A method for regulating and simulating a population ecosystem

Abstract

The application provides a population ecosystem regulation simulation method, wherein historical data of a population ecosystem are acquired, an initial spatial population model is constructed based on the historical data; Sobol indexes of variables in the initial spatial population model are calculated, and key regulation variables are screened from the initial spatial population model based on the Sobol indexes of the variables; observation data of the population ecosystem are acquired, and the key regulation variables are dynamically adjusted based on the observation data to obtain a target spatial population model, so that simulation of the population ecosystem is realized. The above method is used to realize accurate regulation and simulation of the population ecosystem and improve the accuracy of population ecosystem regulation simulation.

Description

Technical Field

[0001] This invention relates to the field of data-driven ecological regulation, and more specifically, to a method for simulating the regulation of a population ecosystem. Background Technology

[0002] Simulation of population ecosystem regulation involves constructing mathematical models to quantify inter-population interactions (such as predator-prey relationships), spatial density distribution, and dynamic evolution. The core function of population ecosystem simulation is to provide quantitative decision-making support for ecological conservation and species management. Therefore, population ecosystem simulation is an indispensable component of ecological environment protection and management.

[0003] Existing population-ecosystem regulation simulation techniques are typically based on static parametric models (such as the classic Lotka-Volterra equation) and a single data source (such as population density statistics). However, research has revealed that static parametric models cannot respond in real time to dynamic factors such as fluctuations in environmental resources and changes in the intensity of interspecies interactions. For example, they cannot quantify the inhibitory effect of prey refuges formed by habitat concealment on predation efficiency, or the decrease in predation success rate caused by prey group defensive behavior. This leads to long-term model predictions deviating from actual ecological trajectories due to parameter fixation, thus failing to accurately simulate population-ecosystem regulation and reducing the accuracy of population-ecosystem regulation simulations. Furthermore, the limitations of a single data source prevent models from integrating multi-dimensional observational information, relying solely on population density statistics, resulting in a single input dimension and further reducing the accuracy of population-ecosystem regulation simulations. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for regulating and simulating population ecosystems, so as to achieve accurate regulation and simulation of population ecosystems and improve the accuracy of population ecosystem regulation and simulation.

[0005] This application provides a method for simulating the regulation of a population ecosystem, the method comprising:

[0006] Acquire historical data on the population ecosystem and construct an initial spatial population model based on the historical data;

[0007] Calculate the Sobol index of each variable in the initial spatial population model, and select key regulatory variables from the initial spatial population model based on the Sobol index of each variable;

[0008] Observational data of the population ecosystem are obtained, and the key regulatory variables are dynamically adjusted based on the observational data to obtain a target spatial population model, thereby simulating the population ecosystem.

[0009] Optionally, the historical data includes the spatial density distribution of prey / predators and the population density of prey / predators. The construction of an initial spatial population model based on the historical data includes:

[0010] Based on the historical data, the initial prey spatial density distribution equation and the initial predator spatial density distribution equation are constructed respectively.

[0011] The spatial density distribution equation of the target prey is determined based on the prey's half-saturation coefficient and the initial prey spatial density distribution equation.

[0012] The target predator spatial density distribution equation is determined based on the prey's anti-predator rate and the initial predator spatial density distribution equation.

[0013] The initial spatial population model is constructed based on the spatial density distribution equation of the target prey and the spatial density distribution equation of the target predator.

[0014] Optionally, calculating the Sobol index of each variable in the initial spatial population model includes:

[0015] Define an output target, where the output target is system stability or outbreak risk;

[0016] The total variance of the initial spatial population model is determined based on the output target;

[0017] The total variance is decomposed to obtain the Sobol index of each variable, where the Sobol index of each variable represents the independent contribution of that variable to the output target.

[0018] Optionally, the Sobol index based on each variable selects key regulatory variables from the initial spatial population model, including:

[0019] Several preferred control variables were selected based on the Sobol index of each variable;

[0020] The total Sobol effect index is determined based on the Sobol index of each preferred control variable;

[0021] When the total Sobol effect index meets the preset threshold, each preferred control variable is determined as a key control variable.

[0022] Optionally, the step of dynamically adjusting the key control parameters based on the observation data to obtain the target spatial population model includes:

[0023] Construct a parameter set based on each key regulatory variable;

[0024] Based on the parameter set, the predicted values ​​of prey and predator density distributions are obtained by solving the initial spatial population model;

[0025] The matching probability between the observed data and the predicted value is calculated using an error model to form a local likelihood function;

[0026] The parameter set is updated based on the local likelihood function and the Hamiltonian Monte Carlo (HMC) sampling method.

[0027] The key control parameters are adjusted based on the updated parameter set and the dynamic adjustment target.

[0028] Optionally, the method further includes:

[0029] After each acquisition of observational data on the population ecosystem, a step is performed to dynamically adjust the key regulatory variables based on the observational data to obtain a target spatial population model.

[0030] The target spatial population model obtained from this dynamic adjustment was used to simulate the ecosystem of the population, and the simulation results were obtained.

[0031] The simulation results are compared with the observation data obtained in the next iteration, and the accuracy of the simulation results is verified based on the comparison results.

[0032] Optionally, the method further includes:

[0033] The population distribution status of the population ecosystem is predicted based on the target spatial population model.

[0034] The management strategy for the population ecosystem is dynamically adjusted based on the predicted results of the population distribution status.

