4 DISCUSSION

4.1 Influencing factors of network stability

Our study shows that the structure and function of the ESN in the UAHB had improved significantly in the past 20 years. But how about the anti-jamming ability of the network? What were the factors that affected the network’s connectivity and stability?
The network stability was closely related to the number of deleted nodes. In terms of the number of deleted nodes (Figure 7a,b,c,d),R 1 and R 2 under different disturbance scenarios were correlated with the number of deleted nodes, and both showed a decreasing trend. The overall trend ofR 1 and R 2 in the same year was roughly the same, but there were local differences. In 1995 (Figure 7a,c), when the node failure ratio (NFR, the ratio of the number of the deleted nodes to the total number of the initial nodes in the network) did not exceed 15% (12 nodes), the values ofR 1 and R 2 almost remained unchanged and the number of the connected components did not change, either (Figure 7e). The results show that the network structure was relatively complete, while the network was in a relatively stable state. When the NFR was at 15%-46%, R 1 andR 2 took different values under the two different disturbance scenarios (Figure 7a,c) and the number of the connected components increased, indicating that the degree of network fragmentation increased (Figure 7e). When the NFR was between 46% to 95%, the network complexity declined significantly with bothR 1 and R 2 reducing to less than half of their initial values and the network was extremely sensitive. When the NFR exceeded 95%, the number of the connected components in the two disturbance scenarios dropped to 0. At this time, there were only a few isolated nodes in the network, and the exchange and transmission of information and energy could not be carried out between the nodes, and the network was in a state of paralysis. Compared to 1995, the network structure in 2015 was relatively complete and the network was in a relatively stable state (Figure 7b,d,f). When more than 25% of nodes were deleted, the disturbance of the network structure became obvious, and the network started to break down. With increasing NFR, network stability declined, the number of the connected components increased rapidly, and the network fragmentation increased until the network was finally paralyzed.
In summary, it was found that the number of nodes influenced the integrity and complexity of the network and had an impact on the stability of the network. In 2015, the NFRs in the network characteristics including stable state, sensitive state, and paralytic state were all greater than that in 1995, indicating that the stability of the ecological security network in 2015 was better than that in 1995. Table 5 further describes the relationship between network robustness and the number of deleted nodes.
The way of nodes deletion was related to the stability of the network . As discussed above, the disturbance scenarios represented different ways of removing nodes from the network, i.e., NHD representing random deletion, whereas HD deleting the nodes with the higher level comprehensive importance first. As shown in Figure 7a,b,c,d, although the values of bothR 1 andR 2 eventually dropped to zero in both disturbance scenarios, the curves of the HD scenario had more fluctuation. For example, R 1 andR 2 of the HD scenario decreased more rapidly than that of the NHD scenario (Figure 7), when more than 15% of the important nodes were deleted. The results indicate that the stability of the ESN was more sensitive to human disturbance than to nonhuman disturbance. Especially, the nodes with a high level of comprehensive importance had a greater influence on R 2, meaning a greater impact on network efficiency.
Table 6 further illustrates the relationship between the network robustness and the way of node deletion. The stability of the ESN depended on the number of interactions of network nodes. The process of nodes deletion based on the level of comprehensive importance of the nodes usually represented the impact of the purposeful disturbance that was mainly caused by human activities. The network of good spatial structure can maintain high stability under any disturbance scenarios.

