Title: Bayesian inference in Y-linked two-sex branching processes with mutations: ABC approach,
Abstract: A Y-linked two-sex branching process with mutations and blind choice of males
is a suitable model for analyzing the evolution of the number of carriers of an
allele and its mutations of a Y-linked gene. Considering a two-sex monogamous
population, in this model each female chooses her partner from among the male
population without caring about his type (i.e., the allele he carries). In this
work, we deal with the problem of estimating the main parameters of such model
developing the Bayesian inference in a parametric framework. Firstly, we
consider, as sample scheme, the observation of the total number of females and
males up to some generation as well as the number of males of each genotype at
last generation. Later, we introduce the information of the mutated males only
in the last generation obtaining in this way a second sample scheme. For both
samples, we apply the Approximate Bayesian Computation (ABC) methodology to
approximate the posterior distributions of the main parameters of this model.
The accuracy of the procedure based on these samples is illustrated and
discussed by way of simulated examples.