The goal of livestock genetic improvement is maximun increase in the economic efficiency of production (economic merit). When several traits contribute to economic merit, optimum genetic improvement can often be achieved by use of a discriminant function of available information (known as a selection index) which maximises expected genetic progress in the aggregate genotype, economic merit. This approach assumes that economic merit is a linear function of genetically controlled outputs. Although this may not always be true, since genetic responses are usually relatively small (0.005 to 0.020 of the mean per year) any non-linear effects are second-order and can generally be ignored. Economic optimization procedures which match production environments to genotypes would generate effectively non-linear functions, such non-linearity will generally be small. Thus the selection index approach can be applied, provided that functions describing economic merit are based on previously optimized production environments.