[0035] The technical solution provided in this application includes, but is not limited to, the following beneficial effects:

[0036] This application first obtains historical data of the population ecosystem, and constructs an initial spatial population model based on the historical data. It can build a preliminary virtual ecosystem model based on information such as past population distribution and quantity, so that the model can simulate the survival, predation and dispersal process of prey and predators, taking into account their possible hiding places or counterattack behaviors, so that the simulation is closer to the real situation.

[0037] Then, the Sobol index of each variable in the initial spatial population model is calculated. Based on the Sobol index of each variable, key regulatory variables are screened out from the initial spatial population model. By calculating the importance of each influencing factor, the key factors that have the greatest impact on ecosystem stability or risk can be identified, such as which factors will directly lead to fluctuations in prey populations or predator outbreaks. In this way, these key factors can be focused on in subsequent adjustments to avoid blind adjustments.

[0038] Finally, observational data of the population's ecosystem are obtained, and the key regulatory variables are dynamically adjusted based on the observational data to obtain a target spatial population model, thereby simulating the population's ecosystem. The model can use the latest observational data to adjust the key factors in the model in real time, making the model more consistent with the current actual ecological conditions, thus simulating ecosystem changes more accurately and providing a more reliable reference for protection and management.

[0039] Using the above method, an initial spatial population model is constructed by acquiring historical data, the Sobol index is calculated to screen key regulatory variables, and then the variables are dynamically adjusted using observational data to obtain the target model. This achieves accurate and efficient regulation and simulation of the population ecosystem, and improves the accuracy of population ecosystem regulation simulation.

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 A flowchart of a population ecosystem regulation simulation method provided in Embodiment 1 of the present invention is shown;

[0043] Figure 2 The flowchart of an initial spatial population model construction method provided in Embodiment 1 of the present invention is shown;

[0044] Figure 3 A flowchart of a method for determining the Sobol index of a variable provided in Embodiment 1 of the present invention is shown;

[0045] Figure 4 The flowchart of a method for determining key regulatory variables provided in Embodiment 1 of the present invention is shown;

[0046] Figure 5 The flowchart of a method for determining a target spatial population model provided in Embodiment 1 of the present invention is shown;

[0047] Figure 6 A flowchart of a simulation result verification method provided in Embodiment 1 of the present invention is shown;

[0048] Figure 7A flowchart of an ecosystem management strategy adjustment method provided in Embodiment 1 of the present invention is shown. Detailed Implementation

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0050] Example 1

[0051] To facilitate understanding of this application, the following is combined with... Figure 1 The flowchart illustrating a population ecosystem regulation simulation method provided in Embodiment 1 of the present invention will be described in detail for Embodiment 1 of this application.

[0052] See Figure 1 As shown, Figure 1 A flowchart of a population ecosystem regulation simulation method provided in Embodiment 1 of the present invention is shown, wherein the method includes steps S101 to S104:

[0053] S101: Obtain historical data on the population ecosystem and construct an initial spatial population model based on the historical data.

[0054] Specifically, the initial approach involves acquiring raw data on various populations within a specified spatial area of ​​the ecosystem, including population density, environmental resources, lifestyle habits, food chain relationships, and topographic maps, to identify key indicators such as birth rate, death rate, competition intensity, and predation efficiency. Based on this data and indicators, an initial spatial population model is constructed. This model describes the spatial density distribution and dynamic changes of prey and predators through a reaction-diffusion equation, while also considering the impact of resource constraints and refuge mechanisms. The prey equation introduces an additive term to reflect the impact of limited resources on survival and reproduction (strong or weak effects), and uses a Type II functional response function and a refuge coefficient to reflect the protection of prey populations by refuges. The predator equation, in a bilinear form, considers the effect of prey anti-predation behavior on predator density, ultimately forming an initial model that incorporates the interactions of biological processes, resource constraints, and refuge mechanisms.

[0055] S102: Calculate the Sobol index of each variable in the initial spatial population model, and select key regulatory variables from the initial spatial population model based on the Sobol index of each variable.

[0056] Specifically, taking system stability or outbreak risk as the output target, a model function Y = f(X) is defined, where X is the input variable. The Sobol index of each variable is calculated through variance decomposition. The first-order index measures the independent contribution of a single variable to the output, while the total effect index measures the combined contribution of the variable and its interaction terms with other variables. Specifically, the first-order index is calculated by fixing the means of other variables, and the total effect index is calculated using conditional variance. First, parameters with significant influence are selected as preferred control variables based on the first-order index. Then, the total effect index is calculated for these preferred variables. When the total effect index exceeds a preset threshold, it is identified as a key control factor and used as a focus parameter for subsequent dynamic adjustments.

[0057] S103: Obtain observational data of the population ecosystem, dynamically adjust the key regulatory variables based on the observational data to obtain a target spatial population model, and realize the simulation of the population ecosystem.

[0058] Specifically, observational data is collected through multiple means: high-resolution images are acquired using drones equipped with multispectral cameras, and activity hotspots of prey and predators are identified by combining spectral features and terrain data; cameras are deployed to count the frequency of species occurrence and generate density heatmaps; adult individuals are tagged with collars or bio-recorders to record their activity range, shelter and other behavioral data, and readers are used to count the survival rate and shelter rate of juveniles; food composition is determined by fecal sequencing and stomach contents analysis, and habitat utilization index is calculated by combining trajectory data.

