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A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

Published online by Cambridge University Press:  14 April 2009

Derek J. Pike
Derek J. Pike
Affiliation:
Department of Applied StatisticsUniversity of Reading
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Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.

These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.

It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

Type
Research Article
Information
Genetics Research , Volume 13 , Issue 2 , April 1969 , pp. 117 - 126
Copyright
Copyright © Cambridge University Press 1969

References

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