Spatial models for hybrid zones

We introduce a spatially explicit model of natural hybrid zones that allows us to consider how patterns of allele frequencies and linkage disequilibria change over time. We examine the influence of hybrid zone origins on patterns of variation at two loci, a locus under selection in a two-patch environment, and a linked neutral locus. We consider several possible starting conditions that represent explicit realizations of two alternative scenarios for hybrid zone origins: primary intergradation and secondary contact. Our results indicate that in some circumstances, differences in hybrid zone origins will result in substantially different patterns of variation that may persist for thousands of generations. Our conclusions are generally similar to those previously derived from partial differential equations, but there are also some important differences.