A method of assessing the effect of submersed plant restoration on phytoplankton

Abstract

The application discloses a method for evaluating the influence of submerged plant restoration on phytoplankton, comprising the following steps: obtaining monitoring data of a target lake, identifying a critical point and a threshold range of submerged plant coverage based on the phytoplankton community data, including: using a Gaussian mixture model to perform cluster analysis on the phytoplankton community data to identify a bimodal distribution pattern of the phytoplankton community with the change of the submerged plant coverage, performing potential energy analysis to obtain the critical point and the steady-state restoring force, and generating a stability landscape graph; and evaluating the relative contribution of random and deterministic processes in the construction mechanism of the phytoplankton community to explain the community construction. After the bimodal distribution pattern is identified, the stability landscape graph is generated based on the potential energy analysis, the community construction can be explained, and thus the quantitative threshold of the submerged plant driving the steady-state conversion of the lake is clear, and a clear and quantifiable target is provided for ecological restoration.

Description

Technical Field

[0001] This invention relates, and more particularly, to a method for assessing the impact of submerged plant restoration on phytoplankton. Background Technology

[0002] High-altitude lakes, due to their unique geographical and climatic environments, have formed special ecosystems. Compared with lakes in plains areas, high-altitude lakes are characterized by high altitude, low air pressure, strong ultraviolet radiation, and large diurnal temperature variations. In recent years, with the intensification of human activities, the ecosystems of high-altitude lakes are transforming from a grass-dominated clear-water state to an algae-dominated turbid-water state, which exacerbates eutrophication and severely damages the ecosystems of high-altitude lakes. Submerged plant restoration, as a biological regulation method based on ecological principles, is widely used for the restoration and reconstruction of lake ecosystems. Submerged plants can promote phytoplankton growth by improving the optical environment and lake nutrient structure, thereby improving the ecological environment of lakes. Studies have found that submerged plants may influence the succession of phytoplankton communities through multidimensional pathways, ultimately achieving the steady-state reconstruction of lake ecosystems. However, traditional restoration practices often lack precise regulatory thresholds and are somewhat indiscriminate, leading to poor lake restoration results, high costs, or long-term stagnation of the ecosystem in a transitional state.

[0003] Currently, many technologies mainly focus on whether submerged plants can survive during lake restoration and their initial improvement of water quality. However, they lack a deep understanding of the intrinsic laws that drive fundamental changes in phytoplankton community structure, assembly mechanisms, and interspecific interaction networks, and have failed to propose quantitative regulatory thresholds. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for assessing the impact of submerged plant restoration on phytoplankton. Through data monitoring, model analysis, and ecological mechanism analysis, the key thresholds of submerged plant coverage are quantitatively determined, thereby guiding the ecological restoration of plateau lakes.

[0005] The objective of this invention is achieved through the following technical solution: This application discloses a method for assessing the impact of submerged plant restoration on phytoplankton, comprising the following steps: acquiring monitoring data of a target lake, the monitoring data including ammonia nitrogen concentration, total nitrogen concentration, total phosphorus concentration, nitrogen-to-phosphorus ratio, and phytoplankton community; identifying the critical point and threshold range of submerged plant coverage based on the phytoplankton community data, including: performing cluster analysis on the phytoplankton community data using a Gaussian mixture model, wherein the cluster analysis uses a Gaussian mixture model to model the phytoplankton community data to identify the bimodal distribution pattern of the phytoplankton community as submerged plant coverage changes, and then performing potential energy analysis to obtain the critical point and steady-state resilience, generating a stability landscape map; assessing the relative contributions of stochastic and deterministic processes in the phytoplankton community building mechanism to explain community building.

[0006] Furthermore, the Gaussian mixture model uses the Bayesian information criterion for model selection, establishing single-component and two-component models respectively, and employing the expectation-maximization algorithm for parameter estimation, selecting the model with the smallest BIC value as the optimal model; wherein, when the difference ΔBIC between the single-peaked model and the two-peaked model is greater than 2, the two-peaked model is determined to be significantly better than the single-peaked model.

