Method and system for predicting secondary productivity under toxin stress, terminal and medium

Abstract

The invention discloses a method and system for predicting secondary productivity under toxin stress, a terminal and a medium, and the method comprises the steps: inputting the ecological data of a zooplankter population into a pre-constructed optimized Logistic population growth model, and obtaining an optimized population number, the secondary productivity of the zooplankton under the specified toxin concentration condition is calculated in combination with individual biomass data and is used for reflecting the biomass accumulation level change of the zooplankton population under the toxin stress condition; the construction of the optimized Logistic population growth model comprises the following steps: constructing a preliminary Logistic population growth model based on the preprocessed zooplankton population ecological data, wherein the output result of the Logistic population growth model is the predicted population number; and optimizing parameters of the Logistic population growth model by adopting a neural network, and converging an error between a predicted population number and an actual population number of the Logistic population growth model to be below a preset threshold value through iterative training to obtain an optimized Logistic population growth model. The invention provides a more reliable secondary productivity prediction means.

Description

Technical Field

[0001] The invention relates to a method, system, terminal and medium for predicting secondary productivity under toxin stress, and belongs to the field of environmental science. Background Art

[0002] Zooplankton are important primary consumers in aquatic ecosystems, and their population dynamics and productivity changes directly influence the structure of the aquatic food web and ecological balance. Secondary productivity, a key indicator of the energy conversion efficiency of zooplankton populations, is widely used in studies of aquatic ecosystem health, fishery resource management, and water environmental change. In aquatic ecosystems, environmental factors such as temperature, dissolved oxygen, and nutrient concentrations, as well as exogenous pollutants such as heavy metals, organic pollutants, and marine toxins, can affect the growth, reproduction, and survival of zooplankton populations to varying degrees. Toxins produced by red tide organisms, in particular, can significantly stress zooplankton populations when accumulated in high concentrations, even leading to colony collapse and, consequently, compromising the stability of the entire aquatic ecosystem. Therefore, studying the population dynamics and secondary productivity changes of zooplankton under varying environmental pressures is crucial for understanding the response mechanisms of aquatic ecosystems.

[0003] Currently, research on zooplankton population dynamics primarily relies on a combination of experimental monitoring and mathematical modeling. Traditional ecotoxicology experiments typically measure zooplankton growth, reproduction, and survival rates through indoor simulations, and use mathematical models to predict population trends. However, due to the complexity of environmental variables and the nonlinear nature of zooplankton population responses to external pressures, traditional models have limitations in describing zooplankton population dynamics. During data processing, outliers, missing values, and scale differences between variables can also affect model accuracy. Therefore, improving data processing accuracy and optimizing population prediction models to predict zooplankton population dynamics and changes in secondary productivity are important areas of current ecological research. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies in the prior art and provide a method, system, terminal and medium for predicting secondary productivity under toxin stress, which solves the adaptability defects of the existing static model in toxin stress prediction and realizes dynamic and accurate secondary productivity prediction.

[0005] To achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0006] In a first aspect, the present invention provides a method for predicting secondary productivity under toxin stress, comprising:

[0007] The zooplankton population ecological data were input into the pre-built optimized logistic population growth model to obtain the optimized population size. The secondary productivity of zooplankton under the specified toxin concentration conditions was calculated by combining the individual biomass data.

[0008] The construction of the optimized Logistic population growth model includes:

[0009] Collect and pre-process zooplankton population ecological data;

[0010] A preliminary logistic population growth model was constructed based on the pre-processed zooplankton population ecological data. The output of the logistic population growth model was the predicted population size.

[0011] A neural network is used to optimize the parameters of the Logistic population growth model. Through iterative training, the error between the population size predicted by the Logistic population growth model and the actual population size converges to below a preset threshold, thereby obtaining an optimized Logistic population growth model.

[0012] Furthermore, the population growth equation of the Logistic population growth model is as follows:

[0013] ;

[0014] Where: represents the intrinsic growth rate of the population, represents the environmental carrying capacity, Indicates time, represents the zooplankton population;

[0015] As the concentration of toxins increases, the environmental carrying capacity The dynamic change equation is shown as follows:

[0016] ;

[0017] Where: Indicates the time when the toxin begins to take effect. Indicates the rate of toxin accumulation, Indicates the maximum population size in the absence of toxins.

