A dynamical analysis of allele frequencies in populations evolving under assortative mating and mutations

We study the evolution of allele frequencies for infinitely large populations subjected to mutations and assortative mating. Haploid individuals are described by two biallelic genes, and assortativity is introduced by preventing mating between individuals whose alleles differ at both loci. In the absence of mutations, evolution leads to the disappearance of one of the alleles. However, a particular combination of the allele frequencies at the two loci is maintained constant. We show that this combination remains constant even when mutations are present, revealing the robustness of the epistatic correlation introduced by the non-random mating mechanism. We obtain the equilibrium solutions for arbitrary values of the mutation rate and provide a description of the dynamics on the basis of a bifurcation analysis.