A method and system for regulating and repairing population natural regeneration through interaction of allium victorialis and competitive species

Abstract

The application relates to the technical field of ecological protection and restoration, and discloses a multi-star lily and competitive species interaction regulation and population natural renewal restoration method and system, which comprises the following steps: based on multi-period sample plot monitoring data, a multi-star lily-competitive species dynamic model containing non-integer time lag and nonlinear density index is established; nonlinear filtering is adopted to perform state online estimation on noise-containing monitoring data, and state estimation values and uncertainty measurements thereof are output; according to the state estimation values and the uncertainty measurements thereof, rolling optimization regulation and decision-making are performed through scene analysis and weight construction based on gradient difference; the natural renewal restoration potential is evaluated, and the grade of auxiliary measures is determined; and the restoration scheme is dynamically adjusted in a monitoring-estimation-decision-implementation-remonitoring closed loop. The application can be used for competitive regulation and ecological restoration of a multi-star lily degraded population in a karst mountain meadow, and the stability of the multi-star lily degraded population restoration is improved.

Description

Technical Field

[0001] This invention relates to the field of ecological protection and restoration technology, specifically to a method and system for regulating and restoring multi-species chive populations based on state estimation and rolling optimization decision-making. Background Technology

[0002] The degradation of *Allium chinense* populations is influenced by multiple factors: in the peripheral areas of the population, competing species such as *Phyllostachys shuichengensis* and *Dipsacus asper* encroach on the living space of *Allium chinense* with their developed root systems and rapid reproductive capabilities; in the core distribution area, the plant density of *Allium chinense* can reach 80-100 plants / m², resulting in fierce intraspecific competition; at the same time, the lack of humus layer and the obstruction of soil nutrient cycling in the degraded areas inhibit the natural regeneration of the population.

[0003] Current technical solutions address degradation identification and early warning, but these only focus on soil improvement and nutrient regulation. They do not involve a quantitative description of the competitive relationship between *Leekia scabra* and competing species, nor do they address the dynamic impact on the natural regeneration process. The elimination of competing species still relies on empirical judgment, and there is a lack of scientific regulatory decision-making methods based on population dynamics prediction.

[0004] Interspecific competition in the wild exhibits two characteristics that cannot be ignored in practice: first, the inhibitory effect of competing species on the growth of *Allium tuberosum* has a time lag, which is influenced by plant phenological rhythms and often spans the growing season boundary; second, the intensity of interspecific competition varies non-linearly with population density. The classic Lotka-Volterra model, which assumes linear density constraints and instantaneous responses, is difficult to accurately describe these characteristics. Furthermore, field monitoring data are inevitably affected by random factors such as interannual climate fluctuations and sampling errors, introducing noise into population status observations and impacting the reliability of regulatory decisions.

[0005] Therefore, a restoration method is needed that can utilize noise-containing monitoring data to predict interspecific competition dynamics and optimize regulatory measures accordingly. Summary of the Invention

[0006] To address the aforementioned technical problems, the purpose of this invention is to provide a method for regulating the interaction between *Allium chinense* and competing species, as well as for the natural regeneration and restoration of its population. This method involves constructing a population dynamics model describing the time lag and nonlinear effects of competition, combining online state estimation with noisy monitoring data, and implementing rolling optimization decisions based on risk assessment. This allows for the scientific formulation and dynamic adjustment of competing species regulation and natural regeneration support measures, contributing to improved stability in the restoration of degraded *Allium chinense* populations. This invention is applicable to the population rejuvenation and ecological restoration of *Allium chinense* populations in karst alpine grasslands under the influence of competing species.

[0007] To achieve the above objectives, the following technical solution is adopted:

[0008] In a first aspect, embodiments of the present invention provide a method for regulating the interaction between *Allium chinense* and competing species and for restoring the natural regeneration of the population, comprising the following steps:

[0009] S1: Acquire population status data of *Lepidium apetalum* and its competing species in multiple monitoring periods, and establish an improved dynamic model describing the density changes of *Lepidium apetalum* and its competing species.

