Quadratic Genomic Selection Index Boosts Multi-Trait Genetic Gain in Modern Plant Breeding

Selection index theory is a cornerstone of multi-trait genetic improvement, yet classical linear indices are limited by assumptions of additivity and fixed trait weights. These limitations hinder their ability to capture complex genetic architectures involving non-linear trait interactions and intermediate optima. To address this, we introduce the Quadratic Genomic Selection Index (QGSI)—a novel index that integrates genome-wide marker information with quadratic modeling to improve accuracy, adaptivity, and selection speed. QGSI retains the desirable statistical properties of traditional indices while enabling non-linear modeling of trait contributions. Using the Quadratic Phenotypic Selection Index (QPSI) theory, simulations, and real datasets from maize and wheat, we show that QGSI achieves the highest selection response, correlation, and the minimum prediction error variance in the genomic selection context; greater ranking fidelity, and more stable predictions than existing QPSI and linear indices. It enables phenotype-free, genome-informed selection, reducing cycle time and supporting rapid, ideotype-targeted breeding. While the QPSI performs best when phenotypic data is available, QGSI becomes the optimal choice in fully genomic cycles. Together, these tools offer a pathway to accelerate multi-trait improvement in modern breeding programs. By increasing the speed, precision, and adaptability of selection, QGSI supports the development of productive and climate-resilient crops.