The Effect of Strongly Selected Substitutions on Neutral Polymorphism: Analytical Results Based on Diffusion Theory

We derived analytical results for the reduction of the level of neutral polymorphism due to genetic hitchhiking using diffusion theory. In the case of a single strongly selected substitution, expected heterozygosity at a linked neutral locus is reduced by a factor (2c/s) aZciSr( 2c/s, l/m), where s is the selective advantage of the favored allele, c is the recombination fraction between the neutral and selected locus, and a = 2Ns, with N as the diploid population size. r denotes the incomplete gamma function. Using this result and assuming that at any one time at most one substitution is on its way to fixation, the effect of recurrent selected substitutions on expected heterozygosity can be approximated by l/Cl -u(v/p) 2(1/a, -2M/s)], where v and p are the expected numbers of selected substitutions and crossovers, respectively, per chromosome, per nucleotide, per generation, and M is the maximal recombination distance from the neutral locus that a selected mutation can be and still have a hitchhiking effect on the neutral locus. This expression involves a special function, I, < 0, which has a simple integral representation. The results are compared with those of deterministic population genetics and coalescent theory.