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 (see González et al. (2012). Extinction conditions for Y-linked mutant-alleles through two-sex branching processes with blind-mating structure. Journal of Theoretical Biology 307, 104-116) 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. In that work, it is assumed a population where females and males coexist and mate without the gene having influence on the mating process. Also, 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. It is shown that the fate of its mutations in the population depends on the survival/extinction of the original allele. The present work focuses on the development of Bayesian inference for this model, considering a parametric framework with the reproduction laws belonging to the power series family of distributions. A sample is considered given by the observation of the total number of females and males of each genotype (original allele and its mutations) up to some generation. Using a simulation method based on the Approximate Bayesian Computation methodology, we approximate the posterior distributions of the main parameters of this model. The accuracy of the procedure based on this sample is illustrated by way of a simulated example.

Acknowledgements: The research is supported by the Ministerio de Economía y Competitividad, Junta de Extremadura and the FEDER through the grants MTM2012-31235 and GR10118.