Dynamic simulation method for structural stability of water ecological network

Abstract

The invention provides a dynamic simulation method for structural stability of a water ecological network, belongs to the technical field of ecological environments, can dynamically simulate the change condition of a water environment, considers the comprehensive influence of spatial distribution, pollutants and environmental factors of aquatic organisms in the water environment, and provides a dynamic simulation method for the structural stability of the water ecological network. And the simulation analysis result of the water ecological network structure stability is more accurate. According to the method, a water ecological network is constructed based on ecological information in a water environment, nodes in the water ecological network are removed according to importance indexes of the water ecological network, the structure of the water ecological network is dynamically adjusted so as to simulate the change condition of the water environment along with time, and a survivability threshold value of the water ecological network is obtained on the basis; and taking the survivability threshold as a simulation analysis result of the structural stability of the water ecological network.

Description

Technical Field

[0001] The present invention relates to the technical field of water environment, and specifically relates to a dynamic simulation method for the stability of a water ecological network structure. Background Art

[0002] At present, the assessment of the stability of the water ecological network in the water environment has become an important research direction in the field of environmental science. The ecological network is a mathematical model established based on ecological principles to describe the mutual relationship between biological populations in water bodies, and it can effectively reflect the functional structure and material cycle of the water ecosystem. The traditional methods for assessing the ecological network structure mainly measure the stability of the system through the quantity, species composition, and interaction relationships of biological populations.

[0003] However, these methods usually rely on the physical distribution and population dynamics of species, lack a comprehensive analysis of the ecological network structure, and are prone to ignoring the comprehensive impacts of the spatial distribution of aquatic organisms, pollutants, and environmental factors in the water environment on the water ecological environment, making the simulation analysis results of the stability of the water ecological network structure inaccurate. Summary of the Invention

[0004] The present invention proposes a dynamic simulation method for the stability of a water ecological network structure, which can dynamically simulate the changes in the water environment and take into account the comprehensive impacts of the spatial distribution of aquatic organisms, pollutants, and environmental factors in the water environment on the water ecological environment, making the simulation analysis results of the stability of the water ecological network structure more accurate.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a dynamic simulation method for the stability of a water ecological network structure, including:

[0007] Constructing a water ecological network based on the ecological information in the water environment;

[0008] Among them, the ecological information includes species information, environmental factors, and pollutant information; the species information includes the spatial distribution of various aquatic organisms existing in the water environment, the environmental factors include: the temperature, pH value, and dissolved oxygen of the water environment, and the pollutant information includes: the concentrations of various pollutants contained in the water environment; the various pollutants include heavy metals, organic pollutants, and nutrient salts; the water ecological network includes multiple nodes and multiple edges connecting the multiple nodes;

[0009] According to the preset removal ratio and the importance index of each node in the water ecological network, iteratively remove at least one node in the water ecological network and at least one edge connected to the at least one node, and calculate the stability index value of the water ecological network after each removal;

[0010] When the stability index value of the aquatic ecological network is less than or equal to the stability threshold after removal until the nodes are removed, determine the vulnerability threshold of the aquatic ecological network according to the number of nodes removed from the aquatic ecological network and the total number of nodes in the aquatic ecological network before iterative removal; use the vulnerability threshold of the aquatic ecological network as the simulation analysis result of the structural stability of the aquatic ecological network.

[0011] In one implementation of the first aspect, multiple nodes of the aquatic ecological network correspond one-to-one with various aquatic organisms, environmental factors, and various pollutants; an edge of the aquatic ecological network represents the ecological interaction relationship between two nodes connected by the edge; the ecological interaction relationships include: predation, symbiosis, competition, endangering survival, and mutual influence; among them, the ecological interaction relationship is determined by the spatial distribution of various aquatic organisms, environmental factors, and the concentrations of various pollutants contained in the water environment.

[0012] In one implementation of the first aspect, according to the preset removal ratio and the importance index of each node in the aquatic ecological network, iteratively remove at least one node in the aquatic ecological network and at least one edge connected to the at least one node, and calculate the stability index value of the aquatic ecological network after each removal, including:

[0013] Calculate the importance index of each node in the aquatic ecological network, and the importance index satisfies the following formula:

[0014] I i =α1k i +α2B i +α3C i

[0015] where, I i represents the importance index of the i-th node in the aquatic ecological network, k i represents the node degree of the i-th node in the aquatic ecological network, B i represents the node betweenness of the i-th node in the aquatic ecological network, C i represents the node connectivity of the i-th node in the aquatic ecological network; α1 represents the weight of the node degree, α2 represents the weight of the node betweenness, and α3 represents the weight of the node connectivity;

