Inferring the Joint Demographic History of Multiple Populations: Beyond the Diffusion Approximation

Genetics. 2017 Jul;206(3):1549-1567. doi: 10.1534/genetics.117.200493. Epub 2017 May 11.


Understanding variation in allele frequencies across populations is a central goal of population genetics. Classical models for the distribution of allele frequencies, using forward simulation, coalescent theory, or the diffusion approximation, have been applied extensively for demographic inference, medical study design, and evolutionary studies. Here we propose a tractable model of ordinary differential equations for the evolution of allele frequencies that is closely related to the diffusion approximation but avoids many of its limitations and approximations. We show that the approach is typically faster, more numerically stable, and more easily generalizable than the state-of-the-art software implementation of the diffusion approximation. We present a number of applications to human sequence data, including demographic inference with a five-population joint frequency spectrum and a discussion of the robustness of the out-of-Africa model inference to the choice of modern population.

Keywords: demographic inference; diffusion approximation; joint allele frequency spectrum; moments equations.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • African Continental Ancestry Group / genetics
  • Gene Frequency*
  • Human Migration*
  • Humans
  • Models, Genetic*
  • Mutation Rate
  • Population / genetics*