Optimizing the Allocation of Trials to Sub-regions in Multi-environment Crop Variety Testing

New crop varieties are extensively tested in multi-environment trials order to obtain a solid empirical basis for recommendations farmers. When the target population of environments is large and heterogeneous, division into sub-regions often advantageous. designing such trials, question arises how allocate different sub-regions. We consider solution this problem assuming linear mixed model. propose an analytical approach computation optimal designs best unbiased prediction genotype effects their pairwise contrasts illustrate obtained results by real data example from Indian nation-wide maize variety trials. It shown that, except simple cases as compound symmetry model, allocation depends on variance–covariance structure genotypic nested within