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The probability of survival of a mutant gene in an age-structured population and implications for the evolution of life-histories

Published online by Cambridge University Press:  14 April 2009

Brian Charlesworth  and
John A. Williamson
Brian Charlesworth
Affiliation:
Department of Genetics, University of Liverpool and Department of Mathematics, University of Colorado, Boulder, Colorado, U.S.A.
John A. Williamson
Affiliation:
Department of Genetics, University of Liverpool and Department of Mathematics, University of Colorado, Boulder, Colorado, U.S.A.

Summary

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An expression is derived for determining the probability of survival of a new favourable mutation in a large random-mating population with overlapping generations. For a gene of small effect, in a near-stationary population, an approximate formula similar to the usual one for discrete generations is obtained. The implications of these results for the evolution of life histories are discussed, using the partial derivatives of the chance of survival of a gene, with respect to changes in age-specific fecundities and survival probabilities. The properties of these derivatives are very similar to those of the derivatives of the intrinsic rate of increase, analysed by Hamilton (1966), thus providing a genetical basis for his conclusions concerning the evolution of life histories.

Type
Research Article
Information
Genetics Research , Volume 26 , Issue 1 , August 1975 , pp. 1 - 10
Copyright
Copyright © Cambridge University Press 1975

References

REFERENCES

Charlesworth, B. (1973). Selection in populations with overlapping generations. V. Natural selection and life histories. American Naturalist 107, 303–311.CrossRefGoogle Scholar
Ewens, W. J. (1969). Population Genetics. London: Methuen.CrossRefGoogle Scholar
Feller, W. (1966). An Introduction to Probability Theory and its Applications, vol. II. New York: John Wiley.Google Scholar
Fisher, R. A. (1922). On the dominance ratio. Proceedings of the Royal Society of Edinburgh 52, 399–433.CrossRefGoogle Scholar
Gadgil, M. & Bossert, W. H. (1970). Life historical consequences of natural selection. American Naturalist 104, 1–26.CrossRefGoogle Scholar
Goodman, L. A. (1971). On the sensitivity of the intrinsic growth rate to changes in the age specific birth and death rates. Theoretical Population Biology 2, 339–354.CrossRefGoogle Scholar
Grenville, T. R. E. (1946). U.S. Life Tables and Actuarial Data. Washington D.C.: U.S. Government Printing Office.Google Scholar
Haldane, J. B. S. (1927). A mathematical theory of natural and artificial selection. Part V: Selection and Mutation. Proceedings of the Cambridge Philosophical Society 28, 838–844.CrossRefGoogle Scholar
Hamilton, W. D. (1966). The moulding of senescence by natural selection. Journal of Theoretical Biology 12, 12–45.CrossRefGoogle ScholarPubMed
Jacquard, A. (1974). The Genetic Structure of Populations. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713–719.CrossRefGoogle ScholarPubMed
Leslie, P. H. (1945). On the use of matrices in certain population mathematics. Biometrika 33, 183–212.CrossRefGoogle ScholarPubMed
Lewontin, R. C. (1965). Selection for colonizing ability. In The Genetics of Colonizing Species (ed. Baker, H. G. and Stebbins, G. L.), pp. 77–94. New York: Academic Press.Google Scholar
Robertson, A. (1960). A theory of limits in artificial selection. Proceedings of the Royal Society of London, B 153, 234–249.Google Scholar
Smith, J. Maynard (1971). On Evolution. Edinburgh: Edinburgh University Press.Google ScholarPubMed
Williams, G. C. (1957). Pleiotropy, natural selection, and the evolution of senescence. Evolution 11, 398–411.CrossRefGoogle Scholar