[0059] After integrating and cleaning / standardizing multi-source data, key parameters are dynamically adjusted using Bayesian inference: First, a normal prior distribution of the key parameters is set, and the model is solved based on the current parameters to generate predicted values. Assuming that the observation error follows a Gaussian or Poisson distribution, a dynamic likelihood function is constructed. Real-time data is sequentially fused, and the posterior distribution of the previous time step is used as the current prior. The posterior distribution is updated in combination with the likelihood function (using Hamiltonian Monte Carlo sampling to improve computational efficiency). Finally, the optimal parameter set is generated based on the statistical characteristics of the posterior distribution, such as the mean and confidence interval, and injected into the model to form a target space population model, thereby realizing the dynamic simulation of the population ecosystem.

[0060] In an optional implementation, see Figure 2 As shown, Figure 2The flowchart illustrates a method for constructing an initial spatial population model according to Embodiment 1 of the present invention. The historical data includes the spatial density distribution of prey / predators and the population density of prey / predators. The construction of the initial spatial population model based on the historical data includes steps S201 to S204.

[0061] S201: Construct the initial prey spatial density distribution equation and the initial predator spatial density distribution equation based on the historical data.

[0062] Specifically, using historical data on the spatial density distribution of prey and predators, and population density, we construct initial prey spatial density distribution equations and initial predator spatial density distribution equations to describe basic biological processes. The initial prey spatial density distribution equation characterizes the natural growth of prey, population loss due to predation, and spatial dispersal, considering the intrinsic growth rate of prey, intraspecific competition intensity (carrying capacity), predator predation rate, and dispersal ability. The initial predator spatial density distribution equation describes the predator's dependence on prey for growth, natural mortality, and spatial dispersal, involving predation conversion efficiency, natural mortality rate, and dispersal coefficient. These two equations provide a preliminary simulation of predator-prey relationships and population spatial distribution through reactive diffusion.

[0063] More specifically, the process first involves acquiring historical data on various populations within a specified spatial area of ​​the ecosystem, including population density, environmental resources, lifestyle habits, food chain relationships among species, and topographic maps. Key indicators are then identified, including birth rate, death rate, competition intensity, and predation efficiency. Based on the collected data and historical population data, a basic spatial population model is constructed to describe the biological processes among populations, the interactions of resource constraints and refuge mechanisms, and density distribution. The biological processes in the spatial population model focus on the dynamic changes of prey and predators within the population ecosystem, using reaction-diffusion equations to describe the spatial density distribution of the population, specifically including:

[0064] Initial prey spatial density distribution equation:

[0065]

[0066] Where x(x,y) represents the spatial density distribution of prey, x represents the density of the prey population, y is the density of the predator population, a represents the intrinsic growth rate of prey, b1 represents the competition coefficient within the prey population, c represents the predation rate of the predators, d1 represents the diffusion coefficient of prey, and the Laplace operator... It describes the spatial diffusion behavior of prey population density, where Ω represents the region where the ecosystem population is located, and t represents time.

[0067] Initial predator spatial density distribution equation:

[0068]

[0069] Among them, y(x, y) represents the spatial density distribution of predators, x represents the density of the prey population, y is the density of the predator population, d represents the natural mortality rate of predators, b2 represents the competition coefficient within the predator population, β represents the predation conversion efficiency, d2 represents the diffusion coefficient of predators, c represents the predation rate of predators, and the Laplace operator describes the diffusion behavior of the predator population density in space, Ω represents the area where the ecosystem population is located, and t represents time.

[0070] S202: Determine the target prey spatial density distribution equation according to the half-saturation coefficient of the prey and the initial prey spatial density distribution equation.

[0071] Specifically, to reflect the inhibition of the prey refuge mechanism (such as habitat shelter) on the predation process, the half-saturation coefficient of the prey is introduced into the initial prey spatial density distribution equation, and the predation efficiency is adjusted through a non-linear function. The half-saturation coefficient reflects the characteristic that it is difficult for prey to be predated due to the protection of the refuge at low density - the larger this coefficient is, the stronger the protection effect of the prey at low population density. The modified equation more realistically simulates the ecological strategy of the prey using the refuge to maintain the population size by depicting the phenomenon that "the predation efficiency decreases significantly when the prey density is low".

[0072] More specifically, consider the impact of resource limitation on biological processes: when environmental resources are limited, the prey population is often more affected. When the population density is low, the individual survival and reproduction success rate shows a downward trend. The impact of resource limitation on the prey in biological processes can be considered by introducing the Allee effect, and the prey spatial density distribution equation considering the impact of resource limitation on biological processes can be obtained:

[0073]

[0074] Among them, represents the additive Allee term. When ah < n, it shows a strong Allee effect. When 0 < n < ah, it shows a weak Allee effect. h represents the half-saturation constant, and n is the maximum Allee effect intensity.

[0075] Consider the impact of refuge mechanisms on biological processes: In complex ecosystems, not all prey can be caught by predators because prey usually have various refuge mechanisms that provide them with different levels of protection. For example, almost all prey populations have habitats or refuges, which effectively protect them and help maintain high biomass levels within the ecosystem. In addition to using refuges to escape predators, prey also exhibit anti-predation behavior, which is a form of self-defense for species and mainly acts on predators.

[0076] Considering the spatial density distribution equation of prey and the influence of refuges: refuges have a direct impact on maintaining prey numbers, this can be addressed by introducing a Holling-II type functional response function. To consider the impact of shelters on the spatial density distribution of prey, we obtain the equation for the spatial density distribution of target prey that takes into account the influence of shelters:

[0077]

[0078] Where m represents the refuge coefficient. denoted as Holling-II type functional response function, and b represents the prey half-saturation coefficient.

[0079] S203: Determine the target predator spatial density distribution equation based on the prey's counter-predation rate and the initial predator spatial density distribution equation.

