Multistage selection for genetic gain by orthogonal transformation.

An exact transformed culling method for any number of traits or stages of selection with explicit solution for multistage selection is described in this paper. This procedure does not need numerical integration and is suitable for obtaining either desired genetic gains for a variable proportion selected or optimum aggregate breeding value for a fixed total proportion selected. The procedure has similar properties to multistage selection index and, as such, genetic gains from use of the procedure may exceed ordinary independent culling level selection. The relative efficiencies of transformed to conventional independent culling ranged from 87% to over 300%. These results suggest that for most situations one can chose a multistage selection scheme, either conventional or transformed culling, which will have an efficiency close to that of selection index. After considering cost savings associated with multistage selection, there are many situations in which economic returns from use of independent culling, either conventional or transformed, will exceed that of selection index.