General theory for stochastic admixture graphs and F-statistics

TL;DR

This paper develops a comprehensive mathematical framework for admixture graphs using graphical models, analyzing properties of F-statistics and the Wright-Fisher model to understand population genetics and gene flow.

Contribution

It introduces a general theoretical approach to admixture graphs, linking them with F-statistics and heterozygosity loss, advancing the mathematical understanding of population genetics models.

Findings

Mathematical properties of admixture graphs are characterized.

A general expression for heterozygosity loss is derived.

The framework connects F-statistics with population structure analysis.

Abstract

We provide a general mathematical framework based on the theory of graphical models to study admixture graphs. Admixture graphs are used to describe the ancestral relationships between past and present populations, allowing for population merges and migration events, by means of gene flow. We give various mathematical properties of admixture graphs with particular focus on properties of the so-called $F$-statistics. Also the Wright-Fisher model is studied and a general expression for the loss of heterozygosity is derived.