  We study the evolution of allele frequencies in a large population where
random mating is violated in a particular way that is related to recent works
on speciation. Specifically, we consider non-random encounters in haploid
organisms described by biallelic genes at two loci and assume that individuals
whose alleles differ at both loci are incompatible. We show that evolution
under these conditions leads to the disappearance of one of the alleles and
substantially reduces the diversity of the population. The allele that
disappears, and the other allele frequencies at equilibrium, depend only on
their initial values, and so does the time to equilibration. However, certain
combinations of allele frequencies remain constant during the process,
revealing the emergence of strong correlation between the two loci promoted by
the epistatic mechanism of incompatibility. We determine the geometrical
structure of the haplotype frequency space and solve the dynamical equations,
obtaining a simple rule to determine equilibrium solution from the initial
conditions. We show that our results are equivalent to selection against double
heterozigotes for a population of diploid individuals and discuss the relevance
of our findings to speciation.