[0016] Sort the removal order of nodes in the water ecological network according to the magnitude of the importance index, and then iteratively remove at least one node in the water ecological network that is consistent with the preset removal ratio, and at least one edge connected to the at least one node; and after each removal operation, calculate the stability index value of the water ecological network after each removal; wherein, the stability index value of the water ecological network after each removal includes the network efficiency of the water ecological network after each removal and the maximum connectivity of the water ecological network after each removal; wherein, the preset removal ratio is the ratio of the number of nodes removed each time to the total number of nodes in the water ecological network before iterative removal, and the preset removal ratio is 1%, 2%, 3% or 5%;

[0017] The network efficiency of the water ecological network after each removal satisfies the following formula;

[0018]

[0019] Wherein, E represents the network efficiency of the water ecological network after each removal, N represents the total number of nodes in the water ecological network before iterative removal, and d ji represents the shortest path length between node i and node j in the water ecological network after each removal;

[0020] The maximum connectivity of the water ecological network after each removal satisfies the following formula;

[0021]

[0022] Wherein, S represents the maximum connectivity of the water ecological network after each removal, and |C max | represents the total number of nodes in the largest connected subgraph of the water ecological network after each removal.

[0023] In one implementation manner of the first aspect, the stability threshold includes a network efficiency threshold and a maximum connectivity threshold; the value range of the network efficiency threshold is 0.10 - 0.15, and the value range of the maximum connectivity threshold is 0.4 - 0.6.

[0024] In one implementation manner of the first aspect, until the stability index value of the water ecological network after removal is less than or equal to the stability threshold, determine the vulnerability threshold of the water ecological network according to the number of nodes removed from the water ecological network and the total number of nodes in the water ecological network before iterative removal, including:

[0025] When the network efficiency of the water ecological network after removal is less than or equal to the network efficiency threshold, or the maximum connectivity of the water ecological network after removal is less than or equal to the maximum connectivity threshold, use the number of nodes removed from the water ecological network and the total number of nodes in the water ecological network before iterative removal to calculate the vulnerability threshold of the water ecological network, and the vulnerability threshold of the water ecological network satisfies the following formula:

[0026]

[0027] Among them, fa represents the invulnerability threshold, Nr represents the number of nodes removed from the water ecological network, and N represents the total number of nodes in the water ecological network before iterative removal.

[0028] In an implementation manner of the first aspect, the method further includes:

[0029] When the stability index value of the water ecological network after removal is less than or equal to the stability threshold, determine the resilience of the water ecological network according to the number of nodes removed from the water ecological network, and use the resilience of the water ecological network and the invulnerability threshold of the water ecological network together as the simulation analysis result of the structural stability of the water ecological network; the resilience of the water ecological network is used to describe the tolerance and recovery ability of the water ecological network to ecological environment changes; the resilience of the water ecological network satisfies the following formula:

[0030]

[0031] Among them, R represents the resilience of the water ecological network, Nr represents the number of nodes removed from the water ecological network, and d ji represents the shortest path length between node i and node j in the water ecological network after removal.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] In a method for dynamically simulating the structural stability of a water ecological network provided by the present invention, a water ecological network is constructed according to ecological information in the water environment, and based on a preset removal ratio and the importance index of each node in the water ecological network, at least one node in the water ecological network and at least one edge connected to the at least one node are removed multiple times by iterative removal, and after each removal, the stability index value of the water ecological network after removal is calculated. Until the stability index value of the water ecological network after removal is less than or equal to the stability threshold, it is determined that the overall function of the ecological system of the water environment corresponding to the water ecological network is damaged and cannot maintain normal operation, that is, the water ecological network is no longer stable. Then, the invulnerability threshold of the water ecological network is calculated by using the number of removed nodes and the total number of nodes in the water ecological network before iterative removal, and the invulnerability threshold is used as the simulation analysis result of the structural stability of the water ecological network. In the process of constructing the water ecological network, the above method takes into account species information, environmental factors, and pollutant information in the water environment. On this basis, at least one node in the water ecological network and at least one edge connected to the at least one node are removed multiple times, which can dynamically simulate the changes in the water environment caused by natural or human factors in the real situation (including species changes, environmental factor changes, and pollutant changes), thereby making the simulation analysis result of the structural stability of the water ecological network more accurate. Description of the Drawings

[0034] Figure 1 It is one of the schematic diagrams of a method for dynamically simulating the stability of a water ecological network structure provided by an embodiment of the present application;

