The Unified AMMI-GGE (UAG) Model: A Continuous Framework for Integrating Yield Stability and Adaptability in Multi-Environment Trials

Understanding and modeling genotype–environment interaction (GEI) remains a cornerstone of plant breeding, directly influencing cultivar recommendation and mega-environment delineation. The Unified AMMI-GGE (UAG) framework developed in this study generalizes two of the most widely used GEI models—the Additive Main effects and Multiplicative Interaction (AMMI) and the Genotype + Genotype–Environment (GGE)—into a parametric continuum governed by the tuning parameter α ∈ [0, 1]. Within a single singular-value decomposition (SVD) structure, UAG retains the inferential rigor of AMMI while recovering the decision-oriented visualization of GGE. Cross-validation experiments across multiple schemes identified intermediate α values (0.1–0.3) and rank K = 2 as optimal, minimizing root-mean-square error while maintaining interpretability. The model was empirically validated using multi-environment yield data from triticale (×Triticosecale Wittmack), demonstrating its capacity to classify genotypes by adaptation type and stability. At α = 0.3, genotypes G3, G5, and G8 exhibited broad adaptation, whereas G10 and G11 showed high yield potential under favorable environments. The key novelty of UAG lies in formalizing a continuous parametric path between AMMI and GGE within a single SVD structure, enabling cross-validated model selection rather than arbitrary choice between the two paradigms. The Unified AMMI-GGE Index (UAGI) provided coherent yield–stability rankings across α-values, avoiding the inconsistencies typical of separate AMMI and GGE metrics. Overall, UAG bridges interpretability and predictive validation within a single analytical framework, offering a flexible, cross-validated, and theoretically consistent tool for modern breeding programs seeking to optimize both stability and productivity under variable environments.