## 3 Results
### Response Curves of ES Trade-Offs/Synergies  
A nonlinear relationship between ES trade-offs/synergies and the change values of each ES was established based on a smooth function of each explanatory variable, where the horizontal coordinate is the value of change in ESs and the vertical coordinate is ESTD. Analysis of the results in Figure 8a shows that the increase in negative variation of WY makes WY gradually converge with FP. Since the negative variation of WY tends from \(-1300\) m\({}^{3}\)/ha to \(-3000\) m\({}^{3}\)/ha, WY and FP gradually convert from a synergy to a trade-off. The positive increase in WY makes it gradually tend to synergize with FP, shifting to a trade-off trend when the positive change is greater than \(1800\) m\({}^{3}\)/ha. As FP increases, the trade-off with WY gradually increases; an increase in the negative change in FP tends to be synergistic. Figure 6: Spatial distribution of trade-offs/synergies for five ecosystem services. WYFP is the ESTD of WY and FP. WYSC is the ESTD of WY and SC. Same for the rest. In Figure 8b, when the negative change in WY increases or the positive change is insignificant, the ESTD interaction remains relatively unchanged. As the positive change in  
Figure 8: Relationship between trade-offs/synergies among ESs (**a–j**). Figure 7: ES variation kernel density estimation map. (**a**) shows the kernel density estimates for the interaction trade-off relationship. (**b**) shows the kernel density estimates for the interaction synergy relationship. Here, white dots in the center of each violin shape represent the median of data, which can reflect the overall situation of the data. The length of the violin body indicates the degree of dispersion of the data, while the highest and lowest points of the body indicate 25% and 75% of the values, respectively. The top and bottom extend to a maximum of 1.5 \(\times\) IQR (interquartile range). the WY increased to 1500 m\({}^{3}\)/ha, a synergistic effect with SC began to arise. Changes in SC had little effect on ESTD. In Figure 8c, an increase in the negative change in WY promotes a synergistic relationship with CS. The increase in positive variation will lead to the generation of synergy before the appearance of a trade-off; the synergy peaks when increasing to 1500 m\({}^{3}\)/ha, after which a trade-off trend will appear. Changes in CS showed very little effect on their ESTD. In Figure 8d, as the positive change in WY increases, the synergistic relationship with HQ becomes clearer; however, when increased to 2500 m\({}^{3}\)/ha, the synergy begins to decline. After 3500 m\({}^{3}\)/ha, the trade-off trend begins, and the increase in negative changes will have some synergistic effect. Changes in HQ showed very little effect on ESTD. Figure 8a-d show that the effect of changes in the volume of WY dominated the ESTD with other ESs; except for FP, changes in all three ESs do not show a large impact on ESTD. In Figure 8e, as the negative change in FP increases, a peak in the trade-off relationship with SC is reached around 400 t/hm\({}^{2}\), after which the trend becomes synergistic. Positive increases in SC show synergistic effects, and negative increases show trade-offs. In Figure 8f, trends in FP are relatively similar to those in CS. An increase in positive changes produces a synergistic effect between them, and an increase in negative changes produces a trade-off trend. In Figure 8g, a positive increase in FP shows synergies, and a negative increase appears as a trade-off trend. The trade-off increases gradually as the change in HQ increases from \(-0.17\) to \(-0.2\); the negative change from 0 to \(-0.17\) produces a trend of trade-offs followed by synergies, with the dividing line at approximately \(-0.1\). The value of positive changes in HQ (greater than 0.2) tends to be a trade-off from a synergy. The synergy and trade-off trend between CS and SC in Figure 8h is similar to that between FP and SC in Figure 8e.