population expansion

Jouganous J, Long W, Ragsdale AP & Gravel S 2017 Inferring the joint demographic history of multiple populations: beyond the diffusion approximation. Genetics 206:1549-1567.

  • 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
  • biases inherent to Kingman's coalescent or the diffusion approximation, which are benign in small samples, can become important in contemporary data sets
  • we used our method to update the out-of-Africa expansion model described in Gutenkunst et al. (2009) and Gravel et al. (2011)
  • these models are used in a wide variety of medical and evolutionary applications
  • we updated the mutation coefficient and the generation time to more realistic values
  • μ = 1.44 × 10−8
  • Tg = 29 year
  • Zivković et al. (2015) [...] also proposed a truncation approach to resolve the moment closure problem
  • this truncation approach would not be practical in the moment representation of Equation 5
  • setting high-order terms to zero would amount to neglecting selection altogether
  • the Evans et al. (2007) equations and the ones presented here are algebraically equivalent
  • the main advantages of the present formulation is numerical stability, ease of generalization, and the availability of the moment closure approach
  • we described a highly accurate and numerically robust approach to simulate the evolution of allele frequency distributions over time in a discrete Wright-Fisher model
  • this approach can be used wherever the diffusion approximation is applicable
  • it typically provides faster, more accurate, and more robust solutions
  • the choice of a "representative" population in out-of-Africa models can substantially affect the inferred parameters, even ones not directly involving the population
  • the choice of the African population has the largest impact on the inferred demography
  • previous out-of-Africa models may be applicable to many Eurasian populations, but not to other African populations
  • building models including more than one African population will likely provide much more information about human ancestry both in Africa and across the world