Prediction and evaluation of response to selection with overlapping generations

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Abstract
SUMMARY In a population in which generations overlap the improvement in performance in successive years resulting from a single year of selection is not constant, for the genes from a group of selected individuals may take many years to pass through the population. A formal method is developed for predicting responses and discounted returns from improvement in populations with overlapping generations including, if necessary, generations of multiplication of breeding stock. The method is based on a matrix which specifies the passage of genes between the different age groups and sexes. Simple matrix operations can be used to compute the proportion of genes in animals of both sexes and each age in the population at any time which derive from a group of selected animals at an earlier time. The response produced by these selected animals equals the product of their genetic selection differential and the proportion of genes deriving from them. Comparisons are made between responses predicted using this theory and the classical theory of uniform rates of response, and a method is given for computing the time lag of genes passing through the population. The results are extended to enable computation of discounted returns from improvement.