## 2 Materials and Methods
### Methods
#### 2.3.3 Ecological Corridor Extraction Based on Multi-Objective Optimization  
1. Potential ecological corridor identification based on MCR. On the basis of determining the resistance value of land use types, the ecosystem service value of each land use type is taken as the weight to correct the resistance value of land use type, and the index system of ecological resistance factor is constructed by combining five resistance factors, including elevation, slope, distance from highway and distance from water (Table 5) [22]. Then, the comprehensive ecological resistance value of the Taishan area is obtained by the ArcGIS overlay analysis. The minimum cumulative resistance (MCR) model is used to generate the resistance surface of the study area, and the minimum cumulative cost distance between the source and the target source is calculated. Then, the potential ecological corridor between the ecological source areas in the Taishan area is obtained (Figure 6). The model considers three factors--source attributes, source-to-source distance and landscape interface characteristics--by calculating the probability of the movement of matter, energy and species in each landscape element type. The ecological resistance surface is constructed, and the minimum cumulative resistance path of the source and target points is obtained. The formula for calculating the minimum cumulative resistance model is [23]  
\[\text{MCR}=fmin\sum_{j=n}^{i=m}\left(D_{ij}\times R_{i}\right) \tag{3}\]  
In Equation (3), MCR is the value of the minimum cumulative resistance; \(f\) denotes the positive correlation between the minimum cumulative resistance and the ecological process; \(D_{ij}\) is the distance traveled by a species from its point of origin \(i\) to a point \(j\) in space; \(R_{i}\) is the resistance coefficient of the landscape \(i\) to the movement of species [24]. Although the function \(f\) is usually unknown, the cumulative value of \((D_{ij}\times R_{i})\) can be \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Resistance Factor** & **Classification Index** & **Loss Coefficient** & **Weight** \\ \hline \multirow{4}{*}{types of land use} & construction land & 1000 & \multirow{4}{*}{0.49} \\  & water & 400 & \\  & cultivated land & 90 & 0.49 \\  & grassland & 11 & \\  & woodland & 5 & \\ \hline \multirow{4}{*}{elevation} & \(>\)1000 m & 100 & \multirow{4}{*}{0.17} \\  & 800–1000 m & 80 & \\  & 400–800 m & 50 & 0.17 \\  & 200–400 m & 30 & \\  & \(<\)200 m & 10 & \\ \hline \multirow{4}{*}{gradient} & \(>\)25\({}^{\circ}\) & 100 & \multirow{4}{*}{0.21} \\  & 15\({}^{\circ}\)–25\({}^{\circ}\) & 70 & \\  & 10\({}^{\circ}\)–15\({}^{\circ}\) & 40 & \\  & 5\({}^{\circ}\)–10\({}^{\circ}\) & 10 & \\  & \(<\)5\({}^{\circ}\) & 5 & \\ \hline \multirow{4}{*}{distance from water} & \(>\)2000 & 100 & \multirow{4}{*}{0.06} \\  & 1000–2000 m & 70 & \\ \cline{1-1}  & 500–1000 m & 50 & \\ \cline{1-1}  & 200–500 m & 30 & \\ \cline{1-1}  & \(<\)200 m & 10 & \\ \hline \multirow{4}{*}{distance from road} & \(<\)100 & 100 & \multirow{4}{*}{0.07} \\  & 100–250 & 80 & \\ \cline{1-1}  & 250–500 & 60 & \\ \cline{1-1}  & 500–1000 & 40 & \\ \cline{1-1}  & \(>\)1000 & 10 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Ecological resistance factor grading assignment and weight. considered a measure of the relative accessibility of a species' path from its source to a point in space. 2. The importance identification of ecological corridor based on gravity model. Based on the gravity model, the interaction matrix between 19 ecological sources in the Taishan area is constructed to quantitatively evaluate the connection intensity between the sources, and the ecological corridor with a high action intensity is selected as an important ecological corridor. The gravity model is used to analyze and predict the mathematical equation of the spatial interaction level.