4.1 Construction and Analysis of Ecological Spatial Network in Xuzhou City
Ecological spatial network is the result of combining traditional ecological network with complex network theory.We believe that ecological spatial network is a kind of network that reflects the geographical location relationship and topological properties of each ecological element in the landscape space.It consists of ecological nodes and ecological corridors,where ecological nodes are the result of abstraction of ecological sources and ecological corridors are the result of abstraction of material and energy flows.In this study,ecological nodes are divided into forest patches,shrub and grassland patches,wetland and lake patches.
4.1.1 Screening of ecological sources
We imported the foreground data and background data into Guidos and obtained seven types of patches according to MSPA analysis,among which core patches and islets patches accounted for a large area,22.4% and 47.4% of the total area,respectively.The core patch is a large ecological patch,which has an important influence on the ecological environment and energy flow.It is usually used as an ecological source.Islet patches are mainly distributed among the core patches and its area is small and numerous which is a more isolated patch type.Islet patches are usually considered as the best choice for ecological stepping stones.Based on the actual situation of the study area,we selected core area patches with an area larger than 0.4 as ecological sources.Finally,7 forest patches,16 shrub and grassland patches,58 wetland and lake patches were selected,for a total of 81 ecological sources(Fig.5).
4.1.2 Minimum cumulative ecological resistance surface analysis
We obtained the minimum cumulative ecological resistance surface after superimposing the resistance values of the eight resistance factors by cost distance analysis (Fig.6).From the figure,it can be seen that the resistance values are lower in the central and eastern parts of the study area and higher in the south and northwest,with the maximum value up to 2082515.75.The area is located in Feng County and Pei County,with key rock salt mining areas in Feng County and key coal mining areas in Pei County.Due to the long-term exploitation of natural resources,the ecological environment in this area is of poor quality and the resistance values of NDVI,MNDWI,water network density and other factors are very high.Besides this area is far away from the existing ecological source,which causes a large accumulation of resistance.
4.1.3 Xuzhou Ecological Spatial Network
Through the iterator tool of ArcGIS platform,the obtained ecological sources and cumulative ecological resistance surfaces were used to generate ecological corridors in the study area through the cost-path model,then a total of 151 ecological corridors were obtained.We combined the ecological corridors with the screened ecological sources to jointly construct the ecological spatial network of Xuzhou City(Fig.7).As can be seen from the figure,the ecological sources are mainly located in the south-central and southeastern areas of Xuzhou,while the sources in the northwest are more sparse.Overall,the ecological sources in Xuzhou are small in area and fragmented in distribution.The majority of the sources types are wetland and lake patches,which are more widely distributed.Forest patches,shrubs and grassland patches are fewer in number and more concentrated in the central part of Xuzhou.Ecological corridors are more dense in the central part of Xuzhou,with shorter corridor lengths,while those in the north-western part of the city are sparser and longer,suggesting that ecological circulation is poor in the north-western part of the city and that the initial ecological base of the area is poor and in need of upgrading.
The ID1 and ID2 of ecological corridors in ArcGIS were imported into the complex network visualization software Gephi and obtained the abstract topological feature map and community topology map of Xuzhou ecological spatial network(Fig.8).From the figure,it can be seen that nodes 40,51,60,and 80 are located in the central area of the network and play an important connecting role.The rest of the nodes are scattered in the network and connected to each other to transmitting information.In the community network,the Xuzhou ecological space network is divided into 7 communities according to the size of modularity and according to the definition of modularity,the nodes in each community have strong connectivity,the nodes are closely connected to each other,so they have strong resistance in the face of attacks.As can be seen from the figure,the seven node communities also have certain relationships in geographic space.Nodes of the same community are adjacent to each other in spatial location.Therefore,within a certain geographical range,the ecological nodes in the area possess strong stability in the face of damage.The maximum value of modularity in the ecological spatial network of Xuzhou is 6 and the community node is located in the southeast area of Xuzhou,indicating the strongest stability in this area.The lowest value of modularity is 0,which is located in the northwest area of Xuzhou city,indicating that the community nodes in this area are less stable and more vulnerable and they are more likely to be destroyed when under attack.
