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The genetic variability of polygenic characters under optimizing selection, mutation and drift

Published online by Cambridge University Press:  14 April 2009

M. G. Bulmer
Affiliation:
Department of Biomathematics, University of Oxford
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Summary

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The effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci with equal effects without dominance was investigated theoretically. Conditions for a stable equilibrium under selection and mutation, in the absence of drift, have been obtained, and hence the amount of genetic variability which can be maintained by mutation has been determined. An approximate expression for the average amount of genetic variability to be expected in the presence of drift in a population of finite size has also been obtained and evaluated.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1972

References

REFERENCES

Airey, J. R. (1926). The confluent hypergeometric function. British Association Reports, pp. 276294.Google Scholar
Airey, J. R. (1927). The confluent hypergeometric function. British Association Reports, pp. 220244.Google Scholar
Bulmer, M. G. (1971 a). The stability of equilibria under selection. Heredity 27, 157162.CrossRefGoogle ScholarPubMed
Bulmer, M. G. (1971 b). Stable equilibria under the two island model. Heredity 27, 321330CrossRefGoogle ScholarPubMed
Erdélyi, A. (1954). Tables of Integral Transforms. (Bateman Manuscript Project.) New York: McGraw-Hill.Google Scholar
Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford: Clarendon Press.CrossRefGoogle Scholar
Haldane, J. B. S. (1932). The Causes of Evolution. London: Longmans, Green.Google Scholar
Haldane, J. B. S. (1953). The measurement of natural selection. Proceedings of the IXth International Congress of Genetics, pp. 480483.Google Scholar
Kimura, M. (1964). Diffusion models in population genetics. Journal of Applied Probability 1, 177232.CrossRefGoogle Scholar
Kimura, M. (1965). A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proceedings of the National Academy of Sciences, U.S.A. 54, 731736.CrossRefGoogle ScholarPubMed
Latter, B. D. H. (1960). Natural selection for an intermediate optimum. Australian Journal of Biological Sciences 13, 3045.CrossRefGoogle Scholar
Latter, B. D. H. (1969). Models of quantitative variation and computer simulation of selection response. In Computer Applications in Genetics (ed. Morton, N. E.), pp. 4960. University of Hawaii Press.Google Scholar
Latter, B. D. H. (1970). Selection in finite populations with multiple alleles. II. Centripetal selection, mutation, and isoallelic variation. Genetics 66, 165186.CrossRefGoogle ScholarPubMed
Robertson, A. (1956). The effect of selection against extreme deviants based on deviation or on homozygosis. Journal of Genetics 54, 236248.CrossRefGoogle Scholar
Rushton, S. & Lang, E. D. (1954). Tables of the confluent hypergeometric function. Sankhyā: The Indian Journal of Statistics 13, 377411.Google Scholar
Slater, L. J. (1964). Confluent hypergeometric functions. In Handbook of Mathematical Functions (ed. Abramowitz, M. & Stegun, I. A.), pp. 503535. National Bureau of Standards, Applied Mathematics Series 55.Google Scholar
Wright, S. (1935). Evolution in populations in approximate equilibrium. Journal of Genetics 30, 257266.CrossRefGoogle Scholar
Wright, S. (1937). The distribution of gene frequencies in populations. Proceedings of the National Academy of Science 23, 307320.CrossRefGoogle ScholarPubMed