MAST: Phylogenetic Inference with Mixtures Across Sites and Trees
Hundreds or thousands of loci are now routinely used in modern phylogenomic studies. Concatenation approaches to tree inference assume that there is a single topology for the entire dataset, but different loci may have different evolutionary histories due to incomplete lineage sorting, introgression, and/or horizontal gene transfer; even single loci may not be treelike due to recombination. To overcome this shortcoming, we introduce the mixture across sites and trees (MAST) model, which uses a mixture of bifurcating trees to represent multiple histories in a single concatenated alignment. The MAST model allows each tree to have its own topology, branch lengths, substitution model, nucleotide or amino acid frequencies, and model of rate heterogeneity across sites. We implemented the MAST model in a maximum-likelihood framework in the popular phylogenetic software, IQ-TREE. Simulations show that we can accurately recover the true model parameters, including branch lengths and tree weights (i.e. frequencies) for a given set of tree topologies. We also show that we can use standard statistical inference approaches to reject a single-tree model when data are simulated under multiple trees (and vice versa). We applied the MAST model to multiple primate datasets and found that it can recover the signal of incomplete lineage sorting in the Great Apes, as well as the asymmetry in minor trees caused by introgression among several macaque species. When applied to a dataset of four Platyrrhine species for which standard concatenated maximum likelihood and gene tree approaches disagree, we find that MAST gives the highest weight to the tree favored by gene tree approaches. These results suggest that the MAST model is able to analyse a concatenated alignment using maximum likelihood, while avoiding some of the biases that come with assuming there is only a single tree. The MAST model can therefore offer unique biological insights when applied to datasets with multiple evolutionary histories. We discuss how it can be extended in the future.