## 3 Materials and Methods
### Measuring Land Use Conflicts  
Land use conflict and the landscape ecological risk are closely related, so the evaluation dimensions of the two can correspond to each other [8; 42]. Based on existing studies [8; 13; 23; 43], we constructed the spatial conflict index (LUCI) to measure the regional and use conflicts while considering three dimensions, i.e., complexity (risk sources), fragility (risk receptors), and stability (risk effects) of the land system. From the perspective of the evaluation dimension of land use conflicts, the effective diagnosis and evaluation of land use conflict require a characterization of pressure from human disturbance and the deterioration of natural conditions. Likewise, it demands an evaluation of the ability of land resources themselves to withstand the pressure of conflicts and an indication of the stability of the land system [23]. The pressure from conflict reflects the impact and pressure of human activities on the land system and can be represented by the landscape complexity index. The areas with lower intensity of landscape disturbance are less pressed by human demands, so the corresponding conflict pressure is smaller. The intensity of land use conflict is also related to the attributes of land resources, which can be expressed through the vulnerability of the landscape. Different types of land resource use have different functions and their ability to withstand conflicts is different as well. The stability of land use under conflict stress is also an important aspect of land use conflict assessment. The more fragmented the landscape, the poorer the stability of landscape components and the more intense the conflicts. Areas of increased landscape fragmentation, complexity, and vulnerability instigate ecological risk and land use conflict. Therefore, the complexity, vulnerability, and fragmentation of the landscape were considered as three indices that reflect the risk sources, risk receptors, and risk effects of the ecological risk, respectively. The mathematical expression can be expressed as follows:  
\[LUCI=CI+FI-SI \tag{6}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Road** & **Length (km)** & **Weight** \\ \hline Expressway & 2721.64 & 9 \\ National highway & 1080.08 & 7 \\ Provincial highway & 3417.09 & 7 \\ Urban main road & 9178.48 & 5 \\ County highway & 3174.17 & 3 \\ Urban road & 39,980.66 & 3 \\ Country road & 1531.86 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The traffic network information statistical table. where the _LUCI_ is the index of land use spatial conflict; the _CI_, _FI_, and _SI_ are the spatial complexity, spatial fragility, and spatial stability indices respectively. Firstly, landscape complexity is an effective indicator of risk sources. It is used to reflect the spatial complexity of landscape patches and the interference degree of neighborhood landscape on the current spatial landscape units [44] which are defined by the area-weighted average patch fractal index [45]. The equation for the CI can be represented as:  
\[CI=\sum_{i=1}^{m}\sum_{j=1}^{n}\left[\frac{2\ln\bigl{(}0.25P_{ij}\bigr{)}}{\ln \bigl{(}a_{ij}\bigr{)}}\biggl{(}\frac{a_{ij}}{A}\biggr{)}\right] \tag{7}\]  
where \(P_{ij}\) is the patch perimeter; \(a_{ij}\) is the patch area; \(A\) is the grid size of the fishnet; \(m\) is the total number of patches in the grid; \(n\) is the number of land use types. Next, landscape fragility reflects the exposure status of the evaluation unit and the carrying capacity of risk receptors [46]. There are great differences in the resistance of land use types to external disturbance in different stages, such as maintaining ecosystem stability, protecting biodiversity, and improving the overall structure of the ecosystem [8]. To reflect the difference between the responses of land use spatial units to external pressures and land use processes, the landscape fragility index (FI) is used [23].