From the MCR model and the community network structure,it can be seen that the ecological sources in the northwestern part of Xuzhou city have a poor ecological base.The energy and material information transfer and exchange in the area are more difficult.When faced with ecological damage,their resistance is poor and they are not easy for self-ecological restoration.In contrast,the central and south-central areas of Xuzhou have a large number of sources and short ecological corridors,so that energy transfer is more convenient and when faced with external damage,their resistance is stronger and conducive to ecological self-restoration.
4.2 Analysis of the results of the various indicators
4.2.1 Analysis of results for network topology metrics
Degree,average path length and clustering coefficient are the three most basic concepts in portraying the statistical properties of complex network structures.The greater the degree of a node,the more information is exchanged between the node and other nodes,and therefore the more important the node is in the network.The average path length is the average of the distance between any two nodes,the larger the average path length indicates the slower the information transfer between nodes,if the corridor length between two nodes is greater than the average value then the corridor is considered longer and is not conducive to information transfer.The clustering coefficient indicates that the degree of aggregation of the node is measured in the network and the larger the clustering coefficient of the node indicates that it has more similarity and less heterogeneity with similar elements.
As can be seen from the figure 9,there are 7 nodes with degree greater than or equal to 7 in the network,which are nodes 28,30,40,41,50,60,80,indicating that these nodes have an important role in the network,where node 60 has the largest degree,reaching 9.The minimum value of node degree in the network is 1,which is nodes 3,25,51,indicating that these nodes have a smaller role in the network,while the node degree The minimum value of 1 indicates that there is at least one node connected to each node in the Xuzhou ecological spatial network and there are no isolated nodes.The average path length of Xuzhou ecological spatial network is 5.492,62 ecological corridors are lower than this value,and the remaining 90 ecological corridors are higher than this value,which indicates that the nodes connected by these 90 ecological corridors have a slow information transfer rate,so some ecological corridors and nodes should be screened and additional stepping stone sources should be installed to shorten the spacing.Fifteen nodes in the Xuzhou ecological spatial network have a clustering coefficient greater than 0.5,with nodes 13,74 and 77 reaching a clustering coefficient of 1,indicating strong similarity between the nodes connected to them while 13 nodes have a clustering coefficient of 0,demonstrating greater heterogeneity between the nodes connected to them.
Closeness centrality,Betweenness centrality and Eigenvector Centrality reflect the relative importance of each node in the network.They are the important indicators to characterize the structure of complex networks.Closeness centrality indicates the spatial location of a node in the network,the greater the Closeness centrality,the more important the node is in the center of the network.Betweenness centrality refers to the number of shortest paths through the node.Larger Betweenness centrality indicates more interaction between the node and other nodes,which facilitates the transfer of energy between nodes.Eigenvector centrality means that the centrality of a node is a function of the centrality of neighbouring nodes,which means that the more important the nodes connected to that node are,the more important that node is.
As can be seen from the figure 10,the Closeness centrality of the Xuzhou ecological network does not vary greatly,with four nodes having values greater than 0.25,namely nodes 29,40,45 and 60,with node 40 having a maximum Closeness centrality of 0.27,indicating that this node is at the very centre of the network.There are three nodes with a betweenness centrality greater than 1000,namely nodes 40,60 and 80,where node 40 has a maximum betweenness centrality of 1526.14,indicating that this node is conducive to energy transfer.On the contrary,there are 6 nodes with zero betweenness centrality,namely nodes 3,13,25,51,74 and 77,which are not conducive to the exchange of materials and energy.The eigenvector centrality of the Xuzhou ecological spatial network is greater than 0.8 for six nodes,nodes 40,41,43,50,60 and 80,with node 60 reaching a maximum value of 1,indicating that the nodes connected to this node are also more important.
Combining the analysis results of basic topological indicators and important topological indicators of ecological space network,it is found that node 40 and node 60 are the most important nodes in the network.Node 40 is the maximum node in closeness centrality and betweenness centrality.Node 60 is the maximum node in degree and eigenvector centrality.Changing these two nodes will affect the topological properties of the whole network. Meanwhile, we found that the values of clustering coefficient and betweenness centrality of nodes 3,25,36,and 51 are very low and increasing the values of their topological indicators will strengthen the topological properties of the network.
