Effect of strong directional selection on weakly selected mutations at linked sites: Implication for synonymous codon usage

The fixation of weakly selected mutations can be greatly influenced by strong directional selection at linked loci. Here, I investigate a two-locus model in which weakly selected, reversible mutations occur at one locus and recurrent strong directional selection occurs at the other locus. This model is analogous to selection on codon usage at synonymous sites linked to nonsynonymous sites under strong directional selection. Two approximations obtained here describe the expected frequency of the weakly selected preferred alleles at equilibrium. These approximations, as well as simulation results, show that the level of codon bias declines with an increasing rate of substitution at the strongly selected locus, as expected from the well-understood theory that selection at one locus reduces the efficacy of selection at linked loci. These solutions are used to examine whether the negative correlation between codon bias and nonsynonymous substitution rates recently observed in Drosophila can be explained by this hitchhiking effect. It is shown that this observation can be reasonably well accounted for if a large fraction of the nonsynonymous substitutions on genes in the data set are driven by strong directional selection.