Shifting Balance on a Static Mutation–Selection Landscape: A Novel Scenario of Positive Selection

A version of the mechanistic mutation-selection (MutSel) model that accounts for temporal dynamics at a site is presented. This is used to show that the rate ratio dN/dS at a site can be transiently > 1 even when fitness coefficients are fixed or the fitness landscape is static. This occurs whenever a site drifts away from its fitness peak and is then forced back by selection, a process reminiscent of shifting balance. Shifting balance is strongest when the substitution process is not dominated by selection or drift, but admits interplay between the two. Under this condition, site-specific changes in dN/dS were inferred in 78-100% of trials, and positive selection (i.e., dN/dS > 1) in 10-40% of trials, when sequence alignments generated under MutSel were fitted to two popular phenomenological branch-site models. These results demonstrate that positive selection can occur without a change in fitness regime, and that this is detectable by branch-site models. In addition, MutSel is used to show that a site can be occupied by a sub-optimal amino acid for long periods on a fixed landscape when selection is stringent. This has implications for the interpretation of constant-but-different site patterns typically attributed to changes in fitness. Furthermore, a version of MutSel with episodic changes in fitness coefficients is used to illustrate systematic differences between parameters used to generate data under MutSel and their counterparts estimated by a simple codon model. Motivated by a discrepancy in the literature, interpretation of dN/dS in the context of MutSel is also discussed.