4.2.2 The results analysis of the coupling between RSEI and dIIC models
Coupling WET,NDBSI,LST,and NDVI,we obtained the results shown in Fig.11.We found that there are areas with low RSEI values in the northwest,central,and east of Xuzhou City and these lower values are mainly concentrated on the urban areas of each county,while the higher values of RSEI are distributed around the urban areas.This indicates that with the development of human construction,the ecological environment quality of the area has been reduced and the quality level of the source area is low.We also found that the RSEI in non-urban areas of Feng County,Pei County and Jiawang County is still at a low value which is due to the local coal mining,thus causing the destruction of the ecological environment,the original landscape becomes fragmented and the ecological environment quality is at a low level.The quality of the regional ecological sources are poor and the ecological background needs to be improved urgently.
We obtained the dIIC values of each source site by using conefor2.6 software and we found that the dIIC values of nodes 47,80,81 were significantly higher than those of other nodes.This indicates that the connectivity of these nodes is higher and the ecological sources are functional.dIIC values are lower than 0.01 for a total of 14 nodes which indicates that these nodes are less connected and less capable of material-energy transfer.
We coupled the RSEI with the dIIC(Fig.12) and normalized the indices.At the same time we classify all nodes and extracting the nodes in the top 10% and the bottom 10% of the coupling values.We identify them as ecologically functional strong nodes and ecologically functional weak nodes and the rest of the nodes are considered as ecologically functional general nodes.Finally,8 nodes with strong functionality,8 nodes with weak functionality,and 65 nodes with general functionality were obtained.Among the ecologically weak nodes,node 26 has low clustering coefficient and eigenvector centrality and node 75 has low proximity centrality.To optimize them will increase their importance in the network and thus enhance the stability of the network.Node 60 is more important in the network and its optimisation will further enhance its role in the network.We have adopted a strategy of adding edges to poorly functioning ecological nodes,linking fragmented sources and enhancing connectivity between nodes to improve the functionality of ecological sources.Additional stepping stone patches are also added to shorten the length of ecological corridors and further enhance the ecological background of the area.
4.2.3 Carbon sink correlation analysis
Through the formula,we obtained the carbon sinks of each ecological source and also identified the nodes in the top 10% of carbon sink values as strong carbon sinks and the nodes in the bottom 10% of carbon sink values as weak carbon sinks.To further investigate the reasons affecting the amount of carbon sinks,we conducted Pearson correlation coefficient analysis between carbon sinks and various topological indicators of complex networks (Fig.13).From the figure,it can be seen that the carbon sinks of forest nodes,shrub and grassland nodes and lake and wetland nodes showed highly significant positive correlation and significant positive correlation with betweenness centrality,respectively.Therefore,increasing the betweenness centrality of the nodes with weak carbon sinks can enhance the carbon sink capacity of the nodes.
4.3 Analysis of the effects of the SEEC optimisation model
We classified the nodes and obtained 5 nodes with only weak ecological functionality(Nodes 15,24,30,60,75) 5 nodes with only weak carbon sinks (Nodes 6,12,21,33,52) and 3 nodes with poor ecological functionality and low carbon sinks (Nodes 17,26,27).For the nodes with weak ecological functionality,we have taken measures to increase the number of stepping stones and ecological corridors.According to the previous study on the ecological community network in Xuzhou,the ecological sources in close geographical proximity are highly modular,closely connected to each other and more resistant to external damage.Therefore,we selected Islet patches with LSI greater than 1.95 around ecologically functional weak nodes as ecological stepping stones through the patch shape index LSI and added ecological corridors according to the MCR model.For nodes with low carbon sinks,we took the measure of increasing their betweenness centricity to enhance their carbon sink capacity.The Betweenness centricity is the number of shortest paths through the point,so we used the nodes with low carbon sinks as bridges to build links with the surrounding nodes and constructed the shortest cost paths according to the modified MCR resistance values.For nodes with weak ecological functionality and low carbon sinks,we also added stepping stones,ecological corridors and shortest paths.In the end,we successfully added 16 new ecological stepping stones and 55 new shortest paths and ecological corridors(Fig.14).The optimised ecological spatial network of Xuzhou is shown in the figure,which clearly shows that the nodes are more closely connected and the length of the ecological corridors has been effectively reduced,further promoting the flow of energy and the exchange of material information.