[0010] S2: The improved dynamic model is expressed as a stochastic form containing process noise and observation noise, and a filtering algorithm is used to estimate the population state online, outputting the state estimate and its uncertainty measure;

[0011] S3: Based on the state estimate and its uncertainty measure, generate multiple scenarios for simulating future population evolution. Construct an objective function based on the scenarios to balance degradation risk and regulation cost. Search for the optimal sequence of regulation measures through an optimization algorithm. The regulation measures include the intensity of elimination of competing species.

[0012] S4: Based on soil seed bank survey data and the reproductive index of *Leekia spicata*, calculate the natural regeneration recovery potential index of the population, and classify the regeneration auxiliary level according to the conservative estimate of the recovery potential index.

[0013] S5: Spatially match and implement the current periodic measures in the optimal control measure sequence with the update assistance level. After acquiring new population state data in the next monitoring cycle, return to step S2 to update the state estimate and re-execute steps S3 and S4 to dynamically adjust subsequent control and update schemes.

[0014] Furthermore, in step S1, the improved dynamic model includes a first nonlinear exponent characterizing the intraspecific nonlinear effect of competition, a second nonlinear exponent characterizing the interspecific nonlinear effect of competition, and a time delay term characterizing the delayed characteristics of the competition effect. The discrete form of the improved dynamic model is as follows:

[0015]

[0016] in, The monitoring period number is 'm', where 'm' represents *Allium chinense* and 'j' represents the code for competing species. For multi-star chive density, For the density of competing species j, The intrinsic growth rate For environmental carrying capacity, It is an intraspecific nonlinear density index. and These are the nonlinear competition index and competition coefficient of competing species j against multiple species of chives, respectively. The number of delay periods for the competition effect. This is an environmental stress index. The stress response coefficient; The population density of *Leekia multiflora* during the kth monitoring period; For the first The predicted population density of *Leekia scabra* over a monitoring period.

[0017] Furthermore, in step S1, when estimating the model parameters, a multi-initialization local optimization strategy is adopted: multiple initial values ​​are selected within a reasonable parameter range, and the error between the model prediction value and the measured value is minimized through optimization algorithms. The parameter combination with the smallest error is then taken as the estimated value.

[0018] Furthermore, step S2 specifically includes: expressing the improved dynamic model as a stochastic form containing process noise and observation noise as follows:

[0019]

[0020] in, : No. Predicted state vector for each monitoring cycle; Let be the state vector consisting of multi-star chives and the densities of each competing species; The set of historical state vectors considering time delay effects, containing all time delays. Species density; This represents a vector of regulatory measures that include the intensity of competing species elimination. For the improved dynamic model, is the vector-valued function; To characterize the process noise vector that the model fails to capture random fluctuations; This represents the actual observation vector for the kth monitoring period; The observation noise vector characterizing sampling and measurement errors;

[0021] Online estimation of population state is performed using the unscented Kalman filter algorithm, including: generating Sigma points through unscented transformation, and then applying the vector-valued function. After propagation, the state mean and covariance matrix are reconstructed, and new observations are obtained in each monitoring period. Then, a measurement update is performed, and the state estimate is output. and its estimated error covariance matrix The initial values ​​of the process noise covariance matrix and the observation noise covariance matrix of the unscented Kalman filter algorithm are estimated by the model fitting residual covariance and the intra-sample repeated measurement variance, respectively, and are updated by a sliding window during operation.

[0022] Furthermore, step S3, which involves constructing an objective function to balance degradation risk and control costs based on the scenarios, specifically includes: generating multiple scenarios subject to noise disturbance to simulate future population evolution based on the current period's state estimate and its uncertainty measure; for each scenario, simulating the trajectory of multi-star density changes during the prediction period, statistically analyzing the proportion of scenarios with multi-star density below a preset threshold during the prediction period as a degradation risk indicator, and calculating the cost of control measures; assigning different scenario weights to each scenario, with scenarios having higher prediction uncertainty receiving higher weights, and constructing a weighted objective function based on the degradation risk indicator, control costs, and scenario weights.

