Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T07:05:34.207Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantitative genetic variability maintained by mutation-stabilizing selection balance in finite populations

Published online by Cambridge University Press:  14 April 2009

Peter D. Keightley  and
William G. Hill
Peter D. Keightley
Affiliation:
Department of Genetics, University of Edinburgh, West Mains Road, Edinburgh EH9 3JN
William G. Hill
Affiliation:
Department of Genetics, University of Edinburgh, West Mains Road, Edinburgh EH9 3JN
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Models of variability in quantitative traits maintained by a balance between mutation and stabilizing selection are investigated. The effects of mutant alleles are assumed to be additive and to be randomly sampled from a stationary distribution. With a two-allele model the equilibrium genetic variance in an infinite population is independent of the distribution of mutant effects, and dependent only on the total number of mutants appearing per generation. In a finite population, however, both the shape and standard deviation of the distribution of mutant effects are important. The equilibrium variance is lower when most of the mutational variance is contributed by few genes of large effect. Genes of small effect can eventually contribute substantially to the variance with increasing population size (N.) The equilibrium variance can be higher in a finite than an infinite population since near-neutral alleles can drift to intermediate frequencies where selection is weakest. Linkage leads to a reduction in the maintained variance which is small unless linkage is very tight and selection is strong, but the reduction becomes greater with increasing N since more mutants segregate. A multi-allele model is simulated and it is concluded that the two-allele model gives a good approximation of its behaviour. It is argued that the total number of loci capable of influencing most quantitative traits is large, and that the distribution of mutant effects is highly leptokurtic with the effects of most mutants very small, and such mutants are important in contributing to the maintained variance since selection against them is slight. The weakness of the simple optimum model is discussed in relation to the likely consequences of pleiotropy.

Type
Research Article
Information
Genetics Research , Volume 52 , Issue 1 , August 1988 , pp. 33 - 43
Copyright
Copyright © Cambridge University Press 1988

