The time of detection of recessive visible genes in small populations

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Abstract
SUMMARY: Homozygotes for recessive visible genes have often been discovered in lines under artificial selection, sometimes many generations from the start. As a help in the interpretation of this phenomenon, the distribution of the time to first detection as a homozygote of a recessive gene occurring only once in the initial generation has been obtained. Alternatively the results may be considered as referring to the time of first appearance as a homozygote of a new mutation occurring in a finite population. For a monoecious random mating population of size N with selfing permitted, the mean time to detection is very close to 2N⅓ over a range of N from 1 to 500 with a coefficient of variation of roughly 2/3 and a 95% upper limit about 2·5 times the mean. If selfing is prohibited, the mean time is increased by a little over 1 generation. The treatment is extended to cover the effects of artificial selection in favour of the heterozygote, of the frequency of occurrence in the initial generation and of the examination of more individuals each generation than are used as parents.