Optimizing training sets for genomic selection to identify superior genotypes across multiple environments

Genomic selection (GS) is a promising strategy in plant breeding for identifying superior genotypes with high true breeding values (TBVs) across multiple environments. However, the relative performance of candidate genotypes often varies due to complex genotype-by-environment (G×E) interactions in multi-environment trials (METs). To address this challenge, we employed a GS prediction model incorporating fixed environment-specific means, random additive genetic effects, and random additive G×E interaction effects to develop training set optimization methods for GS in METs. Two optimization methods derived from the generalized coefficient of determination (CD) criterion-CDmean(v2) (Chen et al. 2024, equivalent to Rincent et al. 2012) and CD(mean.MET) (Rio et al. 2022)-were evaluated and compared with random sampling. Rather than relying on prediction accuracy-focused correlation metrics, we assessed training set performance using selection-focused ranking metrics, including normalized discounted cumulative gain, Spearman's rank correlation, and rank sum ratio. Because TBVs are latent and unobservable, simulation experiments were conducted using real genotype data from diverse crop datasets, including rice (Oryza sativa L.), barley (Hordeum vulgare L.), and maize (Zea mays L.). Among the evaluated approaches, CDmean(v2) consistently showed high efficiency in identifying top-performing genotypes. In practice, CDmean(v2), implemented using the optimization algorithm provided in the TrainSel package (Akdemir et al. 2021), is recommended for GS-assisted breeding programs, as it produced superior training sets for identifying elite genotypes with reasonable computational cost.