Bayesian Least-Squares Supertrees (BLeSS): flexible inference of large time-calibrated phylogenies

Abstract

AO_SCPLOWBSTRACTC_SCPLOWTime-calibrated phylogenies are key to macroevolutionary hypothesis testing and parameter inference, but their estimation is difficult when the number of tips is large. Despite its attractive properties, the joint Bayesian inference of topology and divergence times remains computationally prohibitive for large supermatrices. Historically, supertrees represented a popular alternative to supermatrix-based phylogenetic methods, but most of the existing supertree techniques do not accommodate branch lengths or topological uncertainty, rendering them unfit to supply input for modern comparative methods. Here, we present Bayesian Least-Squares Supertrees (BLeSS), a new approach that takes a profile of time trees with partially overlapping leaf sets as its input, and returns the joint posterior distribution of supertree topologies and divergence times as its output. Building upon the earlier exponential error model and average consensus techniques, BLeSS transforms the profile into path-length distance matrices, computes their arithmetic average, and uses MCMC to sample time-calibrated supertrees according to their least-squares fit to the average distance matrix. We provide a fast, flexible, and validated implementation of BLeSS in the program RevBayes, and test its performance using a comprehensive set of simulations. We show that the method performs well across a wide range of conditions, including variation in missing data treatment and the steepness of the error function. Finally, we apply BLeSS to an empirical dataset comprising 33 time trees for 260 species of carnivorans, illustrating its ability to recover well-supported clades and plausible node ages, and discuss how the method can best be used in practice, outlining possible extensions and performance boosts.