[0007] Furthermore, the potential energy function U(x) = -ln(P(x)) is calculated, where P(x) is the empirical probability density function between the key state variables obtained by fitting a Gaussian mixture model and the submerged plant cover. The potential energy function is scaled to obtain the scaled potential energy U'(x) = U(x) / σ, where σ is the standard deviation of the noise level. The local minimum on the potential energy curve corresponds to the stable state of the ecosystem, and the local maximum corresponds to the critical point.

[0008] Furthermore, a neutral model was used to fit the species abundance distribution, the migration rate parameter m was iteratively optimized, and the goodness-of-fit R² value was used to quantify the proportion of neutral processes that explain the community structure. A null model was used to perform phylogenetic signal analysis, and the dominance of deterministic and stochastic processes was determined by calculating the βNTI index (nearest taxonomic unit index) and the RCBray index (matrix index) and combining them with preset thresholds.

[0009] Furthermore, the method also includes: constructing a species correlation matrix using Spearman rank correlation coefficient and performing co-occurrence network analysis; constructing a phytoplankton species co-occurrence network through co-occurrence network analysis and evaluating the network's topology and stability; and verifying the causal path of submerged plant coverage on phytoplankton community stability by integrating the monitoring data, cluster analysis results, potential energy analysis results, and co-occurrence network analysis results through ecological causal path verification.

[0010] Furthermore, the Spearman rank correlation coefficient is used to construct a species correlation matrix for co-occurrence network analysis, which includes setting a significance level of p < 0.05 and a correlation strength threshold of |r| > 0.6 as criteria for constructing effective connections; and constructing a weighted undirected network based on the effective connections, where nodes represent phytoplankton species, node weights are the average relative abundance of species, and edge weights are the absolute values ​​of the correlation coefficients between species.

[0011] Furthermore, the input data is preprocessed, including outlier handling, Z-score standardization, and Box-Cox transformation when the data does not meet the normal distribution assumption. A structural equation model is established, which defines a multi-level influence path of submerged plant cover on aquatic environmental conditions, aquatic environmental conditions on phytoplankton community characteristics, and phytoplankton community characteristics ultimately on network stability. The Bootstrap method is used for multiple resampling to test the significance of the coefficients of each path in the multi-level influence path.

[0012] Furthermore, it also includes preprocessing the phytoplankton species abundance data, including performing a Hellinger transform, where the Hellinger transform formula is: in, X ij Let be the original abundance of the j-th species in the i-th sample. Y ij is the transformed value, and p is the total number of species.

[0013] The beneficial effects of this invention are as follows: After identifying the bimodal distribution pattern, this application generates a stability landscape map based on potential energy analysis, which can explain community building and thus clarify the quantitative thresholds for submerged plants driving the steady-state transition of lakes, such as the 38.48% critical point, the 30-60% bistable zone, and the >60% clear water state; thereby providing clear and quantifiable targets for ecological restoration. Furthermore, starting from deep ecological mechanisms such as community assembly (dominated by deterministic processes) and network structure (increased complexity), it ensures that the restored ecosystem has inherent stability and resilience; by exceeding the bistable range and maintaining above the target threshold, it can effectively prevent the ecosystem from reverting to an algal-dominated turbid water state, ensuring the long-term stability of the clear water state and reducing the cost of repeated remediation. Attached Figure Description

[0014] Figure 1 This is a schematic flowchart of a method for assessing the impact of submerged plant restoration on phytoplankton according to an embodiment of this application. Detailed Implementation

[0015] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] Before introducing the embodiments of this application, some technical terms will be explained: Gaussian Mixture Model (GMM): A probabilistic model that assumes all data points are generated by a mixture of several different "Gaussian distributions" (i.e., "normal distributions").

[0017] Probability density distribution: used to describe the likelihood (density) of a continuous random variable at different values.

[0018] Z-score standardization: Converts variables with different units and dimensions (e.g., concentration is mg / L, coverage is %, and the index is dimensionless) into a uniform, comparable standard score; this results in a mean of 0 and a standard deviation of 1, eliminating the influence of dimensions.

