Deterministic evolution of an asexual population under the action of beneficial and deleterious mutations on additive fitness landscapes

The divergence of mean phenotypes under persistent directional selection

Numerous organismal traits, particularly at the cellular level, are likely to be under persistent directional selection across phylogenetic lineages. Unless all mutations affecting such traits have large enough effects to be efficiently selected in all species, gradients in mean phenotypes are expected to arise as a consequence of differences in the power of random genetic drift, which varies by approximately five orders of magnitude across the Tree of Life. Prior theoretical work examining the conditions under which such gradients can arise focused on the simple situation in which all genomic sites affecting the trait have identical and constant mutational effects. Here, we extend this theory to incorporate the more biologically realistic situation in which mutational effects on a trait differ among nucleotide sites. Pursuit of such modifications leads to the development of semi-analytic expressions for the ways in which selective interference arises via linkage effects in single-effects models, which then extend to more complex scenarios. The theory developed clarifies the conditions under which mutations of different selective effects mutually interfere with each others' fixation and shows how variance in effects among sites can substantially modify and extend the expected scaling relationships between mean phenotypes and effective population sizes.

Fixation probability of a nonmutator in a large population of asexual mutators

In an adapted population of mutators in which most mutations are deleterious, a nonmutator that lowers the mutation rate is under indirect selection and can sweep to fixation. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large population of asexual mutators. We show that when beneficial mutations are absent, the fixation probability is a nonmonotonic function of the mutation rate of the mutator: it first increases sublinearly and then decreases exponentially. We also find that beneficial mutations can enhance the fixation probability of a nonmutator. Our analysis is relevant to an understanding of recent experiments in which a reduction in the mutation rates has been observed.