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Regression of a Sire's Breeding Value on Various Functions of Daughters' and Herd-Mate Production

Animal Husbandry Research Division, Agricultural Research Service, U. S. Department of Agriculture, Beltsville, Maryland

ABSTRACT

Given some criterion of a sire's transmitting ability for production, I, for example, the predicted breeding value of that sire is given by=µ_G + ß_GI (I–µ_I where is the estimate of the sire's breeding value, µ_G is the population average additively genetic value, ß_GI is the regression of breeding value on I, and µ_I is the population average of the criterion employed. Many such criteria have been employed for sire selection purposes. The most familiar of these are the daughter-dam comparison, the daughter average, and the daughter-herd-mate or contemporary comparison.

In this discussion, interest shall be in three criteria: the average production of daughters,
, the mean difference between daughters and their herd-mates, (C), and Henderson's Adjusted Daughter Average (A). Data are available on r daughters of sire j', each of which has n_j'k records Y_ij'kl. Corresponding to each such record there is a herd-mate average production (H_kl) based upon the average of m_j'kl nonpaternally related cows freshening in the same herd, year, and season as the daughter in question.