[0023] Furthermore, the method of assigning different scenario weights to each scenario is as follows: calculate the gradient vector of the objective function of each scenario with respect to the control variable, and set the weight according to the magnitude of the gradient vector and the angle between it and the average gradient direction, so that scenarios with larger magnitudes or larger angles with the average gradient direction receive higher weights; or, use the principal component analysis method to calculate the score of each scenario on the first principal component, and use the normalized value of the absolute deviation of the score from the mean as the weight.

[0024] Furthermore, in step S3, the optimization algorithm is an adaptive evolution strategy for the covariance matrix.

[0025] Furthermore, in step S4, when calculating the conservative estimate of the population natural regeneration recovery potential index, if each basic indicator has at least 4 periods of historical observation data and the distribution is approximately symmetrical, the mean of the data of each indicator over multiple periods is taken minus one standard deviation; if the data distribution is skewed, a logarithmic transformation is performed first before calculating the conservative estimate.

[0026] Furthermore, in step S4, the step of classifying the update assistance level based on the conservative estimate of the recovery potential index includes: if the conservative estimate is higher than the first threshold, then a light assistance measure mainly based on protective enclosure is adopted; if the conservative estimate is between the second threshold and the first threshold, then seed rain is added on the basis of enclosure; if the conservative estimate is lower than the second threshold, then artificial reseeding of multi-spotted chive seeds is further added; wherein, the first threshold is greater than the second threshold.

[0027] Secondly, embodiments of the present invention also provide a system for regulating the interaction between *Allium chinense* and competing species and for the natural regeneration and restoration of its population, comprising:

[0028] The data acquisition module is used to acquire population status data of *Lepidium apetalum* and its competing species over multiple monitoring periods;

[0029] The model building module is used to establish an improved dynamic model describing the density changes of the multi-star chives and competing species;

[0030] The state estimation module is used to express the improved dynamic model as a stochastic form containing process noise and observation noise, and to use a filtering algorithm to estimate the population state online, outputting the state estimate and its uncertainty measure.

[0031] The rolling optimization module is used to generate multiple scenarios for simulating future population evolution based on the state estimate and its uncertainty measure, construct an objective function to balance degradation risk and regulation cost based on the scenarios, and search for the optimal sequence of regulation measures through an optimization algorithm; the regulation measures include the intensity of elimination of competing species;

[0032] The updated assessment module is used to calculate the natural regeneration recovery potential index of the population based on soil seed bank survey data and the reproductive indicators of *Leekia spicata*, and to classify the regeneration auxiliary level according to the conservative estimate of the recovery potential index.

[0033] The collaborative execution module is used to spatially match and implement the current periodic measures in the optimal control measure sequence with the update assistance level, and after acquiring new population state data in the next monitoring cycle, it triggers the state estimation module, rolling optimization module and update evaluation module to update, so as to dynamically adjust the subsequent control and update schemes.

[0034] Compared with existing technologies, the main beneficial effects of this invention are as follows:

[0035] (1) Improved accuracy of population dynamics prediction. By introducing non-integer time delay and nonlinear density terms into the competition model, the delay and intensity saturation characteristics of the competition effect are described more accurately. In leave-one-out cross-validation in a demonstration plot, the predicted MAPE of the improved model of this invention is 16.0%, while that of the classic LV model is 18.3%, which improves the prediction accuracy and provides a more reliable prediction basis for regulatory decisions.

[0036] (2) Enhanced the adaptability of the remediation scheme to noise interference. Through state filtering and scenario-based optimization methods, monitoring noise and prediction uncertainty are explicitly considered in the decision-making process, so that the control measures can maintain a relatively stable remediation effect under the influence of random factors such as interannual climate fluctuations.

[0037] (3) Dynamic closed-loop adjustment of restoration strategies has been achieved. Through the rolling optimization mechanism, decisions are updated based on new monitoring data in each cycle, so that restoration measures can be continuously optimized as the ecosystem evolves, which helps to overcome the shortcomings of one-off solutions in terms of timeliness.