[0018] Furthermore, a neural network is used to optimize the parameters of the Logistic population growth model, and the error between the prediction result of the Logistic population growth model and the actual observation data is converged to below a preset threshold through iterative training, including:

[0019] The ecological data of zooplankton populations under specified toxin concentrations are used as training samples to train a neural network model. The input layer of the neural network includes a time variable t, which is used to represent the ecological process evolution stage of the zooplankton population under toxin stress. The output layer is the model parameter vector of the Logistic population growth model. θ = [r , b, α , t 0 , N 0 ] ;

[0020] Where: represents the initial population size;

[0021] Calculate the output model parameter vector through linear transformation :

[0022] ;

[0023] Where: represents the weight matrix, b represents the bias vector;

[0024] The mean square error (MSE) is used as the loss function L to measure the error between the predicted value and the true value:

[0025] ;

[0026] Where: m represents the number of time points, represents the actual population size, represents the population size predicted by the model, Indicates a point in time;

[0027] Iteratively update network parameters through gradient descent , including calculating the gradient of the loss function L with respect to the weight W according to the following formula:

[0028] ;

[0029] Where: Represents the loss function L for the model's predicted output The partial derivative of Represents the predicted output Parameters The partial derivative of Represents a vector Partial derivative with respect to weight W;

[0030] According to the set learning rate Update network parameters:

[0031] ;

[0032] Where: represents the updated weight, Represents the weight before gradient update;

[0033] By repeatedly performing the loss function calculation and gradient update process, the optimization process continues to iterate until the loss value L drops below the preset threshold. The optimized parameter vector Using the Logistic population growth model to predict zooplankton population size , and serves as input for secondary productivity calculations.

[0034] Furthermore, the calculation obtains the secondary productivity of zooplankton under the conditions of specified toxin concentration, and the formula is:

[0035] ;

[0036] ;

[0037] ;

[0038] Where: represents the individual growth rate, Indicates the individual growth rate when there is no toxin influence, represents the individual biomass corresponding to the population size, Represents the individual biomass increment.

[0039] Furthermore, the data preprocessing includes:

[0040] Statistical methods are used to identify and remove outliers from the collected zooplankton ecological data, including the number of zooplankton populations. , individual biomass , YTXs toxin concentrations and environmental variables affecting ecological processes;

[0041] Interpolation algorithms were used to complete missing items in the ecological data after outlier processing, including linear interpolation of missing zooplankton populations, environmental variables affecting ecological processes, and toxin concentration data at different time points to restore data integrity.

[0042] The completed ecological data are normalized and uniformly mapped to the interval [0,1] to eliminate the influence of different variable dimensions on modeling accuracy;

[0043] The normalized data is organized into a standardized input format, with unified time steps and feature arrangement order to meet the data input requirements of the Logistic population growth model and the neural network optimization module.

[0044] In a second aspect, the present invention provides a prediction system for secondary productivity under toxin stress, characterized by comprising:

[0045] Data collection unit, which collects ecological data of zooplankton populations and performs preprocessing;

[0046] The calculation unit constructs a preliminary logistic population growth model based on the preprocessed zooplankton population ecological data, and calculates the zooplankton population size using the logistic population growth model;

[0047] an optimization unit, which optimizes the parameters of the Logistic population growth model using a neural network, and makes the error between the prediction result of the Logistic population growth model and the actual observation data converge to below a preset threshold through iterative training, thereby obtaining an optimized Logistic population growth model;

[0048] The prediction unit inputs the ecological data of zooplankton population into the optimized Logistic population growth model to obtain the optimized population size. Combined with the individual biomass data, the secondary productivity of zooplankton under specified toxin concentration conditions is calculated to reflect the changes in the biomass accumulation level of zooplankton populations under toxin stress conditions.

[0049] In a third aspect, the present invention provides an electronic terminal comprising a processor and a memory connected to the processor, wherein a computer program is stored in the memory. When the computer program is executed by the processor, the steps of the method for predicting secondary productivity under toxin stress as described in any one of claims 1 to 5 are executed.

