## 4 Discussion
### GAM Response Curves  
Based on the study of simple trade-off/synergistic relationships among ESs, the drivers of these relationships were further explored. [PERSON] et al. [45] compared ESs in the lower reaches of the Pearl River at different levels of urbanization; [PERSON] et al. [46] researched the relationship between ESs and urbanization in the mountainous regions of southwest China; [PERSON] et al. [47] analyzed the impact of land use change on the trade-offs of ESs in the Chishui River basin; [PERSON] et al. [48] explored the human- and climate-driven mechanisms of changes in trade-offs between ESs in the Chengdu-Chongqing urban agglomeration, and the influence of national policies; and [PERSON] et al. [49] analyzed the effects of topographic factors, soil texture, and human activities on trade-offs of ESs in different climatic zones in Shaanxi Province. This study used a GAM to establish a nonlinear relationship between ESTD and the changing values of each ES, based on a smooth function of eachexplanatory variable. By plotting response curves, we can identify the dominant services in the trade-off/synergistic relationship between ESs, which assists the macro-regulation of ESs. We found that WY dominated most of the trade-off/synergistic relationships, and the influence of FP was relatively large, with SC and HQ usually having a comparatively smaller influence. Such research provides important information for ecological conservation and restoration, thus helping understand human and natural impacts on ecosystems. For example, Figure 8a shows that the trade-off/synergy relationship between WY and FP gradually decreases from higher synergy when WY changes up to a certain level. As WY increases, the synergistic relationship changes to a trade-off relationship. Such regularity provides a quantitative reference for the agricultural rationalization of irrigation and drainage, providing inspiration for the change in trade-off/synergy between ESs.  
[PERSON] [50] explained that rapid changes in potential drivers or interactions among drivers may lead to abrupt ecosystem changes without positive feedback mechanisms. The nonparametric smoothing approach of the GAM describes some of the potential nonlinear response patterns that are not captured by linear models, such as fluctuating increases or decreases. Such fluctuations, however, are very likely due to data instability, higher dispersion, or random errors, potentially introducing misunderstandings in the interpretation of the synergistic response implications of ES trade-offs. Regardless of this, additive models have high application value and can be used as exploratory tools. Many scholars have improved upon this model, e.g., [PERSON] and [PERSON] [51] studied a semiparametric generalized additive model (GACM) that generalizes the prediction function in a conventional GAM to an unknown function that depends on some covariates to overcome the \"curse of dimensionality\" problem when the tuning variables are large. [PERSON] et al. [52] proposed a method for efficient selection of model smoothness for GAM, which yields reliable results by optimizing the entire model; the authors also investigated a GAM model for large data sets [53].  
Figure 8 shows that there are some response curves fitted using the GAM for which the results are already close to a linear relationship (i.e., edf = 1); results are still linear when the number of basic smoothing functions is further adjusted using the guarantee of smoothness test. The linearity result proves that there is no overfitting problem and highlights the dominance of nonlinear ES variation in ESTD. Thus, the use of a GAM in the search for the dominant influence amongst various ESs' trade-offs/synergies can still be relatively obvious. This facilitates further conclusions and lays the foundation for future research.