Can reinforcement complete speciation?

Hybridization is common in nature, even between "good" species. This observation poses the question of why reinforcement is not always successful in leading to the evolution of complete reproductive isolation. To study this question, we developed a new "quasi-linkage disequilibrium" (QLD) approximation to obtain the first analytic results for the evolution of modifiers that increase mate discrimination against hybrids and heterospecifics. When such modifiers have small effects, they evolve more readily under a one-allele than a two-allele mechanism (sensu Felsenstein 1981). The strength of selection on the modifier decreases as hybrids decrease in frequency, and so further reinforcement may not occur once hybridization is sufficiently rare. The outcome is qualitatively different when modifiers have large effects, however, for example when a single mutation can cause complete reproductive isolation. In this case modifiers in a two-allele mechanism can be selected as or more strongly than those in a one-allele mechanism. Further, they can spread under quite general conditions. Thus whether complete closure of genetic introgression by reinforcement occurs may depend on the size of effects that mutations have on the sensory systems used in mate choice.