[0050] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for predicting secondary productivity under toxin stress as described in any one of claims 1 to 5.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] The present invention analyzes the population dynamics of zooplankton and further quantifies the impact of YTXs toxins on secondary productivity, thereby improving the accuracy of zooplankton population dynamics prediction and providing a more reliable means of secondary productivity prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A flow chart of a method for predicting secondary productivity under toxin stress provided in Example 1 of the present invention;

[0054] Figure 2 A diagram showing the predicted effect of secondary productivity provided by the first embodiment of the present invention;

[0055] Figure 3 This is a diagram showing the predicted zooplankton population growth rate provided in Example 1 of the present invention;

[0056] Figure 4 This is a diagram showing the prediction effect of zooplankton reproduction rate provided in Example 1 of the present invention; DETAILED DESCRIPTION

[0057] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations on the technical solution of the present application. Unless there is a conflict, the embodiments of the present application and the technical features in the embodiments can be combined with each other.

[0058] The terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the technical features being referred to. Thus, a feature designated "first," "second," etc., may explicitly or implicitly include one or more of such features. Throughout this disclosure / application, unless otherwise specified, "plurality" means two or more.

[0059] Example 1:

[0060] Figure 1 This is a flow chart of a method for predicting secondary productivity under toxin stress in the first embodiment of the present invention. This flow chart only shows the logical sequence of the method described in this embodiment. Under the premise of no conflict, in other possible embodiments of the present invention, different methods can be used. Figure 1 The steps shown or described are accomplished in the order shown.

[0061] This example is applied to a fishery in the Yellow Sea and Bohai Sea. In this ecosystem, the keystone rotifer, Ankylosaurus plicatilis, is the primary feed for commercial fish species, and the dominant zooplankton species in the fishery is Daphnia japonica. Together, these two zooplankton species constitute a significant component of the fishery's secondary productivity, playing a key role in the early growth of commercial fish and energy transfer in the ecosystem.

[0062] First, an experimental environment was constructed to simulate a marine ecosystem under YTXs stress. The algae samples used in this example included Chlorella vulgaris and Protoceratops reticulateum (YTXs-producing), and the zooplankton were Daphnia japonica and Brachionus plicatilis. The experimental seawater was artificially prepared and sterilized. Protoceratops reticulateum, Chlorella vulgaris, Isochrysis galbana, and Platymonas were cultured in f / 2 medium. Daphnia japonica and Brachionus plicatilis were cultured in sterile seawater (salinity: 25‰, DO > 6 mg / L). Daphnia japonica were fed with Chlorella vulgaris, Protoceratops reticulateum, Isochrysis galbana, and Platymonas every 12 hours at a 1:1:1:1 ratio by volume, with a concentration of 3 × 10⁵ cells / mL for each of the four algae solutions. The rotifers were fed with 3 × 10⁵ cells / mL of Chlorella vulgaris every 12 hours. Algae and zooplankton were cultured in a constant temperature and illumination incubator at (25 ± 1) ℃ with a light intensity of 4,500 lx and a photoperiod of 12 L:12 D.

[0063] The experimental groups were fed Brachionus plicatilis and Daphnia japonica with single and mixed solutions of Protoceratops reticulate TIO863 (homo-YTX-producing) and TIO520 (YTX-producing), respectively. Brachionus plicatilis and Daphnia japonica served as controls, fed with Chlorella vulgaris. The algae solution volume for each experimental group was 2 mL. The experimental and control group settings are shown in Table 1. Raw zooplankton data from the simulated environment were also recorded and stored.

[0064] Table 1 Settings of experimental and control groups

[0065]

[0066] like Figure 1 As shown in Figure 2, collecting ecological data of zooplankton populations and preprocessing them include:

[0067] Use a microscopic imaging system to record data on individual zooplankton morphology and behavior;

[0068] In a simulated water environment, representative zooplankton populations (e.g., copepods and cladocerans) were selected and their dry weights determined using the filtration method. Samples were collected using a plankton net (50-200 μm mesh) and rinsed with 0.22 μm-filtered artificial seawater or distilled water to remove adhering impurities and particulate matter. Samples were filtered through a glass fiber filter (GF / C, 1.2 μm pore size), ensuring that the filter membrane was pretreated to a constant weight (drying at 60-80°C for 2 hours).

[0069] During filtration, a certain volume of zooplankton suspension is passed through the filter membrane using a vacuum filtration device to ensure that the sample is evenly distributed on the filter membrane surface.

