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The effect of random selection coefficients on populations of finite size – some particular models

Published online by Cambridge University Press:  14 April 2009

P. J. Avery
P. J. Avery
Affiliation:
Department of Biomathematics, University of Oxford, Pusey St., OxfordOX1 2JZ
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The model of random selection coefficients is considered in the context of a finite population of diploids. The selection coefficients of the homozygotes are allowed to vary with equal variance while the fitness of the heterozygote is kept fixed. Steady-state solutions are found in the case of equal two-way mutation rates with particular reference to the expected heterozygosity. Increasing the variance of the selection coefficients of the homozygotes is found to uniformly increase the heterozygosity for all values of the average selection coefficients and its effect is largest when the selection coefficients of the homozygotes are fully correlated. The fate of mutant genes is also considered in the case of random selection coefficients by looking at the probability of ultimate fixation and the mean times to fixation and extinction. The errors in previous calculations (e.g. Kimura, 1954; Ohta, 1972) are pointed out. It is found that a small average heterozygote advantage together with a reasonable degree of variance in the coefficients can cause an unexpectedly large amount of heterozygosity to be maintained. It is also seen that probabilities of fixation and mean times to boundaries are usually increased by increasing the variance showing that it in fact helps to keep the population heterozygous for much longer than the non-random case. This is in contradiction to some conclusions of Karlin & Levikson (1974) because their haploid results are not easily extendable to the consideration of this sort of diploid model.

Type
Research Article
Information
Genetics Research , Volume 29 , Issue 2 , April 1977 , pp. 97 - 112
Copyright
Copyright © Cambridge University Press 1977

References

REFERENCES

Fisher, R. A. & Ford, E. B. (1947). The spread of a gene in natural conditions in a colony of the moth Panamixia dominula L. Heredity 1, 143–174.CrossRefGoogle Scholar
Gillespie, J. H. (1973). Natural selection with varying selection coefficients – a haploid model. Genetical Research 21, 115–120.CrossRefGoogle Scholar
Hartl, D. L. & Cook, R. D. (1973). Balanced polymorphisms of quasi-neutral alleles. Theoretical Population Biology 4, 163–172.Google Scholar
Hartl, D. L. & Cook, R. D. (1974). Stochastic selection in large and small populations. Theoretical Population Biology 7, 55–64.Google Scholar
Hartl, D. L. & Cook, R. D. (1975). Stochastic selection and the maintenance of genetic variation. In Population Genetics and Ecology (ed. Karlin, S. and Nevo, E.). Academic Press, London and New York.Google Scholar
Jensen, L. (1973). Random selection advantages of genes and their probability of fixation. Genetical Research 21, 215–219.CrossRefGoogle Scholar
Karlin, S. & Levikson, B. (1974). Temporal fluctuations in selection intensities: case of small population size. Theoretical Population Biology 6, 383–412.Google Scholar
Kimura, M. (1954). Process leading to quasi-fixation of genes in natural populations due to random fluctuation of selection intensities. Genetics 39, 280–295.Google Scholar
Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713–719.CrossRefGoogle ScholarPubMed
Kimura, M. (1964). Diffusion models in Population Genetics. Journal of Applied Probability 1, 177–232.Google Scholar
Kimura, M. & Ohta, T. (1969 a). The average number of generations until fixation of a mutant gene in a finite population. Genetics 61, 763–771.Google Scholar
Kimura, M. & Ohta, T. (1969 b). The average number of generations until extinction of an individual mutant gene in a finite population. Genetics 63, 701–709.CrossRefGoogle Scholar
Nei, M. (1971). Extinction times of deleterious mutant genes in large populations. Theoretical Population Biology 2, 419–425.CrossRefGoogle ScholarPubMed
Ohta, T. (1972). Fixation probability of a mutant influenced by random fluctuation of selection intensity. Genetical Research 19, 33–38.CrossRefGoogle Scholar
Ohta, T. & Kimura, M. (1972). Fixation time of overdominant alleles influenced by random fluctuation of selection intensity. Genetical Research 20, 1–7.Google Scholar
Powell, J. R. (1971). Genetic polymorphisms in varied environments. Science 174, 1035–1036.CrossRefGoogle ScholarPubMed
Smith, D. A. S. (1975). Sexual selection in a wild population of the butterfly Danaus chrysippus L. Science 187, 664–665.Google Scholar
Takahata, N., Ishii, K. & Matsuda, H. (1975). Effect of temporal fluctuation of selection coefficient on gene frequency in a population. Proceedings of the National Academy of Sciences 72, 4541–4545.CrossRefGoogle ScholarPubMed
Wright, S. (1938). The distribution of gene frequencies under irreversible mutation. Proceedings of the National Academy of Sciences 24, 253–259.CrossRefGoogle ScholarPubMed
Wright, S. (1949). Adaptation and selection. In Genetics, Palaeontology and Evolution (ed. Jepson, et al. ). Princeton University Press, Princeton, New Jersey, U.S.A.Google Scholar