Random selective advantages of a gene in a finite population
- 1 April 1969
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 6 (1), 19-37
- https://doi.org/10.2307/3212274
Abstract
A problem of interest to many population geneticists is the process of change in a gene frequency. A popular model used to describe the change in a gene frequency involves the assumption that the gene frequency is Markovian. The probabilities in a Markov process can be approximated by the solution of a partial differential equation known as the Fokker-Planck equation or the forward Kolmogorov equation. Mathematically this equation is where subscripts indicate partial differentiation. In this equation,f(p, x; t)is the probability density that the frequency of a gene isxat timet, given that the frequency waspat timet= o. The expressions MΔXand VΔxare, respectively, the first and second moments of the change in the gene frequency during one generation. A rigorous derivation of this equation was given by Kolmogorov (1931).Keywords
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