Effects of Selection on Estimates of Variance Components Using Gibbs Sampling and Restricted Maximum Likelihood

The effect of selection on estimates of variance components using Gibbs sampling mean and mode, REML, and minimum variance quadratic unbiased estimation was examined through simulation. One hundred replicates were generated for 27 combinations of three levels each of selection schemes, population structures, and heritabilities. All populations consisted of 400 animals. All methods were empirically unbiased, except for the Gibbs sampling estimate of the mode for small variance components, for which the posterior distribution was skewed. Mean squared errors decreased for Gibbs sampling and REML estimates when data were selected, but mean squared errors increased with selection and were largest for minimum variance quadratic unbiased estimation. No pattern existed for differences in mean squared errors for randomly mated and unselected data, suggesting that the differences were due to the direct effect of selection rather than to changes in population structure. Based on these results, the use of minimum variance quadratic unbiased estimation of variance components may be less accurate than other methods for potentially selected field data. Advantages of Gibbs sampling to estimate variance compo-