The use of constrained selection indexes in breeding for economic merit

Various methods exist for the derivation of restricted and/or desired gains selection indexes, and their use in applied breeding has been advocated. It is shown that there exists a set of implied linear economic weights for all constrained indexes and their derivation is given. Where economic weights are linear and known, a standard selection index is, by definition, optimal and thus a constrained index will usually be suboptimal. It is argued that economic weights can always be estimated and that the effects of uncertain weights can be examined by sensitivity analysis. If economic weights are nonlinear, use of the first order (linear) economic weights or a derived linear index, using previously described methods, will give very close to optimum economic selection responses. Examples from the literature indicate that severe losses of potential economic gain can possibly occur through use of a constrained index. It is concluded that constrained indexes should be avoided for economic genetic selection.