Time required for allele frequency change

Taihe Fan, Shuhao Sun, Pingan He

Abstract


In evolutionary theory, a key issue in selection theory is the expected time for a given amount of allele frequency change to occur. Crow and Kimura, by assuming weak selection, presented explicit results for several important cases of the directional selection and of the stochastic process. Those results played an important role in the theory of population genetics. In this paper, first we show that the weak selection assumption can be removed from most of the results of Crow and Kimura, and then we generalize those results to the most general selection model. Next, we estimate the errors of the deterministic formulae produced by proving that the deterministic formulae are limits of the corresponding stochastic formulae when the size of the population tends to infinity. Finally, we present a result which removes the restriction of Kimura’s corresponding results for a favourite recessive selection model, and we also observe that the conclusion made by Kimura about the favourite dominant selection might not be correct.



doi:10.1017/S1446181117000050

Keywords


population genetics, allele frequency, natural selection, deterministic, stochastic.



DOI: http://dx.doi.org/10.21914/anziamj.v58i0.11001



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.