Trends in substitution models of protein evolution for phylogenetic inference

Substitution models of protein evolution describe the rates of evolutionary change among amino acids and are essential for a wide range of phylogenetic studies, including the reconstruction of phylogenetic histories and ancestral sequences, among others. The first substitution models of protein evolution were based on empirical protein sequences and, despite their unrealistic assumptions, they continue to be routinely used in protein phylogenetics. Subsequently, the incorporation of additional parameters that reflect evolutionary constraints on the protein structure significantly improved the accuracy of predictions. However, despite the wide variety of substitution models of protein evolution that have been presented, only a few have been implemented into practical evolutionary frameworks useful for phylogenetic inference. In this review, we present general trends in the development and application of substitution models of protein evolution, including their integration into evolutionary frameworks, advantages, and areas for improvement. We also provide detailed practical examples of phylogenetic inference based on advanced substitution models of protein evolution.