Species diversification may be determined by many different variables, including the traits of the diversifying lineages. The State-dependent Speciation and Extinction (SSE) framework contains methods to detect the dependence of diversification on these traits. For the analysis of traits with multiple states, MuSSE (Multiple-States dependent Speciation and Extinction) was developed. However, MuSSE and other state-dependent speciation and extinction models have been shown to yield false positives, because they cannot separate differential diversification rates from dependence of diversification on the observed traits. The recently introduced method HiSSE (Hidden- State dependent Speciation and Extinction) resolves this problem by allowing a hidden state to affect diversification rates. Unfortunately, HiSSE does not allow traits with more than two states, and, perhaps more interestingly, the simultaneous action of multiple traits on diversification. Here, we introduce an R package (SecSSE: Several examined and concealed States-dependent Speciation and Extinction) that combines the features of HiSSE and MuSSE to simultaneously infer state-dependent diversification across two or more examined (observed) traits or states while accounting for the role of a possible concealed (hidden) trait. Moreover, SecSSE also has improved functionality compared to its two 'parents'. First, it allows for an observed trait being in two or more states simultaneously, which is useful for example when a taxon is a generalist or when the exact state is not precisely known. Second, it provides the correct likelihood when conditioned on non-extinction, which has been incorrectly implemented in HiSSE and other SSE models. To illustrate our method we apply SecSSE to 7 previous studies that used MuSSE, and find that in 5 out of 7 cases, the conclusions drawn based on MuSSE were premature. We test with simulations whether SecSSE sacrifices statistical power to avoid the high type I error problem of MuSSE, but we find that this is not the case: for the majority of simulations where the observed traits affect diversification, SecSSE detects this.

Simulated datasetsFor each empirical datasets, we fit three models Constant-rate (CR), Concealed Trait-Dependent (CTD) and Examined Trait-Dependent (ETD) diversification. Using the parameters that maximize the likelihood, we simulated 100 trees under the three models.Supplementary Figures