Kopperud, B. T.; Höhna, S.

Studying rates of species diversification is one of the key themes in macroevolution. In particular, we are interested in if some clades in a phylogeny diversify more rapidly/slowly than others due to branch-specific diversification rates. A common approach in neontological studies is to use a phylogenetic birth-death process to model species diversification. Specifically, the birth-death-shift process is used to model branch-specific shifts in the tempo of diversification. Here, we present Pesto, a new method and software for estimating branch-specific diversification rates that does not rely on Markov chain Monte Carlo simulations for fitting the model and instead deterministically computes the posterior mean branch-specific diversification rates using only two traversals of the tree. This method is blazingly fast: the birth-death-shift model can be fitted to large phylogenies (>20k taxa) in minutes on a personal computer while also providing branch-specific inference of diversification rate shift events. Thus, we can robustly infer branch-specific diversification rates and the number of diversification rate shift events for large-scale phylogenies as well as exploring the characteristic of the birth-death-shift model through complex and large-scale simulations. Here, we first describe the method and the software implementation Pesto and explore its behavior using trees simulated under the birth-death-shift model. Then, we explore the behavior of inferring significant branch-specific diversification rate shifts using both Bayes factors and effect sizes. We find few to none false positive inferences of diversification rate shift events but many false negatives (reduced power). The most difficult parameter to estimate is the rate at which diversification rate shifts occur (shift rate). Despite this, branch-specific diversification rate estimates are precise and nearly unbiased.