Multilocus clines

When two populations which differ at many loci meet, the degree of introgression of alleles across the boundary will depend on the selection acting on each locus (s), the rate of recombination between adjacent loci (r), and the number of loci involved (n). Simple scaling arguments suggest that the behavior of the system should depend on the ratio of selection to recombination (θ = s/r), and on n. This is borne out by mathematical analysis of two demes which exchange individuals at a low rate; when selection is stronger than recombination (θ > 1), the effective selection on each locus is comparable to the total selection over the whole genome (s* ∼ ns). When selection is weaker than recombination (θ < 1), the effective selection is much weaker, but is still stronger than the selection on each locus alone (s* \sim sn20 for small θ). When n is very large, these two regimes are separated by a sharp threshold at θ = 1. The results are extended to two taxa which meet in a continuous habitat; the effective selection pressure, which determines the width of the hybrid zone, behaves in the same way as for the simpler case above. Even when selection is weak compared to recombination, multilocus clines have a sharp step at their center, flanked by tails of introgression in which the alleles behave independently of each other. The set of clines acts as a barrier to gene flow, and it is shown that the barrier is strongest when selection is spread over many loci. The implications of the results for divergence and speciation are discussed.