OPTIMUM LINEAR SELECTION INDEXES FOR MULTIPLE GENERATION OBJECTIVES WITH NONLINEAR PROFIT-FUNCTIONS

A method to obtain linear selectin indexes that maximize objectives that involve average profit in one or more generations within a planning horizon based on non-linear profit functions, was derived through application of optimal control theory. The method involves simultaneous optimization of indexes for each generation in the planning horizon. Optimum linear indexes were found to be conform indexes derived from selection index theory, with economic values equal to a weighted sum of partial derivatives of the profit function at the trait means which result in each generation of the planning horizon. Numerical procedures to derive optimum indexes are presented. Methods and properties of alternative strategies form selection with non-linear profit functions are illustrated for selection on egg weight and rate of lay in poultry. In the example, the additional benefit of selection indexes that maximize cumulative net present value of profit over a planning horizon of 10 years was small relative to use of traditional selection procedures. Optimal indexes were also derived with a derivative-free non-linear programming optimizer, with identical results. The latter method also allows incorporation of additional constraints. Possible extensions of the optimal control methodology to address other problems related to optimization of selection over multiple generations are discussed.