**RAxML Trees:**
The best tree (with bootstrap support) and the set of 100 bootstrap trees (with branch lengths are provided) are provided as separate files.
RAxML methods:
We performed concatenated maximum likelihood phylogenetic analyses using RAxML v8.2 (Stamatakis, 2014) on the Cyberinfrastructure for Phylogenetic Research (CIPRES) Science Gateway (Miller et al., 2010). We chose RAxML for all ML analyses because RaxML was found to obtain better results than IQ-TREE (Nguyen et al., 2015) for phylogenomic datasets containing >200 taxa (Zhou et al., 2018). We conducted 25 alternate runs on distinct starting trees to find the best-scoring ML tree, using the GTR+CAT model (general-time-reversible model with the CAT approximation of the gamma distribution of rates among sites).
We performed partitioned rapid bootstrapping analyses to obtain 100 bootstrap trees with branch lengths (option -k) using RAxML v8.2. This type of bootstrapping analysis requires a parameter optimization under GAMMA at the end of each replicate, which increases run times. However, the estimated branch lengths were necessary to generate a set of 100 time-calibrated trees for use in comparative analyses (see below).
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**TreePL Trees**
The time-calibrated best RAxML tree is provided, and is annotated with dating confidence intervals from the 100 bootstrap time trees. The set of 100 time-calibrated RAxML bootstrap trees is also provided as a file.
TreePL methods:
We conducted divergence-time estimation using penalized likelihood (Sanderson, 2001) implemented with treePL (Smith and O’Meara, 2012). This method is widely used for dating phylogenies that have very large numbers of species. We removed non-amphibian outgroups prior to conducting divergence time estimation. We used 28 calibration points based on fossil evidence (Appendix S1). Using the best ML tree obtained from RAxML, we ran a thorough analysis and cross validation in treePL. We determined that the optimal smoothing parameter was 1,000. We used this analysis to time-calibrate branches in our primary analysis. We then inferred branch lengths for 100 bootstrap trees in RAxML and then ran these trees iteratively through treePL to obtain a distribution of 100 time-calibrated trees. For this latter analysis, we assumed that the optimal smoothing parameter for the original data also applied to the bootstrapped trees. Hypothetically, we could have determined the optimal smoothing parameter separately for each replicate, but the cross-validation analysis was extremely time intensive. Furthermore, the optimal smoothing parameter for the observed data should be the best for datasets based on resampling the observed data.
We used the 100 time-calibrated bootstrap trees to generate confidence intervals for the divergence times of all nodes in the best ML tree. Divergence time confidence intervals (95% highest posterior density) were generated using TreeAnnotator 1.10.4 (Drummond and Rambaut, 2007).