[0080] Specifically, to address the inhibitory effect of prey's proactive defensive behaviors (such as group counterattacks) on predators, the prey counter-predation rate is introduced into the initial predator equation. A bilinear term quantifies the intensity of prey counter-predation behavior. The counter-predation rate represents the negative feedback effect on predators per unit prey density (such as increased predator mortality or decreased reproduction), expanding the model from "one-way predation" to "two-way interaction between prey and predator," thus more accurately describing the complex dynamic relationships between species in the ecosystem.

[0081] More specifically, the spatial density distribution equation of predators considers the influence of prey anti-predation behavior: the prey's anti-predation behavior is mainly considered in a bilinear form based on state variables x (prey) and y (predator) to determine the effect on the spatial density distribution of predators, thus obtaining the target predator spatial density distribution equation:

[0082]

[0083] Where η represents the prey's counter-predation rate against the predator.

[0084] S204: Construct the initial spatial population model based on the spatial density distribution equation of the target prey and the spatial density distribution equation of the target predator.

[0085] Specifically, the corrected prey and predator equations are联立 to form an initial spatial population model that integrates biological processes (predation, competition, diffusion) and ecological mechanisms (refuge protection, anti-predation behavior). This model calibrates key parameters (such as growth rate, predation rate, refuge coefficient, etc.) through historical data, and can simulate the density distribution and dynamic interactions of prey and predators in space, providing a basic framework for subsequent parameter sensitivity analysis (screening key regulatory variables) and Bayesian inference dynamic calibration, and realizing a preliminary quantitative simulation of the predation-prey process and stability in the population ecosystem. The initial spatial population model is as follows:

[0086]

[0087] where x(x, y) represents the spatial density distribution of prey, y(x, y) represents the spatial density distribution of predators, a represents the intrinsic growth rate of prey, b1 and b2 respectively represent the competition coefficients within the prey and predator populations, c represents the predation rate of predators, b represents the half-saturation coefficient of prey, and the additive Allee term is: When ah < n, it shows a strong Allee effect. When 0 < n < ah, it shows a weak Allee effect. m represents the refuge coefficient, d represents the natural mortality rate of predators, β represents the predation conversion efficiency, η represents the anti-predation rate of prey against predators, d1 represents the diffusion coefficient of prey, d2 represents the diffusion coefficient of predators, and the Laplace operator describes the diffusion behavior of population density in space, and Ω represents the area where the ecosystem population is located.

[0088] In an optional embodiment, refer to Figure 3 as shown Figure 3 shows a flowchart of a method for determining the Sobol index of a variable provided in Embodiment 1 of the present invention. Among them, calculating the Sobol index of each variable in the initial spatial population model includes steps S301 to S303:

[0089] S301: Define the output target, where the output target is system stability or outbreak risk.

[0090] Specifically, first clarify the evaluation direction of the model, and set the stability of the ecosystem (such as the fluctuation range of population density, species coexistence state) or outbreak risk (such as the possibility of prey being on the verge of extinction due to over-reproduction of predators) as the output target of quantitative analysis. This target needs to be reflected by specific indicators output by the model, such as the spatio-temporal distribution uniformity of prey and predator densities, the fluctuation threshold of population growth rate, etc. By defining the output target, a clear analysis dimension is provided for subsequent parameter impact evaluation, ensuring that the sensitivity analysis focuses on the core needs of ecosystem management (such as preventing species outbreaks or maintaining community stability).

[0091] More specifically, first define the model and input variables: Suppose there is a function f(x1,x2,…x…). d ), where x1, x2, ... x d Let f represent the input variables, d represent the output target, and d represent the number of input variables. Here, system stability or outbreak risk is taken as the output target. The Sobol index evaluates each input variable x. i Or the effect of their combination on f. Then construct the Sobol exponent: the first-order Sobol exponent S. i Indicates the input variable x i Independent contribution to the output; the total Sobol effect index STi represents the input variable x. i The contribution of all its interaction terms to the output;

[0092] S302: Determine the total variance of the initial spatial population model based on the output target.

[0093] Specifically, after defining the output target, the total variance of the initial spatial population model output is calculated. The total variance reflects the overall uncertainty of the model output (such as a system stability index or outbreak risk value), encompassing the combined impact of all input parameters and their interactions on the output. For example, if the output target is a "predator outbreak risk index," the total variance can be calculated by measuring the fluctuation range of this index in multiple simulations. This step provides a benchmark for subsequent variance decomposition; the total variance quantifies the contribution of each parameter to the output.

[0094] More specifically, the Sobol exponent is calculated through variance decomposition:

[0095] Assume the model's output Y = f(x1, x2, ... x d The total variance Var(Y) can be expressed as:

[0096] Var(Y) = Var(f(x1,x2,…x) d ))=E[(f(x1,x2,…x d )-E[f]) 2 ];

[0097] Where E represents the expectation operator, and E[f] represents the function f(x1,x2,…x) d ) expectations.

[0098] S303: Decompose the total variance to obtain the Sobol index of each variable, where the Sobol index of each variable represents the independent contribution of that variable to the output target.

[0099] Specifically, variance decomposition techniques are used to allocate the total variance to each input parameter, yielding the first-order Sobol exponent for each variable. This exponent measures the independent contribution of a single parameter to the output target (i.e., the effect of the parameter's interaction with other parameters). Specifically, by fixing the mean of other parameters and allowing the target parameter to vary only within its range, the proportion of the output variance to the total variance is calculated; this is the first-order Sobol exponent for that parameter. A larger exponent value indicates a stronger independent impact of the parameter on system stability or outbreak risk. For example, if the Sobol exponent for predation rate is 0.4, it means that 40% of the system output variation can be explained by changes in predation rate alone. This step helps identify key parameters that dominate ecosystem dynamics, providing a targeted basis for subsequent regulatory strategies.

