**Trait-Dependent Diversification Analyses** **HiSSE:** We performed hidden state speciation and extinction (HiSSE) analyses using the R package HISSE (Beaulieu & O’Meara 2016) to identify if sexual dichromatism in Afrobatrachian frogs is associated with increased diversification rates, and to reconstruct ancestral states while accounting for transition rate and diversification rate heterogeneity. The HiSSE model builds upon the popular binary-state speciation and extinction (BiSSE) model (Maddison et al. 2007) by incorporating ‘hidden states’ representing unmeasured traits that could impact the diversification rates estimated for states of the observed trait. The HiSSE model is therefore able to account for diversification rate heterogeneity that is not linked to the observed trait, while still identifying trait-dependent processes. The HiSSE framework also includes a set of null models that explicitly assume the diversification process is independent from the observed trait, without constraining diversification rates to be homogenous across the tree. The inclusion of these character-independent models circumvents a significant problem identified in the BiSSE framework, in which the simple ‘null’ model of constant diversification rates is typically rejected in favor of trait-dependent diversification when diversification rate shifts unrelated to the trait occur in the phylogeny (Rabosky & Goldberg 2015; Beaulieu & O’Meara 2016). The improved character-independent diversification models, referred to as CID-2 and CID-4, contain the same number of diversification rate parameters as the BiSSE and HiSSE models, respectively. We fit 26 different models to our sexual dichromatism data set (Table 1): six represent BiSSE-like models, four are variations of the CID-2 model, five are variations of the CID-4 model, nine are various HiSSE models with two hidden states, and two are HiSSE models with a single hidden state. Within each of these classes, the models vary mainly in the number of distinct transition rates (q), extinction fraction rates (ε), and net turnover rates (τ), and the most complex HiSSE model includes four net turnover rates, four extinction fraction rates, and eight distinct transition rates. We enforced a monochromatic root state for all models and evaluated the fit of the 26 models using AIC scores, ΔAIC scores, and Akaike weights (ωi) (Burnham & Anderson 2002). From the best-fit model, we estimated confidence intervals for relevant parameters and transformed ε and τ to obtain speciation (λ), extinction (μ), and net diversification rates using the ‘SupportRegion’ function in HISSE (Beaulieu & O’Meara 2016). We performed ancestral state estimations for each of the 26 models using the marginal reconstruction algorithm implemented in the ‘MarginRecon’ function of HISSE, again enforcing a monochromatic root state. Our final estimation and visualization of diversification rates and node character states on the Afrobatrachian phylogeny took model uncertainty into account by using the model averaging approach described by Beaulieu and O’Meara (2016), such that model contributions to rates and states were proportional to their likelihoods. All R scripts (including those from Harrington & Reeder 2017) and data required to run these analyses are included in the *HiSSE* folder, along with saved R data. **BiSSE:** We did not actually include the results of BiSSE in our paper due to the issues described above, but we did run these analyses and so for the sake of completeness we include our script and data here in the *BiSSE* folder.