Approximate Bayesian Computation for Two-Sex Branching Processes: Modeling X-linked Inheritance

M. González Velasco, C. Gutiérrez Pérez, R. Martínez Quintana

X-linked two-sex branching processes offer a probabilistic framework to study the evolution of two X-linked alleles in a population. We consider a dominant allele and a recessive allele associated with a severe disorder, where affected individuals have very limited reproductive success or do not reach reproductive age. We propose a nonparametric Bayesian inference approach to estimate key population parameters, including the sex ratio, recessive allele transmission rate, and mean offspring numbers by genotype. Since the likelihood is analytically intractable due to partial observation and unobserved branching structure, we apply Approximate Bayesian Computation (ABC). Carefully chosen summary statistics based on the process’s asymptotic behavior allow us to handle identifiability issues. The method’s performance is demonstrated through an extensive simulation study in R. This work is supported by grant PID2023-152359NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by ERDF/EU.

Keywords: Two-sex branching processes, X-linked genes, Approximate Bayesian computation

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