## 3 Results
### Analysis of Local Ecosystem Service Trade-Offs and Synergies
#### 3.3.3 Spatial Differences in Ecosystem Service Trade-Offs and Synergies  
Figure 9 illustrates significant variations in the Moran's I indices for ecosystem services across various ecological restoration zones, which are consistent with the patterns noted in the Pearson correlation analysis. The analysis reveals that food production is generally associated with negative Moran's I indices when compared to the other four services, suggesting consistent trade-offs. Conversely, indices for soil conservation, water yield, habitat quality, and carbon sequestration are positive, indicating prevalent synergistic interactions across these services. This pattern underscores that synergistic interactions are more common than trade-offs in these zones. Notably, the interaction between soil conservation and water yield displays the strongest synergy with a Moran's I index of  
Figure 8: Pearson correlation coefficient: HQ: habitat quality; WY: water yield; CS: carbon storage; FD: food production; SC: soil conservation. 0.402, aligning with Pearson correlation findings to highlight a robust cooperative relationship. Following this, the synergy between habitat quality and soil conservation is also significant, with an index of 0.206. Other synergistic relations among these services have Moran's I indices ranging from 0.1 to 0.2, showing less pronounced synergies. The synergy between habitat quality and carbon sequestration, though positive, is the weakest with an index of 0.119. On the contrary, the Moran's I indices for food production in relation to other services vary from \(-0.3\) to \(-0.1\), indicating differing levels of trade-offs. The most substantial trade-off occurs between food production and soil conservation, with an index of \(-0.281\). Following this, the trade-offs decrease in intensity with habitat quality, water yield, and carbon sequestration, respectively, where the least significant trade-off is observed with carbon sequestration, marked by an index of \(-0.183\). The bivariate local Moran's I index reflects the trade-offs and synergies between paired ecosystem services and their statistical significance, aligning closely with the results from Pearson correlation coefficients. This consistency confirms that the bivariate local Moran's I index effectively captures the spatial trade-offs and synergies within the layout of national ecological restoration areas. However, the correlations derived from the bivariate local Moran's I index are generally lower than those from Pearson correlation coefficients. This primarily stems from the inclusion of the spatial weighting matrix \(W_{\bar{\mathrm{ij}}}\) in the formulation of the local Moran's I index, which introduces spatial lags into the interactions between ecosystem services. However, this incorporation of spatial lags effectively captures the spatial dependencies and interconnections that exist among different ecosystem services. As illustrated in the figure (Figure 10), there is significant spatial heterogeneity among the local ecosystem services across the five ecological restoration zones. To enhance the clarity of these results, the administrative districts within each ecological restoration zone were used as the fundamental unit of analysis for a bivariate local spatial autocorrelation assessment. This approach allowed for a more detailed investigation of the trade-offs and synergies among ecosystem services within each zone. Overall, the areas exhibiting synergies between local ecosystem services were more extensive than those showing trade-offs across the ecological restoration zones. Apart from food production, habitat quality, water  
Figure 9: Local bivariate Moran’s I HQ: habitat quality; WY: water yield; CS: carbon storage; FD: food production; SC: soil conservation. yield, carbon sequestration, and soil conservation generally displayed varying degrees of synergy. The spatial distribution patterns of local and global ecosystem services effects exhibit distinct characteristics of spatial differentiation.