**Bayesian Ancestral State Reconstruction** We reconstructed the evolution of sexual dichromatism on the time-calibrated phylogeny of Afrobatrachia using Bayesian ancestral state reconstruction in BEAST. We performed Bayesian ancestral state reconstructions using several combinations of clock and character models in BEAST v1.8.1 (Drummond et al. 2012) following King and Lee (2015). The topology and branch lengths were fixed by removing all tree operators, and sexual dichromatism was treated as a binary alignment. Because all outgroup families are monochromatic, we fixed the root state by adding a placeholder monochromatic taxon to the root with a zero branch length, creating a hard prior distribution on the root where P(monochromatic root) = 1, and P(dichromatic root) = 0. A stochastic Mk model of character evolution (Lewis 2001) was used with symmetrical (Mk1) or asymmetrical (Mk2) transition rates between states, and each character model was analyzed using a strict clock model (enforcing a homogenous trait rate) and a random local clock model (allowing for heterotachy), resulting in four analysis combinations (RLC_mk1, RLC_mk2, SC_mk1, SC_mk2). The analyses involving the random local clock allowed estimation of the number and magnitude of rate changes using MCMC. All analyses were run for 200 million generations with sampling every 20,000 generations, resulting in 10,000 retained samples. We used the marginal likelihood estimator with stepping stone sampling, with a chain length of 1 million and 24 path steps, to estimate the log marginal likelihood of each run (Baele et al. 2012, 2013). We performed five replicates per analysis combination to ensure consistency in the estimated log marginal likelihood, and subsequently compared the four different analyses using log Bayes factors, calculated as the difference in log marginal likelihoods, to select the best fit clock model and character model combination. The replicate folders contain the input xml file and all outputs for each of the analysis combinations. We summarized transitions between character states and created consensus trees to estimate the posterior probabilities of a character states across nodes. The posterior probabilities for each state across nodes were visualized using FigTree, in which node circles were drawn proportional to the posterior probability for a given state.