The divergence of mean phenotypes under persistent Gaussian selection.

Although multigenic traits are often assumed to be under some form of stabilizing selection, numerous aspects of the population-genetic environment can cause mean phenotypes to deviate from presumed optima, often in ways that effectively transform the fitness landscape to one of directional selection. Focusing on an asexual population, we consider the ways in which such deviations scale with the relative power of selection and genetic drift, the number of linked genomic sites, the magnitude of mutation bias, and the location of optima with respect to possible genotypic space. Even in the absence of mutation bias, mutation will influence evolved mean phenotypes unless the optimum happens to coincide exactly with the mean expected under neutrality. In the case of directional mutation bias and large numbers of selected sites, effective population sizes (Ne) can be dramatically reduced by selective interference effects, leading to further mismatches between phenotypic means and optima. Situations in which the optimum is outside or near the limits of possible genotypic space (e.g. a half-Gaussian fitness function) can lead to particularly pronounced gradients of phenotypic means with respect to Ne, but such gradients can also occur when optima are well within the bounds of attainable phenotypes. These results help clarify the degree to which mean phenotypes can vary among populations experiencing identical mutation and selection pressures but differing in Ne, and yield insight into how the expected scaling relationships depend on the underlying features of the genetic system.