Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-24T00:23:09.124Z Has data issue: false hasContentIssue false
  • English
  • Français

Models of long term artificial selection in finite population

Published online by Cambridge University Press:  14 April 2009

William G. Hill  and
Jonathan Rasbash
William G. Hill
Affiliation:
Institute of Animal Genetics, University of Edinburgh, West Mains Road, Edinburgh EH9 3JN
Jonathan Rasbash
Affiliation:
Institute of Animal 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.

The effects of population size and selection intensity, which are in the breeder's control, are investigated for ranges of values of quantities outside his control, namely the number, initial distribution of frequencies and effects of genes influencing the trait. Two alleles are assumed to be initially segregating at each locus, with no linkage, dominance or epistasis. The effects are assumed to follow a gamma distribution, using a wide range of its two parameters which specify both mean gene effect or selective value and the shape of the distribution, or the ratio of Wright's effective number to actual number of genes. The initial gene frequencies (q) are assumed to be either 0·5 at all loci, uniformly distributed over the range 0–1, or to have a U-shaped distribution, proportional to [q(1 − q)]−1 such as derives from neutral mutation, with gene effect and frequency distributions independent. The mean and variance of selection response and limits, in the absence of new mutation, are derived.

The shape of the distribution of effects is not usually important even up to the selection limit. With appropriate parametrization, the influence of the initial frequency distribution is small over a wide range of parameters. For reasonable choices of parameters, the effects of changing population size from those typically used in animal breeding programmes are likely to be small, but not negligible. For the initial U-shaped frequency distribution, further increases in population size are always expected to give a greater limit, regardless of present value, but not for the other distributions.

Type
Research Article
Information
Genetics Research , Volume 48 , Issue 1 , August 1986 , pp. 41 - 50
Copyright
Copyright © Cambridge University Press 1986

References

Crow, J. F. & Kimura, M. (1970). An Introduction to Population Genetics Theory. New York: Harper & Row.Google Scholar
Dudley, J. W. (1977). Seventy-six generations of selection for oil and protein percentage in maize. In Proceedings of the International Conference on Quantitative Genetics (ed. Pollak, E., Kempthorne, O. and Bailey, T. B. Jr.), pp. 459–473. Ames: Iowa State University Press.Google Scholar
Ewens, W. J. (1979). Mathematical Population Genetics. Berlin: Springer-Verlag.Google Scholar
Falconer, D. S. (1981). Introduction to Quantitative Genetics, 2nd edn.London: Longman.Google Scholar
Hill, W. G. (1969). On the theory of artificial selection in finite populations. Genetical Research 13, 143–163.CrossRefGoogle ScholarPubMed
Hill, W. G. (1982). Predictions of response to artificial selection from new mutations. Genetical Research 40, 255–278.CrossRefGoogle ScholarPubMed
Jinks, J. L. & Towey, P. (1976). Estimating the number of genes in a polygenic system by genotype assay. Heredity 37, 69–81.CrossRefGoogle Scholar
Kimura, M. (1955). Solution of a process of random genetic drift with a continuous model. Proceedings of the National Academy of Sciences USA 41, 144–150.CrossRefGoogle ScholarPubMed
Kimura, M. (1957). Some problems of stochastic processes in genetics. Annals of Mathematical Statistics 28, 882–901.CrossRefGoogle Scholar
Kimura, M. (1979). Model of effectively neutral mutations in which selective contrast is incorporated. Proceedings of the National Academy of Sciences USA 76, 3440–3444.CrossRefGoogle Scholar
Kimura, M. & Crow, J. F. (1964). The number of alleles that can be maintained in a finite population. Genetics 49, 725–738.CrossRefGoogle Scholar
Patterson, T. N. L. (1968). The optimum addition of points to quadrature formulae. Mathematical Computing 22, 847–856.CrossRefGoogle Scholar
Robertson, A. (1960). A theory of limits in artificial selection. Proceedings of the Royal Society of London B 153, 234–249.Google Scholar
Robertson, A. (1970). A theory of limits in artificial selection with many linked loci. In Mathematical Topics in Population Genetics (ed. Kojima, K.), pp. 246–268. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Thoday, J. M. (1961). Location of polygenes. Nature, London 191, 368–370.CrossRefGoogle Scholar
Wright, S. (1952). The genetics of quantitative variability. In Quantitative Inheritance (ed. Reeve, E. C. R and Waddington, C. H.), pp. 5–41. London: Her Majesty's Stationery Office.Google Scholar
Zeng, Z.-B. & Hill, W. G. (1986). The selection limit due to conflict between truncation and stabilizing selection with mutation. Genetics (submitted).CrossRefGoogle Scholar