[0070] Place the filtered membrane in an oven and dry it at 60-80℃ for 6-24 hours until constant weight is reached, i.e. the difference between two weighings is less than 0.1 mg. Then use an electronic balance with an accuracy of 0.1 mg to weigh the membrane. The formula for calculating the dry weight of zooplankton is as follows:

[0071] ;

[0072] Where: represents the dry weight of zooplankton, It represents the total mass of the filter membrane and sample after drying. Indicates the blank mass of the filter membrane;

[0073] ;

[0074] Where: represents individual biomass, and N represents the total number of zooplankton individuals after counting;

[0075] Statistical methods are used to identify and remove outliers from the collected zooplankton ecological data, including the number of zooplankton populations. , individual biomass , YTXs toxin concentrations and environmental variables affecting ecological processes;

[0076] An interpolation algorithm was used to complete missing items in the ecological data after outlier processing. This included linear interpolation of missing zooplankton populations, environmental variables affecting ecological processes, and toxin concentrations at different time points to restore data integrity. The completed ecological data were normalized and uniformly mapped to the [0,1] interval to eliminate the impact of different variable dimensions on modeling accuracy. The normalized data were organized into a standardized input format with a unified time step and feature order to meet the data input requirements of the logistic population growth model and the neural network optimization module.

[0077] During the experiment, sterile seawater was replaced every 12 hours, and the experimental and control groups were fed with algae solution. Zooplankton were systematically sampled every 12 hours every 24 hours to ensure data integrity and temporal consistency. The algae solution concentration in each treatment group was 3×10⁵ cells / mL. Six replicates were performed in both the experimental and control groups, and the experimental period was 156 hours. Because zooplankton completely died after the experimental period exceeded 96 hours, population reproduction and growth rates in this experiment were calculated within 96 hours.

[0078] A preliminary Logistic population growth model was constructed based on the pre-processed zooplankton population ecological data. The output of the Logistic population growth model was the predicted population size. The population growth equation of the Logistic population growth model is shown as follows:

[0079] ;

[0080] Where: represents the intrinsic growth rate of the population, represents the environmental carrying capacity, Indicates time, represents the zooplankton population;

[0081] As the concentration of toxins increases, the environmental carrying capacity The dynamic change equation is shown as follows:

[0082] ;

[0083] Where: Indicates the time when the toxin begins to take effect. Indicates the rate of toxin accumulation, Indicates the maximum population size in the absence of toxins.

[0084] The raw data collected during the experiment were input into a logistic model. A neural network was used to optimize the parameters of the logistic population growth model. Through iterative training, the error between the predicted population size and the actual population size was converged to below a preset threshold, resulting in an optimized logistic population growth model. A neural network method was used to perform a nonlinear fit of population growth under YTXs toxin stress. During the training process, a loss function was set to minimize the error between the predicted value and the experimental data. A gradient descent algorithm was used to optimize the model parameters to improve prediction accuracy. Cross-validation was then performed to prevent overfitting.

[0085] The ecological data of zooplankton populations under specified toxin concentrations are used as training samples to train a neural network model. The input layer of the neural network includes a time variable t, which is used to represent the ecological process evolution stage of the zooplankton population under toxin stress. The output layer is the model parameter vector of the Logistic population growth model. θ = [r , b, α , t 0 , N 0 ] ;

[0086] Where: represents the initial population size;

[0087] Calculate the output model parameter vector through linear transformation :

[0088] ;

[0089] Where: represents the weight matrix, b represents the bias vector;

[0090] The mean square error (MSE) is used as the loss function L to measure the error between the predicted value and the true value:

[0091] ;

[0092] Where: m represents the number of time points, represents the actual population size, represents the population size predicted by the model, Indicates a point in time;

[0093] Iteratively update network parameters through gradient descent , including calculating the gradient of the loss function L with respect to the weight W:

[0094] ;

[0095] Where: Represents the loss function L for the model's predicted output The partial derivative of Represents the predicted output Parameters The partial derivative of Represents a vector Weight The partial derivative of

[0096] According to the set learning rate Update network parameters:

[0097] ;

[0098] Where: represents the updated weight, Represents the weight before gradient update;

[0099] By repeatedly performing the loss function calculation and gradient update process, the optimization process continues to iterate until the loss value L drops below the preset threshold. The optimized parameter vector Used to predict zooplankton populations , and used as the input for the calculation of secondary productivity, we finally obtained a mathematical model that can accurately describe the changes in zooplankton populations under YTXs toxin stress. The specific parameters are retained to two decimal places, as shown in Table 2.