[0100] More specifically, the calculated total variance is decomposed to obtain the Sobal exponent for each input variable, where the first-order Sobal exponent S... i It is calculated by fixing the mean of other variables: Total Sobol effect index Among them, Var(ff) i ) indicates that x is removed from the total variance. i Residual variance after individual contribution; Var i (f) indicates that when other input variables are fixed as the mean, only the i-th variable x is considered. i The resulting output variance; Var(f) represents the total variance of the model output; f i It is based on a fixed x i The output under the following conditions.

[0101] In an optional implementation, see Figure 4 As shown, Figure 4 The flowchart of a method for determining key regulatory variables provided in Embodiment 1 of the present invention is shown, wherein the key regulatory variables are screened from the initial spatial population model based on the Sobol index of each variable, including steps S401 to S403:

[0102] S401: Select several preferred control variables based on the Sobol index of each variable.

[0103] Specifically, the first step is to calculate the first-order Sobol exponent of all input variables in the initial spatial population model. This exponent measures the independent contribution of a single variable to system stability or outbreak risk. By comparing the first-order exponent values ​​of each variable, variables with larger exponent values ​​are selected as preferred control variables. For example, if the first-order exponents of predation rate, refuge coefficient, and intrinsic prey growth rate rank highly (e.g., all greater than 0.2), they are included in the preferred variable set as candidate parameters for further analysis. This step, by quantifying the influence strength of individual parameters, eliminates redundant variables with weak contributions to system output, thus narrowing down the range of control parameters.

[0104] S402: Determine the total Sobol effect index based on the Sobol index of each preferred control variable.

[0105] Specifically, for the selected preferred control variables, their total Sobol effect index is further calculated. The total effect index not only includes the independent contribution of the variable but also covers the interaction effects of that variable with all other variables. For example, predation rate may have a synergistic effect with refuge coefficient—when the refuge coefficient is high, the impact of changes in predation rate on system stability may be amplified or weakened. Using variance decomposition, the combined effect of each preferred variable after considering all interaction terms is calculated to obtain the total effect index, thereby comprehensively assessing the complex impact of parameters on the system.

[0106] S403: When the total Sobol effect index meets the preset threshold, each preferred control variable is determined as a key control variable.

[0107] Specifically, a preset threshold (e.g., 0.1) is set to determine whether a preferred variable is a key regulatory factor. If the total effect index of a preferred variable exceeds the threshold, the variable is considered to have a dominant impact on system stability or outbreak risk and is identified as a key regulatory variable. For example, if the total effect index of predation rate is 0.3 (greater than the threshold of 0.1), it indicates that its independent effect and interaction with other variables together explain 30% of the system output variation and should be used as a core parameter for subsequent dynamic regulation. Conversely, variables that do not reach the threshold are considered secondary parameters and are not included in the key regulation scope for the time being. This process ensures that the regulation strategy focuses on the key factors that play a decisive role in ecosystem dynamics by quantifying the comprehensive impact of parameters.

[0108] In an optional implementation, see Figure 5 As shown, Figure 5 The flowchart of a method for determining a target spatial population model according to Embodiment 1 of the present invention is shown, wherein the step of dynamically adjusting the key control parameters based on the observation data to obtain the target spatial population model includes steps S501 to S505:

[0109] S501: Construct a parameter set based on each key regulatory variable.

[0110] Specifically, parameters that significantly impact system stability or outbreak risk (such as predation rate, refuge coefficient, and prey predation rate) are extracted from the global parameter sensitivity analysis results to form a set of key regulatory parameters to be adjusted. A parameter set θ = {θ1, θ2, ... θ} is constructed based on the parameters that show a significant impact after sensitivity analysis. n}, and choose a normal distribution θ i ~N(μ,σ 2 ) is the prior distribution, where μ represents the mean, determined based on historical data or preliminary model calibration results; θ i Let σ represent the i-th parameter to be estimated; N represents the normal distribution, and n is the number of parameters; 2 The variance represents the initial parameter uncertainty. Simultaneously, constraints m1∈(0,1) are imposed on the parameters based on ecological significance and the range of observational data (e.g., non-negative predation rate and refuge coefficient between 0 and 1) to ensure the parameter set remains within a reasonable biological range.

[0111] S502: Based on the parameter set, the predicted values ​​of prey and predator density distributions are obtained by solving the initial spatial population model.

[0112] Specifically, the parameters in the current parameter set are substituted into the initial spatial population model (i.e., the target prey / predator equation including refuge mechanisms and anti-predation behaviors), and the partial differential equations are solved using numerical methods (such as the finite difference method) to generate the predicted density distribution values ​​x of prey and predators in space. model (t,Ω,θ),y model (t,Ω,θ), where θ represents the parameter to be estimated, t is time, Ω is the sample space, and x... model y model These represent model predictions for prey and predators, respectively. For example, based on current predation rates and refuge coefficients, these predictions simulate the density distribution of prey in habitat hotspots at the next moment, or predict population dispersal trends caused by predator counter-hunting behavior. These predictions serve as theoretical estimates of the ecosystem's state and are used to compare with actual observational data.

[0113] S503: Calculate the matching probability between the observed data and the predicted value using an error model to form a local likelihood function.

