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On sojourn times at particular gene frequencies

Published online by Cambridge University Press:  14 April 2009

Edward Pollak  and
Barry C. Arnold
Edward Pollak
Affiliation:
Department of Statistics, Iowa State University, Ames, Iowa 50010, U.S.A.
Barry C. Arnold
Affiliation:
Department of Statistics, Iowa State University, Ames, Iowa 50010, U.S.A.

Summary

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The distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

Type
Research Article
Information
Genetics Research , Volume 25 , Issue 2 , April 1975 , pp. 89 - 94
Copyright
Copyright © Cambridge University Press 1975

References

REFERENCES

Abramowitz, M. & Stegun, I. A. (Eds.) (1968). Handbook of Mathematical Functions. New York: Dover Publications, Inc.Google Scholar
Ewens, W. J. (1973). Conditional diffusion processes in population genetics. Theoretical Population Biology 4, 21–30.Google Scholar
Kemeny, J. G. & Snell, J. L. (1960). Finite Markov Chains. New York: D. van Nostrand Company.Google Scholar
Maruyama, T. (1972). 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. Genetical Research 19, 109–113.Google Scholar
Maruyama, T. (1973). The variance of the number of loci having a given gene frequency. Genetics 73, 361–366.Google Scholar
Maruyama, T. & M., Kimura (1971). Some methods for treating continuous stochastic processes in population genetics. Japanese Journal of Genetics 46, 407–410.Google Scholar
Nagylaki, T. (1974). The moments of stochastic integrals and the distribution of sojourn times. Proceedings of the National Academy of Sciences U.S.A. 71, 746–749.Google Scholar