[0019] Box-Cox transformation: When data does not meet the normality assumption (judged by skewness, kurtosis, or Shapiro-Wilk test), this transformation is used to make it closer to a normal distribution to meet the requirements of statistical methods.

[0020] The bootstrap method for significance testing is a resampling technique. 999 new samples are randomly drawn with replacement from the original data, and the path coefficients are recalculated each time to obtain the distribution of the path coefficients.

[0021] Coupled Neutral Model (NCM) and Null Model: The existing literature, "Quantifying the roles of immigration and chance in shaping prokaryote community structure" (doi.org / 10.1111 / j.1462-2920.2005.00956.x), discloses specific content regarding the application of the Coupled Neutral Model (NCM). In this prior art, the Coupled Neutral Model (NCM) is based on neutral theory, assuming all species are ecologically equivalent, and that community structure is driven by random birth, death, and immigration processes. It uses the migration rate m (immigration probability) to fit the observed species abundance distribution and uses the coefficient of determination R² to quantify the model's goodness of fit, thereby assessing the extent to which random processes explain community structure. The existing literature, "Quantifying community assembly processes and identifying features that impose them" (doi.org / 10.1038 / ismej.2013.93), discloses specific content regarding the application of a null model of phylogenetic signals. In this prior art, based on the null model, a desired distribution is generated through randomized resampling, and ecological processes are inferred by comparing the deviations between observed and desired values. Specifically, the selection process is detected using the βNTI index (β nearest classifier index) (|βNTI|>2 indicates selection dominance) and the diffusion process is detected using the RCbray index (Raup-Crick index based on Bray-Curtis) (|RCbray|>0.95 indicates diffusion restriction or homogenization diffusion dominance).

[0022] Bray-Curtis distance: This measures the similarity of community structure within an ecosystem. If the species composition of samples is exactly the same, their β-diversity distance is 0; the greater the difference, the larger the distance value.

[0023] RCbray index: The Raup-Crick index is based on the Bray-Curtis distance. The Raup-Crick index is used to determine whether the difference in species composition between two communities is significantly greater than the difference that a random process could produce, through a null model randomization test.

[0024] A method for assessing the impact of submerged plant restoration on phytoplankton according to an embodiment of this application includes the following steps: S1. Conduct periodic monitoring of key indicators for the target lake. Taking a monitoring cycle of four times per month as an example, this should continue for at least four to six months to ensure data coverage of two seasons (e.g., spring / summer or autumn / winter) to capture dynamic changes in the ecosystem. Key monitoring indicators include ammonia nitrogen concentration, total nitrogen concentration, total phosphorus concentration, nitrogen-to-phosphorus ratio (N / P), and phytoplankton community. In some examples, phytoplankton monitoring should focus on recording cyanobacteria abundance and calculating submerged plant cover.

[0025] Among them, plant coverage The calculation is as follows: In the formula, S1 is the total area covered by submerged plants in the quadrat, and S2 is the total area of ​​the quadrat.

[0026] S2. Cluster analysis of phytoplankton community data based on Gaussian Mixture Model (GMM). The phytoplankton community data includes the relative abundance or biomass of major phyla such as cyanobacteria, green algae, and diatoms. Specifically, GMM is used to model the distribution of phytoplankton community data under different submerged plant cover gradients, capturing potential patterns in the data by fitting multiple Gaussian distribution components.

[0027] In this example, the Gaussian Mixture Model (GMM) is used to extract the probability density distribution under each submerged plant cover gradient, transforming discrete ecological observations into continuous probability distribution functions to form key indicators characterizing the system state. The optimal GMM component number is determined based on the Bayesian Information Criterion (BIC). Single-component (K=1) and two-component (K=2) models are established respectively. After parameter estimation using the expectation-maximization algorithm, the model with the smallest BIC value is selected as the optimal model. To quantify the significance of model selection, the ΔBIC index is introduced, which is the difference in BIC values ​​between the single-peak and two-peak models.

