Hybrid Mendelian–Bayesian Algorithm for Probabilistic Inference of Genotypes in Pedigrees

Abstract

This study presents a hybrid algorithm—grounded in Mendelian inheritance and Bayesian updating—to infer genotype probability distributions from observable phenotypes (coat color) and pedigree structures when direct genetic data are unavailable. Each individual is represented by a genotype distribution (with fully known genotypes modeled as degenerate distributions), and a distribution-based “cross” operator combines parental distributions to obtain the expected genotype distribution in the offspring. Phenotypic constraints are incorporated by filtering out incompatible genotypes and renormalizing, while both downward and upward inference are supported: offspring evidence updates parental beliefs and vice versa. Validated on simulated populations (small nuclear families and deeper pedigrees) for a single biallelic locus, the algorithm reproduces classical Mendelian proportions under parental certainty, coherently propagates uncertainty when parents are partially specified, and converges steadily under repeated observations. Although current assumptions (single locus, no mutation or recombination, perfect phenotype observation) limit immediate applicability to complex real data, the method’s clarity, interpretability, and ease of implementation make it a practical and explainable tool for breeding programs, conservation planning, and education. It also provides a transparent foundation for future multilocus extensions and models incorporating observation noise.