A spatially explicit individual-based model of reinforcement in hybrid zones

An individual-based model consisting of two dioecious populations in a two-dimensional environmental grid was constructed. Each population began with, and never exceeded, 1000 individuals; extinction was allowed. Genomes consisting of 30 biallelic loci for male sexual advertisement call, female mate preference, and population origin were constructed, and lineages of each individual in the starting populations were followed for 2000 generations. Type and level of hybrid disadvantage, initial population distribution, patchiness of environmental resources, and level of mate choice were varied. Persistence of bimodal hybrid zones was nonexistent at low levels of hybrid disadvantage and universal at high levels of hybrid disadvantage, with a narrow threshold in which persistence was unpredictable. Persistence occurred at lower levels of hybrid disadvantage when populations were initially parapatric rather than sympatric, and environments were patchy rather than homogeneous. Increased divergence in mating systems occurred when hybrid disadvantage was high, hybrids were infertile, populations were initially parapatric, and increased female choice was allowed. Mating system divergence was much higher in interacting populations compared with noninteracting populations, indicating that reinforcement caused most of the observed divergence. When hybrids were infertile, reinforcement contributed to speciation, because under hybrid infertility the probability of persistence at low levels of hybrid disadvantage was positively related to mate choice. The results agree with previous one-dimensional spatial models in finding that population persistence is more likely in parapatric and patchy population distributions. In addition, the results show that hybrid infertility may facilitate the process of reinforcement and speciation.