Hybrid zone dynamics under weak Haldane's rule

The ability of genetic isolation to block gene flow plays a key role in the speciation of sexually reproducing organisms. This paper analyses the hybrid zone dynamics affected by "weak" Haldane's rule, namely the incomplete hybrids inferiority (sterility/inviability) against the heterogametic (XY or ZW) sex caused by a Dobzhansky-Muller incompatibility. Different strengths of incompatibility, dispersal and density-dependent regulation are considered; and the gene flow and clinal structures of allele frequencies in the presence of short-range dispersal (the stepping-stone model) are examined. I show that a weak heterogametic hybrid incompatibility could constitute a substantial barrier that could reduce gene flow and result in non-coincident and discordant clines of alleles. It is found that the differential gene flow is more pronounced under a stronger density-dependent regulation. This study provides a mechanistic explanation for how an adaptive mutation, which may only have a marginal fitness effect, could set a gene up as an evolutionary hot-spot.