Method for analyzing the stability of reef fish communities based on symbiotic graphs

Abstract

The present invention provides a method for analyzing the stability of reef fish communities based on a symbiotic graph, comprising the steps of: S1: Analyzing the stability of reef fish communities, comprehensively considering the dependence relationship and the trophic relationship to quantify the relationship between coral reefs and fish populations; constructing a symbiotic graph and using the PMA graph kernel method for similarity calculation; S2: Identifying the priority areas for protecting reef fish communities, and using the Louvain algorithm to divide the module structure of the communities in unstable years. The method for analyzing the stability of reef fish communities based on a symbiotic graph according to the present invention addresses the problems of single and less objective calculation methods for interspecies relationships in previous studies, and proposes a model that can effectively express the biological relationships of reef fish communities; addresses the problem of low accuracy of the methods for measuring community changes in previous studies, and designs a method that can effectively measure community changes to analyze the stability of the communities; and further identifies the areas that need to be protected first according to the analysis results of community stability.

Description

Technical Field

[0001] The present invention relates to the technical field of coral reef ecological protection, and particularly relates to a method for analyzing the stability of reef fish communities based on a co-occurrence graph. Background Art

[0002] Coral reefs provide ideal habitats for various marine organisms while also providing livelihoods, medicine, and economic services for millions of people. However, due to natural and human factors, coral reefs in many regions of the world are currently facing a serious survival crisis. Therefore, it is urgent to protect the coral reef ecosystem and maintain the ecological stability of coral reef areas.

[0003] Coral reef fish, as an important part of the coral reef ecosystem, plays an important role in maintaining the ecological balance of the system. Its diversity can reflect the health of the system and is an important reef-dwelling organism often used to evaluate the health of coral reefs. Therefore, the present invention focuses on the reef fish community (i.e., the combined community of coral reefs and fish). The temporal and spatial changes of the reef fish community are important reflections of community stability. The measurement of its inter-annual changes can be achieved by calculating the similarity of the community over multiple years, and the spatial changes can be obtained by analyzing the distribution changes of community modules. Therefore, two main tasks need to be considered in the study of reef fish community stability: one is to clearly express the inter-species relationship, and the other is to effectively measure the changes in the community.

[0004] Graph theory, as an effective tool for organizing and analyzing relational data, has been increasingly widely used in ecological protection research due to its unique advantages.

[0005] For the expression of inter-species relationships, Zhao et al. quantified the dependence relationship based on the Euclidean distance between coral reefs and fish populations and established a competition graph model of coral reefs and fish. Lin et al. established an ecological network model of fish communities through trophic relationships. However, these calculation methods of inter-species relationships are single and have weak objectivity.

[0006] For the measurement of community changes, existing methods mostly achieve it based on comparing the structural characteristics of ecological networks, such as degree distribution, nestedness, modularity, etc. However, these methods ignore the attribute information contained in the organisms themselves, have low accuracy, and cannot quickly and effectively quantify the changes in the community. Summary of the Invention

[0007] Aiming at the deficiencies in the above-mentioned prior art, the present invention provides a method for analyzing the stability of reef fish communities based on symbiotic graphs. Aiming at the problems of single calculation method and weak objectivity in the previous research on interspecies relationships, a model that can effectively express the biological relationships of reef fish communities is proposed; aiming at the problem of low accuracy in the previous methods for measuring community changes, a method that can effectively measure community changes is designed to analyze the stability of the community; and according to the analysis results of the community stability, the areas that need to be protected preferentially are further identified.

[0008] To achieve the above object, the present invention provides a method for analyzing the stability of reef fish communities based on symbiotic graphs, including the steps:

[0009] S1: Analysis of the stability of the reef fish community. Select the distance value and trophic level difference between a fixed coral reef and fish populations as the criteria for measuring the existence of the dependence relationship and trophic relationship therebetween, and comprehensively consider the dependence relationship and the trophic relationship to quantify the relationship between the coral reef and the fish populations; select a target coral reef and a target fish population to construct a symbiotic graph, and use the PMA graph kernel method to calculate the similarity of the constructed symbiotic graphs of multiple years to obtain the community similarity results of multiple years.

[0010] S2: Identification of the priority protection areas of the reef fish community. According to the calculated community similarity results of multiple years, screen out the communities in the relatively most unstable years; use the Louvain algorithm to perform module partitioning on the communities in the most unstable years and the communities in the adjacent years before and after them, and finally use the PMA graph kernel method to measure the changes of multiple sub-modules between adjacent years to obtain the similarity results of multiple sub-modules.

