Bayesian modelling of compositional heterogeneity in molecular phylogenetics

In molecular phylogenetics, standard models of sequence evolution generally assume that sequence composition remains constant over evolutionary time. However, this assumption is violated in many datasets which show substantial heterogeneity in sequence composition across taxa. We propose a model which allows compositional heterogeneity across branches, and formulate the model in a Bayesian framework. Specifically, the root and each branch of the tree is associated with its own composition vector whilst a global matrix of exchangeability parameters applies everywhere on the tree. We encourage borrowing of strength between branches by developing two possible priors for the composition vectors: one in which information can be exchanged equally amongst all branches of the tree and another in which more information is exchanged between neighbouring branches than between distant branches. We also propose a Markov chain Monte Carlo (MCMC) algorithm for posterior inference which uses data augmentation of substitutional histories to yield a simple complete data likelihood function that factorises over branches and allows Gibbs updates for most parameters. Standard phylogenetic models are not informative about the root position. Therefore a significant advantage of the proposed model is that it allows inference about rooted trees. The position of the root is fundamental to the biological interpretation of trees, both for polarising trait evolution and for establishing the order of divergence among lineages. Furthermore, unlike some other related models from the literature, inference in the model we propose can be carried out through a simple MCMC scheme which does not require problematic dimension-changing moves. We investigate the performance of the model and priors in analyses of two alignments for which there is strong biological opinion about the tree topology and root position.