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Adapting best linear unbiased prediction (BLUP) for timely genetic evaluation: I. Progeny traits in a single contemporary group for each sex.

The first step of a procedure to partially circumvent the voluminous calculations with extremely large matrices for the usual algorithms for a BLUP (best linear unbiased prediction) approach is presented. This procedure, specific for a hierarchical portion of a model relevant to many animal breeding populations, is pertinent especially for polytocous species such as swine and poultry. For these, the occurrence of full-sib families makes the inclusion of dam effects in the model more necessary than in dairy or beef cattle models, where dam effects often are omitted. The formulas are derived for the hierarchical model for sires, dams within sires, individuals within full-sib family, and records within individuals, showing a relatively simple structure for such predictors. These formulas provide the basis for an alternative computing algorithm for obtaining evaluations having the statistical properties of best linear unbiased prediction. Formulas also are developed to approximate the prediction error variances for such models. Following this, the methodology for combining separate BLUP predictors, both error-independent and correlated, is developed.