Skip to main content Accessibility help
×
Home

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

  • Motoo Kimura (a1)

Extract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

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

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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

Copyright

References

Hide All
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), 449450.
Clayton, G. & Robertson, A. (1955). Mutation and quantitative variation. Am. Nat. 89, 151158.
Crick, F. H. C. (1966). The genetic code: III Scient. Am. 215 (4), 5562.
Crow, J. F. & Kimura, M. (1956). Some genetic problems in natural populations. Proc. Third Berkeley Syrup. on Math. Stat. and Prob. 4, 122.
Ewens, W. J. (1964). The maintenance of alleles by mutation. Genetics 50, 891898.
Ewens, W. J. & Ewens, P. M. (1966). The maintenance of alleles by mutation—Monte Carlo results for normal and self-sterility populations. Heredity 21, 371378.
Fisher, R. A. (1930). The Genetical Theory of Natural Selection. Oxford: Clarendon Press.
Goldberg, A. L. & Wittes, R. E. (1966). Genetic code: Aspects of organization. Science, N.Y. 153, 420424.
Harris, H. (1966). Enzyme polymorphism in man. Proc. Boy. Soc. B 164, 298310.
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, 864875.
Kimura, M. (1964). Diffusion models in population genetics. J. appl. Probability 1, 177232.
Kimura, M. (1967). On the evolutionary adjustment of spontaneous mutation rates. Genet. Res. 9, 2334.
Kimura, M. & Crow, J. F. (1963). The measurement of effective population number. Evolution 17, 279288.
Kimura, M. & Crow, J. F. (1964). The number of alleles that can be maintained in a finite population. Genetics 49, 725738.
Kimura, M. & Maruyama, T. (1966). The mutational load with epistatic gene interactions in fitness. Genetics 54, 13371351.
Kimura, M. & Weiss, G. H. (1964). The stepping stone model of population structure and the decrease of genetic correlation with distance. Genetics 49, 561576.
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, 595609.
Mukai, T. (1964). The genetic structure of natural populations of Drosophila melanogaster. I. Spontaneous mutation rate of polygenes controlling viability. Genetics 50, 119.
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. 419447. Madison: Univ. of Wisconsin Press.
Robertson, A. (1962). Selection for heterozygotes in small populations. Genetics 47, 12911300.
Robertson, A. (1967). The nature of quantitative genetic variation. In Heritage from Mendel, pp. 265280. (ed. Brink, R. A.). Madison: Univ. of Wisconsin Press.
Shaw, C. R. (1965). Electrophoretic variation in enzymes. Science, N.Y. 149, 936943.
Smith, M. H. (1966). The amino acid composition of proteins. J. Theoret. Biol. 13, 261282.
Sonneborn, T. M. (1965). Degeneracy of the genetic code: Extent, nature, and genetic implications. In Evolving Genes and Proteins, pp. 377397 (ed. Bryson, V. and Vogel, H. J.), New York: Academic Press.
Sueoka, N. (1965). On the evolution of informational macromolecules. In Evolving Genes and Proteins (ed. Bryson, V. and Vogel, H. J.), pp. 479496. New York: Academic Press.
Watson, J. D. (1965). Molecular Biology of the Gene. New York: Benjamin.
Weiss, G. H. & Kimura, M. (1965). A mathematical analysis of the stepping stone model of genetic correlation. J. appl. Probability 2, 129149.
Wright, S. (1931). Evolution in Mendelian populations. Genetics 16, 97159.
Wright, S. (1938 a). The distribution of gene frequencies under irreversible mutation Proc. Natn. Acad. Sci. U.S.A. 24, 253259.
Wright, S. (1938 b). Size of population and breeding structure in relation to evolution. Science, N.Y. 87, 430431.
Wright, S. (1949). Genetics of populations. Encyclopaedia Britannica 10, 111112.
Wright, S. (1951). The genetical structure of populations. Ann. Eugen. 15, 323354.
Wright, S. (1966). Polyallelic random drift in relation to evolution. Proc. Natn. Acad. Sci. U.S.A. 55, 10741081.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed