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Proc Natl Acad Sci U S A. Nov 1977; 74(11): 5096–5098.
PMCID: PMC432106

Error estimate for the diffusion approximation of the Wright--Fisher model.

Abstract

The Wright--Fisher model and its approximating diffusion model are compared in terms of the expected value of a smooth but arbitrary function of nth-generation gene frequency. In the absence of selection, this expectation is shown to differ in the two models by at most a linear combination (with coefficients depending only on the derivatives of the smooth function involved) of the maximum mutation rate and the reciprocal of the population size.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.
  • Wright S. Evolution in Mendelian Populations. Genetics. 1931 Mar;16(2):97–159. [PMC free article] [PubMed]
  • Wright S. The Differential Equation of the Distribution of Gene Frequencies. Proc Natl Acad Sci U S A. 1945 Dec;31(12):382–389. [PMC free article] [PubMed]
  • EWENS WJ. THE ADEQUACY OF THE DIFFUSION APPROXIMATION TO CERTAIN DISTRIBUTIONS IN GENETICS. Biometrics. 1965 Jun;21:386–394. [PubMed]

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