Estimation of Response to Selection Using Least-Squares and Mixed Model Methodology

Abstract

Properties of least-squares and mixed model estimators of response to selection are discussed. The least-squares estimator is unbiased provided that the records have been properly adjusted for fixed effects (for example, using a control line), that selection is within generations and that there is only one record/candidate for selection. In the case of the mixed model estimator, it is unbiased and individual breeding values have minimum variance of prediction error provided that selection is within levels of fixed effects and the variances of the random effects before selection are known. If certain conditions are met, the mixed model approach does not require the use of a control line in order to partition adequately phenotypic trend into its genetic and environmental components. Henderson's results are extended to a model that includes several cycles of selection. It is shown that the relationship matrix accounts for the decline in variance due to genetic drift and it circumvents further reduction in variance due to gametic disequilibrium. Results are illustrated with Monte Carlo simultation.