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Quantitative genetic variability maintained by mutation-stabilizing selection balance: sampling variation and response to subsequent directional selection

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
*
† Corresponding author.

Summary

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A model of genetic variation of a quantitative character subject to the simultaneous effects of mutation, selection and drift is investigated. Predictions are obtained for the variance of the genetic variance among independent lines at equilibrium with stabilizing selection. These indicate that the coefficient of variation of the genetic variance among lines is relatively insensitive to the strength of stabilizing selection on the character. The effects on the genetic variance of a change of mode of selection from stabilizing to directional selection are investigated. This is intended to model directional selection of a character in a sample of individuals from a natural or long-established cage population. The pattern of change of variance from directional selection is strongly influenced by the strengths of selection at individual loci in relation to effective population size before and after the change of regime. Patterns of change of variance and selection responses from Monte Carlo simulation are compared to selection responses observed in experiments. These indicate that changes in variance with directional selection are not very different from those due to drift alone in the experiments, and do not necessarily give information on the presence of stabilizing selection or its strength.

Type
Research Article
Information
Genetics Research , Volume 54 , Issue 1 , August 1989 , pp. 45 - 58
Copyright
Copyright © Cambridge University Press 1989

References

Atkins, K. D. & Thompson, R. (1986). Predicted and realised responses to selection for an index of bone length and body weight in Scottish Blackface sheep. Animal Production 43, 421–435.Google Scholar
Avery, P. J. & Hill, W. G. (1977). Variability in genetic parameters among small populations. Genetical Research 29, 193–213.CrossRefGoogle ScholarPubMed
Avery, P. J. & Hill, W. G. (1979). Variance in quantitative traits due to linked dominant genes and variance in heterozygosity in small populations. Genetics 91, 817–844.CrossRefGoogle ScholarPubMed
Barton, N. H. (1986). The maintenance of polygenic variation through a balance between mutation and stabilizing selection. Genetical Research 47, 209–216.CrossRefGoogle ScholarPubMed
Barton, N. H. & Turelli, M. (1987). Adaptive landscapes, genetic distance and the evolution of quantitative characters. Genetical Research 49, 157–173.CrossRefGoogle ScholarPubMed
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. (1976). The effect of selection on genetic variability: a simulation study. Genetical Research 28, 101–117.CrossRefGoogle ScholarPubMed
Bulmer, M. G. (1980). The Mathematical Theory of Quantitative Genetics. Oxford: Clarendon Press.Google Scholar
Burger, R. E., Wagner, G. P. & Stettinger, F. (1988). How much heritable variation can be maintained in finite populations by a mutation selection balance? Evolution (in the press).Google Scholar
Clayton, G. A., Morris, J. A. & Robertson, A. (1957). An experimental check on quantitative genetical theory. I. Short-term responses to selection. Journal of Genetics 55, 131–151.CrossRefGoogle Scholar
Cockerham, C. C. & Tachida, H. (1987). Evolution and maintenance of quantitative genetic variation by mutations. Proceedings of the National Academy of Sciences, USA 84, 6205–6209.CrossRefGoogle ScholarPubMed
Falconer, D. S. (1973). Replicated selection for body weight in mice. Genetical Research 22, 291–321.CrossRefGoogle ScholarPubMed
Frankham, R., Jones, L. P. & Barker, J. S. F. (1968). The effects of population size and selection intensity in selection for a quantitative character in Drosophila. I. Short term response to selection. Genetical Research 12, 237–248.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, 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. (1989). Mutation and maintenance of quantitative genetic variation. In: Evolution and Animal Breeding (ed. Hill, W. G. and Mackay, T. F. C.). Wallingford, Oxford: C.A.B. International (in the press).Google Scholar
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. Weir, B. S., Eisen, E. J., Goodman, M. M. and Namkoong, G.), pp. 57–70. Sunderland, Massachusetts: Sinauer.Google Scholar
Hill, W. G. & Rasbash, J. (1986). Models of long term artificial selection in finite populations. Genetical Research 48, 41–50.CrossRefGoogle Scholar
Kacser, H. & Burns, J. A., (1981). The molecular basis of dominance. Genetics 97, 639–666.CrossRefGoogle ScholarPubMed
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
Keightley, P. D. & Hill, W. G. (1988). Quantitative genetic variability maintained by mutation-stabilizing selection balance in finite populations. Genetical Research 52, 33–43.CrossRefGoogle ScholarPubMed
Kingman, J. F. C. (1978). A simple model for the balance between selection and mutation. Journal of Applied Probability 15, 1–12.CrossRefGoogle Scholar
Kimura, M. (1965). A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proceedings of the National Academy of Sciences, 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
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. (1988). Quantitative genetics and evolutionary theory. In Proceedings of the Second International Conference on Quantitative Genetics (ed. Weir, B. S., Eisen, E. J., Goodman, M. M. and Namkoong, G.), pp. 71–85. Sunderland, Massachusetts: Sinauer.Google Scholar
Latter, B. D. H. (1960). Natural selection for an intermediate optimum. Australian Journal of Biological Science 13, 30–35.CrossRefGoogle Scholar
Lynch, M. & Hill, W. G. (1986). Phenotypic evolution by neutral mutation. Evolution 40, 915–935.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. (1959). The sampling variance of the genetic correlation coefficient. Biometrics 15, 219–226.CrossRefGoogle Scholar
Robertson, A. (1967). The nature of quantitative genetic variation. In Heritage from Mendel (ed. Brink, R. A.), pp. 265–280. University of Wisconsin Press, Madison, Milwaukee and London.Google Scholar
Robertson, A. (1973). The validity of the optimum model. Advances in Applied Probability 6, 17–18.CrossRefGoogle Scholar
Robertson, A. (1978). The time of detection of recessive visible genes in small populations. Genetical Research 31, 255–264.CrossRefGoogle Scholar
Ruano, R. G., Orozco, F. & Lopez-Fanjul, C. (1975). The effect of different selection intensities on selection responses in egg-laying of Tribolium castaneum. Genetical Research 25, 17–27.CrossRefGoogle Scholar
Shrimpton, A. E. & Robertson, A. (1988). The isolation of polygenic factors controlling bristle score in Drosophila melanogaster. II. Distribution of third chromosome bristle effects within chromosome sections. Genetics 118, 445–459.CrossRefGoogle ScholarPubMed
Thoday, J. M., Gibson, J. B. & Spickett, S. G. (1964). Regular responses to selection. 2. Recombination and accelerated response. Genetical Research 5, 1–19.CrossRefGoogle Scholar
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
Yoo, B. H. (1980). Long-term selection for a quantitative character in large replicate populations of Drosophila melanogaster. Genetical Research 35, 1–17.CrossRefGoogle Scholar