[0028] When ΔBIC > 2, the bimodal model is considered significantly superior to the unimodal model, indicating a clear steady-state transition characteristic of the phytoplankton community with changes in cover. In this example, a bimodal coefficient BC can also be calculated to quantify the degree of bimodality. The formula for calculating the bimodal coefficient BC is as follows: Where m3 is skewness, m4 is kurtosis, and n is the number of samples. Skewness reflects the asymmetry of the data distribution, and kurtosis reflects the sharpness of the distribution. Here, skewness m3 and kurtosis m4 are calculated based on the probability distribution fitted by GMM or the distribution of the original phytoplankton community data on the cover gradient, and are used to describe the morphological characteristics of the distribution. The number of samples n is used for standardization calculations.

[0029] In this embodiment of the application, potential energy analysis and critical point identification are performed on the dynamic behavior of phytoplankton community state on the submerged plant coverage gradient, i.e., the probability density distribution function extracted by the Gaussian mixture model. The specific steps include the following: Define potential energy U: Here, P is the empirical probability density between key state variables and environmental conditions. P is a probability density function obtained by fitting a Gaussian Mixture Model (GMM) onto the submerged plant cover gradient, representing the probability of phytoplankton community states (such as the relative abundance of cyanobacteria) occurring under different cover levels. Key state variables refer to quantitative indicators that characterize the overall state of the ecosystem and change regularly with environmental gradients; in this example, they refer to the structural characteristics of the phytoplankton community, such as the relative abundance of cyanobacteria. The empirical probability density refers to the probability density function estimated using statistical methods based on actual observation data; it describes the probability of state variables occurring under different conditions. Specifically, it is the probability density distribution obtained by fitting a Gaussian Mixture Model (GMM) onto the submerged plant cover gradient. This distribution is directly obtained from measured phytoplankton community data and submerged plant cover data through statistical calculations, hence the term "empirical" probability density.

[0030] The scaled potential energy calculation formula is as follows: Here, σ is the noise level, expressed as the standard deviation. σ is usually estimated as the standard deviation of the probability density distribution P, or determined through residual analysis to reflect the random variation in the data.

[0031] Thus, on the potential energy curve U'(x) (where x is the horizontal axis variable), local minima correspond to stable states, and local maxima correspond to unstable states (i.e., critical points). Through potential function reconstruction, a two-dimensional stability landscape map of the phytoplankton community under the submerged plant cover gradient can be generated, with potential energy peaks corresponding to the critical points of state transition. Simultaneously, the potential energy difference ΔU between the critical point and the stable state is calculated to quantitatively characterize the resilience of each stable state. Based on the above analysis, key threshold parameters are derived. For example, a submerged plant cover of 38.48% is identified as the critical point for a steady-state transition in the phytoplankton community; a cover of 30% to 60% represents a bistable range where the system may coexist in both "turbid water" (dominated by cyanobacteria) and "clear water" (dominated by green algae and diatoms); and a cover greater than 60% is the recommended threshold for the system to stably maintain a clear water state.

[0032] S3. Based on the analysis of the ecological mechanisms of community construction, this study uses a coupled neutral model (NCM) and null model framework to preliminarily assess the impact of increased dormant plant cover on lake phytoplankton, in order to evaluate the evolution of phytoplankton community construction mechanisms under submerged plant cover gradients. Specifically, this includes: First, the input data includes a standardized preprocessed phytoplankton species abundance matrix and sample groups divided by submerged plant cover intervals (e.g., 20%, 40%, 60%, 80%, 100%). In the phytoplankton species abundance matrix, each row represents a water sample, each column represents a phytoplankton species, and each value represents the quantity or relative proportion (i.e., abundance) of that species in the sample.

[0033] Based on this, the neutral process fitting of phytoplankton species abundance distribution within each interval was analyzed. First, a neutral community model was fitted for the phytoplankton species abundance data of each ecological state interval. This model is based on the neutral theory framework, and its core parameter mobility m is optimized using the maximum likelihood estimation method to find the optimal parameter value that can best explain the observed species abundance distribution.