4.3.1 Robustness comparison analysis
The random and malicious attacks of the network can be used in the ecological spatial network to simulate the ecological damage suffered by the landscape space,and the resistance to external damage can be expressed by the robustness of the network.The change of the robustness of the ecological spatial network in Xuzhou before and after optimization by random and malicious attacks(Fig.15).From the figure,it can be seen that the recovery robustness of nodes,the recovery robustness of edges and the connection robustness are all enhanced to some extent,with the optimization effect of connection robustness being the most obvious.With the increasing number of nodes subjected to random and malicious attacks,the robustness of the network before and after optimization shows a decreasing trend,but the stability of the network subjected to random attacks is significantly stronger than that of the network subjected to malicious attacks and the change of robustness of different types also shows a difference.
In the recovery robustness of the nodes,the network robustness values before and after optimization are first kept constant at 1,and then start to decline from slow to fast.The optimized network curve is more convex than the pre-optimized network curve,which indicates that the optimized network declines more slowly and the inflection point of the decline is delayed.When the pre-optimized network is subjected to random and malicious attacks,the robustness starts to fall below 1 at the 18th and 24th nodes,respectively,and falls below 0.1 at the 79th and 77th nodes,the network eventually collapses.The robustness of the optimized network starts to fall below 1 at the 38th and 37th nodes and falls below 0.1 at the 96th and 94th nodes,respectively.When the attack reaches the last node,the robustness of the optimized network can be maintained at 0.12 and 0.03 after random and malicious attacks,both of which are better than the robustness of the pre-optimized network.
In the recovery robustness of the edges,the robustness values before and after optimization decreases from 1.When subjected to random attacks,the robustness decreases from slow to fast but in the case of malicious attacks,the robustness decreases at a more stable rate.In the random attack,it is also found that the robustness of the optimized network decreases significantly less than that of the pre-optimized network.When the robustness falls below 0.1, the network starts to collapse and only three nodes of the optimized network remain, while four nodes of the pre-optimized network are still below 0.1.When subjected to malicious attacks,the rate of decline before and after optimization is approximately the same,and there are 12 nodes with network robustness below 0.1 both before and after optimization,but the number of nodes increases after optimization,so the optimized network is still more stable than the network before optimization.
The initial robustness of the pre-optimised network was 0.98,while the initial robustness of the post-optimised network reached 1.The robustness of the network decreased in waves after both random and malicious attacks,but the post-optimised robustness decreased at a significantly slower rate than the pre-optimised network.The optimised network maintained a robustness of 1 after a random attack up to 30 nodes,and made several attempts to recover from subsequent attacks,eventually recovering to 0.67 at node 91,and below 1 after a malicious attack starting at node 11,after which several attempts were made to recover,most notably at node 54 (recovering to 0.37),node 74 (recovering to 0.35),and node 90 (recovery to 0.29).The pre-optimised network fell faster under random attacks,recovering to 0.18 by the 70th node.When subjected to a malicious attack,the robustness of the network falls rapidly to 0.5 at the 10th node and eventually recovers to 0.3 at the 71st node.Thus,the optimised network outperforms the pre-optimised network both in terms of the rate of decline and in terms of robustness recovery.
The results of the node recovery robustness,edge recovery robustness and connection robustness show that the optimization of the SEEC model can strengthen the ability of the Xuzhou ecological network to resist external damage and improve the stability of the network.The analysis of the connection robustness results shows that the optimised network can attempt to automatically recover robustness in the face of ecological damage in order to maintain the smooth operation of the network and the recovered robustness can reach a high value,which reflects that the ecological resilience of the Xuzhou ecological spatial network has been improved to a certain extent.
4.3.2 Carbon sink
In the current study,there are various ways to calculate carbon sink.This paper adopts the method of estimating carbon sink through land use and the carbon sink value before and after the optimization of ecological spatial network in Xuzhou City is obtained by the formula(Table.3). From the table,it can be seen that the carbon sink of the ecological sources are improved by 352.04 tons and the carbon sink of the ecological corridor is improved by 25.56 tons.The carbon sink of the ecological sources are improved by about 14 times of the ecological corridor and the improvement effect is more significant.
Table 3.Changes in carbon sinks before and after optimization of Xuzhou's ecological spatial network.
Ecological Sources Carbon Sink（t）
Ecological Corridor Carbon Sink（t）