[0011] Preferably, the step S1 further includes the steps:

[0012] S11: Quantification of interspecies relationships;

[0013] A dependence criterion and a trophic criterion are proposed. Without considering the dependence relationship between the coral reefs for the time being, only when the distance between two different objects is less than or equal to the corresponding dependence criterion, it is considered that there is a dependence relationship therebetween; only when the trophic level difference between two different objects is greater than or equal to the trophic criterion, it is considered that there is a trophic relationship therebetween;

[0014] Establish a relationship strength formula:

[0015]

[0016] Among them, W(x,y) represents the relationship strength between organisms, e represents the natural constant, λ represents the exponent, and G(x,y) represents the sum of the dependence distance and the trophic level difference; d'(x,y) and ΔTL'(x,y) are the normalized dependence distance and trophic level difference respectively; α is the weight coefficient;

[0017] S12: Construction of the symbiotic graph model;

[0018] Taking one of the coral reefs or one of the fish populations as a node, setting the corresponding node label information according to its role, and taking its relevant biological information as node attribute information; Only when the dependence criterion and the nutrition criterion are simultaneously satisfied between two nodes, an edge is connected from the node with a lower trophic level to the node with a higher trophic level, and the edge weight is calculated according to formula (1);

[0019] S13: PMA graph kernel.

[0020] Preferably, the step S13 further includes the steps:

[0021] S131: Generate the graph node embedding of the symbiotic graph and map it to a multi-resolution histogram;

[0022] S132: Calculate the similarity of multiple symbiotic graphs.

[0023] Preferably, the step S131 further includes the steps:

[0024] S1311: Extract the graph attribute features and generate the attribute embedding vector matrix of the symbiotic graph;

[0025] S1312: Extract the graph structure features and generate the structure vector matrix of the symbiotic graph;

[0026] S1313: Fuse the attribute embedding vector matrix and the structure vector matrix to generate the vector representation of the entire graph;

[0027] S1314: Map the vector set of the graph to a multi-resolution histogram.

[0028] Preferably, in the step S132:

[0029] The similarity of multiple symbiotic graphs can be obtained by weighted intersection summation of point sets at different resolutions:

[0030]

[0031] Among them, H l (G1), H l (G2) are the histograms corresponding to the node embeddings of G1 and G2 at the l-th layer resolution; I(H l (G1), Hl (G2) is the matching value of G1 and G2 on the l-th layer; ω is the weight value, ω l = 1 / 2 l ; S Δ S(G1,G2) represents the similarity between nodes G1 and G2; L represents the total number of levels;

[0032]

[0033] wherein, lab represents the number of label categories; represents the similarity values of multiple said symbiotic graphs.

[0034] Preferably, in the S2 step:

[0035] First, use the Louvain algorithm to divide the modules of the communities in unstable years, and then use the PMA method to measure the changes of the sub-modules between adjacent years.

[0036] Due to the adoption of the above technical solutions, the present invention has the following beneficial effects:

[0037] The present invention proposes a symbiotic graph model that can effectively express the biological relationships in reef fish communities, and realizes the quantification of the intensity of biological relationships, which can provide a reference for the modeling of community structures to a certain extent.

[0038] The present invention transforms the problem of measuring community changes into the problem of calculating the similarity of its relational graph model, and designs a new pyramid matching (PMA) graph kernel method that combines graph attributes and structural information. This method can not only quickly and effectively achieve the accurate measurement of reef fish community changes, but also flexibly select the attributes to be compared to measure the differences in multiple aspects of the community, and can provide a new auxiliary evaluation method for the stability analysis of the community.

[0039] Based on the similarity calculation results of the communities in multiple years, the present invention performs sub-module division and its sub-module change measurement on the communities in unstable years, and initially identifies the areas that need to be prioritized, which can provide auxiliary decision-making for relevant conservation personnel in the supervision and protection planning of coral reef ecosystems. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flowchart of the method for analyzing the stability of reef fish communities based on symbiotic graphs according to an embodiment of the present invention;

[0041] Figure 2 is a comparison graph of the two measurement results according to an embodiment of the present invention;

[0042] Figure 3 is a graph of the diversity index values of each year according to an embodiment of the present invention;

[0043] Figure 4 Calculation result diagram of different version graph kernels of the embodiment of the present invention;

[0044] Figure 5 Similarity calculation result diagram of the community module of the embodiment of the present invention;

[0045] Figure 6 Comparison diagram of module similarity results of two measures in 2006 - 2007 of the embodiment of the present invention.

