Hidden state models improve the adequacy of state-dependent diversification approaches using empirical trees, including biogeographical models

The state-dependent speciation and extinction models (SSE) have recently been criticized due to their high rates of "false positive" results and many researchers have advocated avoiding SSE models in favor of other "non-parametric" or "semi-parametric" approaches. The hidden Markov modeling (HMM) approach provides a partial solution to the issues of model adequacy detected with SSE models. The inclusion of "hidden states" can account for rate heterogeneity observed in empirical phylogenies and allows detection of true signals of state-dependent diversification or diversification shifts independent of the trait of interest. However, the adoption of HMM into other classes of SSE models has been hampered by the interpretational challenges of what exactly a "hidden state" represents, which we clarify herein. We show that HMM models in combination with a model-averaging approach naturally account for hidden traits when examining the meaningful impact of a suspected "driver" of diversification. We also extend the HMM to the geographic state-dependent speciation and extinction (GeoSSE) model. We test the efficacy of our "GeoHiSSE" extension with both simulations and an empirical data set. On the whole, we show that hidden states are a general framework that can generally distinguish heterogeneous effects of diversification attributed to a focal character.