Optimum truncation points for independent culling level selection on a multivariate normal distribution, with an application to dairy cattle selection
Résumé
Independent culling level selection is often practiced in breeding programs because extreme animals for some particular traits are rejected by breeders or because records on which genetic evaluation is based are collected sequentially. Optimizing these selection procedures for a given overall breeding objective is equivalent to finding the combination of truncation thresholds or culling levels which maximizes the expected value of the overall genetic value for selected animals. A general Newton-type algorithm has been derived to perform this maximization for any number of normally distributed traits and when the overall probability of being selected is fixed. Using a powerful method for the computation of multivariate normal probability integrals, it has been possible to undertake the numerical calculation of the optimal truncation points when up to 6 correlated traits or stages of selection are considered simultaneously. The extension of this algorithm to the more complex situation of maximizing annual genetic response subject to nonlinear constraints is demonstrated using a dairy cattle model involving milk production and a secondary trait such as type. Consideration is given to three of the four pathways of selection: dams of bulls; sires of bulls; and sires of cows.