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.