Reinforcement and divergence under assortative mating

Traits that cause assortative mating such as the flowering time in plants and body size in animals can produce reproductive isolation between hybridizing 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 another. The partial pre-zygotic isolation between the two populations is caused by assortative mating for a trait that is influenced by any number of genes with additive effects. The post-zygotic isolation is caused by selection against genetic incompatibilities that can involve any form of selection on individual genes and gene combinations (epistasis). The analysis assumes that the introgression rate and selection coefficients are small. The results show that the assortment trait mean will not diverge from the immigrants 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 equilibrium is determined by a balance between direct selection on the assortment trait and introgression from the other population. Additional selection against hybrid genetic incompatibilities reduces the effective migration rate and allows greater divergence. The role of assortment in speciation is discussed in the light of these results.