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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