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

Miguel González, Cristina Gutiérrez and Rodrigo Martínez
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Miguel González: Department of Mathematics and ICCAEx, Faculty of Sciences, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain
Cristina Gutiérrez: Department of Mathematics and ICCAEx, Faculty of Business, Finance and Tourism, University of Extremadura, Avda. de la Universidad s/n, 10071 Cáceres, Spain
Rodrigo Martínez: Department of Mathematics and ICCAEx, University Center of Plasencia, University of Extremadura, Avda. Virgen del Puerto 2, 10600 Plasencia, Spain

Mathematics, 2021, vol. 9, issue 2, 1-19

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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