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Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles*

Published online by Cambridge University Press:  14 April 2009

Motoo Kimura
Motoo Kimura
Affiliation:
National Institute of Genetics, Mishima, Japan
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1. The average and the effective numbers of alleles maintained in a finite population due to mutational production of neutral isoalleles were studied by mathematical analysis and computer simulation.

2. The exact formula was derived for the effective number (ne) of alleles maintained in a population of effective size Ne, assuming that there are K possible allelic states and mutation occurs with equal frequency in all directions. If the number of allelic states is so large that every mutation is to a new, not pre-existing, allele, we have ne = 4Neu+1 − 2Neu2, where u is the mutation rate. Thus, the approximation formula, ne = 4Neu+1, given by Kimura & Crow (1964) is valid as long as 2Neu2 ≪ 1.

3. The formula for the average number of alleles (na) maintained in a population of actual size N and effective size Ne was derived by using the method of diffusion approximation. If every mutation is to a new, not pre-existing, allele, we obtain

where M = 4Neu. The average number of alleles as a function of M and N is listed in Table 1.

4. In order to check the validity of the diffusion approximations, Monte Carlo experiments were carried out using the computer IBM 7090. The experiments showed that the approximations are satisfactory for practical purposes.

5. It is estimated that among the mutations produced by DNA base substitutions, synonymous mutations, that is, those which cause no alterations of amino acids, amount roughly to 0·2–0·3 in vertebrates. Incompletely synonymous mutations, that is, those which lead to substitution of chemically similar amino acids at a different position of the polypeptide chain from the active site and therefore produce almost no phenotypic effects, must be very common. Together with synonymous mutations, they might constitute at least some 40% of all mutations. These considerations suggest that neutral and nearly neutral mutations must be more common than previously considered.

Type
Research Article
Information
Genetics Research , Volume 11 , Issue 3 , June 1968 , pp. 247 - 270
Copyright
Copyright © Cambridge University Press 1968

References

REFERENCES

Brenner, S., Barnett, L., Katz, E. R. & Crick, F. H. C. (1967). UGA: A third nonsense triplet in the genetic code. Nature, Lond. 213 (5075), 449–450.CrossRefGoogle Scholar
Clayton, G. & Robertson, A. (1955). Mutation and quantitative variation. Am. Nat. 89, 151–158.CrossRefGoogle Scholar
Crick, F. H. C. (1966). The genetic code: III Scient. Am. 215 (4), 55–62.CrossRefGoogle Scholar
Crow, J. F. & Kimura, M. (1956). Some genetic problems in natural populations. Proc. Third Berkeley Syrup. on Math. Stat. and Prob. 4, 1–22.Google Scholar
Ewens, W. J. (1964). The maintenance of alleles by mutation. Genetics 50, 891–898.CrossRefGoogle ScholarPubMed
Ewens, W. J. & Ewens, P. M. (1966). The maintenance of alleles by mutation—Monte Carlo results for normal and self-sterility populations. Heredity 21, 371–378.CrossRefGoogle ScholarPubMed
Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford: Clarendon Press.CrossRefGoogle Scholar
Goldberg, A. L. & Wittes, R. E. (1966). Genetic code: Aspects of organization. Science, N.Y. 153, 420–424.CrossRefGoogle ScholarPubMed
Harris, H. (1966). Enzyme polymorphism in man. Proc. Boy. Soc. B 164, 298–310.Google ScholarPubMed
Josse, J., Kaiser, A. D. & Kornberg, A. (1961). Enzymatic synthesis of deoxyribonucleic acid VIII. Frequencies of nearest neighbour base sequences in deoxyribonucleic acid. J. Biol. Chem. 236, 864–875.CrossRefGoogle ScholarPubMed
Kimura, M. (1964). Diffusion models in population genetics. J. appl. Probability 1, 177–232.CrossRefGoogle Scholar
Kimura, M. (1967). On the evolutionary adjustment of spontaneous mutation rates. Genet. Res. 9, 23–34.CrossRefGoogle Scholar
Kimura, M. & Crow, J. F. (1963). The measurement of effective population number. Evolution 17, 279–288.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
Kimura, M. & Maruyama, T. (1966). The mutational load with epistatic gene interactions in fitness. Genetics 54, 1337–1351.CrossRefGoogle ScholarPubMed
Kimura, M. & Weiss, G. H. (1964). The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561–576.CrossRefGoogle ScholarPubMed
Lewontin, R. C. & Hubby, J. L. (1966). A molecular approach to the study of genic heterozygosity in natural populations. II. Amount of variation and degree of heterozygosity in natural populations of Drosophila pseudoobscura. Genetics 54, 595–609.CrossRefGoogle Scholar
Mukai, T. (1964). The genetic structure of natural populations of Drosophila melanogaster. I. Spontaneous mutation rate of polygenes controlling viability. Genetics 50, 1–19.CrossRefGoogle ScholarPubMed
Muller, H. J. (1967). The gene material as the initiator and the organizing basis of life. In Heritage from Mendel (ed. Brink, R. A.), pp. 419–447. Madison: Univ. of Wisconsin Press.Google Scholar
Robertson, A. (1962). Selection for heterozygotes in small populations. Genetics 47, 1291–1300.CrossRefGoogle ScholarPubMed
Robertson, A. (1967). The nature of quantitative genetic variation. In Heritage from Mendel, pp. 265–280. (ed. Brink, R. A.). Madison: Univ. of Wisconsin Press.Google Scholar
Shaw, C. R. (1965). Electrophoretic variation in enzymes. Science, N.Y. 149, 936–943.CrossRefGoogle ScholarPubMed
Smith, M. H. (1966). The amino acid composition of proteins. J. Theoret. Biol. 13, 261–282.CrossRefGoogle Scholar
Sonneborn, T. M. (1965). Degeneracy of the genetic code: Extent, nature, and genetic implications. In Evolving Genes and Proteins, pp. 377–397 (ed. Bryson, V. and Vogel, H. J.), New York: Academic Press.CrossRefGoogle Scholar
Sueoka, N. (1965). On the evolution of informational macromolecules. In Evolving Genes and Proteins (ed. Bryson, V. and Vogel, H. J.), pp. 479–496. New York: Academic Press.CrossRefGoogle Scholar
Watson, J. D. (1965). Molecular Biology of the Gene. New York: Benjamin.Google Scholar
Weiss, G. H. & Kimura, M. (1965). A mathematical analysis of the stepping stone model of genetic correlation. J. appl. Probability 2, 129–149.CrossRefGoogle Scholar
Wright, S. (1931). Evolution in Mendelian populations. Genetics 16, 97–159.CrossRefGoogle ScholarPubMed
Wright, S. (1938 a). The distribution of gene frequencies under irreversible mutation Proc. Natn. Acad. Sci. U.S.A. 24, 253–259.CrossRefGoogle Scholar
Wright, S. (1938 b). Size of population and breeding structure in relation to evolution. Science, N.Y. 87, 430–431.Google Scholar
Wright, S. (1949). Genetics of populations. Encyclopaedia Britannica 10, 111–112.Google Scholar
Wright, S. (1951). The genetical structure of populations. Ann. Eugen. 15, 323–354.CrossRefGoogle ScholarPubMed
Wright, S. (1966). Polyallelic random drift in relation to evolution. Proc. Natn. Acad. Sci. U.S.A. 55, 1074–1081.CrossRefGoogle ScholarPubMed