References

Abramowitz, M. & Stegun, I. A.). (1965). Handbook of Mathematical Functions. New York: Dover.Google Scholar
Bulmer, M. G. (1972). The genetic variability of polygenic characters under optimizing selection, mutation and drift. Genetical Research 19, 17–25.CrossRefGoogle ScholarPubMed
Bulmer, M. G. (1980). The Mathematical Theory of Quantitative Genetics. Oxford: Clarendon Press.Google Scholar
Bürger, R. (1986). On the maintenance of genetic variation: Global analysis of Kimura's continuum of alleles model. Journal of Mathematical Biology 24, 341–351.CrossRefGoogle ScholarPubMed
Bürger, R. E., Wagner, G. P. & Stettinger, F. (1988). How much heritable variation can be maintained in finite populations by a mutation selection balance? (In preparation.)CrossRefGoogle Scholar
Clayton, G. A. & Robertson, A. (1955). Mutation and quantitative variation. American Naturalist 89, 151–158.CrossRefGoogle Scholar
David, J. R. & Bocquet, C. (1975). Similarities and differences in latitudinal adaptation of two Drosophila sibling species. Nature 257, 588–590.CrossRefGoogle ScholarPubMed
Falconer, D. S. (1981). Introduction to Quantitative Genetics, 2nd ed.London: Longman.Google Scholar
Gibson, J. B. & Bradley, B. P. (1974). Stabilizing selection in constant and fluctuating environments. Heredity 33, 293–302.CrossRefGoogle ScholarPubMed
Hill, W. G. (1982 a). Rates of change in quantitative traits from fixation of new mutations. Proceedings of the National Academy of Sciences of the USA 79, 142–145.CrossRefGoogle ScholarPubMed
Hill, W. G. (1982 b). Predictions of response to artificial selection from new mutations. Genetical Research 40, 255–278.CrossRefGoogle ScholarPubMed
Hill, W. G. & Keightley, P. D. (1988). Interrelations of mutation, population size, artificial and natural selection. In Proceedings of the Second International Conference on Quantitative Genetics (ed. Eisen, E. J., Goodman, M. M., Namkoong, G. and Weir, B. S.). (In the Press.)Google Scholar
Hill, W. G. & Rasbash, J. (1986). Models of long-term artificial selection in finite populations. Genetical Research 48, 41–50.CrossRefGoogle Scholar
Hyytia, P., Capy, P., David, J. R. & Singh, R. S. (1985). Enzymatic and quantitative variation in European and African populations of Drosophila simulans. Heredity 54, 209–217.CrossRefGoogle ScholarPubMed
Kacser, H. & Burns, J. A. (1973). The control of flux. Symposium of the Society for Experimental Biology 32, 65–104.Google Scholar
Kaufman, P. K., Enfield, F. D. & Comstock, R. E. (1977). Stabilizing selection for pupal weight in Tribolium castaneum. Genetics 87, 327–341.CrossRefGoogle Scholar
Keightley, P. D. & Hill, W. G. (1983). Effects of linkage on response to directional selection from new mutations. Genetical Research 42, 193–206.CrossRefGoogle ScholarPubMed
Keightley, P. D. & Hill, W. G. (1987). Directional selection and variation in finite populations. Genetics 117, 573–582.CrossRefGoogle ScholarPubMed
Kemeny, J. F. & Snell, J. L. (1960). Finite Markov Chains. Princeton: Van Nostrand.Google Scholar
Kimura, M. (1965). A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proceedings of the National Academy of Sciences of the USA 54, 731–736.CrossRefGoogle ScholarPubMed
Kimura, M. (1969). The number of heterozygous nucleotide sites maintained in a finite population due to a steady flux of mutations. Genetics 61, 893–903.CrossRefGoogle Scholar
Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge University Press.CrossRefGoogle Scholar
Kingman, J. F. C. (1978). A simple model for the balance between selection and mutation. Journal of Applied Probability 15, 1–12.CrossRefGoogle Scholar
Lack, D. (1968). Ecological Adaptation for Breeding in Birds. London: Methuen.Google Scholar
Lande, R. (1976). The maintenance of genetic variability by mutation in a polygenic character with linked loci. Genetical Research 26, 221–235.CrossRefGoogle Scholar
Lande, R. (1980). The genetic covariance of characters maintained by pleiotropic mutations. Genetics 94, 203–215.CrossRefGoogle ScholarPubMed
Latter, B. D. H. (1960). Natural selection for an intermediate optimum. Australian Journal of Biological Science 13, 30–35.CrossRefGoogle Scholar
Latter, B. D. H. (1970). Selection in finite populations with multiple alleles. II. Centripetal selection, mutation and isoallelic variation. Genetics 66, 165–186.CrossRefGoogle ScholarPubMed
Mackay, T. F. C. (1987). Transposable element-induced polygenic mutations in Drosophila melanogaster. Genetical Research 49, 225–233.CrossRefGoogle Scholar
McClintlock, B. (1950). The origin and behavior of mutable loci in maize. Proceedings of the National Academy of Sciences of the USA 36, 344–355.CrossRefGoogle Scholar
Mousseau, T. A. & Roff, D. A. (1987). Natural selection and the heritability of fitness components. Heredity 59, 181–197.CrossRefGoogle ScholarPubMed
Mukai, T. & Cockerham, C. C. (1977). Spontaneous mutation rates at enzyme loci in Drosophila melanogaster. Proceedings of the National Academy of Sciences of the USA 74, 2514–2517.CrossRefGoogle ScholarPubMed
Robertson, A. (1956). The effect of selection against extreme deviants based on deviation or on homozygosis. Journal of Genetics 54, 236–248.CrossRefGoogle Scholar
Robertson, A. (1967). The nature of quantitative genetic variation. In Heritage from Mendel (ed. Brink, R. A.), pp. 265–280. Madison, Milwaukee and London: University of Wisconsin Press.Google Scholar
Robertson, A. (1973). The validity of the optimum model. Advances in Applied Probability 6, 17–18.CrossRefGoogle Scholar
Roff, D. A. & Mousseau, T. A. (1987). Quantitative genetics and fitness: Lessons from Drosophila. Heredity 58, 103–118.CrossRefGoogle ScholarPubMed
Rose, M. R. (1982). Antagonistic pleiotropy, dominance and genetic variation. Heredity 48, 63–78.CrossRefGoogle Scholar
Russell, W. A., Sprague, G. F. & Penny, L. H. (1963). Mutations affecting quantitative characters in long-time inbred lines of maize. Crop Science 3, 175–178.CrossRefGoogle Scholar
Slatkin, M. (1987). Heritable variation and heterozygosity under a balance between mutations and stabilizing selection. Genetical Research 50, 53–62.CrossRefGoogle Scholar
Sprague, G. F., Russell, W. A. & Penny, L. H. (1960). Mutations affecting quantitative traits in selfed progeny of doubled monoploid maize stocks. Genetics 45, 855–866.CrossRefGoogle ScholarPubMed
Turelli, M. (1984). Heritable genetic variation via mutation-selection balance: Lerch's zeta meets the abdominal bristle. Theoretical Population Biology 25, 138–193.CrossRefGoogle Scholar
Turelli, M. (1985). Effects of pleiotropy on predictions concerning mutation-selection balance for polygenic traits. Genetics 111, 165–195.CrossRefGoogle ScholarPubMed