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