4.2 Ecological security network optimization

System scientists believe that restructuring is to reframe the system’s structure to promote an optimal combination of the system’s internal elements and to achieve the system’s fundamental transformation (Zhou, Xu, & Lin, 2016). The optimization and reconstruction of the ESNs provide spatial planning methods to integrate ecological processes, spatial scales, and ecosystems. The complexity and uncertainty of the network’s structure should be considered in the reconstruction of the ESNs. Combined with the reconstruction of the ESNs and the difference in ecological space protection strategy, we propose five measures to improve the regional ESN of the UAHB based on our research findings.
The first measure is to protect the important ecological sources.As the important network nodes, the ecological sources are the important habitats for the living beings in a region. Increasing their quantities and improving their quality is particularly important for the protection of the regional ecological environment and biodiversity. Compared with 1995, the area of ecological sources of the UAHB increased significantly in 2015 (Figure 3), but the increment was mainly concentrated in Hangzhou, while the areas of the sources in Jiaxing and Huzhou were small, and the corridor length between the sources in these two cities and other sources and nodes was considerable long. Therefore, we suggest that the integrity of national or provincial natural reserves, forest parks, large forest land, and wetlands should be strictly protected, and the forest land around them should be considered as part of the network, to increase sources area, to enrich the biological species, to improve the quality of the habitat, and to increase the suitability of the habitat (Liang, Liu, Liu, Qi, & Liu, 2018; Yin et al., 2011).
The second measure is to improve the effectiveness of connectivity between nodes . Nodes are the key to ensuring network connectivity. Their interactivity, importance, and quantity are important factors to maintain the integrity and complexity of the network structure. As displayed in Figure S2, there were two isolated nodes in Jiaxing (see also Figure S1). Although there were potential ecological corridors in Jiaxing, Huzhou, and other areas (see also Figure 3), only a fewkey ecological corridors existed due to large landscape resistance, so the ESN was not fully connected. On the one hand, the protection of the key nodes will not only help to improve landscape connectivity but also promote the virtuous cycle of logistics and energy flow in the network. On the other hand, we should implement spatially distributed control and protection measures based on the distribution characteristics of the important nodes to change the formation mechanism of the network and to realize the reconstruction of the ESN. At least three reconstruction strategies may be adopted based on the node importance: individual protection, general protection, and extensive protection. According to the needs of biological diffusion and the possibility of ecological construction, we suggest planning corridors to connect the two currently isolated sources in Jiaxing to promote their connection with the nearest nodes and to improve the ESN’s structure.
The third measure is to restore ecological breaking points . Ecological corridors are an important part of the regional ESN, which can improve the overall quality of the regional ecological environment (Li, Han, & Tong, 2009). However, the more landscape types the ecological corridors cross, the greater the accumulated resistance of the landscape will be, which, in turn, will reduce the effectiveness of the functions of the ecosystem. Roads, especially high-grade road networks, have a certain barrier effect on the transfer of material and energy flows in the ESN, which may cause ecological breakpoints and habitat fragmentation. We conducted the overlay analysis of railway, expressway, national road, provincial road, and important ecological corridors in the network of the UHAB. The intersections of railways, expressways, and corridors were regarded as the main breaking points, while the intersections of national roads, provincial roads, and corridors were regarded as secondary breaking points. Overall, 36 main breaking points and 23 secondary breaking points were extracted (Figure 8). Currently, many scholars have called to include wildlife passageways such as underground passageways, tunnels, and overpasses in the construction codes of the high-grade roads (Chen, Yin, Kong, & Yao, 2015; Yin et al., 2011). According to the current economic and social development level of the UAHB, it is suggested that the high-grade roads network should avoid the areas where wildlife activities are frequent and provide more access to wildlife by restoring ecological breakpoints.
The fourth measure is to strengthen the protection and planning of steppingstones . The steppingstones can provide temporary habitats for migrating species, especially for the species with long migration distances. The quantity, quality, and spatial locations of the steppingstones are important factors that affect the time, frequency, and success rate of species migration and increase the regional biodiversity (Yin et al., 2011). Therefore, it is necessary to strengthen the protection of the existing steppingstones and the planning and construction of future steppingstones. When combined with the intersection of important ecological corridors and the nodes’ comprehensive importance in the network, the nodes with high comprehensive importance are selected as steppingstones. As a result, 21 steppingstones are identified and selected in our study (Figure 9).
The fifth measure is to connectthe ESNs with the surrounding areas at different scales . The interconnection of the networks inside and outside the region can contribute to the material exchange and energy transfer, enhancing the ecosystem stability (Yin et al., 2011). At present, the surrounding areas of the UAHB, such as Jiangsu, Anhui, Jiangxi, Fujian, and Shanghai, also have a good ecological environment. Therefore, in the process of improving the internal network of the UAHB, it is suggested to strengthen the connection of the ESNs between the UAHB and the surrounding areas at different scales. This will not only help to improve the stability of the ecosystems but also enable the ESNs to have longer buffer zones and recovery times when they are damaged by external disturbances.

4.3 Limitations

Our case study in the UAHB may provide empirical evidence and support in terms of space optimization, planning, and protection of the ESNs in other regions where are also experiencing rapid urbanization. However, our study is not without limitations. First, the assessment indexes of ESNs can be further improved. The area and shape of ecological sources have important influences on the structure and function of an ESN, but these influences cannot be reflected merely based on the analysis of network topology. Second, we assume that nodes and edges are not functioning when they are disturbed and ignore the situations when they may partially or fully recover from disturbance.