A modified Wright-Fisher model that incorporates Ne: A variant of the standard model with increased biological realism and reduced computational complexity

Journal of Theoretical Biology
Lei ZhaoDavid Waxman

Abstract

The Wright-Fisher model is an important model in evolutionary biology and population genetics. It has been applied in numerous analyses of finite populations with discrete generations. It is recognised that real populations can behave, in some key aspects, as though their size that is not the census size, N, but rather a smaller size, namely the effective population size, Ne. However, in the Wright-Fisher model, there is no distinction between the effective and census population sizes. Equivalently, we can say that in this model, Ne coincides with N. The Wright-Fisher model therefore lacks an important aspect of biological realism. Here, we present a method that allows Ne to be directly incorporated into the Wright-Fisher model. The modified model involves matrices whose size is determined by Ne. Thus apart from increased biological realism, the modified model also has reduced computational complexity, particularly so when Ne⪡N. For complex problems, it may be hard or impossible to numerically analyse the most commonly-used approximation of the Wright-Fisher model that incorporates Ne, namely the diffusion approximation. An alternative approach is simulation. However, the simulations need to be sufficiently detailed that they y...Continue Reading

References

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Aug 5, 2006·Theoretical Population Biology·Steven N EvansMontgomery Slatkin
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May 20, 2015·Ecology Letters·Dena GrossenbacherYaniv Brandvain

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Citations

Apr 18, 2020·Frontiers in Genetics·David Waxman, Andrew D J Overall

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