[0046] Figure 7 Comparison diagram of module similarity results of two measures in 2007 - 2008 of the embodiment of the present invention. Detailed implementation manner

[0047] Next, according to the attached Figures 1 to 7 , the preferred embodiment of the present invention is given and described in detail to better understand the functions and features of the present invention.

[0048] Please refer to Figure 1 , a method for analyzing the stability of reef fish communities based on symbiotic graphs according to an embodiment of the present invention includes the steps:

[0049] S1: Stability analysis of reef fish communities. Select the distance value and trophic level difference between a fixed coral reef and a fish population as the criteria for measuring the existence of the dependence relationship and trophic relationship therebetween, and comprehensively consider the dependence relationship and the trophic relationship to quantify the relationship between the coral reef and the fish population; select a target coral reef and a target fish population to construct a symbiotic graph, and use the PMA graph kernel method to calculate the similarity of the constructed symbiotic graphs of multiple years to obtain the community similarity results of multiple years;

[0050] S2: Identification of priority areas for reef fish community protection. According to the calculated community similarity results of multiple years, screen out the communities in the relatively most unstable years; use the Louvain algorithm to perform module partitioning on the communities in the most unstable years and their adjacent years before and after, and finally use the PMA graph kernel method to measure the changes of multiple sub - modules between adjacent years to obtain the similarity results of multiple sub - modules.

[0051] Step S1 further includes the steps:

[0052] S11: Quantification of inter - species relationships;

[0053] A dependence criterion and a trophic criterion are proposed. Without considering the dependence relationship between the coral reefs for the time being, only when the distance between two different objects is less than or equal to the corresponding dependence criterion, it is considered that there is a dependence relationship therebetween; only when the trophic level difference between two different objects is greater than or equal to the trophic criterion, it is considered that there is a trophic relationship therebetween;

[0054] Establish a relationship strength formula:

[0055]

[0056] Among them, W(x,y) represents the relationship strength between organisms, e represents the natural constant, λ represents the exponent, and G(x,y) represents the sum of the dependence distance and the trophic level difference; d'(x,y) and ΔTL'(x,y) are the dependence distance and the trophic level difference after normalization respectively; α is the weight coefficient;

[0057] S12: Construction of the symbiotic graph model;

[0058] Take a coral reef or a fish population as a node, set the corresponding node label information according to its role, and use its relevant biological information as node attribute information; Only when both the dependence criterion and the nutrition criterion are met between two nodes, connect an edge from the node with a lower trophic level to the node with a higher trophic level, and calculate the weight value on the edge according to formula (1);

[0059] S13: PMA graph kernel.

[0060] Step S13 further includes the steps:

[0061] S131: Generate the graph node embedding of the symbiotic graph and map it to a multi-resolution histogram;

[0062] Step S131 further includes the steps:

[0063] S1311: Extract the graph attribute features and generate the attribute embedding vector matrix of the symbiotic graph;

[0064] S1312: Extract the graph structure features and generate the structure vector matrix of the symbiotic graph;

[0065] S1313: Fuse the attribute embedding vector matrix and the structure vector matrix to generate the vector representation of the entire graph;

[0066] S1314: Map the vector set of the graph to a multi-resolution histogram.

[0067] S132: Calculate the similarity of multiple symbiotic graphs.

[0068] In step S132:

[0069] The similarity of multiple symbiotic graphs can be obtained by weighted intersection summation of point sets at different resolutions:

[0070]

[0071] Among them, H l (G1), H l(G2) is the histogram corresponding to the node embeddings of G1 and G2 at the l-th layer resolution; I(H l (G1), H l (G2) is the matching value of G1 and G2 at the l-th layer; ω is the weight value, ω l = 1 / 2 l ; S Δ (G1, G2) represents the similarity between nodes G1 and G2; L represents the total number of levels;

[0072]

[0073] Among them, lab represents the number of label categories; represents the similarity values of multiple said co-occurrence graphs.

[0074] In step S2:

[0075] First, use the Louvain algorithm to divide the modules of the communities in unstable years, and then use the PMA method to measure the changes of sub-modules between adjacent years.

[0076] A method for analyzing the stability of reef fish communities based on co-occurrence graphs according to an embodiment of the present invention is specifically implemented as follows:

[0077] Adopt the dataset of coral reefs and fish in St. John's Island in summer from 2004 to 2010. After preprocessing the original dataset, construct it into a graph dataset suitable for the embodiment. On this basis, use the proposed PMA graph kernel method to perform similarity calculations on multiple co-occurrence graphs to obtain the similarity results of the communities over the years.

