General theory for stochastic admixture graphs and F-statistics

Theor Popul Biol. 2019 Feb;125:56-66. doi: 10.1016/j.tpb.2018.12.002. Epub 2018 Dec 15.


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.

Keywords: -statistic; Genetic drift; Heterozygosity; Introgression; Markov graphical model; Wright–Fisher model.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Genetic Drift*
  • Genetics, Population* / statistics & numerical data
  • Heterozygote
  • Humans
  • Models, Theoretical
  • Stochastic Processes*