Coordinated management of ecosystem service Supply–Demand and trade-offs based on nonlinear responses across multiple scales

Ecosystem service (ES) supply–demand balance is essential for regional sustainability, yet simultaneously optimizing multiple ESs remains challenging due to inherent trade-offs. This study investigates ES supply–demand patterns, trade-offs and synergies across multiple scales in the Loess Plateau (LP) in 2020, employing Generalized Additive Models (GAMs) to quantify nonlinear responses and identify model-derived breakpoints of socio-ecological drivers affecting both the overall ES supply–demand ratio (CESDR) and trade-offs (ES trade-off ). Results showed that CESDR and ES trade-off exhibited a southeast–northwest gradient, with surplus and synergistic areas concentrated in the southeastern LP and deficits and stronger trade-offs in urbanized and northwestern regions. Based on ES supply–demand ratio (ESDR) bundles, the LP was delineated into four, five, and six sub-zones at the city, county, and town scales, respectively. GAM analyses revealed widespread nonlinear responses of CESDR and ES trade-off to socio-ecological drivers, with human activity-related factors exhibiting dominant negative influences. CESDR generally exhibited hump-shaped responses to forest and grassland proportions in most sub-zones, with diminishing or negative responses beyond certain ranges. By integrating multi-scale pattern analysis, ESDR-based zoning, and nonlinear response assessment, this study advances understanding of ES supply–demand dynamics and provides insights for ecological management in the LP.