[0034] Then, a null model analysis method based on phylogenetic signals is used to analyze the relative contributions of deterministic and stochastic processes. Input data includes a standardized phytoplankton species abundance matrix, sample grouping by coverage interval, and a phylogenetic tree of phytoplankton groups (used to calculate the β-diversity distance containing phylogenetic information).

[0035] Specifically, during the model fitting process, the expectation-maximization algorithm is used to iteratively calculate the probability of species occurrence in the community, and the difference between the observed species abundance and the model-predicted distribution is compared. The goodness of fit of the model is quantified by calculating the coefficient of determination R², which represents the proportion of community structure variation that can be explained by the neutral process.

[0036] R² is calculated using the following formula: R² = 1 - (sum of squared residuals / total sum of squares) When the R² value is close to 1, it indicates that the observed community structure pattern is mainly driven by stochastic processes (diffusion restriction and ecological drift); while when the R² value is low, it means that deterministic processes (environmental selection and competitive exclusion) need to be introduced to explain the community building mechanism. This quantitative analysis provides a statistical basis for understanding the phytoplankton community building mechanism under different submerged plant cover conditions.

[0037] In some cases, as submerged plant cover increases, the phytoplankton community building mechanism gradually shifts from being dominated by stochastic processes to being dominated by deterministic processes, indicating that submerged plants drive community structure evolution by altering the filtration function of the aquatic environment. In other words, when submerged plant cover is low, the R² value of the neutral model is high, and a stochastic process explanation is adopted. As cover increases, the R² value decreases, and the |βNTI| value in the null model analysis becomes greater than 2, indicating that the contribution of deterministic processes increases significantly.

[0038] In other words, based on the neutral theory framework, assuming that species are ecologically equivalent, community structure is driven by random birth, death, and immigration processes. The core parameter, migration rate *m* (immigration probability), is optimized using maximum likelihood estimation to find the optimal parameter value that best explains the observed species abundance distribution. During model fitting, the expectation-maximization algorithm is used to iteratively calculate the probability of species occurrence in the community, comparing the difference between the observed species abundance and the model-predicted distribution. The coefficient of determination (R²) is used to quantify the model fit, representing the proportion of community structure variation that can be explained by neutral processes. R² indicates that the observed community structure patterns are mainly driven by stochastic processes (diffusion restriction and ecological drift); while a low R² value means that deterministic processes (environmental selection, competitive exclusion) need to be introduced to explain the community building mechanism. This quantitative analysis provides statistical evidence for understanding the construction mechanism of phytoplankton communities under different submerged plant cover conditions.

[0039] Furthermore, a null model analysis method based on phylogenetic signals is used to analyze the relative contributions of deterministic and stochastic processes. Input data includes a standardized phytoplankton species abundance matrix, sample groupings across coverage intervals, and a phylogenetic tree of phytoplankton groups (used to calculate the β-diversity distance containing phylogenetic information). The null model generates the expected distribution through randomized resampling (e.g., 999 times) and calculates the βNTI and RCBray indices. βNTI is based on phylogenetic turnover; |βNTI|>2 indicates selection process dominance. RCBray is based on species composition turnover; |RCbray|>0.95 indicates diffusion process dominance (diffusion restriction or homogenized diffusion). By comparing the changes in these indices across different coverage intervals, the evolution of ecological mechanisms is assessed.

[0040] In this example, the number of resampling iterations for the null model is set to 999 to ensure statistical reliability. The significance threshold for the phylogenetic signal is set to |βNTI|>2 to determine whether a deterministic process dominates; the decision threshold for RCBray is set to |value|>0.95 to distinguish different stochastic processes.

[0041] S4. Based on multidimensional stability assessment, the phytoplankton species abundance data are first standardized and preprocessed using the Hellinger transform. The calculation formula is as follows: in, x ij Let be the original abundance of the j-th species in the i-th sample. y ij is the transformed value, and p is the total number of species. A species correlation matrix is ​​constructed based on the Spearman rank correlation coefficient correlation matrix to perform co-occurrence network analysis.

