Optimum Group Size in Half-Sib Family Selection

Abstract

When indirect methods of selecting breeding stock have to be used there is often a limit to the number of offspring or other relatives that can be examined. Alan Robertson in a recent paper [1957] discussed the problem of deciding how many sires should be tested on how many offspring when selecting by progeny testing with a given size of test population. He shows that a general solution can be arrived at if the number of offspring tested for each sire is expressed in terms of the fraction of sires kept for breeding. If there are S sires kept for breeding and N animals tested all told, n for each sire, the proportion of sires selected, p, is nS/N since N/n is the number of sires tested. N/S, the number of tested animals for each sire kept, is Robertson's testing ratio, K. It turns out that the genotypic superiority of selected sires is proportional to V1 + (alpK) Z/p where a is (4 h2)/h2, h2 is the fraction of variation that is genetic, and Z/p the superiority of selected sires in standard measure. This expression can be differentiated to give a value of K in terms of p, which maximises the genetic superiority of selected sires. Robertson states that exactly the same formulae will hold in half-sib family selection. This is no doubt true enough for most practical purposes but is not strictly true. In progeny testing when a sire is chosen on the performance of his offspring, each being by a different dam, he is chosen to be used again on other dams, or if he is not to be used again his offspring, by dams other than those in the test, are to be kept. It is the assessment of the sire's genotype which is decisive. The dams of his progeny are irrelevant, except as a possible source of error or bias in his evaluation; they cannot contribute to his genotype. On the other hand, in the half-sib family selection system the dams are not irrelevant since it is members of the half-sibship that are used again or kept and, provided the dams