A Bayesian Approach for Estimating Branch-Specific Speciation and Extinction Rates

Species richness varies considerably among the tree of life which can only be explained by heterogeneous rates of diversification (speciation and extinction). Previous approaches use phylogenetic trees to estimate branch-specific diversification rates. However, all previous approaches disregard diversification-rate shifts on extinct lineages although 99% of species that ever existed are now extinct. Here we describe a lineage-specific birth-death-shift process where lineages, both extant and extinct, may have heterogeneous rates of diversification. To facilitate probability computation we discretize the base distribution on speciation and extinction rates into k rate categories. The fixed number of rate categories allows us to extend the theory of state-dependent speciation and extinction models (e.g., BiSSE and MuSSE) to compute the probability of an observed phylogeny given the set of speciation and extinction rates. To estimate branch-specific diversification rates, we develop two independent and theoretically equivalent approaches: numerical integration with stochastic character mapping and data-augmentation with reversible-jump Markov chain Monte Carlo sampling. We validate the implementation of the two approaches in RevBayes using simulated data and an empirical example study of primates. In the empirical example, we show that estimates of the number of diversification-rate shifts are, unsurprisingly, very sensitive to the choice of prior distribution. Instead, branch-specific diversification rate estimates are less sensitive to the assumed prior distribution on the number of diversification-rate shifts and consistently infer an increased rate of diversification for Old World Monkeys. Additionally, we observe that as few as 10 diversification-rate categories are sufficient to approximate a continuous base distribution on diversification rates. In conclusion, our implementation of the lineage-specific birth-death-shift model in RevBayes provides biologists with a method to estimate branch-specific diversification rates under a mathematically consistent model.