Abstract

New crop varieties are extensively tested in multi-environment trials in order to obtain a solid basis for recommendations to farmers. When the target population of environments is large, a division into sub-regions is often advantageous. If the same set of genotypes is tested in each of the sub-regions, a linear mixed model (LMM) may be fitted with random genotype-within-sub-region effects. The first analytical results to optimizing allocation of trials (designs) to sub-regions have been obtained in Prus and Piepho (2021). In that paper the genotype effects are assumed to be uncorrelated. However, this assumption is not always suitable for practical situations. In praxis, genetic markers are often used in plant breeding for determining genetic relationships of genotypes, which helps to model their correlation. In this work a more general LMM with correlated genotype effects is considered. An analytical solution for optimal allocations of trials (optimal designs) is proposed in form of an optimality condition. For small to moderate number of genotypes optimal designs can be determined using the OptimalDesign package in R and the approach proposed in Harman and Prus (2018). The optimization problem becomes more challenging if the number of genotypes is very large. For this situation a new approach for computing optimal designs is proposed. The obtained results are illustrated by real data examples.

Harman, R. and Prus, M. (2018). Computing optimal experimental designs with respect to a compound Bayes Risk criterion. Statistics and Probability Letters, 137, 135-141.

Prus, M. and Piepho, H.-P. (2021). Optimizing the allocation of trials to sub-regions in multi-environment crop variety testing. Journal of Agricultural, Biological and Environmental Statistics, 26, 267–288.