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

• A resolution of the dynamics of a population of two biallelic loci individuals evolving under assortative mating and mutations is provided.
• A bifurcation diagram is constructed to describe the dynamics in a qualitative way.
• The fate of initial conditions is obtained by the employment of a constant of motion.
• A trade-off between assortativity and the effect of mutations is discussed.

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.