[0035] Figure 2 It is the second schematic diagram of a method for dynamically simulating the stability of a water ecological network structure provided by an embodiment of the present application;

[0036] Figure 3 It is a schematic diagram of the node removal process of the water ecological network in an embodiment of the present application;

[0037] Figure 4 It is a schematic diagram of relevant indicators of the water ecological network after node removal in an embodiment of the present application; (a) Connectivity, (b) Relative size of the largest connected subgraph, (c) Network efficiency, (d) Maximum connectivity versus node attack ratio. Detailed implementation manners

[0038] In the embodiments of the present application, words such as "exemplary" or "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as "exemplary" or "for example" in the embodiments of the present application should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Exactly speaking, using words such as "exemplary" or "for example" aims to present relevant concepts in a specific manner.

[0039] In the description of the present invention, unless otherwise specified, the meaning of "a plurality of" refers to two or more. For example, a plurality of nodes refers to two or more nodes. The meaning of "at least one" is one or more, at least one node refers to one or more nodes, and at least one edge refers to one or more edges.

[0040] The method provided by the embodiments of the present application relates to a water ecological network. By removing nodes in the water ecological network, it can dynamically simulate the situation of the water environment corresponding to the water ecological network being disturbed over time, and use the resilience threshold of the water ecological network after being disturbed as the simulation analysis result of the stability of the water ecological network structure, so as to reflect the stability of the water environment.

[0041] It can be understood that a water ecological network refers to a complex system that identifies ecological factors (including environmental factors, pollutants and aquatic organisms) in a water body within a specific water environment spatial scale and connects different ecological factors to reflect the interactions and connections between various ecological elements. The stability of the water ecological network reflects the lasting ability of the ecosystem corresponding to the water ecological network to maintain the normal operation of its functions in the face of natural or human-induced ecological changes. Studying the structural resilience of ecological networks is crucial for ensuring the stability and sustainability of ecosystems, especially in the face of external disturbances such as environmental changes, species invasions or pollution, to maintain the normal functions of ecosystems.

[0042] The spatial distribution of aquatic organisms refers to the distribution pattern and location of aquatic organisms in the water environment, reflecting the aggregation, dispersion or migration patterns of aquatic organisms at different spatial scales. The spatial distribution of aquatic organisms is usually affected by environmental factors, biological interactions and pollutants.

[0043] To solve the problem in the background technology that the existing analysis method for the stability of the water ecological network structure lacks a comprehensive analysis of the ecological network structure and is prone to ignoring the comprehensive influence of ecological relationships and environmental factors at different levels, resulting in inaccurate analysis results for the stability of the water ecological network structure, the embodiments of the present application provide a dynamic simulation method for the stability of the water ecological network structure. During the construction of the water ecological network, species information, environmental factors and pollutant information in the water environment are considered. On this basis, at least one node in the water ecological network and at least one edge connected to at least one node are removed multiple times, which can dynamically simulate the changes in the water environment caused by natural or human factors (including species changes, environmental factor changes and pollutant changes) in the real situation, and thus make the simulation analysis results of the water ecological network structure stability more accurate.

[0044] As Figure 1 shown, a dynamic simulation method for the stability of the water ecological network structure provided by the embodiments of the present application includes S101 - S103.

[0045] S101. Construct a water ecological network based on the ecological information in the water environment.

[0046] Among them, the ecological information includes species information, environmental factors and pollutant information. The species information includes the spatial distribution of various aquatic organisms existing in the water environment, and the various aquatic organisms include algae, fish and aquatic plants. The environmental factors include: the temperature, pH value and dissolved oxygen of the water environment. The pollutant information includes: the concentrations of various pollutants contained in the water environment, the various aquatic organisms include algae, fish and aquatic plants, and the various pollutants include heavy metals, organic pollutants and nutrient salts.

[0047] Optionally, the above-mentioned various aquatic organisms may further include microorganisms; the above-mentioned environmental factors may further include hardness; the above-mentioned various pollutants may further include other pollutants; the embodiments of the present application do not further limit the above-mentioned various aquatic organisms, the above-mentioned environmental factors and the above-mentioned various pollutants. Specifically, in order to obtain the above-mentioned ecological information, remote sensing technology, field sampling and other means can be used to obtain the species information, spatial distribution data and population density of various aquatic organisms in the water environment; environmental factors can be continuously or regularly sampled by water quality monitoring equipment; the concentrations of various pollutants can be obtained by water quality monitoring equipment and laboratory analysis.

