Prediction of response with overlapping generations accounting for multistage selection.

A generalization of Hill's equations predicting response to selection is developed that accounts for multiple stage selection in either or both sexes. The method accounts for the flow of genes for animals selected at later stages. This allows for the use of genetic gains from later stages, which explains the reduction in variance due to previous selection. Genetic gains from different selection differentials in each reproductive pathway are incorporated into the equations. The asymptotic response to a single cycle of selection is shown to agree with classical selection theory.The method is applied to a dairy progeny testing scheme representative of an artificial insemination organization in the USA. Two models were compared: (1) the first model accounted for two-stage selection of males, the first stage being based on pedigree information and the second stage on both pedigree and progeny test information; and (2) the second model assumed single-stage male selection. Selection was based on milk volume, milk fat, and milk protein yields. The predicted asymptotic rates for a single cycle of selection were overestimated by 6% and the cumulative response to continuous selection over 20 years was overestimated by 8% by assuming singlestage male selection.