Crop Adaptation Trajectory Science: Concept, Theoretical Framework, and Mathematical Modeling
Traditional crop physiology and agronomic research predominantly rely on static cross-sectional evaluations to assess stress resistance and yield potential. However, a crop's terminal phenotype and yield are not dictated by its instantaneous status at a single growth stage, but rather represent the cumulative path-integral of dynamic interactions among genotypes, environmental stress, and management practices across the entire life cycle. To bridge this knowledge gap, this paper establishes a novel conceptual framework and interdisciplinary paradigm termed Crop Adaptation Trajectory Science (CATS). CATS shifts the research core from "what state the crop is in" to "how the crop evolved to its current state along a continuous trajectory." We propose a four-stage evolutionary model comprising Establishment, Stress Induction, Recovery and Compensation, and Maturation and Terminal Phase. Furthermore, a quantitative state-space dynamic model based on continuous ordinary differential equations is constructed. The model explicitly incorporates environmental stress force vectors, intrinsic recovery rate matrices, time-decaying cumulative damage integrals, and dual-exponential epigenetic memory kernels. It mathematically demonstrates how stress history, lagged physiological responses, and overcompensation effects govern terminal agronomic traits. Mechanistically, CATS elucidates that the temporal expression of Genotype-Environment-Management (GxExM) interactions is driven by chromatin-level epigenetic memory and metabolic energy reallocation between maintenance and repair. Practically, CATS provides a foundation for real-time trajectory matching and intervention in precision agriculture, while offering new trajectory-based breeding indices—such as Deviation Rate, Recovery Slope, and Memory Efficiency—to decouple environmental resilience from yield penalty. CATS establishes a comprehensive theoretical basis for dynamic crop phenotyping, predictive digital twins, and full-lifecycle crop management.