[0048] For the above water ecological network, the water ecological network includes multiple nodes and multiple edges connecting the multiple nodes. The multiple nodes of the water ecological network correspond one-to-one with multiple aquatic organisms, environmental factors, and multiple pollutants. An edge of the water ecological network represents the ecological interaction relationship between the two nodes connected by the edge. The ecological interaction relationships include: predation, symbiosis, competition, survival hazard, and mutual influence. Among them, the ecological interaction relationship is determined by the spatial distribution of multiple aquatic organisms, environmental factors, and the concentrations of multiple pollutants contained in the water environment.

[0049] Exemplarily, for an edge, there are the following six situations regarding the ecological interaction relationship represented by the edge.

[0050] The first situation: When both of the two nodes connected by an edge are aquatic organisms, the ecological interaction relationship represented by the edge is one of predation, symbiosis, and competition. The ecological interaction relationship represented by the edge is determined by the spatial distribution of multiple aquatic organisms in the water environment.

[0051] The second situation: When one of the two nodes connected by an edge is an aquatic organism and the other node is an environmental factor, the ecological interaction relationship represented by the edge is survival hazard, which means that the above environmental factor will endanger the survival of the above aquatic organism. The ecological interaction relationship represented by the edge is determined by the environmental factor.

[0052] The third situation: When one of the two nodes connected by an edge is an aquatic organism and the other node is a pollutant, the ecological interaction relationship represented by the edge is survival hazard, which means that the above pollutant will endanger the survival of the above aquatic organism. The ecological interaction relationship represented by the edge is determined by the concentration of the above pollutant among the multiple pollutants contained in the water environment.

[0053] The fourth situation: When both of the two nodes connected by an edge are environmental factors, the ecological interaction relationship represented by the edge is mutual influence. The ecological interaction relationship represented by the edge is determined by the environmental factor.

[0054] The fifth situation: When both of the two nodes connected by an edge are pollutants, the ecological interaction relationship represented by the edge is mutual influence. The ecological interaction relationship represented by the edge is determined by the concentrations of the above two pollutants among the multiple pollutants contained in the water environment.

[0055] The sixth situation: When one of the two nodes connected by an edge is an environmental factor and the other node is a pollutant, the ecological interaction relationship represented by the edge is mutual influence.

[0056] It should be noted that in the above water ecological network, each node also includes node features, which can be used as auxiliary information in the process of simulating the water ecological network. Specifically, when the node is an aquatic organism, the node features of this node can be the species name, spatial distribution, and population density of the aquatic organism; when the node is an environmental factor, the node features of this node can be the values of the environmental factor sampled continuously or regularly; when the node is a pollutant, the node features of this node can be the concentration of the pollutant sampled continuously or regularly.

[0057] In an application scenario, the embodiment of the present application constructs a water ecological network by using graph theory. The composition of the obtained water ecological network is shown in Table 1.

[0058] Table 1: Information Table of the Composition of the Ecological Network

[0059]

[0060]

[0061] In the above application scenario, after obtaining the water ecological network, an adjacency matrix is constructed through the connection weight w between the nodes in the water ecological network, and the shortest path matrix W between each node is determined through the Floyd-Warshall algorithm. The shortest path matrix W between each node is as follows.

[0062] W = [w ij

[0063] where w ij is the path length between nodes i and j.

[0064] S102. According to the preset removal ratio and the importance index of each node in the water ecological network, at least one node in the water ecological network and at least one edge connected to the at least one node are iteratively removed, and the stability index value of the water ecological network after each removal is calculated.

[0065] It can be understood that iteration is an activity of repeating the feedback process. Each repetition of the process is called an iteration, and the result obtained from each iteration will be used as the initial value for the next iteration. In the embodiment of the present application, the iterative removal of nodes and edges in the water ecological network is to repeatedly perform the removal operation on the nodes and edges in the water ecological network, and the water ecological network obtained after each removal operation will be used as the object for the next iterative removal.

[0066] Optionally, in combination with Figure 1 , as Figure 2 shown, S102 includes S1021 - S1022.

[0067] S1021. Calculate the importance index of each node in the water ecological network.​

[0068] Optionally, the above importance index can be calculated from the node degree, node betweenness, and node connectivity degree of the nodes in the water ecological network. The above importance index satisfies the following formula:

[0069] I i = α1k i + α2B i + α3C i where I i represents the importance index of the i-th node in the water ecological network, k i represents the node degree of the i-th node in the water ecological network, B i represents the node betweenness of the i-th node in the water ecological network, C i represents the node connectivity degree of the i-th node in the water ecological network; α1 represents the weight of the node degree, α2 represents the weight of the node betweenness, and α3 represents the weight of the node connectivity degree.

