## 4 Results
### Synergies between Ecosystem Services
#### 4.2.2 Synergies  
Assuming the accuracy of our DMC analysis, we selected four pairs of ecosystem services that exhibit average correlation coefficients greater than 0.3, and eliminated those between P export, NPP and soil conservation amount. In addition, to further analyze differences in synergy effects, we also established DMCs for different LULCs (i.e., cultivated land, forested land and grassland) and ranges of altitude (i.e., less than 3500 m, between 3500 and 4500 m, between 4500 and 5500 m and greater than 5500 m). Results show that DMCs of NPP versus water yield for the TRHR conform to a linear relationship, indicating the presence of a fixed synergistic effect between the two services (Figure 8). Compared with data for 2000, the DMC of NPP and water yield for 2012 is extended, indicating an increased amount of accumulated NPP and water yield. This paired increasing trend in water yield and NPP for each LULC in 2012 shows that forested land and grassland are almost equivalent to one another and that both have larger values than cultivated land (Figure 10a). In addition, the DMC slope of these data increases in concert with altitude (Figure 10b), indicating that an improvement in NPP in high-altitude areas is favorable for enhancing water yields. Between 2000 and 2012, the total water yield amount and NPP both increased with altitude up to 5500 m, while a negative correlation was also present as amplitude and altitude increased. The slope rates of lines for all LULC types and ranges of altitude also decreased slightly compared with 2000, indicating a decreasing trend in water yield changes caused by unit changes in NPP. The DMC graphs generated in this study to illustrate the amount of soil conservation versus NPP are characterized by some convex curve shapes, indicating the presence of a significant synergistic effect between this pair of services. Amongst different LULC types, the services provided by forested land were the highest (Figure 11a), followed successively by grassland and cultivated land. Thus, from the perspective of synergistic effects, as NPP decreased, the concomitant trend in reduction of the amount of soil conservation for each LULC was (from highest to lowest) forested land, grassland and cultivated land. Similarly, synergy between NPP and the amount of soil conservation is also positively correlated with altitude (Figure 11b). Results show that between 2000 and 2012, synergy between NPP and soil conservation for cultivated land decreased, while that for forested land and grassland remained broadly consistent. The change in synergies between NPP and soil conservation was, however, inconsistent for different altitude ranges; below 4500 m, synergy between the two services increased, but decreased at ranges above 4500 m. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Year** & **Ecosystem Service** & **NPP** & **Water Yield** & **Soil Conservation** & **P Export** \\ \hline \multirow{4}{*}{2000} & NPP & 1 & & & & \\  & Water yield & 0.699 *** & 1 & & & \\  & Soil conservation & 0.383 *** & 0.407 *** & 1 & & \\  & P export & 0.309 *** & 0.500 *** & 0.224 *** & 1 \\ \hline \multirow{4}{*}{2012} & NPP & 1 & & & & \\  & Water yield & 0.761 *** & 1 & & & \\ \cline{1-1}  & Soil conservation & 0.338 *** & 0.294 *** & 1 & & \\ \cline{1-1}  & P export & 0.095 *** & 0.178 *** & 0.066 *** & 1 \\ \hline \hline \end{tabular} Note: *** Correlation is significant at the 0.01 level (two-tailed).  
\end{table} 
Table 1: Correlation matrix between various ecosystem services of the TRHR. The DMC graphs generated in this study to illustrate the amount of soil conservation versus water yield for different LULCs corroborate the fact that the highest volume of services is provided by forested land, followed by grassland and cultivated land. In terms of synergistic effects, water yield amounts decrease in concert with soil conservation amounts with cultivated land greater than grassland, which is greater than forested land (Figure 12a).