## 3 Results
### Analysis of Global Ecosystem Service Trade-Offs and Synergies  
In Liaoning Province, the interactions between various ecosystem services are predominantly marked by strong trade-offs, weak trade-offs, high synergies, and low synergies (Figure 5). The distribution of these relationships, ranked by proportion, is as follows: strong trade-offs (35.51%) > weak trade-offs (33.17%) > low synergies (29.09%) > high synergies (2.24%). The spatial distribution of global ecosystem service trade-offs and synergies demonstrates a clear pattern (Figure 6). With the exception of areas characterized by low synergies, the WCR exhibits the highest proportion of regions with the other three types of relationships, making it the most dominant among the five ecological restoration zones. In the five ecological restoration zones, low synergy relationships are primarily concentrated in the SWCR and the IR, with 33.93% of the low synergy areas located in SWCR and 27.73% in IR. Together, these two zones account for over half of the total low synergy areas. The proportion of low synergy areas in the CR and the WPSR is similar. High synergy areas are predominantly located in the WCR, which accounts for 68.15% of the high synergy regions, indicating a prominent presence of high synergy relationships in this zone. Following WCR, the IR and CR also exhibit significant high synergy, with the combined proportion of these three zones exceeding 90% of the total high synergy areas. In contrast, the high synergy regions in SWCR and WPSR are nearly nonexistent. Similarly, weak trade-off relationships are mainly concentrated in WCR, accounting for 59.79% of such regions, with the remaining weak trade-off areas distributed in SWCR and IR. Strong trade-off relationships, however, exhibit a more uniform spatial distribution across the five ecological restoration zones without any significant regional concentration, indicating a more balanced presence across the study area. According to spatial characteristics, the distribution of the four types of relationships exhibits significant spatial heterogeneity. Low synergy relationships are widely distributed across SWCR, IR, and the southwestern part of WSFR, as well as the southern portion of CR, with a scattered distribution throughout the entire study area. High synergy relationships are only present in the southern part of WCR, near the boundary with IR, and in the northeastern part of WCR, with almost no occurrence in other regions. In contrast to synergy relationships, trade-off relationships display a more widespread global distribution. Weak trade-off relationships are primarily located in the eastern part of WCR, with a spatial pattern opposite to that of low synergy relationships. Strong trade-off relationships are concentrated in the northern part of WSFR, the northwestern region of WCR, and the northern boundary area of CR. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Ecosystem Services Type**} & \multirow{2}{*}{**Area**} & \multicolumn{2}{c}{**Per Area Service Capability**} & \multirow{2}{*}{**Proportion of Liaoning Province**} \\ \cline{3-4}  & & **MIN** & **MEAN** & **MAX** \\ \hline \multirow{4}{*}{carbon sequestration (\(\text{t h}\text{m}^{-2}\))} & IR & 0 & 127.98 & 215.84 & 19.34\% \\ \cline{2-4}  & WSFR & 0 & 111.22 & 215.84 & 10.24\% \\ \cline{2-4}  & CR & 0 & 101.20 & 215.84 & 9.53\% \\ \cline{2-4}  & WCR & 0 & 177.25 & 215.84 & 39.64\% \\ \cline{2-4}  & SWCR & 0 & 149.74 & 215.84 & 21.25\% \\ \hline \multirow{4}{*}{Habitat Quality} & IR & 0 & 0.41 & 1 & 18.23\% \\ \cline{2-4}  & WSFR & 0 & 0.39 & 0.97 & 9.36\% \\ \cline{2-4}  & CR & 0 & 0.32 & 0.97 & 8.77\% \\ \cline{2-4}  & WCR & 0 & 0.66 & 0.99 & 43.13\% \\ \cline{2-4}  & SWCR & 0 & 0.50 & 0.87 & 20.51\% \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._Figure 5: Global Ecosystem services trade-off/synergy of Liaoning province (**a**) Low Synergy; (**b**) High Synergy; (**c**) Weak Trade-off; (**d**) Strong trade-off.