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 variety of evolutionary studies, including the reconstruction of phylogenetic histories and ancestral sequences, among others. The earliest substitution models of protein evolution are based on empirical protein sequences and, despite their unrealistic assumptions, are still routinely used in protein phylogenetics. Next, the incorporation of additional parameters that inform about evolutionary constraints on protein stability and protein function provided a significant increase in the accuracy of the modeling. However, despite the wide variety of substitution models of protein evolution that were presented, only a small subset has been implemented in evolutionary frameworks of practical use in phylogenetics. Here, we overview general trends in the development and application of substitution models of protein evolution, including their theoretical fundamentals, goals, areas for improvement, and implementation in phylogenetic frameworks. We also provide detailed practical examples of phylogenetic inference using advanced structurally constrained substitution models.