Empirical substitution models of SARS-CoV-2 protein evolution

Probabilistic phylogenetic inference requires substitution models of molecular evolution, and these models should be as realistic as possible to yield accurate predictions. At the protein level, empirical substitution models are well established in phylogenetics. However, the number of available empirical substitution models remains limited, and only a few focus on rapidly evolving viruses. In this context, no substitution models have yet been developed for SARS-CoV-2 proteins, despite their potential to improve evolutionary predictions. Here, we present a set of empirical substitution models for SARS-CoV-2 proteins, including the main protease, papain-like protease, spike protein, and the complete proteome. We inferred these models using maximum likelihood from thousands of protein sequences and validated them with independent datasets. Overall, the estimated empirical substitution models outperformed currently available empirical models in terms of phylogenetic likelihood and showed that evolutionary patterns vary among SARS-CoV-2 proteins. Additionally, using forward-in-time evolutionary simulations, we found that SARS-CoV-2 proteins modeled with these empirical substitution models generated protein variants with folding stabilities more realistic than those produced under other empirical substitution models. We conclude that evolutionary inferences based on protein-specific substitution models are generally more accurate and biologically realistic than those based on generalist models and recommend the empirical substitution models presented for evolutionary predictions of SARS-CoV-2 proteins.