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 (EStrade-off). Results showed that CESDR and EStrade-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 EStrade-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.