Infinite Mixture Models for Improved Modeling of Across-Site Evolutionary Variation

Abstract Scientific studies in many areas of biology routinely employ evolutionary analyses based on inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly variable, and properly accounting for heterogeneity is crucial for more accurate phylogenetic inference. Nucleotide substitution rates and patterns are known to vary among sites in multiple sequence alignments, and such variation can be modeled by partitioning alignments into categories corresponding to different substitution models. Determining a priori appropriate partitions can be difficult, however, and better model fit can be achieved through flexible Bayesian infinite mixture models that simultaneously infer the number of partitions, the partition that each site belongs to, and the evolutionary parameters corresponding to each partition. Here, we consider several different types of infinite mixture models, including classic Dirichlet process mixtures, as well as novel approaches for modeling across-site evolutionary variation: hierarchical models for data with a natural group structure, and infinite hidden Markov models that account for spatial patterns in alignments. In analyses of several viral data sets, we find that different types of models perform best in different scenarios, but infinite hidden Markov models emerge as particularly promising for larger data sets and complex evolutionary patterns characterized by multiple genes and overlapping reading frames. To enable these models to scale to large data sets, we adapt efficient Markov chain Monte Carlo algorithms and exploit opportunities for parallel computing. We implement this infinite mixture modeling framework in BEAST X, a widely-used software package for phylogenetic inference.