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Fixation of a Mutant Gene

Consider a population of N breeding diploid organisms. Suppose that a new genetic mutation arises in a single gene copy within an individual, producing a new allele A. There is a small probability that the frequency, p, of this mutant allele within the breeding population will increase and become fixed   (i.e. = 1; the population eventually becomes monomorphic). In 1969, Japanese geneticists Motoo Kimura and Tomdko Ohta computed the probability of fixation of such a new mutation (under certain assumptions) as,

equation:  p = (1- e ^-2s)/ (1 - e^-4Ns).

where s is the selective advantage of allele A and N is the number of breeding individuals [1].

Given this equation, find the value of N required for allele A, with selective advantage s = 0.050, to have fixation probability of 0.11.

Be sure to keep your answer exact until the last step to avoid the propagation of round-off errors.

Answer:  ≈
   

Reference
[1] Kimura, M. and T. Ohta (1969). The average number of generations until fixation of a mutant gene in a finite population. Genetics 61:763-771.

 

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February 2005
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