Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-02T23:59:10.736Z Has data issue: false hasContentIssue false

The distribution of allelic effects under mutation and selection

Published online by Cambridge University Press:  14 April 2009

Steven A. Frank*
Affiliation:
Department of Ecology and Evolutionary Biology, University of California, Irvine, CA 92717, USA
Montgomery Slatkin
Affiliation:
Department of Zoology, University of California, Berkeley, CA 94720, USA
*
Corresponding author.

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.

The Price (1970, 1972) equation is applied to the problem of describing the changes in the moments of allelic effects caused by selection, mutation and recombination at loci governing a quantitative genetic character. For comparable assumptions the resulting equations are the same as those obtained by different means by Barton & Turelli (1987; Turelli & Barton, 1989). The Price equation provides a natural framework within which to examine certain kinds of non-additive allelic effects, recombination and assortative mating. The use of the Price equation is illustrated by finding the equilibrium genetic variance under multiplicative dominance and epistasis and under assortative mating at an additive locus. The limitations of the use of recursion equations for the moments of allelic effects are also discussed.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1990

References

Barton, N. H. & Turelli, M. (1987). Adaptive landscapes, genetic distance and the evolution of quantitative characters. Genetical Research 49, 157173.CrossRefGoogle ScholarPubMed
Frank, S. A. (1987). Demography and sex ratio in social spiders. Evolution 41, 12671281.CrossRefGoogle ScholarPubMed
Grafen, A. (1985). A geometric view of relatedness. Oxford Surveys in Evolutionary Biology 2, 2889.Google Scholar
Kendall, M. & Stuart, A. (1977). The Advanced Theory of Statistics, vol. 1, 4th edn.New York: Macmillan Publ. Co.Google Scholar
Kimura, M. (1965). A stochastic model concerning the maintenance of genetic variability in quantitative characters. Proceedings of the National Academy of Science, USA 54, 731736.CrossRefGoogle ScholarPubMed
Lande, R. (1975). The maintenance of genetic variability by mutation in a polygenic character with linked loci. Genetical Research 26, 221235.CrossRefGoogle Scholar
Lande, R. (1977). The influence of mating system on the maintenance of genetic variability in polygenic characters. Genetics 86, 485498.CrossRefGoogle ScholarPubMed
Lande, R. (1980). The genetic covariance between characters maintained by pleiotropic mutations. Genetics 94, 203215.CrossRefGoogle ScholarPubMed
Lande, R. (1984). The genetic correlation between characters maintained by selection, linkage and inbreeding. Genetical Research 44, 309320.CrossRefGoogle ScholarPubMed
Lande, R. & Arnold, S. J. (1983). The measurement of selection on correlated characters. Evolution 37, 12121226.CrossRefGoogle ScholarPubMed
Li, C. C. (1967). Fundamental theorem of natural selection. Nature 214, 505506.CrossRefGoogle ScholarPubMed
Price, G. R. (1970). Selection and covariance. Nature 227, 520521.CrossRefGoogle ScholarPubMed
Price, G. R. (1972). Extension of covariance selection mathematics. Annals of Human Genetics 35, 485490.CrossRefGoogle ScholarPubMed
Robertson, A. (1966). A mathematical model of the culling process in dairy cattle. Animal Productions 8, 95108.Google Scholar
Robertson, A. (1968). The spectrum of genetic variation. In Population Biology and Evolution (ed. Lewontin, R. C.), pp. 516. Syracuse, New York: Syracuse University Press.Google Scholar
Slatkin, M. (1987). Heritable variation and heterozygosity under a balance between mutations and stabilizing selection. Genetical Research 50, 5362.CrossRefGoogle Scholar
Taylor, P. D. (1988). Inclusive fitness models with two sexes. Theoretical Population Biology 34, 145168.CrossRefGoogle ScholarPubMed
Turelli, M. (1984). Heritable genetic variation via mutation- selection balance: Lerch's zeta meets the abdominal bristle. Theoretical Population Biology 25, 138193.CrossRefGoogle Scholar
Turelli, M. (1986). Gaussian versus non-Gaussian genetic analyses of polygenic mutation-selection balance. In Evolutionary Processes and Theory (ed Karlin, S. and Nevo, E.), pp. 607628. New York: Academic Press.CrossRefGoogle Scholar
Turelli, M. (1988). Population genetic models for polygenic variation and evolution. In Proceedings of the Second International Conference on Quantitative Genetics (ed. Weir, B. S., Eisen, E. J., Goodman, M. and Namkoong, G.), pp. 601618. Sunderland, Mass.: Sinauer Associates.Google Scholar
Turelli, M. & Barton, N. H. (1989). Dynamics of polygenic characters under selection. Theoretical Population Biology (in the press).Google Scholar
Uyenoyama, M. K. (1988). On the evolution of genetic incompatibility systems: incompatibility as a mechanism for the regulation of outcrossing distance. In The Evolution of Sex, (ed. Michod, R. E. and Levin, B. R.), pp. 212232. Sunderland, Mass: Sinauer Associates.Google Scholar
Wade, M.J. (1985). Soft selection, hard selection, kin selection, and group selection. American Naturalist 125, 6173.CrossRefGoogle Scholar