[0078] The embodiment of the present invention focuses on the changes of reef fish communities between adjacent years. From the community similarity results of multiple years, it can be seen that the community has changed greatly between 2006 and 2008, and the change is the largest between 2007 and 2008, while the changes in other years are relatively small. By analyzing the fluctuations of six similarity values, it can be found that the community is relatively the most unstable in 2007.

[0079] It is found through investigation that between 2006 and 2008, the overall proportion of herbivorous fish in the study area of the embodiment has changed greatly, and the coverage rate of the dominant species, hard coral, has also changed greatly. This situation is closely related to the heat wave that occurred in the US Virgin Islands that year, and the increase in water temperature led to large-scale coral bleaching in this area.

[0080] In order to further verify the effectiveness of the above results, the present invention calculates the Bray-Curtis distance based on the number of species and species abundances in each year to measure the similarity between communities, and compares the results with the above community similarity results after normalization processing. The comparison results are as Figure 2As shown in the figure. It can be found that the similarity values obtained by the PMA graph kernel method are generally lower than those of the Bray-Curtis similarity method. This is normal because the Bray-Curtis measure method mainly considers the species composition of the community, while the PMA graph kernel method not only considers the species composition of the community, but also considers multiple information such as location and coverage. Among them, the results obtained by the two methods differ particularly greatly in 2006 - 2007 and 2007 - 2008. Considering the reason for this situation may be that the positions of coral reefs and fish populations in the community have changed greatly during this period, and this possibility has been verified in the subsequent measurement of community module changes. The results obtained by the two methods basically maintain the same change trend, proving the effectiveness of the experimental results.

[0081] Since the diversity of the community is an important guarantee for stability, and its fluctuations can indirectly reflect the true stability status of the community, the present invention also separately counted the diversity index information of the coral reef and fish communities each year as shown in Figure 3 the figure. It can be clearly found from Figure 3 that all three index values fluctuate greatly between 2006 and 2008, showing a trend of first decreasing and then increasing as a whole. Among them, 2007 is the inflection point of significant change, that is, the true stability status of the community reflected by the change of community diversity is consistent with the conclusion obtained by the PMA method, proving the effectiveness of the experimental results.

[0082] To verify the effectiveness of the PMA graph kernel, the present invention conducts experiments on the data set by applying PMA, its initial version, and the subsequent version applicable to labeled graphs respectively. For the sake of simplifying the description, here the initial version and the version applicable to labeled graphs are represented by PM and PML respectively. Figure 4 shows the results obtained by the three versions of graph kernels after normalization.

[0083] From Figure 4 it can be found that the results obtained by the PMA graph kernel are basically lower than the similarity values obtained by the other two versions. The lower the similarity value, the more beneficial it is to improve the accuracy of the measurement result. In the calculation of community similarity in 2006 - 2007 and 2007 - 2008, the results obtained by the PM and PML versions are (0.017, 0.024) and (0.015, 0.020) respectively, which do not conform to the actual situation. While the result obtained by PMA is (0.015, 0.003), which conforms to the actual situation, successfully proving the effectiveness of the method proposed by the present invention.

[0084] In the task of identifying community protection priority areas, the present invention first uses the Louvain algorithm to perform module division on communities with large inter-annual variations (co-occurrence graphs corresponding to 2006, 2007, and 2008). On this basis, the changes of multiple modules in the same geographical range in different years are measured respectively. For the convenience of calculation, the new module structures that appeared between 2007 and 2008 are not considered temporarily, and the calculation results are as Figure 5 shown.

[0085] From Figure 5 it can be clearly found that the similarity values before and after Module 2 differ greatly. By analyzing the coral and fish conditions in this range, it can be seen that the types and quantities of coral reefs and fish in Module 2 changed greatly in 2007. In addition, Modules 4, 6, 7, and 9 also need attention because the similarity values were 0 during 2006 - 2007 or 2007 - 2008, which means the disappearance of the modular structure at this place. All these modules with large changes should be concerned.

[0086] To verify the effectiveness of the above results, the present invention calculates the Bray-Curtis distance based on the number of species and species abundance in each year to measure the similarity of multiple modules between adjacent years, and compares the results with those obtained by the PMA graph kernel, as Figure 6 and Figure 7 show the comparison results of the two measures. From Figure 6 and Figure 7 it can be seen that the results obtained by the two methods basically maintain the same change trend, and the similarity values obtained by the PMA graph kernel method are all lower than the Bray-Curtis similarity values, proving its accuracy and effectiveness.

