Should genetic groups be fitted in BLUP evaluation? Practical answer for the French AI beef sire evaluation

Some analytical and simulated criteria were used to determine whether a priori genetic differences among groups, which are not accounted for by the relationship matrix, ought to be fitted in models for genetic evaluation, depending on the data structure and the accuracy of the evaluation. These criteria were the mean square error of some extreme contrasts between animals, the true genetic superiority of animals selected across groups, i.e. the selection response, and the magnitude of selection bias (difference between true and predicted selection responses). The different statistical models studied considered either fixed or random genetic groups (based on six different years of birth) versus ignoring the genetic group effects in a sire model. Including fixed genetic groups led to an overestimation of selection response under BLUP selection across groups despite the unbiasedness of the estimation, i.e. despite the correct estimation of differences between genetic groups. This overestimation was extremely important in numerical applications which considered two kinds of within-station progeny test designs for French purebred beef cattle AI sire evaluation across years: the reference sire design and the repeater sire design. When assuming a priori genetic differences due to the existence of a genetic trend of around 20% of genetic standard deviation for a trait with h2=0.4, in a repeater sire design, the overestimation of the genetic superiority of bulls selected across groups varied from about 10% for an across-year selection rate p=1/6 and an accurate selection index (100 progeny records per sire) to 75% for p=1/2 and a less accurate selection index (20 progeny records per sire). This overestimation decreased when the genetic trend, the heritability of the trait, the accuracy of the evaluation or the connectedness of the design increased. Whatever the data design, a model of genetic evaluation without groups was preferred to a model with genetic groups when the genetic trend was in the range of likely values in cattle breeding programs (0 to 20% of genetic standard deviation). In such a case, including random groups was pointless and including fixed groups led to a large overestimation of selection response, smaller true selection response across groups and larger variance of estimation of the differences between groups. Although the genetic trend was correctly predicted by a model fitting fixed genetic groups, important errors in predicting individual breeding values led to incorrect ranking of animals across groups and, consequently, led to lower selection response.