Optimal Design for Multi-Environment Trials

• Applicant: Dr. Maryna Prus
• Subject Area: Plant Breeding and Plant Pathology ; Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 533007746

New crop varieties are extensively tested in multi-environment trials (MET) in order to obtain a solid empirical basis for recommendations to farmers. When the target population of environments is large, a division into sub-regions is often advantageous. When designing such trials, the question arises how to allocate trials to the different sub-regions. For solution to this problem linear mixed models are usually being assumed. The optimal designs (optimal allocations of trials) are determined for best linear unbiased prediction of genotype effects and their pairwise linear contrasts. In the present project it is planned to consider linear mixed models with correlated genotype effects which may also incorporate the influence of the years and / or environmental factors. Moreover, besides randomized complete block designs, incomplete block designs (alpha designs, row-column designs) are planned to be considered. Furthermore, we will explore the design of MET for sparse testing when marker data is available. Sparse testing involves testing each genotype only in a subset of the trials, thereby allowing more environments to be sampled and better precision to be achieved for marker effect estimates. The design problem here is how to allocate genotypes to environments. The linear mixed models used here are so complex that the design problems involved are far from trivial. If the design criteria obtained in this project will have a new structure, i.e., cannot be recognized as particular cases of any criteria available in the literature, new computational methods will be developed. A related open problem that will be addressed in the present research is determining optimal or highly efficient designs, which are independent of, or at least not sensitive with respect to the covariance matrix of random effects. We will solve this problem by using a Bayesian approach and / or by considering minimax and maximin efficiency criteria, which are related to the worst case of the underlined criterion with respect to variance parameters.

• DFG Programme: Research Grants