Approximate Bayesian Computation of diversification rates from molecular phylogenies: introducing a new efficient summary statistic, the nLTT

Molecular phylogenies form a potential source of information on rates of diversification, and the mechanisms that underlie diversification patterns. Diversification models have become increasingly complex over the past decade, and we have reached a point where the computation of the analytical likelihood of the model given a phylogeny is either unavailable or intractable. For such models, a likelihood-free approach such as Approximate Bayesian Computation (ABC) offers a solution. ABC is a Bayesian framework that uses one or more summary statistics instead of the likelihood function. Crucial to the performance of an ABC algorithm is the choice of summary statistics. Here, we analyse the applicability of three traditional and often-used summary statistics (Gamma statistic, Phylogenetic Diversity and tree size) within an ABC framework and propose a new summary statistic: the normalized Lineages-Through-Time (nLTT) statistic. We find that the traditional summary statistics perform poorly and should not be used as a substitute of the likelihood. By contrast, we find that the nLTT statistic performs on par with the likelihood. We suggest to include the nLTT statistic in future ABC applications within phylogenetics. We argue that the use of ABC in diversification rate analysis is a promising new approach, but that care should be taken which summary statistics are chosen.