Statistical Inferences in Populations Undergoing Selection or Non-Random Mating

Abstract

Data available to animal breeders often come from populations undergoing selection and non-random mating (SNRM). Unless this is taken into consideration, inferences based on such data may be misleading. Using a Bayesian setting, it is shown that when the information used to make breeding decisions is available, posterior densities constructed taking into consideration SNRM are identical to those constructed ignoring SNRM. Thus, methods of inference based on posterior densities including all information used to make breeding decisions, can be used ignoring complications due to SNRM. Properties of methods such as maximum likelihood (ML) and best linear unbiased prediction (BLUP) are examined under the assumption of multivariate normality in data from populations undergoing SNRM. Although expressions for ML estimators are identical with or without SNRM, their sampling properties are affected by SNRM. In the presence of SNRM, the matrices appearing in the mixed model equations cannot be considered fixed. However, it is shown under multivariate normality, that the usual expressions lead to BLUP, provided that SNRM decisions are based on translation invariant functions of the data available for calculation of BLUP.