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Extension of the Haldane-Muller principle of mutation load with application for estimating a possible range of relative evolution rate*

Published online by Cambridge University Press:  14 April 2009

Kazushige Ishii  and
Hirotsugu Matsuda
Kazushige Ishii
Affiliation:
College of General Education, Nagoya University, Nagoya 464, Japan
Hirotsugu Matsuda
Affiliation:
Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812, Japan

Summary

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The Haldane-Muller principle of mutation load is generalized so as to be applicable to both cases of strong and very weak selection with any time variation. It is proved that in an infinite asexual haploid population, the average Malthusian parameter m¯ of a population, the evolution rate ν, and the total mutation rate μ satisfy the relation ∂m¯/∂/∂μ = ν/μ−1, so long as each Malthusian parameter is independent of μ. A similar result is also true in a diploid population under genie selection. It is discussed how the above relation gives a restriction on the possible range of values of relative evolution rate ν/μ.

Type
Research Article
Information
Genetics Research , Volume 46 , Issue 1 , August 1985 , pp. 75 - 84
Copyright
Copyright © Cambridge University Press 1985

References

REFERENCES

Crow, J. F. (1970). Genetic loads and the cost of natural selection. In Mathematical Topics in Population Genetics (ed. Kojima, K. I.), pp. 128–177. Heidelberg: Springer.CrossRefGoogle Scholar
Ewens, W. J. (1972). The substitutional load in a finite population. American Naturalist 106, 273–282.Google Scholar
Felsenstein, J. (1971). On the biological significance of the cost of gene substitution. American Naturalist 105, 1–11.Google Scholar
Fisher, R. A. (1958). The Genetical Theory of Natural Selection. New York: Dover.Google Scholar
Haldane, J. B. S. (1937). The effect of variation on fitness. American Naturalist 71, 337–349.Google Scholar
Haldane, J. B. S. (1957). The cost of natural selection. Journal of Genetics 55, 511–524.CrossRefGoogle Scholar
Ishii, K., Matsuda, H. & Ogita, N. (1980). Selection theory of mutation rate. Japanese Journal of Genetics 55, 462.Google Scholar
Ishii, K., Matsuda, H. & Ogita, N. (1982). A mathematical model of biological evolution. Journal of Mathematical Biology 14, 327–353.CrossRefGoogle ScholarPubMed
Kimura, M. (1960). Optimum mutation rate and degree of dominance as determined by the principle of minimum genetic load. Journal of Genetics 57, 21–34.Google Scholar
Kimura, M. (1967). On the evolutionary adjustment of spontaneous mutation rates. Genetical Research 9, 23–34.Google Scholar
Kimura, M. (1968). Evolutionary rate at the molecular level. Nature 217, 624–626.CrossRefGoogle ScholarPubMed
Kimura, M. (1979). The neutral theory of molecular evolution. Scientific American 241, 94–104.Google Scholar
Kimura, M. (1983). The Neutral Theory of Molecular Evolution. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Leigh, E. G. Jr. (1970). Natural selection and mutability. American Naturalist 104, 301–305.CrossRefGoogle Scholar
Leigh, E. G. Jr. (1973). The evolution of mutation rates. Genetics (Supplement) 73, 1–18.Google ScholarPubMed
Lewontin, R. C. (1974). The Genetic Basis of Evolutionary Change. New York: Columbia University Press.Google Scholar
Maynard Smith, J. (1968). ‘Haldane's dilemma’ and the rate of evolution. Nature 219, 1114–1116.Google Scholar
Miyata, T. (1982). Evolutionary changes and functional constraint in DNA sequences. In Molecular Evolution, Protein Polymorphism and the Neutral Theory (ed. Kimura, M.), pp. 233–266. Tokyo: Japan Scientific Societies Press.Google Scholar
Mukai, T., Tachida, H. & Ichinose, M. (1980). Selection for viability at loci controlling protein polymorphisms in Drosophila melanogaster is very weak at most. Proceedings of the National Academy of Science, U.S.A. 77, 4857–4860.Google Scholar
Muller, H. J. (1950). Our load of mutations American Journal of Human Genetics 2, 111–176.Google Scholar
Nei, M. (1971). Fertility excess necessary for gene substitution in regulated populations. Genetics 68, 169–184.CrossRefGoogle ScholarPubMed
Van Valen, L. (1974). Molecular evolution as predicted by natural selection. Journal of Molecular Evolution 3, 89–101.Google Scholar
Zuckerkandl, E. & Pauling, L. (1965). Evolutionary divergence and convergence in proteins. In Evolving Genes and Proteins (ed. Bryson, V. and Vogel, H. J.), pp. 97–166. New York: Academic Press.Google Scholar