Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-09T22:35:17.575Z Has data issue: false hasContentIssue false
  • English
  • Français

On the fixation probability of a gene under random fluctuations in selection intensities in small populations*

Published online by Cambridge University Press:  14 April 2009

Prem Narain  and
Edward Pollak
Prem Narain
Affiliation:
Statistical Laboratory, Iowa State University, Ames, Iowa 50011, U.S.A.
Edward Pollak
Affiliation:
Statistical Laboratory, Iowa State University, Ames, Iowa 50011, U.S.A.
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.

A population with N monoecious individuals, and having two alleles, is considered. The problem of calculating the fixation probability of a particular allele under random fluctuation of selection intensities is re-examined, employing finite Markov chain methods. An approximate but general expression for this probability is obtained and the results obtained by previous workers are shown to be special cases of this result.

Type
Research Article
Information
Genetics Research , Volume 29 , Issue 2 , April 1977 , pp. 113 - 121
Copyright
Copyright © Cambridge University Press 1977

References

REFERENCES

Ewens, W. J. (1973). Conditional diffusion processes in population genetics. Theoretical Population Biology 4, 21–30.CrossRefGoogle ScholarPubMed
Fisher, R. A. (1922). On the dominance ratio. Proceedings of the Royal Society of Edinburgh 42, 321–341.CrossRefGoogle Scholar
Gillespie, J. H. (1973). Natural selection with varying selection coefficients: a haploid model. Genetical Research 21, 115–120.CrossRefGoogle Scholar
Jensen, L. (1973). Random selective advantages of genes and their probabilities of fixation. Genetical Research 21, 215–219.CrossRefGoogle ScholarPubMed
Jensen, L. & Pollak, E. (1969). Random selective advantages of a gene in a finite population. Journal of Applied Probability 6, 19–37.CrossRefGoogle Scholar
Karlin, S. & Levikson, B. (1974). Temporal fluctuations in selection intensities: Case of small population size. Theoretical Population Biology 6, 383–412.CrossRefGoogle Scholar
Kemeny, J. G. & Snell, J. L. (1960). Finite Markov Chains. New York: D. van Nostrand.Google Scholar
Kimura, M. (1962). On the probability of fixation of mutant genes in a population. Genetics 47, 713–719.CrossRefGoogle ScholarPubMed
Kolmogorov, A. (1931). Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung. Mathematische Annalen 104, 415–458.CrossRefGoogle Scholar
Narain, P. & Robertson, A. (1969). Limits and duration of response to selection in finite populations: The use of transition probability matrices. Indian Journal of Heredity 1, 1–19.Google Scholar
Narain, P. (1974). The conditional diffusion equation and its use in population genetics. Journal of the Royal Statistical Society B 36, 258–266.Google Scholar
Ohta, T. (1972). Fixation probability of a mutant influenced by random fluctuation of selection intensity. Genetical Research 19, 33–38.CrossRefGoogle Scholar