The effect of background selection at a single locus on weakly selected, partially linked variants

Previous work has shown that genetic diversity at a neutral locus is affect ed by background selection due to recurrent deleterious mutations as though the effective population size N-e is reduced by a factor that is calculabl e from genetic parameters such as mutation rates, selection coefficients, a nd the rates of recombination between sites subject to selection and the ne utral locus. Given that silent changes at third coding positions are often subject to weak selection pressures, it is important to develop similar qua ntitative predictions of the effects of background selection on variation a nd evolution at weakly selected sites. A diffusion approximation is derived that describes the effects of the presence of a single locus subject to mu tation and strongly deleterious selection on variation and evolution at a p artially linked, weakly selected locus. The results are validated by comput er simulations using the Ito pseudo-sampling method. We show that both nucl eotide site diversity and rates of molecular evolution at a weakly selected locus are affected by background selection as though N-e is reduced in the same way as for a neutral locus. Heuristic arguments are presented as to w hy the change in N-e for the neutral case also applies with weak selection. As in the case of a neutral locus, the number of segregating sites in the population is poorly predicted from the change in N-e, The potential signif icance of the results in relation to the effects of recombinational environ ment on molecular variation and evolution is discussed.