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 required for a wide variety of studies that include 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 are still routinely used in protein phylogenetics. Next, the incorporation of additional parameters that inform about evolutionary constraints on the protein structure provided a significant increase in the accuracy of the predictions. However, despite the wide variety of substitution models of protein evolution that were presented, only a part of them have been implemented into evolutionary frameworks of practical use in phylogenetics. Here, we review general trends in the development and application of substitution models of protein evolution, including their framework implementations, goals, and improvement needs. We also present some detailed practical examples of phylogenetic inference based on advanced substitution models of protein evolution.