[0038] It should be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of the present invention, nor is it intended to restrict the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0039] The above and other features, advantages, and aspects of the various embodiments of the present invention will become more apparent from the accompanying drawings and the following detailed description. The drawings are provided for a better understanding of the invention and are not intended to limit the scope of the invention. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0040] Figure 1 This is a schematic flowchart illustrating the steps of a method for regulating the interaction between *Leekia spicata* and competing species and for natural population regeneration and restoration according to an embodiment of the present invention.

[0041] Figure 2 This is an overall flowchart of a method for regulating the interaction between *Allium chinense* and competing species and for natural population regeneration and restoration, according to an embodiment of the present invention.

[0042] Figure 3 This is a schematic diagram of the structure of a multi-star chive and competing species interaction regulation and natural population renewal and repair system according to an embodiment of the present invention;

[0043] Figure 4 This is a graph showing the fitting results of the improved competitive dynamic model and the classic Lotka-Volterra model of this invention on the changes in multi-star chive density.

[0044] Figure 5 This is a schematic diagram of the optimization decision-making process based on state estimation and scenario generation in an embodiment of the present invention. Detailed Implementation

[0045] 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. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0047] Example 1:

[0048] Figure 1 This is a schematic flowchart illustrating the steps of a method for regulating the interaction between *Leekia spicata* and competing species and for natural population regeneration and restoration according to an embodiment of the present invention. Figure 2This is a flowchart illustrating the overall process of regulating interactions between *Allium chinense* and competing species and promoting natural population regeneration and restoration, according to an embodiment of the present invention. (See also...) Figure 1 and Figure 2 A method for regulating the interaction between *Leekia spicata* and competing species and restoring the natural regeneration of the population includes the following steps:

[0049] S1: Acquire population status data of *Lepidium apetalum* and its competing species in multiple monitoring periods, and establish an improved dynamic model describing the density changes of *Lepidium apetalum* and its competing species.

[0050] Step S1 is used to construct a dynamic model for sample plot monitoring data acquisition and competition. Specifically:

[0051] Within the distribution area of ​​*Allium chinense* in the scenic area, fixed monitoring quadrats are established according to the degree of degradation and differences in the composition of competing species. Based on the actual survey conditions in the scenic area, the quadrat size can be 1m × 1m, with no fewer than 5 replicate quadrats for each habitat type. The monitoring cycle is determined based on the actual feasible survey frequency; for example, surveys can be conducted once a year during the peak growing season (July–August) and the post-fruiting nutrient period (September–October), meaning one calendar year corresponds to two monitoring cycles. This is the monitoring cycle number. Aboveground density and plant height of *Allium chinense* and its competing species were recorded. The thickness of the surface humus layer was also measured, and soil seed bank samples were collected.

[0052] Based on multi-period monitoring data, an improved Lotka-Volterra dynamic model was established to describe the density changes of *Allium chinense* and its competing species. The model incorporates non-integer time delay terms and a density nonlinearity exponent. Furthermore, the improved dynamic model includes a first nonlinearity exponent characterizing the intraspecific nonlinear effect of competition, a second nonlinearity exponent characterizing the interspecific nonlinear effect of competition, and a time delay term characterizing the delayed characteristics of the competition effect. Specifically, the discrete form of the improved dynamic model is as follows:

[0053]

