Technical note: optimization of breed composition to maximize net merit of synthetic populations

Determination of optimal breed (strain or line) composition is important when synthesizing a new population. In this study, the relative proportions of different breed contributions to a synthetic population are derived so that net merit of the resulting synthetic population is at a maximum. Net merit (aggregate genotype) is defined as a linear combination of genotypic values weighted by economic values. Two methods of optimizing breed compositions for multiple traits were derived. The first method was component optimization, which is an extension of a previously derived method for a single trait. A numerical example was given to illustrate the computation. The second method was index optimization, derived from a base index that is defined as a linear combination of phenotypes weighted by the economic values. The two procedures were shown to be equivalent.