Adaptive Tree Proposals for Bayesian Phylogenetic Inference

Bayesian inference of phylogeny with Markov chain Monte Carlo plays a key role in the study of evolution. Yet, this method still suffers from a practical challenge identified more than two decades ago: designing tree topology proposals that efficiently sample tree spaces. In this article, I introduce the concept of adaptive tree proposals for unrooted topologies, that is, tree proposals adapting to the posterior distribution as it is estimated. I use this concept to elaborate two adaptive variants of existing proposals and an adaptive proposal based on a novel design philosophy in which the structure of the proposal is informed by the posterior distribution of trees. I investigate the performance of these proposals by first presenting a metric that captures the performance of each proposal within a mixture of proposals. Using this metric, I compare the performance of the adaptive proposals to the performance of standard and parsimony-guided proposals on 11 empirical data sets. Using adaptive proposals led to consistent performance gains and resulted in up to 18-fold increases in mixing efficiency and 6-fold increases in convergence rate without increasing the computational cost of these analyses. [Bayesian phylogenetic inference; Markov chain Monte Carlo; posterior probability distribution; tree proposals.].