Optimizing the Allocation of Trials to Sub-regions in Crop Variety Testing with Multiple Years and Locations

Field experiments in crop variety testing are conducted in multiple environments. When the targeted growing area can be stratified into sub-regions (zones), a design problem arises regarding the number of trials to be performed in each sub-region. We propose an analytical solution and a computational approach for optimal allocation of trials to sub-regions in multi-environment crop variety testing for multi-year experiments. For our purpose, we use a linear mixed model and we determine allocations that are optimal for the prediction of pairwise linear contrasts of genotype effects. For computations, we use the OptimalDesign package. The analytical results are illustrated by a real data example.