A single locus mass-action model of assortative mating, with comments on the process of speciation

Abstract

Genes that cause positive assortative mating have the potential of effecting reproductive isolation and hence speciation. A one-locus-2-allele model of assortative mating is investigated. In this model, when two individuals encounter, they mate with probability 1, a or ¿3 depending on whether they share 2, 1 or 0 alleles respectively at the assortative mating locus. The special case where a = 0-5; = 0 is investigated extensively. Assortative mating eliminates genetic polymorphisms. The only non-trivial equilibrium occurs when each homozygote has a frequency of 0-5 and there are no heterozygotes, but this equilibrium is unstable. Numerical analysis suggests that this is also true when assortment is only partial (j3>0). When the alleles are allowed to mutate from one form to the other, a stable non-trivial equilibrium results, but one allele or the other is very rare. When the alleles affect fitness in some additional way, the assortative mating locus will be polymorphic provided there is substantial hybrid superiority; e.g. when the homozygotes are equally fit, the heterozygote must be approximately twice as fit. Similarly, favourable mutants at the assortative mating locus cannot enter a population unless they enhance the fitness of both their genotypes rather substantially. Thus, in the hypothesis of speciation where premating isolating mechanisms are supposed to evolve as a response to selection against hybrids, there is some doubt as to whether genetic variation for assortative mating would exist, and, if it did, whether it would always respond to selection. © 1979 The Genetical Society of Great Britain.