Limiting Genotype Frequencies of Y-Linked Genes with a Mutant Allele in a Two-Sex Population

Abstract

A two-type two-sex branching process is considered to model the evolution of the number of carriers of an allele and its mutations of a Y-linked gene. The limiting growth rates of the different types of couples and males (depending on the allele, mutated or not, that they carry on) on the set of coexistence of both alleles and on the fixation set of the mutant allele are obtained. In addition, the limiting genotype of the Y-linked gene and the limiting sex frequencies on those sets are established. Finally, the main results have been illustrated with simulated studies contextualized in problems of population genetics.

Keywords

• two-sex Galton–Watson branching process
• genotype frequencies
• mutant allele
• growth rate
• sex ratio