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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

  • Derek J. Pike (a1)

Extract

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.

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Copyright

References

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Allan, J. S. & Robertson, A. (1964). The effect of initial reverse selection upon total selection response. Genet. Res. 5, 6879.
Baker, L. H. & Curnow, R. N. (1968). Choice of population size and use of variation between replicate populations in plant breeding selection programmes. (In preparation.)
Curnow, R. N. & Baker, L. H. (1968). The effect of repeated cycles of selection and regeneration in populations of finite size. Genet. Res. 11, 105112.
Ewens, W. J. (1963). Numerical results and diffusion approximations in a genetic process. Biometrika 50, 241249.
Hill, W. G. (1968). On the theory of artificial selection in finite populations. Genet. Res. 13, 143163.
Hill, W. G. & Robertson, A. (1966). The effect of linkage on limits to artificial selection. Genet. Res. 8, 269294.
Kendall, M. G. & Stuart, A. (1963). The Advanced Theory of Statistics, Volume 1. London: Griffin.
Kimura, M. (1957). Some problems of stochastic processes in genetics. Ann. Math. Stat. 28, 882901.
Kojima, K. (1961). Effects of dominance and size of population on response to mass selection. Genet. Res. 2, 177188.
Robertson, A. (1960). A theory of limits in artificial selection. Proc. Roy. Soc. B 153, 234249.

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