An efficient deep learning method for amino acid substitution model selection

Amino acid substitution models play an important role in studying the evolutionary relationships among species from protein sequences. The amino acid substitution model consists of a large number of parameters; therefore, it is estimated from hundreds or thousands of alignments. Both general models and clade-specific models have been estimated and widely used in phylogenetic analyses. The maximum likelihood method is normally used to select the best-fit model for a specific protein alignment under the study. A number of studies have discussed theoretical concerns as well as the computational burden of the maximum likelihood methods in model selection. Recently, machine learning methods have been proposed for selecting nucleotide models. In this article, we propose a method to measure substitution rates among amino acids (called summary statistics) from protein alignments to efficiently train a deep learning network of so-called ModelDetector for detecting amino acid substitution models. The ModelDetector network was trained from 2,246,400 alignments on a computer with eight cores (without GPU) in about 3.3 hr. Experiments on simulation data showed that the accuracy of the ModelDetector was comparable with that of the maximum likelihood method ModelFinder. It was orders of magnitude faster than the maximum likelihood method in inferring amino acid substitution models and able to analyze genome alignments with millions of sites in minutes. The results indicate that the deep learning network can play as a promising tool for amino acid substitution model selection.