Article,

On the probability of fixation of mutant genes in a population

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Genetics, (June 1962)

Abstract

HE success or failure of a mutant gene in a population is dependent not only Ton selectio2 but also on chance. This fact was first treated quantitatively by FISHER (1922) who later (1930) worked out the probability of ultimate survival of a mutant gene for the case of genic selection (i.e. no dominance). Equivalent results have been obtained by HALDANE (1927) and WRIGHT (1931). Also the probability was estimated for a recessive mutant gene by HALDANE (1927) and WRIGHT ( 1942). The present author (KIMURA 1957) extended these results to include any level of dominance. The probability of eventual fixation, U (p) , was expressed in terms of the initial frequency, p, the selection coefficients, and the effective population number. This function was used by ROBERTSON (1960) in his theory of selection limits in plant and animal breeding. The purpose of this note is to present a more general formula for ~(p) which exompasses random fluctuations in selection intensity as well as random drift because of small population number. It will also be used to solve a question relating to “quasi-fixation” posed by the author in 1955.

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