[0114] Specifically, based on the type of observed data, an appropriate error model is selected to quantify the difference between predicted and measured values: For continuous data (such as population density heatmaps monitored by UAVs): it is assumed that the error follows a Gaussian distribution, with the mean being the predicted value and the variance reflecting environmental noise or measurement error. For discrete data (such as the number of individuals counted using the label-recapture method): a Poisson distribution or a negative binomial distribution is used to characterize the counting error. The conditional probability of the observed data under the current parameters is calculated using these distributions, forming a local likelihood function. For example, for single-time-step observed data, the likelihood function is the joint probability density of the observation errors at each spatial point; for multi-time-series data, the likelihood values ​​at each time point are multiplied to capture time dependence.

[0115] More specifically, it is assumed that the deviation between observed data and model predictions follows a specific probability distribution—for example, for continuous density data, a Gaussian distribution is typically used to characterize the error, with the mean being the model prediction and the variance reflecting environmental noise or measurement uncertainty: D t =N~(x model (t,θ),σ 2 ), where D t Let D be the error at time t. t Follows a normal distribution N, x model (t,θ) represents the predicted density distribution of prey in space, σ represents the mean of a normal distribution. 2 Let be the variance and t be time. For discrete count data (such as the number of individuals in the label-recapture method), a Poisson distribution or a negative binomial distribution might be chosen. The dynamic likelihood function needs to further incorporate time-series characteristics: for a single time step, the likelihood function can be defined as the joint probability density of the observation errors at each spatial point. The calculation can be simplified using the independent and identically distributed assumption, i.e.: In multi-time sequential scenarios, it is necessary to multiply the likelihood values ​​at each time step, or introduce an autoregressive structure to capture temporal dependencies. Where, x obs,i Let x represent the i-th observation, L represent the likelihood function, and x represent the probability of the i-th observation. model,i Let x represent the i-th model prediction. obs,i -x model,i This represents the difference between the i-th observation and the model prediction. Let T represent the i-th variance, T represent the total time, n represent the number of parameters, and D represent the total variance. 1：T This represents the error of parameter θ at time T.

[0116] S504: Update the parameter set based on the local likelihood function and the Hamiltonian Monte Carlo (HMC) sampling method.

[0117] Specifically, Bayes' theorem is used to combine the prior distribution with the likelihood function, and the Hamiltonian Monte Carlo (HMC) sampling method is employed to efficiently explore the parameter space and update the posterior distribution of the parameters. First, the initial state is determined: the posterior distribution of the previous time step is used as the current prior. Then, new parameters are proposed: a candidate parameter set is generated through HMC sampling, utilizing Hamiltonian dynamics to avoid the inefficiency of random walks and improve sampling efficiency. Next, an acceptance-rejection decision is made: the acceptance rate of the candidate parameters is calculated, and the new parameter set is accepted with probability; otherwise, the original parameters are retained, gradually approximating the high-probability region of the posterior distribution. Through this process, real-time observation data is sequentially incorporated into parameter inference, gradually correcting the uncertainty of the parameters.

[0118] More specifically, when the system acquires observation data for a new time window (such as prey density observation data x) obs (t) and predator density observation data y obs After (t), first assume θ based on the current parameters. t-1 Generative model predicted value x model (t;θ t-1 Then, the matching probability between the observed data and the predicted value is calculated using an error model (Gaussian likelihood), forming the local likelihood function L(θ) at that time (time t). t |D t Then, using Bayes' theorem, this likelihood is compared with the posterior probability P(θ) of the previous time step. t-1 |D 1:t-1 Multiply and normalize, θ t-1 D represents the parameter at time t-1. 1:t-1 This represents the error of the parameters at time t-1, yielding the updated posterior probability distribution P(θ). t |D 1:t )=L(θ t |D t )·P(θ t |D 1:t-1 Then, by combining Hamiltonian Monte Carlo (HMC) sampling or variational inference, a new parameter set θ ~ q(θ|θ) is proposed while maintaining accuracy. t-1 ), calculate the acceptance rate of the new parameters. Accept the parameter set θ with probability α, otherwise retain θ. t-1 , where q(θ) t-1 |θ) represents the parameter value at time t, q(θ|θ) t-1 Let L(θ) represent the parameter value at time t-1, L(θ) represent the prior probability with respect to parameter θ, and P(θ) represent the posterior probability with respect to parameter θ. t-1 ) represents the parameter θ t-1 The prior probability, P(θ) t-1 ) represents the parameter θ t-1 The posterior probability.

[0119] S505: Adjust the key control parameters according to the updated parameter set and dynamic adjustment target.

[0120] Specifically, based on the updated posterior distribution of parameters, optimal control parameters are generated and strategies are formulated. First, statistical feature extraction is performed: the posterior mean (point estimate) or 95% confidence interval of the parameters is calculated (e.g., the mean of the refuge coefficient is 0.6, with a confidence interval of 0.4-0.8). Then, risk-sensitive decision-making is conducted: if stability is prioritized, the posterior median is selected as the adjustment benchmark to reduce the impact of extreme values; if outbreak risk is mitigated, the lower limit of the confidence interval is used (e.g., setting a conservative threshold of predation rate not exceeding 0.3). Next, model injection and validation are performed: the adjusted parameters are input into the initial model to predict future population density distribution, generating control commands (e.g., adjusting the protected area boundaries or fishing quotas), and a closed loop is formed through real-time monitoring feedback (e.g., restarting calibration when the error exceeds 15%) to ensure the model continuously adapts to dynamic changes in the ecosystem.