[0087] The present invention has been described in detail above in combination with the embodiments in the accompanying drawings. Those of ordinary skill in the art can make various variations of the present invention according to the above description. Therefore, some details in the embodiments should not constitute a limitation to the present invention, and the protection scope of the present invention will be defined by the scope of the appended claims.

Claims

1. A method for analyzing the stability of reef fish communities based on co-occurrence graphs, comprising the steps of: S1: Stability analysis of reef fish communities. Select the distance value and trophic level difference between a fixed coral reef and fish populations as the criteria for measuring the existence of the dependence relationship and trophic relationship therebetween, and comprehensively consider the dependence relationship and the trophic relationship to quantify the relationship between the coral reef and fish populations; Selecting a target coral reef and a target fish population to construct a co-occurrence graph, and using the PMA graph kernel method to calculate the similarity of the constructed co-occurrence graphs of multiple years to obtain the community similarity results of multiple years. The S1 step further includes the steps of: S11: Quantifying interspecific relationships; Proposing a dependence criterion and a trophic criterion. Temporarily disregarding the dependence relationships between the coral reefs, only when the distance between two different objects is less than or equal to the corresponding dependence criterion, is it considered that there is a dependence relationship between them; only when the difference in trophic levels between two different objects is greater than or equal to the trophic criterion, is it considered that there is a trophic relationship between them; Establishing a relationship strength formula: where W(x,y) represents the relationship strength between organisms, e represents the natural constant, λ represents the exponent, G(x,y) represents the sum of the dependence distance and the difference in trophic levels; d'(x,y) and ΔTL'(x,y) are the dependence distance and the difference in trophic levels after normalization respectively; α is the weight coefficient; S12: Constructing the co-occurrence graph model; Taking one of the coral reefs or one of the fish populations as a node, setting the corresponding node label information according to its role, and taking its relevant biological information as node attribute information; only when both the dependence criterion and the trophic criterion are satisfied between two nodes, a directed edge is drawn from the node with a lower trophic level to the node with a higher trophic level, and the edge weight is calculated according to formula (1); S13: PMA graph kernel; S2: Identifying the priority areas for protecting reef fish communities. According to the calculated community similarity results of multiple years, screening out the communities in the relatively most unstable years; using the Louvain algorithm to perform module partitioning on the communities in the most unstable years and the communities in the adjacent years before and after them, and finally using the PMA graph kernel method to measure the changes of multiple sub-modules between adjacent years to obtain the similarity results of multiple sub-modules.

2. The method for analyzing the stability of reef fish communities based on the symbiotic graph according to claim 1, wherein The S13 step further includes the steps of: S131: Generating the graph node embedding of the co-occurrence graph and mapping it to a multi-resolution histogram; S132: Calculating the similarity of multiple co-occurrence graphs.

3. The method for analyzing the stability of reef fish communities based on the symbiotic graph according to claim 2, characterized in that The S131 step further includes the steps of: S1311: Extracting graph attribute features to generate the attribute embedding vector matrix of the co-occurrence graph; S1312: Extracting graph structure features to generate the structure vector matrix of the co-occurrence graph; S1313: Fusing the attribute embedding vector matrix and the structure vector matrix to generate the vector representation of the entire graph; S1314: Mapping the vector set of the graph to a multi-resolution histogram.

4. The method for analyzing the stability of reef fish communities based on a symbiotic graph according to claim 3, characterized in that, In the S132 step: The similarity of multiple co-occurrence graphs can be obtained by weighted intersection summation of point sets at different resolutions: Among them, H l (G1), H l (G2) are histograms corresponding to the node embeddings of G1 and G2 at the l-th layer resolution; I(H l (G1), H l (G2) is the matching value of G1 and G2 at the l-th layer; ω is the weight value, ω l = 1 / 2 l ; S Δ (G1, G2) represents the similarity between nodes G1 and G2; L represents the total number of levels; where lab represents the number of label categories; represents the similarity values of multiple said symbiotic graphs.

5. The method for analyzing the stability of reef fish communities based on the symbiotic graph according to claim 4, characterized in that, In the S2 step: First, use the Louvain algorithm to perform module structure partitioning on the communities in the unstable years, and then use the PMA method to measure the changes of the sub-modules between adjacent years.

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