## 4 Discussion  
### Spatial-Temporal Characteristics of ESSI and ESDI  
Our framework of analysis was used to make sense of relationships between ES supply (ESS) and ES demand (ESD) in a complex social-ecological system. Utilizing the ES supply index (ESSI), we have derived the spatiotemporal variation characteristics of ESS (Figure 3). These characteristics provide valuable insights into assessing the level of ES supply, as well as tracking its enhancement or decline in every county within Shanxi Province. We found that high values of ESSI were predominantly observed in mountainous areas with dense forest coverage. In contrast, low values were mainly found in the Fen River basin, which is dominated by cropland and stretches from northeast to southwest. The Fen River basin is the most active area in terms of social and economic activities in Shanxi Province. The extensive human disturbance in this basin, characterized by high population density and economic growth, has led to the rapid expansion of construction land, causing a reduction in ecological land. As a result, the supply of ESs in the counties within this watershed is relatively low. Similarly, the northwestern parts of the study area, dominated by cropland and grassland, also exhibited relatively low ESSI values. This aligns with findings from previous studies [76]. This region represents a transition zone from scrub steppe to typical steppe, and factors such as increasing population, livestock, and desertification posed significant threats to the area for an extended period. Despite the implementation of the GFGP in these northwestern counties of Shanxi Province since 2000, the supply of local ESs continues to deteriorate [77]. Hence, the grass-planting-based GFGP in this region is required to improve efficiency and achieve ecological protection. Additionally, the western area of Mount Luliang exhibited relatively low ESSI values. Figure 7: Interaction-detected results of socio-ecological variables of CCD using GDM for 2000 (**a**) and 2020 (**b**). _“new”_ indicates nonlinear enhancement: \(q\) (X1\(\cap\)X2)\(>q\) (D1) + \(q\) (D2); _“+”_ indicates bivariate enhancement: \(q\) (D1 \(\cap\) D2) \(>q\) (D1) and \(q\) (D2). A deeper shade of blue indicates a smaller interaction coefficient between X1 and X2 on CCD, and a darker shade of red signifies a larger interaction coefficient. This can be attributed to Mount Luliang's location in the loess hilly and gully region, which is characterized by severe soil and water loss [78]. Moreover, these mountainous areas are contiguous to regions with concentrated mineral resources and frequent human activities. As of 2021, there are 91 coal mines in Luliang, accounting for 13.62% of the total number of coal mines in Shanxi. Extensive mining methods and inadequate management measures have imposed a burden on ecosystems, leading to a diminished supply level of regional ESs. Concerning the ES demand index (ESDI), we carefully curated three indicators representing land use, population dynamics, and economic factors (Figure 4). These indicators collectively offer a comprehensive representation of ESD, encompassing preferences and requirements. We found that high values of ESDI were primarily distributed in the central Taiyuan Basin, northern Datong Basin, southern Linfen Basin and Yuncheng Basin, and southeastern Changzhi Basin, while low values were observed in the mountainous areas on the east and west sides. These basin regions, with Taiyuan, Datong, Linfen, Yuncheng, and Changzhi as their central cities, have experienced significant population and industrial concentration, resulting in high demand for ESs. Notably, the spatial pattern of ESDI closely resembles that of the degree of land use development (Figure 3). This finding is consistent with existing studies [79] that indicate a strong correlation between ESDI distribution and land use development degree, population density, and per capita GDP.