Optimizing training sets to identify superior genotypes in hybrid populations

The identification of superior hybrids from candidate populations is a central goal in plant breeding, particularly for commercial applications and large-scale cultivation. In this study, several promising training set optimization methods in genomic selection (GS) are evaluated and extended to construct predictive models for the identification of top-performing genotypes in hybrid populations. The methods investigated include: (i) a ridge regression-based approach, ${\text{MSPE}}_{\left(\text{v}2\right)}^{\text{Ridge}}$ , (ii) a generalized coefficient of determination-based method, ${\text{CD}}_{\text{mean}\left(\text{v}2\right)}$ , and (iii) an A-optimality-like ranking strategy, ${\text{GV}}_{\text{average}}$ . To assess predictive performance in identifying genotypes with the highest true breeding values (TBVs), three evaluation metrics were developed. Since TBVs are latent quantities derived from models, simulation experiments based on real genotype data from wheat (Triticum aestivum L.), maize (Zea mays), and rice (Oryza sativa L.) were carried out to assess the proposed methods. Results demonstrated that ${\text{GV}}_{\text{average}}$ not only achieved substantial computational efficiency but also generally generated highly informative training sets across a broad range of sizes. However, when constructing small training sets, ${\text{GV}}_{\text{average}}$ occasionally failed to maintain adequate genomic diversity. In such cases, ${\text{CD}}_{\text{mean}\left(\text{v}2\right)}$ is recommended as a more reliable alternative. Overall, the proposed framework provides a flexible and effective approach to optimizing training sets for hybrid breeding, thereby enhancing the accuracy of genomic prediction in practical breeding programs.