[0100] Table 2 Parameters of zooplankton population prediction model under different groups

[0101]

[0102] The calculation yields the secondary productivity of zooplankton under specified toxin concentration conditions using the formula:

[0103] ;

[0104] ;

[0105] ;

[0106] Where: represents the individual growth rate, Indicates the individual growth rate when there is no toxin influence, represents the individual biomass corresponding to the population size, represents the individual biomass increment;

[0107] from Figure 3 and Figure 4 In the analysis, under the stress of YTXs toxins, the growth rate and reproduction rate of zooplankton population showed a clear downward trend. Figure 3 As shown in the figure, the population growth rate decreases significantly after 40 hours over time, and the fitting curve can accurately capture this change; Figure 4 The reproductive rate showed obvious fluctuations and declines, especially between 20 and 40 hours. The stress of toxins caused the reproductive capacity to be greatly suppressed. Although the fitting curve could capture the overall trend, it was not accurate enough in some periods with large fluctuations.

[0108] Based on these results, the optimal time for treatment is between 20 and 40 hours, especially when reproduction rates are close to zero. Treatment methods include reducing toxin concentrations in the water through clay adsorption, optimizing water quality, and introducing nutrient supplements or other zooplankton populations to promote recovery.

[0109] like Figure 2As shown in the figure, the secondary productivity of zooplankton in the toxin environment gradually decreased over time, and by about 80 hours, it had almost dropped to zero. This shows that toxin stress has a significant inhibitory effect on the energy accumulation and conversion of zooplankton. The fitting curve is smooth and has a small error with the actual data, indicating that the model has a high accuracy in predicting secondary productivity and can well capture the process of secondary productivity decline. Based on the range of changes in secondary productivity, corresponding analytical indicators can be further developed to quantify the impact of red tide toxins YTXs on marine secondary productivity, as shown in Table 3 below:

[0110] Table 3 Secondary productivity prediction criteria

[0111]

[0112] This demonstrates that the model accurately simulates the decline in zooplankton population growth, reproductive capacity, and secondary productivity under YTXs stress. The model's fitting curve closely matches the real data, particularly in the prediction of secondary productivity.

[0113] Example 2:

[0114] The embodiment of the present invention further provides a system for predicting secondary productivity under toxin stress, comprising:

[0115] Data collection unit, which collects ecological data of zooplankton populations and performs preprocessing;

[0116] The calculation unit constructs a preliminary logistic population growth model based on the preprocessed zooplankton population ecological data, and calculates the zooplankton population size using the logistic population growth model;

[0117] an optimization unit, which optimizes the parameters of the Logistic population growth model using a neural network, and makes the error between the prediction result of the Logistic population growth model and the actual observation data converge to below a preset threshold through iterative training, thereby obtaining an optimized Logistic population growth model;

[0118] The prediction unit inputs the ecological data of zooplankton population into the optimized Logistic population growth model to obtain the optimized population size. Combined with the individual biomass data, the secondary productivity of zooplankton under specified toxin concentration conditions is calculated to reflect the changes in the biomass accumulation level of zooplankton populations under toxin stress conditions.

[0119] Example 3:

[0120] An embodiment of the present invention also provides an electronic terminal, characterized in that it includes a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the method for predicting secondary productivity under toxin stress described in the above embodiment 1 are executed.

[0121] Example 4:

[0122] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the program first implements the steps of the method for predicting secondary productivity under toxin stress described in the first embodiment above.

[0123] The computer-readable storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0124] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0125] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0126] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1The function specified in one or more boxes.

[0127] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0128] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for predicting secondary productivity under toxin stress, characterized in that: include: The zooplankton population ecological data were input into the pre-built optimized logistic population growth model to obtain the optimized population size. The secondary productivity of zooplankton under the specified toxin concentration conditions was calculated by combining the individual biomass data. The construction of the optimized Logistic population growth model includes: Collect and pre-process zooplankton population ecological data; A preliminary logistic population growth model was constructed based on the pre-processed zooplankton population ecological data. The output of the logistic population growth model was the predicted population size. A neural network is used to optimize the parameters of the Logistic population growth model. Through iterative training, the error between the population size predicted by the Logistic population growth model and the actual population size converges to below a preset threshold, thereby obtaining an optimized Logistic population growth model.