[0070] In the above formula, the node degree (Degree) refers to the number of edges directly connecting a node to other nodes. The node betweenness (Betweenness Centrality) is used to measure the frequency of a node appearing in all shortest paths, reflecting its intermediary role in the network. The node connectivity degree (Closeness Centrality) is used to measure the average shortest path length from a node to all other nodes, reflecting its closeness to other nodes. It can be understood that in graph theory, the node degree, node betweenness, and node connectivity degree are common indicators for measuring node importance and network structure, and the definitions and applications of the node degree, node betweenness, and node connectivity degree all belong to the prior art.

[0071] The calculation formula of the node degree k i is as follows.

[0072]

[0073] where N represents the total number of nodes in the water ecological network before removal, a ij represents the adjacency matrix of the water ecological network. If node i is directly connected to node j, then aij = 1; if node i is not directly connected to node j, then aij = 0.

[0074] The calculation formula of the node betweenness B i is as follows.

[0075]

[0076] where n jk represents the number of shortest paths between node j and node k, n jk(i) represents the number of the shortest paths between node j and node k passing through node i.

[0077] Node correlation degree C i The calculation formula is as follows.

[0078]

[0079] Among them, C ij represents the correlation degree between node i and node j, and d ji represents the shortest path length between node i and node j in the water ecological network after removal. In one case, d max = max(d ij ), d max is the maximum value of all effective shortest path lengths in the network. When there is no path connection between node i and node j in the network, the shortest path length between node i and node j is d max .

[0080] S1022. Sort the removal order of the nodes in the water ecological network according to the size of the importance index, and then iteratively remove at least one node consistent with the preset removal ratio from the water ecological network, and at least one edge connected to the at least one node; and after each removal operation, calculate the stability index value of the water ecological network after each removal.

[0081] Among them, the preset removal ratio is the ratio of the number of nodes removed each time to the total number of nodes in the water ecological network before iterative removal. The above preset removal ratio can be set according to the actual situation of the water environment. Optionally, the preset removal ratio can be 1%, 2%, 3% or 5%, or other reasonable values, which are not limited in the embodiments of the present application.

[0082] For example, set the preset removal ratio to 1%. When removing for the first time, remove the nodes ranked in the top 1% of the nodes in the water ecological network before iterative removal according to the size of the importance index value, and calculate the stability index value of the water ecological network after the first removal; when removing for the second time, remove the nodes ranked in the top 1-2% of the nodes in the water ecological network before iterative removal from the water ecological network after the first removal (at this time, the total number of removed nodes is 2% of the total number of nodes in the water ecological network before iterative removal), and calculate the stability index value of the water ecological network after the second removal. And so on, the stability index values of the water ecological network after removal can be obtained when the number of removed nodes is 3%, 4%, 5%... 100% of the total number of nodes in the water ecological network before iterative removal. This removal process can refer to Figure 3 .

[0083] For another example, assume that the preset removal ratio is 5%. During the first removal, remove the nodes that rank in the top 5% among the nodes of the pre-iteration-removal aquatic ecological network according to the magnitude of the importance index value, and calculate the stability index value of the aquatic ecological network after the first removal. During the second removal, remove the nodes that rank in the top 5-10% among the nodes of the pre-iteration-removal aquatic ecological network from the aquatic ecological network after the first removal (at this time, the total number of removed nodes is 10% of the total number of nodes of the pre-iteration-removal aquatic ecological network), and calculate the stability index value of the aquatic ecological network after the second removal. By analogy, when the number of removed nodes is 15%, 20%, 25%... 100% of the total number of nodes of the pre-iteration-removal aquatic ecological network, the stability index values of the aquatic ecological network after removal can be obtained.

[0084] It can be understood that in the above two examples, when removing nodes, the edges connected to the nodes are also removed.

[0085] Furthermore, the stability index value of the aquatic ecological network after each removal includes the network efficiency of the aquatic ecological network after each removal and the maximum connectivity of the aquatic ecological network after each removal.

[0086] It can be understood that the importance index value reflects the key importance of each node in the aquatic ecological network. The higher the importance index value, the more important the node is in the aquatic ecological network, and the greater the impact of removing this node on the aquatic ecological network. Network Efficiency is used to measure the efficiency of information transfer between nodes in the network. Maximum Connectivity refers to the size (i.e., the number of nodes) of the largest connected subgraph in the network.

[0087] The network efficiency of the aquatic ecological network after each removal satisfies the following formula.

