## 2 Materials and Methods
### Methodology
#### 2.2.4 Priority Assessment of Ecological Corridors  
* Calculation of the importance of ecological corridors  
The gravity model determines the importance and protection priority of ecological corridors by comparing the interaction intensity between ecological sources. High intensity indicates that the ecological sources of the corridor connection are of better quality or that the corridor provides a better connection [83]. The formula is as follows:  
\[G_{ab}=\frac{N_{a}\times N_{b}}{D_{ab}^{2}}=\frac{L_{max}^{2}\times\ln S_{a} \times\ln S_{b}}{L_{ab}^{2}\times P_{a}\times P_{b}} \tag{21}\]  
where \(G_{ab}\) is the interaction intensity of the ecological corridors connecting sources \(a\) and \(b\); \(N_{a}\) and \(N_{b}\) represent the weights of ecological sources \(a\) and \(b\), respectively; \(D_{ab}\) is the standardized cumulative resistance of the corridor; \(L_{ab}\) is the minimum cumulative resistance of the corridor connecting sources \(a\) and \(b\); \(L_{max}\) is the maximum cumulative resistance of the corridor in the study area; \(S_{a}\) and \(S_{b}\) are the areas of sources \(a\) and \(b\), respectively; and \(P_{a}\) and \(P_{b}\) are the resistance values of sources \(a\) and \(b\), respectively.
* Calculation of connectivity of ecological corridors  
The Centrality Mapper tool in the Linkage Mapper plug-in can quantify ecological corridor connectivity. Referring to the circuit theoretical model, the Centrality Mapper regards the study area as a conductive surface. It turns the current into different ecological sources and accumulates the currents successively to obtain the cumulative current value of each corridor [84]. The connectivity is determined by comparing the current value of each ecological corridor. The higher the current value is, the more ecological sources are affected by the corridor, and the greater the contribution to the connectivity of the ecological network.
* Priority classification of ecological corridors  
Based on the calculation method above, the calculated interaction intensity and corridor current value were standardized. To reduce the influence of the data magnitude on the evaluation results, we took natural logarithms of the interaction intensity and corridor current value. The formula is as follows:  
\[Z_{i}=\frac{x_{i}-\overline{x}}{s} \tag{22}\]where \(Z_{i}\) is the evaluation index, \(x_{i}\) is the \(i\)-th evaluation indicator (interaction intensity or corridor current value), \(\overline{x}\) is the mean value of the evaluation indicator, and \(s\) is the standard deviation of the evaluation indicator.  
The standardized value of the interaction intensity and corridor current will participate in the priority classification as an importance index and connectivity index of the ecological corridors, respectively. A plane Cartesian coordinate system is established, where the horizontal axis represents the standardized interaction intensity index, and the longitudinal axis represents the standardized corridor current value index. Together, the two indexes form the \"importance-connectivity\" index. According to the quadrant, ecological corridors can be divided into four types: the corridors with an importance index and connectivity index greater than 0 are classified as \"high importance-high connectivity\" ecological corridors. Similarly, the corridors with a negative importance index and positive connectivity index, with a positive importance index and negative connectivity index, and with both a negative importance and connectivity index are categorized as being \"low importance-high connectivity\", \"high importance-low connectivity\", and \"low importance-low connectivity\" ecological corridors, respectively.