Long-term Buildup of Reproductive Isolation Promoted by Disruptive Selection: How Far Does it Go?

We analyze the long-term evolution of a continuous trait subject to frequency-dependent disruptive selection, and controlled by a single diploid, additive locus. Our simple selection model is a mathematical approximation to many complex systems of ecological interactions resulting in disruptive selection, like, for example, scramble competition and habitat heterogeneity. A polymorphism of two specific alleles at equal frequencies is the unique long-term equilibrium, or ESS, of this system. We then study the evolution of direct assortative mating for the selected trait, through mutations of small effect at modifier loci controlling the degree of assortment. The mating process is described by a model that allows for possible costs of assortment. Unless the cost of assortment is too high, strength of assortment always increases in populations where mating is random or weakly assortative, and also in populations that already practice very strong assortative mating. However, even if it has no cost, assortment can increase continuously from random mating to complete isolation, resulting in sympatric speciation, only if selection is sufficiently strong. In fact, only a modest degree of assortment, corresponding to a continuously stable ESS, can be attained from random mating, when selection intensity is below a certain threshold.