Genetic changes with generations of artificial selection.

Using conditional probabilities and moment-generating matrices, I derived approximate algebraic equations that give expectations of gene frequency, population mean, gene frequency variance within lines, or heterozygosity, and gene frequency variance between lines, or drift, for repeated cycles of recurrent selection in populations of finite size. For genes of large effect, the responses to selection differ substantially from the classical expectations, and equations are derived that give quantitative estimates of asymmetry of response when selection is done in opposite directions. Particular cases of the derived formulae yield equations given by other authors. The error involved in the approximations is discussed in the appendix.