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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.
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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

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