Supplementary files from: Improving inference and avoiding over-interpretation of hidden-state diversification models: Specialized plant breeding has no effect on diversification in frogs

The hidden-state speciation and extinction (HiSSE) model helps avoid spurious results when testing whether a character affects diversification rates. However, care must be taken to optimally analyze models and interpret results. Recently, Tonini et al. (2020; TEA hereafter) studied anuran (frog and toad) diversification with HiSSE methods. They concluded that their focal state, breeding in phytotelmata, increases net diversification rates. Yet this conclusion is counterintuitive, because the state that purportedly increases net diversification rates is 14 times rarer among species than the alternative. Herein I revisit TEA's analyses and demonstrate problems with inferring model likelihoods, conducting post-hoc tests, and interpreting results. I also re-evaluate their top models and find that diverse strategies are necessary to reach the parameter values that maximize each model's likelihood. In contrast to TEA, I find no support for an effect of phytotelm breeding on net diversification rates in Neotropical anurans. In particular, even though the most highly supported models include the focal character, averaging parameter estimates over hidden states shows that the focal character does not influence diversification rates. Finally, I suggest ways to better analyze and interpret complex diversification models – both state-dependent and beyond – for future studies in other organisms.