  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.