[0042] For example, for any two species abundance sequences across all samples, they are first converted to rank sequences, and then the Pearson correlation coefficient between these two rank sequences is calculated. (Spearman correlation coefficient) The calculation formula is: in, d i The rank difference between each pair of observations is represented by , where n is the number of samples. When constructing the correlation matrix, a significance level of p < 0.05 is set as the statistical significance threshold, and a correlation strength threshold of |r| > 0.6 is set as the standard for ecologically meaningful correlation. Only species pairs that simultaneously meet both conditions are retained for constructing the weighted undirected network. Nodes are defined as each phytoplankton species or operational taxonomic unit. Node weights are determined by calculating the average relative abundance of that species across all samples. The average relative abundance is calculated as the average of the abundance of each species divided by the total abundance across all samples. Edge weights are taken as the absolute value of the correlation coefficient to reflect the strength of the interaction; positively correlated edges may indicate mutualistic symbiosis or niche overlap between species, while negatively correlated edges may reflect competitive exclusion or niche differentiation.

[0043] Based on the network construction of the model, the system analyzes the network's topological characteristics, including modularity (reflecting the subgroup structure within the network) and connectivity (reflecting the strength of connections between nodes). Modularity is typically calculated using a modularity index (such as Newman modularity), while connectivity is quantified using average degree or density. Furthermore, the ecological stability of the network is quantified from three dimensions: robustness, calculated by simulating random or targeted attacks on nodes to determine the proportion of nodes that need to be removed to reduce network connectivity to 50%; vulnerability, assessed by evaluating the change in average path length or connected components after removing highly central nodes; and durability, evaluated by assessing the network structure's ability to withstand disturbances through network phantom analysis or dynamic simulation. For example, robustness can be calculated by the change in network efficiency after randomly removing nodes; vulnerability is assessed based on node centrality (such as degree centrality); and durability can be quantified by simulating the retention rate of the network structure under disturbances.

[0044] The structural feature detection methods described above, and the three dimensions of ecological stability quantification networks, can all be implemented using any existing quantification method. For example, the detected co-occurrence networks in clear water (coverage > 60%) exhibit higher modularity, robustness, durability, and lower vulnerability, indicating that submerged plant restoration can promote the formation of more complex and stable phytoplankton communities. Therefore, a three-dimensional quantitative network model can be constructed to quantitatively reveal changes in phytoplankton degradation structure during submerged plant restoration, thereby assessing the impact of changes in external environmental factors on lake restoration capacity.

[0045] In step S5, ecological causal path verification is performed based on multi-source data integration. By constructing a partial least squares path model (PLS-PM) to integrate the aforementioned analysis results, the causal path of "submerged plant coverage → aquatic environmental conditions → phytoplankton community characteristics → network stability" is systematically verified.

[0046] Specifically, the data preprocessing was first performed on indicators such as coverage, water quality parameters, phytoplankton diversity index, network complexity, and stability. This included outlier handling, Z-score standardization (making the data mean 0 and the standard deviation 1), and Box-Cox transformation (when the absolute value of the skewness of the variable is >1 and the absolute value of the kurtosis is >3.5, or after Shapiro-Wilk test (normality test)). p When the value is <0.05, a Box-Cox transformation is required to improve normality. The Box-Cox transformation optimizes the parameter λ to make the data closer to a normal distribution; λ is usually determined by maximum likelihood estimation. Based on this, a structural equation model reflecting ecological theory is established, defining latent variables (such as "water environment conditions" and "community stability"). These latent variables are defined by weighted combinations of multiple observed variables (such as water quality parameters or network indicators). The model quality is comprehensively evaluated by calculating indicators such as goodness of fit, average redundancy, and average variance extraction rate. The significance of path relationships is tested using the Bootstrap method (999 resamplings). After iterative optimization, the causal relationship network among various ecological elements is determined, and the direct and indirect effects of key factors such as submerged plant coverage on network stability are quantified, providing a quantitative basis for determining the optimal recovery threshold for submerged plants.

