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.
Highlights
In many populations, the sex of an individual is determined by a pair of chromosomesX and Y
This work deals with the problem of determining the limiting growth rates and the limiting genotype frequencies of two alleles named R and r of a Y-linked gene, allowing the possibility that the R-allele mutates into the r-form assuming a two-sex population
The model studied in this communication is the so-called Y-linked bisexual branching processes with mutations and blind choice of males defined in [5]
Summary
The sex of an individual is determined by a pair of chromosomes. In this paper it is assumed that R represents the nonmutant allelic form of the gene which can mutate and give rise to new allelic forms, all of them denoted by r and called mutant alleles. The latter can mutate this is ignored in this case because we do not further distinguish between possible types of mutation, and a reversion, i.e., a mutation from r back to R, is not allowed.
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