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Keywords = two-sex Galton–Watson branching process

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19 pages, 874 KiB  
Article
Limiting Genotype Frequencies of Y-Linked Genes with a Mutant Allele in a Two-Sex Population
by Miguel González, Cristina Gutiérrez and Rodrigo Martínez
Mathematics 2021, 9(2), 131; https://doi.org/10.3390/math9020131 - 9 Jan 2021
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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, [...] Read more.
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. Full article
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