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

Area of Science:

• Population Genetics
• Mathematical Biology
• Evolutionary Dynamics

Background:

• Y-linked alleles and their mutations are crucial for understanding male lineage evolution.
• Modeling these processes requires accounting for population structure, mating behavior, and genetic changes.
• Previous models may not fully capture the complexities of Y-linked inheritance with mutations and non-assortative mating.

Purpose of the Study:

• To develop and apply Bayesian inference methods for estimating key parameters in a Y-linked two-sex branching process model.
• To analyze the evolution of Y-linked allele carrier numbers and mutations under specific population dynamics.
• To assess the effectiveness of different data sampling schemes for parameter estimation.

Main Methods:

• A Y-linked two-sex branching process model incorporating mutations and random male choice was utilized.
• Bayesian inference within a parametric framework was developed for parameter estimation.
• Approximate Bayesian Computation (ABC) was applied to approximate posterior distributions using two distinct sample schemes.

Main Results:

• The study demonstrates the feasibility of using Bayesian inference and ABC for parameter estimation in the proposed model.
• Two sample schemes were evaluated: one observing population sizes and genotypes, the other focusing on mutated males in the final generation.
• Simulated examples confirmed the accuracy and utility of the developed estimation procedures.

Conclusions:

• The developed Bayesian inference framework, particularly using Approximate Bayesian Computation (ABC), provides a robust method for analyzing Y-linked genetic evolution.
• The choice of data sampling scheme significantly impacts the precision of parameter estimates.
• This modeling approach offers valuable insights into the dynamics of Y-linked alleles and their mutations within a population.