[0047] Therefore, the method of this application embodiment actively guides the phytoplankton community to transform from a turbid water steady state dominated by cyanobacteria to a clear water steady state dominated by green algae / diatoms by monitoring and regulating the coverage of submerged plants to a specific threshold range. Furthermore, by enhancing the deterministic process of community assembly and network complexity, it ultimately achieves a comprehensive improvement in the stability of the lake ecosystem.

[0048] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for assessing the impact of submerged plant restoration on phytoplankton, comprising the following steps: Acquire monitoring data of the target lake, the monitoring data including ammonia nitrogen concentration, total nitrogen concentration, total phosphorus concentration, nitrogen-to-phosphorus ratio, and phytoplankton community, characterized in that it further includes: Based on phytoplankton community data, the critical point and threshold range of submerged plant coverage are identified. Specifically, cluster analysis is performed on the phytoplankton community data. The cluster analysis uses a Gaussian mixture model to model the phytoplankton community data to identify the bimodal distribution pattern of the phytoplankton community as the submerged plant coverage changes. Then, potential energy analysis is performed to obtain the critical point and steady-state resilience, and a stability landscape map is generated. To assess the relative contributions of stochastic and deterministic processes in the phytoplankton community building mechanism to explain community building.

2. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 1, characterized in that, The Gaussian mixture model uses the Bayesian information criterion for model selection, establishing single-component and two-component models respectively, and employing the expectation-maximization algorithm for parameter estimation, selecting the model with the smallest BIC value as the optimal model; wherein, when the difference ΔBIC between the single-peaked model and the two-peaked model is greater than 2, the two-peaked model is determined to be superior to the single-peaked model.

3. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 1, characterized in that, The potential energy analysis includes: Calculate the potential energy function: Where P is the empirical probability density function between the key state variables obtained by fitting a Gaussian mixture model and the submerged plant coverage; Scaling the potential energy function yields the scaled potential energy: Where σ is the standard deviation of the noise level; Local minima on the potential energy curve correspond to the stable state of the ecosystem, while local maxima correspond to the critical point.

4. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 1, characterized in that: The neutral model was used to fit the species abundance distribution, the migration rate parameter m was optimized iteratively, and the goodness-of-fit R² value was used to quantify the proportion of the neutral process that explains the community structure. Phylogenetic signal analysis is performed using a null model. By calculating the nearest taxonomic unit index and the matrix index, and combining them with preset thresholds, the dominance of deterministic and stochastic processes is determined.

5. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 1, characterized in that, The method also includes: constructing a species correlation matrix using Spearman rank correlation coefficients and performing co-occurrence network analysis; constructing a phytoplankton species co-occurrence network through co-occurrence network analysis and evaluating the network's topology and stability; Then, by integrating the monitoring data, cluster analysis results, potential energy analysis results, and co-occurrence network analysis results, the causal path of submerged plant coverage on phytoplankton community stability was verified.

6. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 5, characterized in that, The process of constructing a species correlation matrix using Spearman's rank correlation coefficient and conducting co-occurrence network analysis includes: A significance level of p < 0.05 and a correlation strength threshold of |r| > 0.6 were set as criteria for constructing effective connections; A weighted undirected network is constructed based on effective connections, where nodes represent phytoplankton species, node weights are the average relative abundance of species, and edge weights are the absolute values ​​of the correlation coefficients between species.

7. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 5, characterized in that: The input data is preprocessed, including outlier handling, Z-score standardization, and Box-Cox transformation when the data does not meet the normal distribution assumption. A structural equation model was established, which defined a multi-level influence path of submerged plant cover on aquatic environmental conditions, aquatic environmental conditions on phytoplankton community characteristics, and phytoplankton community characteristics on network stability. The Bootstrap method was used for multiple resampling to test the significance of the path coefficients in the multi-level influence path.

8. The method for assessing the impact of submerged plant restoration on phytoplankton according to claim 1, characterized in that, This also includes preprocessing of phytoplankton species abundance data, including Hellinger transform, where the Hellinger transform formula is: in, x ij Let be the original abundance of the j-th species in the i-th sample. y ij is the transformed value, and p is the total number of species.

Images