## 3 Research Methods
### Construction of a Composite Index of Conflicts in the PLES  
A spatial grid of 300 m \(\times\) 300 m was chosen as the assessment unit, considering the scope of the study, the characteristics of the data, and the conditions of land patches. This scale was selected for the following reasons: A 300 m \(\times\) 300 m grid provides sufficient spatial resolution to capture variations in land use while maintaining computational feasibility. Finer grids (e.g., 100 m \(\times\) 100 m) may increase computational complexity without significantly improving analytical accuracy, whereas coarser grids (e.g., 500 m \(\times\) 500 m or 1 km \(\times\) 1 km) could obscure localized spatial conflicts. Building on insights from prior research [28; 29], a set of evaluation indicators was developed to measure the intensity of \begin{table}
\begin{tabular}{c c c c} \hline
**PLES Types** & **Secondary-Level Space** & **Current Land-Use Categories** & **Images** \\ \hline  & Forest Ecological Space & Forestland & \\  & Grassland Ecological Space & Grassland & \\ Ecological Space & Waterbody Ecological Space & Rivers, Lakes, Reservoirs, Ponds & \\  & Other Ecological Spaces & Sandy Land, Bare Land, Rocky Land & \\ \hline  & Urban Living Space & Urban Land & \\ Living Space & Rural Living Space & Rural Residential Land & \\  & Industrial Production Space & Construction Land & \\ Production Space & Agricultural Production Space & Paddy Field, Dry Land & \\ \hline \end{tabular}
\end{table} 
Table 1: Zengcheng District PLES Classification System. spatial conflicts among the three functional domains. This intensity is quantified using the Spatial Conflict Composite Index (SCCI). \[\text{SCCI}=\text{CI}+\text{FI}-\text{SI} \tag{1}\]  
The Spatial Conflict Composite Index (SCCI) is a comprehensive metric that combines three critical indices: the Spatial Complexity Index (CI), the Fragility Index (FI), and the Stability Index (SI). Spatial complexity is evaluated through area-weighted sub-dimensions, which provide a quantitative measure of the intricacy of patch boundaries. Higher sub-dimension values signify more complex patch geometries, indicating greater levels of interference and heightened risk. The calculation formula is presented as follows:  
\[\text{AWMPFD}=\sum_{\text{j}=1}^{\text{m}}\sum_{\text{i}=1}^{\text{n}}\left[ \frac{2\text{ln}\left(0.25\text{P}_{\text{ij}}\right)}{\text{ln}\,\text{a}_{ \text{ij}}}\times\frac{\text{a}_{\text{ij}}}{\text{A}}\right] \tag{2}\]  
Here, \(\text{P}_{\text{ij}}\) represents the perimeter of the patch, \(\text{a}_{\text{ij}}\) denotes the area of the patch, A refers to the total area of the spatial unit, m indicates the total number of evaluation units, and n corresponds to the number of landscape types. Vulnerability captures the degree of exposure faced by risk receptors, exhibiting spatial variability across different regions. Drawing on previous studies [30; 31], the spatial vulnerability indices for each category were determined (Table 2). The formulas for their calculation are as follows:  
\[\text{FI}=\sum_{\text{i}=1}^{\text{n}}\left(\text{F}_{\text{i}}\times\frac{ \text{a}_{\text{i}}}{\text{S}}\right) \tag{3}\]  
Stability is evaluated using patch density within the Landscape Index. Higher patch density indicates greater landscape fragmentation, reduced biodiversity, diminished environmental coherence, and heightened ecological risk. The calculation formula is as follows:  
\[\text{SI}=1-\frac{\text{PD}-\text{PD}_{\text{min}}}{\text{PD}_{\text{max}}- \text{PD}_{\text{min}}} \tag{4}\]  
\[\text{PD}=\frac{\text{n}_{\text{i}}}{\text{A}} \tag{5}\]  
\(\text{n}_{\text{i}}\) represents the number of patches of spatial type i within the spatial unit, while A denotes the total area of the spatial unit. The values of the spatial conflict index were normalized to fall within the range of 0 to 1. Conflict levels are categorized using the equal-interval method, with the thresholds and characteristics of each level detailed in Table 3.