[0088]

[0089] Among them, E represents the network efficiency of the aquatic ecological network after each removal, N represents the total number of nodes of the pre-iteration-removal aquatic ecological network, and d ji represents the shortest path length between node i and node j in the aquatic ecological network after each removal.

[0090] The maximum connectivity of the aquatic ecological network after the above removal satisfies the following formula.

[0091]

[0092] Among them, S represents the maximum connectivity of the aquatic ecological network after each removal, |C max | is the total number of nodes in the largest connected subgraph of the aquatic ecological network after each removal, and N is the total number of nodes of the pre-iteration-removal aquatic ecological network.

[0093] It is understandable that by analyzing the changing trends of the network efficiency E and the maximum connectivity S of the aquatic ecological network after multiple removals, the connectivity, stability, and recovery ability of the aquatic ecological network under dynamic disturbances (i.e., multiple removals of nodes and edges) can be evaluated. For example, assume that the initial aquatic ecological network consists of several nodes (such as fish, dissolved oxygen, nutrients, etc.), and these nodes form a connected network through mutual connections. Removing a key node (such as the dissolved oxygen node) in the aquatic ecological network will destroy the associated relationships directly connected to this node (such as the relationships with fish survival and pollutant degradation), resulting in a weakened connectivity of the network structure and damage to the overall function of the ecosystem.

[0094] S103. Until the stability index value of the aquatic ecological network after removal is less than or equal to the stability threshold, determine the invulnerability threshold of the aquatic ecological network according to the number of nodes removed from the aquatic ecological network and the total number of nodes in the aquatic ecological network before iterative removal; use the invulnerability threshold of the aquatic ecological network as the simulation analysis result of the structural stability of the aquatic ecological network.

[0095] Among them, the stability threshold includes a network efficiency threshold and a maximum connectivity threshold. The value range of the network efficiency threshold is 0.10 - 0.15, and the value range of the maximum connectivity threshold is 0.4 - 0.6.

[0096] Optionally, the above S103 includes the following content.

[0097] When the network efficiency of the aquatic ecological network after removal is less than or equal to the network efficiency threshold, or the maximum connectivity of the aquatic ecological network after removal is less than or equal to the maximum connectivity threshold, calculate the invulnerability threshold of the aquatic ecological network using the number of nodes removed from the aquatic ecological network and the total number of nodes in the aquatic ecological network before iterative removal. The invulnerability threshold of the aquatic ecological network satisfies the following formula:

[0098]

[0099] Among them, fa represents the invulnerability threshold, Nr represents the number of nodes removed from the aquatic ecological network, and N represents the total number of nodes in the aquatic ecological network before iterative removal.

[0100] Optionally, the above network efficiency threshold can be 0.14, and the above maximum connectivity threshold can be 0.4 or 0.6. The embodiments of the present application do not further limit the values of the above network efficiency threshold and the above maximum connectivity threshold.

[0101] In an application scenario, a certain aquaculture water body in Bishan, Chongqing is used as the water environment, and the ecological network stability of this water environment is analyzed. Among the aquatic organisms included in this water environment, the algae include: Chlorella, Cyanobacteria, Diatoms, Green algae; the fish include: Grass carp, Common carp, Crucian carp, Black carp; the plants include: Water hyacinth, Duckweed, Aquatic plants, Ceratophyllum demersum, Reed. Among the environmental factors, the water temperature is 25°C, the pH value is 7.5, the dissolved oxygen is 8 mg / L, and the hardness is 50 mg / L. Among the various pollutants included in this water environment, the heavy metals include Cadmium, Lead, and Copper; the organic pollutants include Organochlorine pesticides; the nutrient salts include Nitrogen and Phosphorus. In addition, it also includes Zinc, Petroleum pollutants, and Polycyclic aromatic hydrocarbons. Specifically, the concentration of Nitrogen is 10 mg / L, the concentration of Phosphorus is 1.2 mg / L, the concentration of Organochlorine pesticides is 0.05 mg / L, the concentration of Petroleum pollutants is 2.3 mg / L, and the concentration of Polycyclic aromatic hydrocarbons is 3 mg / L; the concentration of Cadmium is 0.2 μg / L, the concentration of Lead is 0.05 μg / L, the concentration of Copper is 0.15 μg / L, the concentration of Zinc is 0.3 μg / L, and the concentration of Heavy metal Chromium is 0.1 μg / L.

[0102] Apply S101 of the method provided in the embodiments of the present application to the above application scenario to obtain the aquatic ecological network of this water environment. Then, perform iterative removal on the aquatic ecological network of this water environment through S102, and use S103 to determine the vulnerability threshold of the aquatic ecological network of this water environment.

