Bayesian Inference in Y-Linked Two-Sex Branching Processes with Mutations: ABC Approach

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 a Y-linked allele and its mutations. Such a model considers a two-sex monogamous population in which 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 these models by developing Bayesian inference in a parametric framework. First, we consider as a 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 in the last generation. Subsequently, we introduce the information on the mutated males in only the last generation, obtaining in this way a second sample scheme. For both samples, we apply the Approximate Bayesian Computation (ABC) method to approximate the posterior distributions of the main parameters of the model. The accuracy of the procedure based on these samples is illustrated and discussed by way of simulated examples.

Automated summary

The study analyzes the evolution of Y-linked allele carriers and mutations using a Y-linked two-sex branching process model, estimating main parameters through Bayesian inference. By observing total number of females, males, males of each genotype in last generation, and introducing information on mutated males in last generation, the study approximates the posterior distributions of model parameters using Approximate Bayesian Computation (ABC). Illustrations and discussion on accuracy of the procedure based on simulated examples are provided.