2 MATERIALS AND METHODS

2.1 Complex network analysis

Network structure analysis is the basis of network function optimization (Wang et al., 2019). As shown in Figure 2(a), a landscape is composed of ecological sources and ecological corridors (Turner, Gardner, & O’Neill, 2001). The constructed ESN of a landscape may be simplified into a topological network of nodes and edges (Figure 2(b)). As more and more topological networks join together, they form a complex network system as shown in Figure 2(c). Therefore, an ESN in this study is a complex spatial network with hierarchy and ecological attributes (Dehmer, Emmert-Streib, & Shi, 2017; Dai, Liu, & Luo, 2020). This study used complex network analysis to explore the spatial topological structure of the ESN. The topological structure of the ESN mainly includes nodes, edges, and the overall network. Nodes represent the basic units of the network and edges indicate the functional relations among the basic units. More details of assessment methods including ecological corridors, ecological nodes, network connectivity, and network robustness can be found in SI Complex network analysis methods and Eq. S1 to S11.

2.2 Disturbance scenarios

In this study, we designed two disturbance scenarios including non-human disturbance (NHD) and human disturbance (HD) based on the robustness assessment. NHD can be regarded as random natural disasters (e.g., forest fire, debris flow), whereas HD can be understood as purposeful human activities (e.g., land use change, urban sprawl).
In terms of NHD, we randomly deleted the nodes in the network by the “online random number generator” tool (https://rand.91maths.com/) to ensure the randomness of disturbance. The corresponding nodes were deleted in random numerical order to calculate the connectivity robustness and vulnerability robustness of the ESN. HD refers to the purposeful deletion of nodes in the ESN. We introduce the “disturbance radius” to control the initial direction of the disturbance. The specific operation in ArcGIS took the boundary of the developed land as the starting point and the value of 500 m as the radius to conduct buffer and spatial overlay analysis and to obtain the corresponding nodes distribution. The nodes within the radius were removed according to the comprehensive importance of the nodes, and then the nodes outside the radius were deleted to calculate the network robustness.
To simplify the problem, the following three assumptions were made when simulating network robustness:

2.3 Data sources and statistical analysis

The UAHB’s ESN in 1995 and 2015 was constructed by Zhou, Lin, Ma, Qi, & Yan (2020), where the details of original data and analysis can also be found. In 1995, 43 ecological sources, 85 ecological nodes, and 134 key ecological corridors were identified or extracted (Figure 3); in 2015, these numbers were 41, 96, and 161, respectively.
In this study, network analyses were mainly performed in ArcGIS® (version 10.6), Excel® (version 2019), Pajek® (version 2.00), SPSS® (version 25.0), and R® (version 36.3). The indexes including degree, clustering coefficient, core of node, and node centrality indexes were calculated using Pajek software. The robustness assessment was achieved using R® and Pajek®. It should be noted that the isolated nodes in the ESNs were not included in calculating clustering coefficient, core of node, node comprehensive importance, and network robustness because their presence does not affect the functions of the network.