## 4 Results Analysis
### Trade-Offs/Synergies Analysis on ESs  
The trade-off and synergy index between ESs can be obtained through Equation (3), as shown in Figure 10.  
An analysis of trade-offs and synergies among TCES in Putian City revealed a dynamic interplay over the 20-year study period. Synergy dominated the relationships, with the strongest association observed between regulating and supporting services. Conversely, trade-offs emerged between provisioning-regulating services and supporting-cultural services, with the most pronounced trade-off occurring between provisioning-regulating services. Specifically, the synergy degree between regulating-supporting services peaked at 1.022 from 2000 to 2010, exceeding the lowest synergy degree of 0.977 observed between supporting and cultural services by a significant margin. This suggests that regulating and supporting services exhibited a mutually reinforcing relationship, where the improvement of one service often led to synergistic benefits for the other. However, trade-offs between provisioning-regulating services and supporting-cultural services highlighted the potential conflicts between different ESs. This underscores the need for careful management to optimize the balance among these services and ensure the sustainability of ecosystems. Interestingly, the synergy degree between supporting and cultural services exhibited a reversal from 2010 to 2020, with the synergy degree decreasing to 0.975. This may be attributed to the increasing pressure on ecological land due to accelerated urbanization and industrialization, which may have disrupted the balance between these services.  
Equation (3) was applied to calculate the trade-off and synergy degree indices for SCES in Putian City, as presented in Figure 11.  
Figure 11 presents the trade-off and synergy patterns among SCES in Putian City from 2000 to 2020. The data reveal a prevalence of synergistic relationships, with 10 negative values out of 55 pairs, indicating that synergistic interactions dominate the ecosystem service network. In the trade-off relationship, the highest trade-off intensity was observed between water supply and maintaining the nutrient cycle (\(-\)7.420), while the lowest trade-off intensity was found between hydrologic adjustment and water supply (\(-\)0.162). Regarding synergy, the synergy degree demonstrated a relatively stable trend over the two study periods, with maintaining the nutrient cycle and hydrologic adjustment exhibiting the highest synergy degree (45.738), followed by gas regulation and water supply (1.319). A comparison of the two stages showcases distinct patterns of change across ecosystem  
Figure 10: ESTD in Putian City from 2000 to 2020. Note: Abbreviations are the same as those given in Table 1. Sources: Drawings from this study.  
services. Out of 55 pairs, 20 experienced an increase in synergy degree, while 35 exhibited a decrease, indicating an overall decline in synergy. This variability highlights the dynamic nature of ESs in Pution City over the past two decades. The trade-off degree between food production and water supply declined by 59.73% from 2000 to 2020, while the synergy degree between gas regulation and water supply increased by 126.08%.