A unified decision framework combines phenotypic and genomic information for nonlinear selection in plant breeding

Abstract Plant breeding traditionally relies on linear selection indices that combine phenotypic and genomic data to predict breeding objectives (also called genetic merits). Many breeding objectives are nonlinear because they include target deviations, curvature, or the joint value of trait combinations. In this work, we develop a unified decision framework for phenotypic, genomic, and combined information and introduce the combined quadratic genomic selection index (CQGSI). The framework separates genomic prediction from the subsequent selection decision and treats nonlinearity as a property of the breeding objective and its predictor, the CQGSI. In simulated maize, real maize, and wheat datasets, adding genomic predictions often improved response and the expected genetic gain per trait within the same objective. Also, we showed mathematically, why the mean square prediction error of CQGSI was higher than the mean square prediction error of linear indices. Comparisons between linear and quadratic indices remained objective specific because the linear genetic merit and the quadratic genetic merit differ in definition and scale. The framework therefore clarifies when phenotypic, genomic, or combined information can support a stated nonlinear breeding objective.