SPIn: model selection for phylogenetic mixtures via linear invariants

Abstract

In phylogenetic inference, an evolutionarymodel describes the substitution processes along each edge of a phylogenetic tree. Misspecification of the model has important implications for the analysis of phylogenetic data. Conventionally, however, the selection of a suitable evolutionary model is based on heuristics or relies on the choice of an approximate input tree. We introduce a method for model Selection in Phylogenetics based on linear INvariants (SPIn), which uses recent insights on linear invariants to characterize a model of nucleotide evolution for phylogenetic mixtures on any number of components. Linear invariants are constraints among the joint probabilities of the bases in the operational taxonomic units that hold irrespective of the tree topologies appearing in the mixtures. SPIn therefore requires no input tree and is designed to deal with nonhomogeneous phylogenetic data consisting ofmultiple sequence alignments showing different patterns of evolution, for example, concatenated genes, exons, and/or introns. Here, we report on the results of the proposedmethod evaluated on multiple sequence alignments simulatedunder a variety of single-tree andmixture settings for both continuous- and discretetime models. In the simulations, SPInsuccessfully recovers the underlying evolutionarymodel and is shown to performbetter than existing approaches.