Relative evolutionary rates in proteins are largely insensitive to the substitution model
The relative evolutionary rates at individual sites in proteins are informative measures of conservation or adaptation. Often used as evolutionarily-aware conservation scores, relative rates reveal key functional or strongly-selected residues. Estimating rates in a phylogenetic context requires specifying a protein substitution model, which is typically a phenomenological model trained on a large empirical dataset. A strong emphasis has traditionally been placed on selecting the \"best-fit\" model, with the implicit understanding that suboptimal or otherwise ill-fitting models can potentially bias inferences. However, the pervasiveness and degree of such bias has not been systematically examined. We investigated how model choice impacts site-wise relative rates from a large set of empirical protein alignments. We compared models designed for use on any general protein, models designed for specific domains of life, and the simple equal-rates Jukes Cantor-style model (JC). As expected, information theoretic measures showed overwhelming evidence that some models fit the data decidedly better than others. By contrast, estimates of site-specific evolutionary rates were impressively insensitive to the substitution model used, revealing an unexpected degree of robustness to potential model misspecification. A deeper examination of the fewer than 5% of sites for which model inferences differed in a meaningful way showed that the JC model can uniquely identify rapidly-evolving sites that models with empirically-derived exchangeabilities fail to detect. We conclude that relative protein rates appear robust to the applied substitution model, and any sensible model of protein evolution, regardless of its fit to the data, should produce broadly consistent evolutionary rates.