On the Construction of an Index for Indirect Selection

We consider artificial selection, aiming at maximum increase per generation of the breeding-value, with respect to an economically valuable quanti-tative character, t, of a strain of a domesticated animal species. Following the well-established conventions we denote this breeding-value by G, , and its increase per generation by AG, . This note refers to the special case when, because of circumstances of physiological and/or of managemental nature, it is preferable not to use t itself as selection-criterion, but to use other measurable characters (genetically correlated with t) for that purpose. Using one such character constitutes the procedure well-known as indirect selection. When, however, several such characters are observable, without undue inconvenience, it is almost always more advantageous to form from them a linear combination as selection-index. The coefficients for that combination are obtainable from the appropriate modification of the formulae of H. Fairfield Smith [1936], who derived them by applying R. A. Fisher's [1936] classical method to a similar (but not identical) problem.