Modeling Y-Linked Pedigrees through Branching Processes

Miguel González, Cristina Gutiérrez and Rodrigo Martínez
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Miguel González: Department of Mathematics and ICCAEx, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain
Cristina Gutiérrez: Department of Mathematics and ICCAEx, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain
Rodrigo Martínez: Department of Mathematics and ICCAEx, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain

Mathematics, 2020, vol. 8, issue 2, 1-17

Abstract: A multidimensional two-sex branching process is introduced to model the evolution of a pedigree originating from the mutation of an allele of a Y-linked gene in a monogamous population. The study of the extinction of the mutant allele and the analysis of the dominant allele in the pedigree is addressed on the basis of the classical theory of multi-type branching processes. The asymptotic behavior of the number of couples of different types in the pedigree is also derived. Finally, using the estimates of the mean growth rates of the allele and its mutation provided by a Gibbs sampler, a real Y-linked pedigree associated with hearing loss is analyzed, concluding that this mutation will persist in the population although without dominating the pedigree.

Keywords: Y-linked genes; pedigree; Markov chains; two-sex branching processes; multi-type branching processes; Gibbs sampler; hearing loss (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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