## 2 Materials and Methods
### Evaluation Indexes of Complex Ecospatial Network  
(1)  
The integrity of the ecospatial network mainly reflects the quantitative relationship between the ecological source patch and the ecological corridor. To a certain extent, it can measure the complexity and ecological efficiency of the network. It mainly includesseveral evaluation indexes including the closure \(\alpha\), the line-point rate \(\beta\) and the network connectivity \(\gamma\). The index \(\alpha\) is used to reflect the degree of loops in the network. The higher the index \(\alpha\), the better the circularity and circulation of the network. The index \(\beta\) is used to reflect the average number of lines connected to each node in the network. The index \(\gamma\) is used to reflect the connectivity of nodes in the network. The above indexes are calculated as follows [39]:  
\[\alpha=\frac{L-V+1}{2V-5} \tag{2}\]  
\[\beta=\frac{L}{V} \tag{3}\]  
\[\gamma=\frac{L}{3(V-2)} \tag{4}\]  
For a network, \(L\) is the number of ecological corridors; \(V\) is the number of ecological nodes. When \(\beta<1\), the network belongs to a tree structure; when \(\beta=1\), the network belongs to a single loop structure; when \(\beta>1\), the complexity of the network connection belongs to a higher level. When \(\gamma=0\), no corridors are connected between nodes; when \(\gamma=1\), nodes in the network are highly connected;  
(2) Ecological node degree and degree distribution  
The number of corridors connected to a node in the ecosspatial network is called the degree of the node, and the average of the degrees of all nodes in the ecosspatial network is called the average degree [40]. The degree of a node reflects the importance of the node in the ecosspatial network in a sense. The greater the degree of a node, the more nodes it is connected to, and the higher the connectivity of that node; the greater the average degree of nodes, the higher the overall connectivity of the network. For a given network adjacency matrix \(A=\big{(}a_{ij}\big{)}_{N\times N}\), the calculation formulas of an average degree are as follows [41]:  
\[\langle k\rangle=\frac{1}{N}{\sum_{i=1}^{N}}k_{i} \tag{5}\]  
where \(k_{i}\) is the degree of the \(i\) node; \(k\) is the average degree of the network; and \(N\) is the total number of nodes in the network. The proportion of nodes with degree k in the entire network is called the degree distribution of nodes in the ecosspatial network;  
(3) Ecological node clustering coefficient  
Based on the complex network theory, it is assumed that the ecological node \(v_{i}\) is connected to the adjacent nodes through \(k_{i}\) ecological corridors, which means that the \(v_{i}\) node has \(k_{i}\) nodes adjacent to it. Note that \(k_{i}\) in this subsection is different from \(k_{i}\) in Section 2. There may be at most \(C\) corridors between these \(k_{i}\) nodes. The ratio of the actual number of corridors \(E_{i}\) between the \(k_{i}\) neighboring nodes of node \(v_{i}\) and the number of corridors that exist at most \(C_{k_{i}}^{2}\) is called the clustering coefficient of this node, and its formula is as follows [42]:  
\[C_{i}=\frac{E_{i}}{C_{k_{i}}^{2}} \tag{6}\]  
The average of the clustering coefficient of all nodes in the network is called the average clustering coefficient \(C\). The average clustering coefficient is used to reflect the closeness of the connections between nodes in the network. The larger \(C\) is, the stronger the small-world property of the network is. When \(C=0\), there is no corridor connection between all nodes; when \(C=1\), all nodes are connected;(4)  
The ability of an ecospatial network to maintain its ecological properties or ecological service functions under the interference and attack of various external factors is called the robustness of the ecospatial network [10; 43]. Analyzing the robustness of an ecospatial network can measure the ability of the ecospatial network to resist external attacks and recover after suffering damage.