Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T15:08:34.429Z Has data issue: false hasContentIssue false

The average number and the variance of generations at particular gene frequency in the course of fixation of a mutant gene in a finite population*

Published online by Cambridge University Press:  14 April 2009

Takeo Maruyama
Affiliation:
National Institute of Genetics, Mishima, Japan
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.

In the case of an allele which is going to become fixed in a population, the average number of generations for which the population assumes particular gene frequencies is investigated, using the diffusion approximation. Explicit formulas were obtained and they were checked by computer simulations. As a particular case, it is shown that if a new mutant that is selectively neutral is eventually fixed in a population of size N, it spends two generations on average at each of the intermediate frequencies (1/2N, 2/2N, …, (2N−1)/2N), and the variance at each frequency is four generations.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1972

References

REFERENCES

Crow, J. F. & Kimura, M. (1970). An Introduction to Population Genetics Theory. New York: Harper and Row.Google Scholar
Dynkin, E. B. (1965). Markov Processes. Berlin: Springer-Verlag.Google Scholar
Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713719.CrossRefGoogle ScholarPubMed
Kimura, M. (1969). The number of heterozygous nucleotide sites maintained in a finite population due to steady flux of mutations. Genetics 61, 893903.CrossRefGoogle Scholar
Kimura, M. (1970). The length of time required for a selectively neutral mutant to reach fixation through random frequency drift in a finite population. Genetical Research 15, 131133.CrossRefGoogle Scholar
Kimura, M. & Ohta, T. (1969 a). The average number of generations until fixation of a mutant gene in a finite population. Genetics 61, 763771.CrossRefGoogle Scholar
Kimura, M. & Ohta, T. (1969 b). The average number of generations until extinction of an individual mutant gene in a finite population. Genetics 63, 701709.CrossRefGoogle Scholar
Maruyama, T. & Kimura, M. (1971). Some methods for treating continuous stochastic processes in population genetics. Japanese Journal of Genetics 46, 407410.Google Scholar
Narain, P. (1970). A note on the diffusion approximation for the variance of the number of generations until fixation of a neutral mutant gene. Genetical Research, 15, 251255.CrossRefGoogle ScholarPubMed