Best Linear Unbiased Prediction of Performance and Breeding Value

Introduction Genetic progress in traits of economic importance has been impressive during the past few decades. This has been due to a combination of (1) selection, primarily on additive genetic merit, (2) changes in breed structure, and (3) crossbreeding; the relative importance of these factors varying from species to species. This paper is concerned with the first of these factors and is restricted to linear models and approximate normality of distributions. It should be understood that a linear model can include dominance and epistasis and also interaction between genotypes and environments. This paper presents methods for predicting both performance and breeding value. This is a somewhat arbitrary dichotomy since breeding values are defined in terms of average performance of progeny, and prediction of breeding values requires performance records. Assuming linearity, the mixed model method for best linear unbiased prediction (BLUP) provides a powerful and flexible tool for predictions that have very desirable properties. I. In the class of linear, translation invariant functions of records, the variances of errors of prediction are smaller than any other such predictor, least-squares or selection index for example. 2. The corelations between predictors and predictands are larger than for any other predictor.