[0103] In the above process, it is set that when the maximum connectivity of the aquatic ecological network after removal is less than or equal to the maximum connectivity threshold (0.5), and the preset removal ratio is 1%, the vulnerability threshold of the aquatic ecological network is calculated using the number of nodes removed from the aquatic ecological network and the total number of nodes in the aquatic ecological network before iterative removal. During the iterative removal process, the removal ratio, the maximum connectivity of the aquatic ecological network, and the network efficiency are shown in Table 1.

[0104] Table 1: Schematic table of removal ratio, maximum connectivity, and network efficiency

[0105]

[0106]

[0107] As can be seen from Table 1, when the removal ratio reaches 24%, the maximum connectivity of the water ecological network after removal is 0.5001, and when the removal ratio reaches 26%, the maximum connectivity of the water ecological network after removal is 0.33435. That is to say, when the removal ratio reaches 24%, it can be considered that the maximum connectivity of the water ecological network after removal reaches the maximum connectivity threshold (0.5), indicating that the network function of the water ecological network after removal is on the verge of collapse at this time; when the removal ratio reaches 26%, the maximum connectivity of the water ecological network after removal is less than the maximum connectivity threshold, indicating that the network function of the water ecological network after removal has collapsed at this time. Thus, it can be seen that the network function of the water ecological network collapses when the removal ratio is between 24% and 26%.

[0108] In order to more accurately represent the stability of the water ecological network, the resilience threshold interval of 0.24 - 0.26 composed of the resilience threshold of 0.24 of the water ecological network when the removal ratio reaches 24% and the resilience threshold of 0.26 of the water ecological network when the removal ratio reaches 26% is used as the simulation analysis result of the structural stability of the water ecological network.

[0109] In one implementation, the above method further includes S104.

[0110] S104. When the stability index value of the water ecological network after removal is less than or equal to the stability threshold, determine the resilience of the water ecological network according to the number of nodes removed from the water ecological network, and use the resilience of the water ecological network and the resilience threshold of the water ecological network together as the simulation analysis result of the structural stability of the water ecological network.

[0111] Among them, the resilience of the water ecological network is used to describe the tolerance and recovery ability of the water ecological network to ecological environment changes. The resilience of the water ecological network satisfies the following formula:

[0112]

[0113] Among them, R represents the resilience of the water ecological network, Nr represents the number of nodes removed from the water ecological network, and d ji represents the shortest path length between node i and node j in the water ecological network after removal.

[0114] In summary, in a dynamic simulation method for the stability of a water ecological network structure provided by an embodiment of the present application, a water ecological network is constructed according to ecological information in the water environment, and based on a preset removal ratio and the importance index of each node in the water ecological network, at least one node in the water ecological network and at least one edge connected to the at least one node are removed multiple times in an iterative removal manner, and after each removal, the stability index value of the water ecological network after removal is calculated. When the stability index value of the water ecological network after removal is less than or equal to the stability threshold, it is determined that the overall function of the ecological system of the water environment corresponding to the water ecological network is damaged and cannot maintain normal operation, that is, the water ecological network is no longer stable. Then, using the number of removed nodes and the total number of nodes in the water ecological network before removal, the vulnerability threshold of the water ecological network is calculated, and the vulnerability threshold is used as the simulation analysis result of the water ecological network structure stability. In the process of constructing the water ecological network, the above method takes into account species information, environmental factors, and pollutant information in the water environment. On this basis, at least one node in the water ecological network and at least one edge connected to the at least one node are removed multiple times, which can dynamically simulate the changes in the water environment caused by natural or human factors in the real situation (including species changes, environmental factor changes, and pollutant changes), thereby making the simulation analysis result of the water ecological network structure stability more accurate.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A dynamic simulation method for the stability of a water ecological network structure, characterized in that, Including: Constructing a water ecological network based on ecological information in the water environment; Wherein, the ecological information includes species information, environmental factors, and pollutant information; the species information includes the spatial distribution of various aquatic organisms existing in the water environment, and the various aquatic organisms include algae, fish, and aquatic plants; the environmental factors include: the temperature, pH value, and dissolved oxygen of the water environment, and the pollutant information includes: the concentrations of various pollutants contained in the water environment; the various pollutants include heavy metals, organic pollutants, and nutrients; the water ecological network includes multiple nodes and multiple edges connecting the multiple nodes; According to a preset removal ratio and the importance index of each node in the water ecological network, iteratively remove at least one node in the water ecological network and at least one edge connected to the at least one node, and calculate the stability index value of the water ecological network after each removal; Until the stability index value of the water ecological network after removal is less than or equal to the stability threshold, determine the vulnerability threshold of the water ecological network according to the number of nodes removed from the water ecological network and the total number of nodes in the water ecological network before iterative removal; take the vulnerability threshold of the water ecological network as the simulation analysis result of the structural stability of the water ecological network.