[0121] More specifically, extracting statistical features of key parameters from the updated posterior distribution. For example, calculating the posterior mean of the shelter rate m2. As a point estimate, or by determining its 95% confidence interval [θ] using quantiles. t,0.025 ,θ t,0.975 The uncertainty range is represented by the 0.025 and 0.975 quantiles, which correspond to the lower and upper limits of the interval, respectively. Decision rules are designed for different risk preferences: if stability is prioritized, the posterior median is selected as the parameter adjustment benchmark to avoid interference from extreme values; if the risk of ecological collapse (such as predator outbreaks) needs to be mitigated, the lower limit of the confidence interval is selected (such as setting a conservative threshold for the predation rate c). The adjusted parameters are input into the spatial population model to predict the future distribution of prey and predator densities, and based on this, executable control instructions (such as the intensity of work to maintain ecosystem stability) or dynamic adjustments to fishing quotas are generated. During implementation, the control effect is monitored in real time through a network of sensors. If the deviation between the observed data and the prediction exceeds the preset tolerance (such as population density error > 15%), a feedback loop is triggered—recalibrating the model parameters, optimizing the prior distribution, or adjusting the weight allocation of the decision rules (such as increasing the priority of ecological protection goals). This process forms a closed loop of "evaluation-correction-revalidation," ensuring that the model continuously adapts in a dynamic environment, ultimately achieving stable and efficient management of the ecosystem.

[0122] Before performing step S501, observational data of the population ecosystem are obtained, including in the following ways:

[0123] Drones and multispectral imaging data collection: High-resolution images are acquired by using drones equipped with multispectral cameras. Spectral features are combined to identify prey and predators in vegetation cover, and animal activity hotspots are identified based on terrain data. Cameras are deployed in the activity range of these hotspots to count the frequency of species occurrence per unit time, and density heatmaps are generated by combining spatial interpolation.

[0124] Individual tagging and tracking collection: Adult individuals are tagged with GPS collars or bio-recorders to record activity range, shelter, reproductive behavior and death signals; RFID readers are deployed in nests or fixed stations to count the survival rate and shelter rate of juveniles.

[0125] Resource utilization overlap analysis: Fecal DNA was sequenced and stomach contents were analyzed based on species diets to determine the food composition of prey and predators; then, GPS trajectory data was used to calculate the habitat utilization index to quantify spatial competition.

[0126] In an optional implementation, see Figure 6 As shown, Figure 6 The flowchart of a simulation result verification method provided in Embodiment 1 of the present invention is shown, wherein the method further includes steps S601 to S603:

[0127] S601: After each acquisition of observational data of the population ecosystem, perform a step of dynamically adjusting the key regulatory variables based on the observational data to obtain a target spatial population model.

[0128] Specifically, whenever new observational data is acquired, such as prey density distribution monitored by drones, x obs (t) and predator density distribution y obs (t) A Bayesian sequential inference process needs to be initiated to dynamically calibrate the model parameters using a sequential posterior update method: First, new data is integrated with historical data, and the data uncertainty is quantified using an error model; then, the posterior distribution of the model parameters from the previous time step is used as the current prior, and a dynamic likelihood function is constructed by combining it with the new data. Hamiltonian Monte Carlo (HMC) sampling is used to update the posterior distribution of the parameters, resulting in a target spatial population model adapted to the latest observations. This process achieves a real-time closed loop of "data acquisition - parameter calibration," ensuring that the model parameters are continuously optimized dynamically with the ecosystem.

[0129] S602: Using the target spatial population model obtained from this dynamic adjustment, the population ecosystem is simulated to obtain the simulation results.

[0130] Specifically, the updated target space population model parameters θ t+1Substituting calibrated predation rates and refuge coefficients into the model, the reaction-diffusion equation is solved numerically to simulate ecological indicators such as the spatial density distribution of prey and predators and population growth rates in the next time period. For example, based on the latest calibrated parameters, the dispersal range of predators in the habitat or the density fluctuation trend of prey due to resource constraints can be predicted within the next month. The simulation results reflect theoretical predictions of the current ecosystem state, providing a forward-looking basis for management decisions.

[0131] S603: Compare the simulation results with the next obtained observation data, and verify the accuracy of the simulation results based on the comparison results.

[0132] Specifically, the simulation results are compared with newly acquired independent observational data (such as population size from field surveys and environmental parameters recorded by sensors), and the model's predictive accuracy is evaluated by calculating error indices (such as root mean square error and absolute percentage error). If the deviation is within a preset tolerance (such as population density error ≤ 15% as mentioned in the document), the model is considered effective; if the deviation exceeds the threshold, a feedback correction mechanism is triggered: the data quality is rechecked, the prior distribution is adjusted, or the decision rule weights are optimized, and the parameter calibration process is repeated until the simulation results match the observational data. This process forms an adaptive cycle of "simulation-validation-correction," ensuring that the model continuously and reliably reflects changes in the population ecosystem in a dynamic environment.

[0133] In an optional implementation, see Figure 7 As shown, Figure 7 The flowchart illustrates an ecosystem management strategy adjustment method provided in Embodiment 1 of the present invention, wherein the method further includes steps S701 to S702:

[0134] S701: Predict the population distribution status of the population ecosystem based on the target spatial population model.

