Epistasis increases the rate of conditionally neutral substitution in an adapting population

Kimura observed that the rate of neutral substitution should equal the neutral mutation rate. This classic result is central to our understanding of molecular evolution, and it continues to influence phylogenetics, genomics, and the interpretation of evolution experiments. By demonstrating that neutral mutations substitute at a rate independent of population size and selection at linked sites, Kimura provided an influential justification for the idea of a molecular clock and emphasized the importance of genetic drift in shaping molecular evolution. But when epistasis among sites is common, as numerous empirical studies suggest, do neutral mutations substitute according to Kimura's expectation? Here we study simulated, asexual populations of RNA molecules, and we observe that conditionally neutral mutations--i.e., mutations that do not alter the fitness of the individual in which they arise, but that may alter the fitness effects of subsequent mutations--substitute much more often than expected while a population is adapting. We quantify these effects using a simple population-genetic model that elucidates how the substitution rate at conditionally neutral sites depends on the population size, mutation rate, strength of selection, and prevalence of epistasis. We discuss the implications of these results for our understanding of the molecular clock, and for the interpretation of molecular variation in laboratory and natural populations.