2. The method for predicting secondary productivity under toxin stress according to claim 1, characterized in that: The population growth equation of the Logistic population growth model is as follows: ； Where: represents the population growth rate, represents the environmental carrying capacity, Indicates time, represents the zooplankton population; As the concentration of toxins increases, the environmental carrying capacity The dynamic change equation is shown as follows: ； Where: Indicates the time when the toxin begins to take effect. Indicates the rate of toxin accumulation, Indicates the maximum population size in the absence of toxins.

3. The method for predicting secondary productivity under toxin stress according to claim 2, characterized in that: A neural network is used to optimize the parameters of the Logistic population growth model, and the error between the prediction results of the Logistic population growth model and the actual observation data is converged to below a preset threshold through iterative training, including: The ecological data of zooplankton populations under specified toxin concentrations are used as training samples to train a neural network model. The input layer of the neural network includes a time variable t, which is used to represent the ecological process evolution stage of the zooplankton population under toxin stress. The output layer is the model parameter vector of the Logistic population growth model. ; Where: represents the initial population size; Calculate the output model parameter vector through linear transformation : ； Where: represents the weight matrix, b represents the bias vector; The mean square error (MSE) is used as the loss function L to measure the error between the predicted value and the true value: ； Where: m represents the number of time points, represents the actual population size, represents the population size predicted by the model, Indicates a point in time; Iteratively update network parameters through gradient descent , including calculating the gradient of the loss function L with respect to the weight W according to the following formula: ； Where: Represents the loss function L for the model's predicted output The partial derivative of Represents the predicted output Parameters The partial derivative of Represents a vector Weight The partial derivative of According to the set learning rate Update network parameters: ； Where: represents the updated weight, Represents the weight before gradient update; By repeatedly performing the loss function calculation and gradient update process, the optimization process continues to iterate until the loss value L drops below the preset threshold. The optimized parameter vector Using the Logistic population growth model to predict zooplankton population size , and serves as input for secondary productivity calculations.

4. The method for predicting secondary productivity under toxin stress according to claim 3, characterized in that: The calculation yields the secondary productivity of zooplankton under specified toxin concentration conditions using the formula: ； ； ； Where: represents the individual growth rate, Indicates the individual growth rate when there is no toxin influence, represents the individual biomass corresponding to the population size, Represents the individual biomass increment.

5. The method for predicting secondary productivity under toxin stress according to claim 1, wherein the data preprocessing comprises: Statistical methods are used to identify and remove outliers from the collected zooplankton ecological data, including the number of zooplankton populations. , individual biomass , YTXs toxin concentrations and environmental variables affecting ecological processes; Interpolation algorithms were used to complete missing items in the ecological data after outlier processing, including linear interpolation of missing zooplankton populations, environmental variables affecting ecological processes, and toxin concentration data at different time points to restore data integrity. The completed ecological data are normalized and uniformly mapped to the interval [0,1] to eliminate the influence of different variable dimensions on modeling accuracy; The normalized data is organized into a standardized input format, with unified time steps and feature arrangement order to meet the data input requirements of the Logistic population growth model and the neural network optimization module.

6. A prediction system for secondary productivity under toxin stress, characterized in that: include: Data collection unit, which collects ecological data of zooplankton populations and performs preprocessing; The calculation unit constructs a preliminary Logistic population growth model based on the pre-processed zooplankton population ecological data, and calculates the zooplankton population size using the Logistic population growth model; an optimization unit, which optimizes the parameters of the Logistic population growth model using a neural network, and makes the error between the prediction result of the Logistic population growth model and the actual observation data converge to below a preset threshold through iterative training, thereby obtaining an optimized Logistic population growth model; The prediction unit inputs the ecological data of zooplankton population into the optimized Logistic population growth model to obtain the optimized population size. Combined with the individual biomass data, the secondary productivity of zooplankton under specified toxin concentration conditions is calculated to reflect the changes in the biomass accumulation level of zooplankton populations under toxin stress conditions.

7. An electronic terminal, characterized in that: The method comprises a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the method for predicting secondary productivity under toxin stress according to any one of claims 1 to 5 are executed.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for predicting secondary productivity under toxin stress according to any one of claims 1 to 5 are realized.

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