Bayesian Cross-Validation Comparison of Amino Acid Replacement Models: Contrasting Profile Mixtures, Pairwise Exchangeabilities, and Gamma-Distributed Rates-Across-Sites

Models of amino acid replacement are central to modern phylogenetic inference, particularly so when dealing with deep evolutionary relationships. Traditionally, a single, empirically derived matrix was utilized, so as to keep the degrees-of-freedom of the inference low, and focused on topology. With the growing size of data sets, however, an amino acid-level general-time-reversible matrix has become increasingly feasible, treating amino acid exchangeabilities and frequencies as free parameters. Moreover, models based on mixtures of multiple matrices are increasingly utilized, in order to account for across-site heterogeneities in amino acid requirements of proteins. Such models exist as finite empirically-derived amino acid profile (or frequency) mixtures, free finite mixtures, as well as free Dirichlet process-based infinite mixtures. All of these approaches are typically combined with a gamma-distributed rates-across-sites model. In spite of the availability of these different aspects to modeling the amino acid replacement process, no study has systematically quantified their relative contributions to their predictive power of real data. Here, we use Bayesian cross-validation to establish a detailed comparison, while activating/deactivating each modeling aspect. For most data sets studied, we find that amino acid mixture models can outrank all single-matrix models, even when the latter include gamma-distributed rates and the former do not. We also find that free finite mixtures consistently outperform empirical finite mixtures. Finally, the Dirichlet process-based mixture model tends to outperform all other approaches.