Selection and mutation at a diallelic \(X\)-linked locus (Q1177000)

The evolution at a diallelic \(X\)-linked locus under the influence of (constant) selection and mutation is studied, and extensive results on equilibria and convergence of gene frequencies to equilibria are given. The model considered is the classical model of an infinite diploid population with non-overlapping discrete generations and random mating. It is proved that if mutation rates are less than one third, then (in most cases) there exist at most three equilibria and global convergence of gene frequencies to equilibria occurs. This convergence is shown to be monotone from a certain generation on if every other generation is skipped. Phase portraits for the allelic frequencies are determined. Finally, the maintained results are applied to the inheritance dynamics of human hemophilia.