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Y-linked two-sex branching processes with mutations

The genetic causes of infertility in males or the history of paternal lineages are some relevant problems directly related to mutations in Y-linked genes. The interest of how these genes and their mutations evolve in a population leads us to introduce a new two-sex two-type branching process to model the evolution of the number of carriers of an allele (and its mutations) of a Y-linked gene. It is assumed a population where females and males coexist and mate without the gene having influence on the mating process. In this work it is proved that the key to determine conditions for the extinction / survival of such allele are given by the probability of an offspring to be female, the rate of mutation and the mean number of offspring per couple. Also, it shown that the fate of its mutations in the population depends on the survival / extinction of the original allele. Finally, the theoretical results are illustrated by means of simulated examples.
 
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