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Modeling Y-Linked Pedigrees through Branching Processes

Author

Listed:
  • Miguel González

    (Department of Mathematics and ICCAEx, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain
    All the authors contributed equally to this work.)

  • Cristina Gutiérrez

    (Department of Mathematics and ICCAEx, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain
    All the authors contributed equally to this work.)

  • Rodrigo Martínez

    (Department of Mathematics and ICCAEx, University of Extremadura, Avda. Elvas s/n, 06006 Badajoz, Spain
    All the authors contributed equally to this work.)

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.

Suggested Citation

  • Miguel González & Cristina Gutiérrez & Rodrigo Martínez, 2020. "Modeling Y-Linked Pedigrees through Branching Processes," Mathematics, MDPI, vol. 8(2), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:256-:d:321079
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    References listed on IDEAS

    as
    1. Neves, Armando G.M. & Moreira, Carlos H.C., 2006. "Applications of the Galton–Watson process to human DNA evolution and demography," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 132-146.
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