[0054] In the formula, The monitoring cycle number is a dimensionless integer representing the k-th discrete monitoring time; m represents multi-star chives, and j represents the code of the competing species. For multi-star chive density; The population density of *Leekia spicata* during the kth monitoring period, expressed in units of plants. ; : No. The predicted population density of *Leekia scabra* for a monitoring period, with units of plants. ; Population density of competing species in the kth monitoring period, in units of plants. or cluster ; The intrinsic growth rate of multi-star chives represents the maximum instantaneous growth rate under conditions of no density constraints and environmental stress. The carrying capacity of *Leekia polymorpha* indicates the maximum density that *Leekia polymorpha* can achieve under current habitat conditions, expressed in units of 1 / 2π and 1 / 3π ... Consistent; : Intraspecific nonlinear density index of *Allium chinense*, dimensionless, characterizing the degree of nonlinearity of intraspecific competition intensity with density; : The nonlinear interspecific competition index of competing species j against *Leekia multiflora*, dimensionless, characterizing the degree of nonlinearity of competition intensity with the density of competing species; : Interspecific competition coefficient of competing species j against *Leekia multiflora*, dimensionless, reflecting the inhibitory effect of competing species per unit density on the growth of *Leekia multiflora*; The number of delayed periods during which competing species exert a competitive effect on *Leekia multiflora*, i.e., the number of delayed periods of the competitive effect, can be a non-integer, and the unit is the number of monitoring periods; : Environmental stress index for the kth monitoring period (composed of normalized weighted average of annual precipitation anomaly and tourist volume, optional), dimensionless composite index; The response coefficient of *Leuciscus polymorpha* to environmental stress represents the contribution of a unit stress index to the density change of *Leuciscus polymorpha*. : High density of star chives Power functions are used to express the nonlinear strength of intraspecific density constraints; Density of competing species j at the delayed time Power functions are used to express the nonlinear intensity of time-delayed interspecies competition; : Delay time index, when it is not an integer, the corresponding density value is obtained by linear interpolation of adjacent integer period data; : The summation operator that iterates through all competing species except for the multi-star chive; The product of the environmental stress index and the density of the multi-star chives represents the population decline caused by stress.

[0055] Environmental stress index Determine the annual precipitation anomaly as follows: Normalized value of tourist volume Perform a weighted summation, that is ,in, and For the preset weighting coefficients, and When reliable stress data is unavailable, i.e., reliable precipitation and visitor volume data cannot be obtained, take... At this point, the improved dynamic model degenerates into a basic form that does not include environmental stress terms.

[0056] Within the parameter search space And apply nonnegativity constraints to the relevant density terms, , Limit it to a reasonable range (e.g., 0.8~2.0) to ensure the economy and explainability of changes in competition intensity; It is not advisable to exceed 3 to 4 monitoring cycles.

[0057] For time delay terms ,when When the values ​​are non-integer, linear interpolation of adjacent integer periods is used for calculation. When estimating model parameters, a multi-initialization local optimization strategy is employed: multiple sets of initial values ​​are selected within a reasonable parameter range, and the mean absolute percentage error between the model prediction and the measured values ​​is minimized using optimization algorithms such as Nelder-Mead. The parameter combination with the smallest error is then taken as the estimated value. Optionally, confidence interval estimation of the model parameters is performed using Bootstrap resampling to assess prediction uncertainty.

[0058] S2: The improved dynamic model is expressed as a stochastic form containing process noise and observation noise, and a filtering algorithm is used to estimate the population state online, outputting the state estimate and its uncertainty measure;

[0059] Step S2 is used to perform state estimation of noisy observations. The specific process is as follows:

[0060] Considering that actual monitoring data contains sampling errors and random environmental fluctuations, the improved dynamic model in step S1 is expressed as a stochastic form including process noise and observation noise as follows:

[0061]

[0062] in, : The state vector of the kth monitoring period, which is composed of the density of multiple species and each competing species; : No. Predicted state vector for each monitoring cycle; Consider the set of historical state vectors with time delays, containing data at each delay time. Species density; : The regulatory measures vector for the kth monitoring period, which includes the removal intensity of each competing species and the indication of enclosure measures; Step S1: The vector-valued function of the dynamic model maps the current state, historical time-delay state, and control input to the state of the next cycle. : Process noise vector, representing environmental random fluctuations and dynamic simplification errors not captured by the model; : The observed noise vector characterizes the sampling error and density measurement error of the quadrat. : The actual observation vector for the kth monitoring period is composed of the measured density values ​​of each species obtained from the fixed quadrat survey; : Process noise covariance matrix, describing the variance and covariance of each component of the process noise; : Observation noise covariance matrix, which describes the variance and covariance of each component of the observation noise; The state estimate after measurement update in the kth cycle is the optimal state estimate of the filtered output. : The state estimation error covariance matrix for the k-th period, which quantifies the uncertainty of the current estimate.

