Inferring state‐dependent diversification rates using approximate Bayesian computation

Abstract State‐dependent speciation and extinction (SSE) models are a popular framework for quantifying whether species traits have an impact on evolutionary rates and how this shapes the variation in species richness among clades in a phylogeny. However, SSE models are becoming increasingly complex, limiting the application of likelihood‐based inference methods. Approximate Bayesian computation (ABC), a likelihood‐free approach, is a potentially powerful alternative for estimating parameters. Here, we develop an ABC framework to estimate state‐dependent speciation, extinction and transition rates from phylogenetic trees in BiSSE (binary state dependent speciation and extinction), GeoSSE (geographic state dependent speciation and extinction) and MuSSE (multiple state‐dependent speciation and extinction) models. Using different sets of candidate summary statistics, we then compare the inference ability of ABC with that of using likelihood‐based maximum likelihood (ML) and Markov chain Monte Carlo (MCMC) methods to identify the combinations that best capture the complex relationships between rates of diversification and species traits. Our results show the ABC algorithm can accurately estimate state‐dependent diversification rates for most of the model parameter sets we explored. The inference error of the parameters associated with the species‐poor state is larger with ABC than in the likelihood estimations only when the speciation rate ( λ ) is highly asymmetric between states in all three models. We suggest that the combination of normalized lineage‐through‐time (nLTT) statistics and phylogenetic signal constitutes efficient summary statistics for the ABC method. By providing an efficient algorithm and a set of suitable summary statistics, our work aims to contribute to the use of the ABC approach in the development of complex SSE models, for which a likelihood is not available.