclear and mitochondrial 63 genes. We deleted 4 nuclear genes that lacked sequences for any of these taxa (CXCR4, 64 NCX1, POMC, SCL8A3), which left 3 mitochondrial genes (12S, 16S, cytb) and 5 65 nuclear genes (H3A, RAG1, Rhod, SIA, Tyrosinase). However, not all genes were 66 sampled for all species (although most taxa were sampled for 12S and 16S), and all 67 nuclear genes were present in only a subset of species. 68 The phylogeny was estimated using the Bayesian uncorrelated lognormal 69 approach (Drummond et al. 2006) implemented in BEAST version 1.5.4 (Drummond & 70 Rambaut 2007). We used separate substitution models for each gene and partition, but 71 with a tree model and clock model shared among genes. Following Pyron & Wiens 72 (2011), we used the GTR+I+gamma for all genes and partitions, with separate partitions 73 for stems and loops in 12S, separate stem and loop partitions in 16S, and separate 74 partitions for genes and codons in the protein-coding genes. We used estimated base 75 frequencies and used four-rate categories for gamma. We used a relaxed, uncorrelated, 76 clock model with an estimated clock rate and randomly generated trees with a Yule 77 speciation tree prior. Wiens et al. (2009) estimated common ancestor of clade of North 78 America species at 34.14 Myr, based on analyses using BEAST. We used this date as a 79 secondary calibration point, with normal distribution and standard deviation of 1 (95% 80 prior distribution: 32.5--35.8 Myr). Analyses were run for 20 million generations, 81 sampling every 1000 generations 82 Initial analyses yielded trees with higher-level relationships that were somewhat 83 inconsistent with those of Pyron & Wiens (2011) and Wiens et al. (2009). We therefore 84 performed analyses with the following clades constrained to be monophyletic: (1) boylii 85 group, (2) all New World Rana excluding the boylii group, (3) the clade of the catesbiana 86 group + R. sylvatica, (4) palmipes group + tarahumarae group+ leopard frog clade 87 (Nenirana, Scurillirana, Stertirana), (5) palmipes group + tarahumarae groups, and (6) 88 the leopard frog clade. 89 Given these constraints, we then performed two analyses of 20 million 90 generations each. Using Tracer (the BEAST package), we identified the first 2 million 91 generations of each analysis as burnin, and excluded these results. The two analyses 92 yielded similar trees and clade ages. We then combined the estimated post-burnin trees 93 and parameters using LogCombiner in the BEAST package. Using Tracer in the BEAST 94 package, we found the combined results yielded an effective sample size >200 on all ages 95 and parameters. The estimated tree was based on the tree with the highest clade 96 credibility and ages were estimated based on mean ages across the postburnin trees. 97 The final estimated tree was similar to that from Wiens et al. (2009), Pyron & 98 Wiens (2011), and earlier studies, and was generally strongly supported. The estimated 99 tree, including posterior probabilities of clades and mean estimated divergence times is 100 shown in Fig. S3. 101 102 Additional references (not in main text). 103 Drummond, A.J. & Rambaut, A. (2007). BEAST: Bayesian evolutionary analysis by 104 105 106 107 sampling trees. BMC Evol. Biol., 7, 214. Drummond, A.J., Ho, S.Y.W., Phillips, M.J., & Rambaut, A. (2006). Relaxed phylogenetics and dating with confidence. 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