GTRpmix: A linked general-time reversible model for profile mixture models

Profile mixture models capture distinct biochemical constraints on the amino acid substitution process at different sites in proteins. These models feature a mixture of time-reversible models with a common set of amino acid exchange rates (a matrix of exchangeabilities) and distinct sets of equilibrium amino acid frequencies known as profiles. Combining the exchangeability matrix with each profile generates the matrix of instantaneous rates of amino acid exchange for that profile. Currently, empirically estimated exchangeability matrices (e.g., the LG or WAG matrices) are widely used for phylogenetic inference under profile mixture models. However, such matrices were originally estimated using site homogeneous models with a single set of equilibrium amino acid frequencies; therefore unlikely to be optimal for site heterogeneous profile mixture models. Here we describe the GTRpmix model, implemented in IQ-TREE2, that allows maximum likelihood estimation of a common set of exchangeabilities for all site classes under any profile mixture model. We show that exchangeability matrices estimated in the presence of a site-heterogeneous profile mixture model differ markedly from the widely used LG matrix and dramatically improve model fit and topological estimation accuracy for empirical test cases. Because the GTRpmix model is computationally expensive, we provide two exchangeability matrices estimated from large concatenated phylogenomic supermatrices under the C60 profile mixture model that can be used as fixed matrices for phylogenetic analyses. One of these, called Eukaryotic Linked Mixture (ELM), is designed for phylogenetic analysis of proteins encoded by nuclear genomes of eukaryotes, and the other, Eukaryotic and Archeal Linked mixture (EAL), for reconstructing relationships between eukaryotes and Archaea. These matrices when combined with profile mixture models fit data much better and have improved topology estimation relative to the empirical LG matrix combined with the same underlying mixture models. Version v2.3.1 of IQ-TREE2 implementing these models is available at www.iqtree.org.