SINGLE LOCUS MASS-ACTION MODEL OF ASSORTATIVE MATING, WITH COMMENTS ON THE PROCESS OF SPECIATION

Genes that cause positive assortative mating have the potential of effecting reproductive isolation and hence speciation. A 1-locus-2-allele model of assortative mating is investigated. In this model, when 2 individuals encounter, they mate with probability 1, .alpha. or .beta. depending on whether they share 2, 1 or 0 alleles, respectively, at the assortative mating locus. The special case where .alpha. = 0.5; .beta. = 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 (.beta. > 0). When the alleles are allowed to mutate from one form to the other, a stable non-trivial equilibrium results, but 1 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, favorable mutants at the assortative mating locus cannot enter a population unless they enhance the fitness of both their genotypes rather substantially. 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.