A comparison of multilocus clines maintained by environmental adaptation or by selection against hybrids

There has recently been considerable debate over the relative importance of selection against hybrids ("endogenous" selection) vs. adaptation to different environments ("exogenous") in maintaining stable hybrid zones and hence in speciation. Single-locus models of endogenous and exogenous viability selection generate clines of similar shape, but the comparison has not been extended to multilocus systems, which are both quantitatively and qualitatively very different from the single-locus case. Here we develop an analytical multilocus model of differential adaptation across an environmental transition and compare it to previous heterozygote disadvantage models. We show that the shape of clines generated by exogenous selection is indistinguishable from that generated by endogenous selection. A stochastic simulation model is used to test the robustness of the analytical description to the effects of drift and strong selection, and confirms the prediction that pairwise linkage disequilibria are predominantly generated by migration. However, although analytical predictions for the width of clines maintained by heterozygote disadvantage fit well with the simulation results, those for environmental adaptation are consistently too narrow; reasons for the discrepancy are discussed. There is a smooth transition between a system in which a set of loci effectively act independently of each other and one in which they act as a single nonrecombining unit.