Abstract:Trade-offs and synergistic relationships among ecosystem service pose a significant challenge to ecosystem service management. With the enhancement of ecosystem services, trade-offs or synergies between different ecosystem services may change nonlinearly, i.e., threshold effects. Herein, remove sensing data, field observation data and field survey data have been collected from 1990 to 2020. Four ecosystem services, such as carbon sequestration, water production, soil conservation and food production have been quantified based on the CASA (Carnegie-Ames-Stanford Approach), the InVEST (Integrated Valuation of Ecosystem Services and Tradeoffs ), the CSLE (China Soil Lose Equation) and the PD (Pixel decomposition) model, respectively. The spatial and temporal trade-offs and synergies of ecosystem services were quantified based on correlation analysis and spatial statistics methods. Finally, the thresholds of ecosystem services were extracted using breakpoint analysis. The results showed as follows: (1) All four ecosystem services, namely carbon sequestration, water production, soil conservation and food production, showed a trend of decreasing and then increasing, with an overall increase. In particular, the average annual carbon sequestration of the Yanhe basin is about 200-450 g C/m2, and the increase in carbon sequestration is the largest compared with other ecosystem services. However, the increase of carbon sequestration service is not the result from expansion of vegetation coverage but the improvement of vegetation quality. (2) There are high synergistic relationships among carbon sequestration, water production and soil conservation in the Yanhe basin, and all three have trade-off relationships with food production. In general, the synergistic relationship is weakening and the trade-off relationship is increasing in the Yanhe basin. At the same time, there is a scale effect in this relationship, which gradually strengthens or weakens or even reverses as the scale increases. (3) Most relationships among ecosystem services existed threshold effects with the increase of ecosystem services. For example, at water yields around 150 t/hm2, its synergistic relationship with carbon sequestration shifts to a trade-off, while its trade-off relationship with food production shifts to a synergistic one. When ecosystem services are small, fewer resources are needed to maintain such services, resulting in services that tend to exhibit synergistic relationships with each other. When ecosystem services increase further, the demand for various resources also gradually increases, leading to a weakening of synergistic relationships and even a shift from synergistic to trade-off relationships. Controlling ecosystem services within certain thresholds can help the synergistic development of ecosystem services and provide a reference for sustainable ecosystem management.