Reinforcement and divergence under assortative mating

Traits that cause assortative mating such as the flowering time in plants a nd body size in animals call produce reproductive isolation between hybridi zing populations. Can selection against unfit hybrids cause two populations to diverge in their mean values for these kinds of traits? Here I present a haploid analytical model of one population that receives gene flow from a nother. The partial pre-zygotic isolation between the two populations is ca used by assortative mating for a trait that is influenced by any number of genes with additive effects. The post-zygotic isolation is caused by select ion against genetic incompatibilities that can involve any form of selectio n on individual genes and gene combinations (epistasis). The analysis assum es that the introgression rate and selection coefficients are small. The re sults show that the assortment trait mean will not diverge from the immigra nts unless there is direct selection on the trait favouring it to do so or there are genes of very large effect. The amount of divergence at equilibri um is determined by a balance between direct selection on the assortment tr ait and introgression from the other population Additional selection agains t hybrid genetic incompatibilities reduces the effective migration rate and allows greater divergence. The role of assortment in speciation is discuss ed in the light of these results.