A Mutation–Selection Model of Protein Evolution under Persistent Positive Selection

We use first principles of population genetics to model the evolution of proteins under persistent positive selection (PPS). PPS may occur when organisms are subjected to persistent environmental change, during adaptive radiations, or in host–pathogen interactions. Our mutation–selection model indicates protein evolution under PPS is an irreversible Markov process, and thus proteins under PPS show a strongly asymmetrical distribution of selection coefficients among amino acid substitutions. Our model shows the criteria [Formula: see text] (where ω is the ratio of nonsynonymous over synonymous codon substitution rates) to detect positive selection is conservative and indeed arbitrary, because in real proteins many mutations are highly deleterious and are removed by selection even at positively selected sites. We use a penalized-likelihood implementation of the PPS model to successfully detect PPS in plant RuBisCO and influenza HA proteins. By directly estimating selection coefficients at protein sites, our inference procedure bypasses the need for using ω as a surrogate measure of selection and improves our ability to detect molecular adaptation in proteins.