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THE TIME REQUIRED FOR ALLELE FREQUENCY CHANGE

Published online by Cambridge University Press:  13 March 2017

TAI-HE FAN ,
SHUHAO SUN  and
PING-AN HE
TAI-HE FAN*
Affiliation:
Faculty of Sciences, Zhejiang Sci-Tech University, Hangzhou, 310018, China email [email protected], [email protected]
SHUHAO SUN
Affiliation:
School of Mathematical Science, Monash University, Australia email [email protected]
PING-AN HE
Affiliation:
Faculty of Sciences, Zhejiang Sci-Tech University, Hangzhou, 310018, China email [email protected], [email protected]
*
✉[email protected]
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Abstract

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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.

Keywords

population geneticsallele frequencynatural selectiondeterministicstochastic

MSC classification

Primary: 92D10: Genetics
Secondary: 92D15: Problems related to evolution 92D25: Population dynamics (general)
Type
Research Article
Information
The ANZIAM Journal , Volume 58 , Issue 3-4 , April 2017 , pp. 464 - 473
Copyright
© 2017 Australian Mathematical Society 

References

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