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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup><mml:mrow><mml:mtext>MSPE</mml:mtext></mml:mrow> <mml:mrow><mml:mo>(</mml:mo> <mml:mtext>v</mml:mtext> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo></mml:mrow> <mml:mrow><mml:mtext>Ridge</mml:mtext></mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> , (ii) a generalized coefficient of determination-based method, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mtext>CD</mml:mtext></mml:mrow> <mml:mrow><mml:mtext>mean</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>v</mml:mtext> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:msub> </mml:mrow> </mml:math> , and (iii) an A-optimality-like ranking strategy, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mtext>GV</mml:mtext></mml:mrow> <mml:mrow><mml:mtext>average</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> </mml:math> . 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 (<i>Triticum aestivum</i> L.), maize (<i>Zea mays</i>), and rice (<i>Oryza sativa</i> L.) were carried out to assess the proposed methods. Results demonstrated that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mtext>GV</mml:mtext></mml:mrow> <mml:mrow><mml:mtext>average</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> </mml:math> 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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mtext>GV</mml:mtext></mml:mrow> <mml:mrow><mml:mtext>average</mml:mtext></mml:mrow> </mml:msub> </mml:mrow> </mml:math> occasionally failed to maintain adequate genomic diversity. In such cases, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub><mml:mrow><mml:mtext>CD</mml:mtext></mml:mrow> <mml:mrow><mml:mtext>mean</mml:mtext> <mml:mo>(</mml:mo> <mml:mtext>v</mml:mtext> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo></mml:mrow> </mml:msub> </mml:mrow> </mml:math> 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.