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

中文翻译：

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优化在多环境作物品种测试中将试验分配到子区域

新作物品种在多环境试验中进行了广泛测试，以获得向农民推荐的坚实经验基础。当环境的目标群体很大且具有异质性时，划分子区域通常是有利的。在设计此类试验时，问题是如何将试验分配到不同的子区域。我们假设一个线性混合模型来考虑这个问题的解决方案。我们提出了一种计算最佳设计的分析方法，以实现基因型效应的最佳线性无偏预测及其成对线性对比，并通过来自印度全国玉米品种试验的真实数据示例说明获得的结果。结果表明，除了复合对称模型等简单情况外，