**Trait-Dependent Diversification Analyses with Simulations** The identified bias towards the detection of trait-dependent diversification in the BiSSE framework (Rabosky & Goldberg 2015; Beaulieu & O’Meara 2016) prompted us to investigate if a similar outcome would be detected in our data set, and whether the HiSSE framework could improve our ability to distinguish whether the observed states are correlated with diversification rates. One concern raised by Beaulieu and O’Meara (2016) is that neutrally evolving traits simulated on trees generated from a complex heterogenous rate branching process can lead to false signals of trait-dependent diversification, signifying the HiSSE framework may be sensitive to particular types of tree shapes. To evaluate the performance of these methods given our empirical tree topology, we simulated neutrally evolving traits on the Afrobatrachian frog phylogeny and tested for trait-dependent diversification using both the BiSSE and HiSSE frameworks. **Simulating Trait Data:** We conducted independent simulations of a binary trait with the ‘sim.history’ function in R package PHYTOOLS (Revell 2012) using the unequal rates q-matrices obtained from our empirical data and enforcing a root state of trait absence. We required a minimum of 10% of taxa to exhibit the derived state and conducted simulations until we obtained 1,500 replicates meeting this criterion. The R script and tree file used to generate simulation data can be found in the *Simulating Trait Data/Run Simulations* folder. We generated 5000 simulations. These were then filtered to find 1500 simulations meeting our criteria and converted into the proper format using the Simulation_Processing_for_BiSSE.py script. This script and the output text files can be found in the *Simulating Trait Data/Filter Simulation Data* folder. **BiSSE Analyses**: We used maximum likelihood to fit a BiSSE model and the typical ‘null’ model with equal speciation and extinction rates to each simulated trait using the R package DIVERSITREE (Maddison et al. 2007; FitzJohn et al. 2009; FitzJohn 2012). We performed likelihood ratio tests and calculated ΔAIC scores to determine if the constraint model could be rejected with confidence (ΔAIC > 2 or p-value < 0.05), and summarized the number of instances each of the two models was favored across the simulations. The R script, tree file, simulation files, and all outputs for BiSSE can be found in the *BiSSE Analyses for Simulations* folder. **HiSSE Analyses**: We analyzed the simulated data in the HiSSE framework as with our empirical data, but with a reduced set of five models representing each major category of model. This reduced model set included two BiSSE-like models that differed only in the constraint of τ, a CID-2 and CID-4 model, and a HiSSE model with two hidden states, three transition rates, equal τ, and distinct τ. We set a probability of one for trait absence at the root state to match the manner in which traits were simulated and evaluated the fit of the 5 models using ΔAIC scores and Akaike weights (ωi) for each simulation, using a threshold of ΔAIC greater than two to favor a model. Specifically, we were interested in whether the unconstrained BiSSE-like or HiSSE models were favored, resulting in the detection of a false pattern of trait-dependent diversification, or if the CID-2 or CID-4 models were selected, capturing the expected pattern where the diversification process was independent from trait evolution. The R script, tree file, simulation files, and all outputs can be found in the *HiSSE Analyses for Simulations* folder. This folder also contains a directory with the R data for each model for each simulation replicate, and a directory with the AIC tables created for each simulation model set, a python script to filter through all these AIC tables, and the final resulting output from this python script that includes model summaries, a script for plotting, and plots.