Accounting for Selection and Mating Biases in Genetic Evaluations

Abstract

When selection has occurred, the means and variances of random variables are different from those under the usual assumptions of mixed linear models. Consequently, the solution to regular mixed model equations sometimes gives biased estimators and predictors. Given multivariate normal distributions and a vector variable used to make selection and mating decisions, the mixed model equations can be modified to yield unbiased estimators and predictors. This modification is described and several examples are given of its application, including cow culling, selection on records not available for analysis, estimation of genetic and environmental trends, association between sire and herd values, genetic groups, differential treatment, and assortative mating with and without selection.