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Diploid populations with selection depending on gene frequency

Published online by Cambridge University Press:  09 April 2009

W. J. Ewens
W. J. Ewens
Affiliation:
Australian National University, Canberra.
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We consider the case of a genetic population for which the selective advantages of the various genotypes are not constant but for each generation depend linearly on the gene frequencies in the population in the previous generation. For such populations, the effect of competition between similar genotypes may be allowed for by suitable choice of the frequency-dependent selective advantages, or, by a reversal of sign, the case where genotypes are favoured by the presence of similar genotypes may also be considered. favoured by the presence of similar genotypes may also be considered. All populations are finite and of constant size so that eventually only one type of gene will survive. The probabilities of survival for each gene are found and compared with the case where there are no frequency-dependent factors. If a small amount of mutation is allowed, gene fixation will not occur and a steady-state distribution of gene frequency will appear. The form of this distribution may be derived simply from the survival probabilities in the corresponding cases where there is no mutation. The main result is that in some cases, frequency-dependent factors have a marked effect on survival probabilities, while in other cases they can be completely ignored. The latter wifi only occur in certain cases where there exists competition between similar genotypes.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 3 , August 1963 , pp. 359 - 374
Copyright
Copyright © Australian Mathematical Society 1963

References

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