2. The method according to claim 1, wherein The multiple nodes of the water ecological network correspond one-to-one with the various aquatic organisms, the environmental factors, and the various pollutants; one edge of the water ecological network represents the ecological interaction relationship between the two nodes connected by the one edge; the ecological interaction relationship includes: predation, symbiosis, competition, endangering survival, and mutual influence; wherein, the ecological interaction relationship is determined by the spatial distribution of various aquatic organisms existing in the water environment, the environmental factors, and the concentrations of various pollutants contained in the water environment.

3. The method according to claim 1, characterized in that, The step of, according to a preset removal ratio and the importance index of each node in the water ecological network, iteratively remove at least one node in the water ecological network and at least one edge connected to the at least one node, and calculate the stability index value of the water ecological network after each removal, includes: Calculating the importance index of each node in the water ecological network, and the importance index satisfies the following formula: I i = α1k i + α2B i + α3C i Among them, I i represents the importance index of the i-th node in the water ecological network, k i represents the node degree of the i-th node in the water ecological network, B i represents the betweenness centrality of the i-th node in the water ecological network, C i represents the node connectivity of the i-th node in the water ecological network; α1 represents the weight of the node degree, α2 represents the weight of the betweenness centrality, and α3 represents the weight of the node connectivity; Sort the removal order of the nodes in the water ecological network according to the magnitude of the importance index, and then iteratively remove at least one node consistent with the preset removal ratio from the water ecological network, and at least one edge connected to the at least one node; and after each removal operation, calculate the stability index value of the water ecological network after each removal, wherein the stability index value of the water ecological network after each removal includes the network efficiency of the water ecological network after each removal and the maximum connectivity of the water ecological network after each removal; wherein, the preset removal ratio is the ratio of the number of nodes removed each time to the total number of nodes in the water ecological network before iterative removal, and the preset removal ratio is 1%, 2%, 3%, or 5%; The network efficiency of the water ecological network after each removal satisfies the following formula; where E represents the network efficiency of the water ecological network after each removal, N represents the total number of nodes in the water ecological network before iterative removal, and d ji represents the shortest path length between node i and node j in the water ecological network after each removal; The maximum connectivity of the water ecological network after each removal satisfies the following formula; Among them, S represents the maximum connectivity of the water ecological network after each removal, and |C max | represents the total number of nodes in the largest connected subgraph of the water ecological network after each removal.

4. The method according to claim 3, wherein The stability threshold includes a network efficiency threshold and a maximum connectivity threshold. The value range of the network efficiency threshold is 0.10 to 0.15, and the value range of the maximum connectivity threshold is 0.4 to 0.

6.

5. The method according to claim 4, wherein When the stability index value of the water ecological network after removal is less than or equal to the stability threshold, according to the number of nodes removed from the water ecological network and the total number of nodes of the water ecological network before iterative removal, determining the vulnerability threshold of the water ecological network includes: When the network efficiency of the water ecological network after removal is less than or equal to the network efficiency threshold, or the maximum connectivity of the water ecological network after removal is less than or equal to the maximum connectivity threshold, using the number of nodes removed from the water ecological network and the total number of nodes of the water ecological network before iterative removal, calculating the vulnerability threshold of the water ecological network, and the vulnerability threshold of the water ecological network satisfies the following formula: Where, fa represents the vulnerability threshold, Nr represents the number of nodes removed from the water ecological network, and N represents the total number of nodes of the water ecological network before iterative removal.

6. The method according to claim 1, wherein The method further includes: When the stability index value of the water ecological network after removal is less than or equal to the stability threshold, according to the number of nodes removed from the water ecological network, determining the resilience of the water ecological network, and taking the resilience of the water ecological network and the vulnerability threshold of the water ecological network together as the simulation analysis result of the structural stability of the water ecological network; the resilience of the water ecological network is used to describe the bearing capacity and recovery ability of the water ecological network to ecological environment changes; the resilience of the water ecological network satisfies the following formula: Wherein, R represents the resilience of the water ecological network, Nr represents the number of nodes removed from the water ecological network, and d ji represents the shortest path length between node i and node j in the water ecological network after removal.

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