Spatiotemporal synergies and trade-offs among food production, water availability, and ecological quality in the Beijing–Tianjin–Hebei Region

Managing interactions among food production, water resources, and ecological systems is a major sustainability challenge in semi-arid and rapidly urbanizing socio-ecological regions. Using Big Earth Data and a two-scale analytical framework, this study quantifies spatiotemporal synergies and trade-offs in the food-water-ecology (FWE) nexus of the Beijing-Tianjin-Hebei region from 2005 to 2022. A mechanical equilibrium model reveals persistent north-south differentiation, with strong trade-offs in mountainous ecological zones and weak synergies across the agricultural plains. XGBoost-SHAP analysis identifies nonlinear ecological and anthropogenic thresholds, including forest cover above 60 %, elevations exceeding 780 m, and development intensity, that influence transitions between synergy and trade-off states. Cross-scale comparison shows that natural constraints dominate grid-level patterns, while human activities increasingly control township-level outcomes. These findings highlight the necessity of threshold-informed and spatially differentiated governance, including groundwater recovery and agricultural intensity management in the plains, long-term ecological stabilization in uplands, and integrated water-ecology regulation in metropolitan areas. The framework provides a tool for advancing coordinated progress toward Sustainable Development Goals 2, 6, 11, and 15.