Probabilistic Phylogenetic Inference with Insertions and Deletions

Abstract

A fundamental task in sequence analysis is to calculate the probability of a multiple alignment given a phylogenetic tree relating the sequences and an evolutionary model describing how sequences change over time. However, the most widely used phylogenetic models only account for residue substitution events. We describe a probabilistic model of a multiple sequence alignment that accounts for insertion and deletion events in addition to substitutions, given a phylogenetic tree, using a rate matrix augmented by the gap character. Starting from a continuous Markov process, we construct a non-reversible generative (birth–death) evolutionary model for insertions and deletions. The model assumes that insertion and deletion events occur one residue at a time. We apply this model to phylogenetic tree inference by extending the program dnaml in phylip. Using standard benchmarking methods on simulated data and a new “concordance test” benchmark on real ribosomal RNA alignments, we show that the extended program dnamlε improves accuracy relative to the usual approach of ignoring gaps, while retaining the computational efficiency of the Felsenstein peeling algorithm. We describe a computationally efficient method to use insertion and deletion events, in addition to substitutions, in phylogenetic inference. To date, many evolutionary models in probabilistic phylogenetic inference methods have only accounted for substitution events, not for insertions and deletions. As a result, not only do tree inference methods use less sequence information than they could, but also it has remained difficult to integrate phylogenetic modeling into sequence alignment methods (such as profiles and profile-hidden Markov models) that inherently require a model of insertion and deletion events. Therefore an important goal in the field has been to develop tractable evolutionary models of insertion/deletion events over time of sufficient accuracy to increase the resolution of phylogenetic inference methods and to increase the power of profile-based sequence homology searches. Our model offers a partial answer to this problem. We show that our model generally improves inference power in both simulated and real data and that it is easily implemented in the framework of standard inference packages with little effect on computational efficiency (we extended dnaml, in Felsenstein's popular phylip package).