Analysis of selection experiments using mixed model methodology.

Use of mixed model techniques to estimate genetic variance and selection response is illustrated by simple examples. A minimum variance quadratic unbiased estimator (MIVQUE) of genetic variance using a reduced animal model is derived. Properties of the mixed model estimator of response are discussed and illustrated with results from Monte Carlo simulation. The mixed model estimator of response requires knowledge of the base population heritability. When the latter is not known, simulation results suggest that using a MIVQUE estimate obtained from the data yields estimates of response in good agreement with the true response. If a number of conditions are satisfied, the mixed model estimator of response partitions the phenotypic trend into its genetic and environmental components, without need for a control population. These conditions are unlikely to hold in long-term selection experiments. More work is needed to understand the implications of finite numbers of loci or the presence of unaccounted natural selection opposing artificial selection, for example, on the properties of the mixed model estimator of response.