Optimal Diallel Cross Designs for the Interval Estimation of Heredity

The results on optimal diallel cross designs are based on standard linear model assumptions where the general combining ability effects are taken as fixed. In many practical situations, this assumption may not be tenable since often one studies only a sample of inbred lines from a possibly large hypothetical population. A random effects model is proposed in this paper that allows us to obtain an interval estimate of a ratio of the variance components. We address the issue of optimal designs by considering the D l-optimality criteria. Designs that are D l-optimal for the estimation of heredity are obtained in the sense that the designs minimize the maximum expected length of the h confidence intervals. The approach leads to certain connections with the optimization problem under the fixed effects model.