Assessment of genomic prediction reliability and optimization of experimental designs in multi-environment trials

New forms of the coefficient of determination can help to forecast the accuracy of genomic prediction and optimize experimental designs in multi-environment trials with genotype-by-environment interactions. In multi-environment trials, the relative performance of genotypes may vary depending on the environmental conditions, and this phenomenon is commonly referred to as genotype-by-environment interaction (G[Formula: see text]E). With genomic prediction, G[Formula: see text]E can be accounted for by modeling the genetic covariance between trials, even when the overall experimental design is highly unbalanced between trials, thanks to the genomic relationship between genotypes. In this study, we propose new forms of the coefficient of determination (CD, i.e., the expected model-based square correlation between a genetic value and its corresponding prediction) that can be used to forecast the genomic prediction reliability of genotypes, both for their trial-specific performance and their mean performance. As the expected prediction reliability based on these new CD criteria is generally a good approximation of the observed reliability, we demonstrate that they can be used to optimize multi-environment trials in the presence of G[Formula: see text]E. In addition, this reliability may be highly variable between genotypes, especially in unbalanced designs with complex pedigree relationships between genotypes. Therefore, it can be useful for breeders to assess it before selecting genotypes based on their predicted genetic values. Using a wheat population evaluated both for simulated and phenology traits, and two maize populations evaluated for grain yield, we illustrate this approach and confirm the value of our new CD criteria.