Extinction conditions for Y-linked mutant-alleles through two-sex branching processes with blind-mating structure

A new two-sex bidimensional branching process is introduced to model the evolution of the number of carriers of an allele and its mutations of a Y-linked gene. A population is assumed in which females and males coexist and mate without the gene influencing the mating process. It is deduced from the model that the key determining conditions for the extinction or survival of the allele are given by the probability that an offspring is female, the rate of mutation, and the mean number of offspring per mating unit. It is also proved that the destiny of the allele's mutations in the population also depends on the survival or extinction of the original allele.