“Restricted Selection Indices”, 1959-03-01 (; similar):
…While use of I will result in best progress in H, the means of the Gi will change in either a positive or negative direction, so that a breeder may well be interested in increasing H as much as possible with a restriction that some Gi or some linear functions of the Gi will not change. For example, a poultry breeder may feel that he should keep mean egg size at a constant intermediate level while using an index to maximize progress in genetic economic value based on egg weight, body weight, and production. It was in fact such a situation which led to the present note.
…The constrained optimization procedure given here [using Lagrange multipliers] permits no genetic change in the chosen attribute, attributes, or linear functions of attributes, and may be unduly restrictive from some points of view. It is not entirely obvious but can be shown that if the restricted index is to keep say attribute 1 constant, then the weight associated with attribute 1 in the genotypic economic value is irrelevant.
Conclusion: The purpose of the present note is to give a derivation and examples of restricted selection indices. A further development of indices requiring some genetic changes to be of particular sign will be presented in a later paper.
View PDF: