## 3 Research Methods
### Construction of a Composite Index of Conflicts in the PLES
\begin{table}
\begin{tabular}{c c} \hline \hline
**Production–Living–Ecological Space Types** & **Landscape Vulnerability Index** \\ \hline Agricultural Production Space & 3 \\ Forest Ecological Space & 1 \\ Grassland Ecological Space & 2 \\ Waterbody Ecological Space & 4 \\ Urban Living Space & 6 \\ Rural Living Space & 6 \\ Industrial Production Space & 6 \\ Other Ecological Spaces & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Landscape Vulnerability Index table. Optimal Parameter Geodetectors extend the functionality of traditional geodetectors by identifying and quantifying the factors influencing spatial distribution variations. They further investigate the influence of various factors and their interactions on spatial dynamics [32; 33]. Factor detection in the Optimal Parameter Geodetector evaluates the extent to which factor X explains the spatial variation in attribute Y through the computation of the q-statistic. The q-value ranges between 0 and 1, with higher values signifying greater explanatory power. The calculation formula is as follows:  
\[\text{q}=1-\frac{1}{\text{N}}\times\frac{\sum_{\text{i}=1}^{\text{n}}{\text{ N}_{\text{i}}}\times{\sigma_{\text{i}}}^{2}}{\sigma^{2}} \tag{6}\]  
where i = 1, 2, \(\ldots\), n represents the stratification or categorization of factor X; N and N\({}_{\text{i}}\) denote the total number of units and the number of units in stratum i, respectively; and \(\sigma^{2}\) and \({\sigma_{\text{i}}}^{2}\) refer to the variances in the overall dataset and in stratum i, respectively. Interaction detection examines the relationships between factors by contrasting the q-values of individual factors with the q-value derived from their interaction. The nature and intensity of these interactions are classified into five distinct categories, as outlined in Table 4. \begin{table}
\begin{tabular}{c c} \hline \hline
**Criteria for Judgment** & **Interaction Types** \\ \hline q(x1/\(\times\)x2) \(<\) Min(q(x1), q(x2)) & Nonlinear Attenuation \\ Min(q(x1)q(x2)) \(<\) q(x1/\(\times\)x2) \(<\) Max(q(x1), q(x2)) & Single-Factor Nonlinear Attenuation \\ q(x1/\(\times\)x2) \(>\) Max(q(x1), q(x2)) & Two-Factor Enhancement \\ q(x1/\(\times\)x2) \(=\) q(x1) \(+\) q(x2) & Independence \\ q(x1/\(\times\)x2) \(>\) q(x1) \(+\) q(x2) & Nonlinear Enhancement \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Interaction detection type. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Conflict Types** & **Threshold Interval** & **Spatial Landscape Patch Performance** \\ \hline Weak Conflict & [0, 0.2) & Relatively undisturbed by human activities, the landscape patches demonstrate structural integrity, robust continuity, and high stability. \\ Weaker Conflict & [0.2, 0.4) & This predominantly coincides with regions of relatively low spatial conflict, characterized by minimal conflict intensity. Landscape patches exhibit increased fragmentation, accompanied by more intricate and irregular boundary configurations. \\ Stronger Conflict & [0.6, 0.8) & Landscape patches exhibit a high degree of fragmentation, characterized by heightened vulnerability and increased structural complexity. \\ Strongest Conflict & [0.8, 1] & The spatial landscape patches are highly fragmented, interspersed with one another, and characterized by intricate structural patterns. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thresholds and characteristics of different levels of spatial conflict.