[0135] Specifically, a dynamically calibrated target spatial population model (i.e., a model updated with the latest observational data) is used to prospectively simulate the future state of the population ecosystem. This involves solving reaction-diffusion equations that incorporate biological processes, resource constraints, and refuge mechanisms to predict key indicators such as the spatiotemporal density distribution of prey and predators, population growth rates, and species coexistence status. For example, it can predict the trend of prey density recovery due to refuge protection in a specific area; simulate changes in predator dispersal paths due to intensified anti-predation behavior; and assess the impact of environmental resource fluctuations (such as drought leading to vegetation reduction) on the risk of population outbreaks. This prediction process, based on the posterior distribution of model parameters, can generate probabilistic results containing uncertainties (such as a 95% confidence interval for population density), providing a quantitative basis for management decisions.

[0136] S702: Dynamically adjust the management strategy of the population ecosystem based on the predicted results of the population distribution status.

[0137] Specifically, based on the prediction results of S701 and combined with ecological protection goals (such as maintaining species diversity and preventing the outbreak of invasive species), the management strategy is dynamically optimized through the following process: (1) Risk assessment: Compare the prediction results with ecological security thresholds (such as minimum survival density of prey and upper limit of predator control) to identify high-risk areas or trends (such as predator density in a certain area exceeding the threshold by 20%). (2) Strategy generation: If the population is predicted to be on the verge of collapse (such as prey density being lower than the critical value), trigger protection measures (such as expanding the scope of refuges and artificially supplementing food resources); if the risk of predator outbreak is predicted to be high, formulate intervention plans (such as adjusting fishing quotas and introducing natural enemies for regulation). (3) Parameter feedback: Transform the management strategy into model parameter adjustment instructions (such as increasing the refuge coefficient to enhance prey protection), re-inject the target model to simulate the effect of the strategy, and form a closed loop of "prediction-decision-simulation verification". (4) Dynamic iteration: The effectiveness of the strategy implementation is evaluated by real-time monitoring data. If the actual population response deviates from the prediction by more than the preset tolerance (e.g., density error > 15%), the parameter calibration and strategy optimization process is restarted to ensure the adaptability and effectiveness of the management measures.

[0138] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In addition, the terms "first", "second", "third", etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0139] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. All should be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for simulating the regulation of a population ecosystem, characterized in that, The method includes: Acquire historical data on the population ecosystem and construct an initial spatial population model based on the historical data; Calculate the Sobol index of each variable in the initial spatial population model, and select key regulatory variables from the initial spatial population model based on the Sobol index of each variable; Observational data of the population ecosystem are obtained, and the key regulatory variables are dynamically adjusted based on the observational data to obtain a target spatial population model, thereby simulating the population ecosystem. The historical data includes the spatial density distribution of prey / predators and the population density of prey / predators. The construction of an initial spatial population model based on the historical data includes: Based on the historical data, the initial prey spatial density distribution equation and the initial predator spatial density distribution equation are constructed respectively. The spatial density distribution equation of the target prey is determined based on the prey's half-saturation coefficient and the initial prey spatial density distribution equation. The target predator spatial density distribution equation is determined based on the prey's anti-predator rate and the initial predator spatial density distribution equation. The initial spatial population model is constructed based on the spatial density distribution equation of the target prey and the spatial density distribution equation of the target predator. The Sobol index, based on each variable, selects key regulatory variables from the initial spatial population model, including: Several preferred control variables were selected based on the Sobol index of each variable; The total Sobol effect index is determined based on the Sobol index of each preferred control variable; When the total Sobol effect index meets the preset threshold, each preferred control variable is determined as a key control variable; The process of dynamically adjusting the key regulatory variables based on the observed data to obtain the target spatial population model includes: Construct a parameter set based on each key regulatory variable; Based on the parameter set, the predicted values ​​of prey and predator density distributions are obtained by solving the initial spatial population model; The matching probability between the observed data and the predicted value is calculated using an error model to form a local likelihood function; The parameter set is updated based on the local likelihood function and the Hamiltonian Monte Carlo (HMC) sampling method. Adjust the key control variables according to the updated parameter set and dynamic adjustment target; The calculation of the Sobol index of each variable in the initial spatial population model includes: Define an output target, where the output target is system stability or outbreak risk; The total variance of the initial spatial population model is determined based on the output target; The total variance is decomposed to obtain the Sobol index of each variable, where the Sobol index of each variable represents the independent contribution of that variable to the output target. The initial spatial population model is as follows: in, Indicates the spatial density distribution of prey. This represents the spatial density distribution of predators. Indicates the intrinsic growth rate of prey. These represent the competition coefficients within the prey and predator populations, respectively. Indicates the predation rate of a predator. The half-saturation coefficient of the prey, additive. The item is: ,when At that time, it manifested as strong Effect, when At that time, it manifested as weakness effect, Indicates the refuge coefficient. Indicates the natural mortality rate of predators. Indicates predator-prey conversion efficiency. This indicates the prey's counter-predation rate against predators. Represents the diffusion coefficient of prey. Represented as the predator's diffusion coefficient, the Laplace operator. It describes the spatial diffusion behavior of population density. Indicates the area where the ecosystem population is located. Indicates the density of the prey population. It is the density of the predator population. Indicates time.

2. The method according to claim 1, characterized in that, The method further includes: After each acquisition of observational data on the population ecosystem, a step is performed to dynamically adjust the key regulatory variables based on the observational data to obtain a target spatial population model. The target spatial population model obtained from this dynamic adjustment was used to simulate the ecosystem of the population, and the simulation results were obtained. The simulation results are compared with the observation data obtained in the next iteration, and the accuracy of the simulation results is verified based on the comparison results.

3. The method according to claim 1, characterized in that, The method further includes: The population distribution status of the population ecosystem is predicted based on the target spatial population model. The management strategy for the population ecosystem is dynamically adjusted based on the predicted results of the population distribution status.

Images