[0063] The unscented Kalman filter algorithm is used to perform online estimation of the population state:

[0064] This filter generates a set of Sigma points through an unscented transform, followed by a nonlinear vector-valued function. After propagation, the state mean and covariance matrix are reconstructed, and new observations are obtained in each monitoring period. Then, a measurement update is performed, and the state estimate is output. and its estimated error covariance matrix , respectively, serve as the state estimate and its uncertainty measure. The process noise covariance matrix of the unscented Kalman filter algorithm. and observation noise covariance matrix The initial values ​​can be estimated from the model fitting residual covariance and the intra-sample repeated measures variance, respectively. During operation, a sliding window of several periods can be used to recalculate the filter residuals and observation error covariance, and the updated matrix can be diagonalized or positive definite to ensure numerical stability. The state estimate output by the filter... and its state estimation error covariance matrix This provides a foundation for subsequent optimization decisions.

[0065] S3: Based on the state estimate and its uncertainty measure, generate multiple scenarios for simulating future population evolution, construct an objective function to balance degradation risk and regulation cost based on the scenarios, and search for the optimal sequence of regulation measures through an optimization algorithm; the regulation measures include the intensity of elimination of competing species and indications of enclosure measures;

[0066] Step S3 is used to implement rolling optimization control decisions based on risk assessment.

[0067] Specifically, the objective function for balancing degradation risk and control costs is constructed based on the aforementioned scenarios. This includes: generating multiple noise-perturbed scenarios to simulate future population evolution based on the current period's state estimate and its uncertainty measure; for each scenario, simulating the change trajectory of multi-star chickpea density during the prediction period, statistically analyzing the proportion of scenarios with multi-star chickpea density below a preset threshold as a degradation risk indicator, and calculating the cost of control measures; assigning different scenario weights to each scenario, with scenarios having higher prediction uncertainty receiving higher weights, and constructing a weighted objective function based on the degradation risk indicator, control costs, and scenario weights. The specific process is as follows:

[0068] Based on the state estimation results, future plans are formulated in each decision-making cycle. The regulatory measures are implemented in several cycles. These measures include the intensity of zonal clearing of competing species and whether or not enclosure measures are implemented.

[0069] The following optimization problem is established: Under the premise that the density of multiple chives (a type of chive) remains above a set threshold with a high probability, minimize the cost of control measures. Specifically, based on the current state estimation... and state estimation error covariance matrix ,generate The future state evolution scenarios are subject to noise disturbances. For each scenario, the trajectory of multi-star chive density change is simulated, and the proportion of scenarios where the multi-star chive density is lower than the minimum survivable density during the prediction period is used as a degradation risk indicator. The control costs are also calculated.

[0070] To guide the optimization search towards scenarios with a higher risk of degradation, scenario weights are constructed based on the differences in the magnitude and direction of the gradient for each scenario. Furthermore, different scenario weights are assigned to each scenario as follows:

[0071] One specific approach is to calculate the gradient vector of the objective function of each scenario with respect to the control variable, and set weights based on the magnitude of the gradient vector of each scenario and the angle between it and the average gradient direction, so that scenarios with larger magnitudes or larger angles with the average gradient direction receive higher weights.

[0072] As an optional implementation, principal component analysis can also be used: calculate the score of each scenario on the first principal component, and use the normalized absolute deviation of this score from the mean as the weight, with larger differences resulting in higher weights. After constructing the weighted objective function, an adaptive evolutionary strategy based on the covariance matrix is ​​preferably used as the optimization algorithm to search for the optimal control sequence. The optimized output will then be the future... The system consists of a series of regulatory measures for each cycle, but only the decisions corresponding to the current cycle are implemented immediately.

[0073] S4: Based on soil seed bank survey data and the reproductive index of *Leekia spicata*, calculate the natural regeneration recovery potential index of the population, and classify the regeneration auxiliary level according to the conservative estimate of the recovery potential index.

[0074] Step S4 is used to assess the natural regeneration capacity. Specifically, when calculating the conservative estimate of the population's natural regeneration recovery potential index, if each basic indicator has at least four periods of historical observation data and its distribution is approximately symmetrical, the mean of the multi-period data for each indicator is taken minus one standard deviation; if the data distribution is skewed, a logarithmic transformation is performed before calculating the conservative estimate. The specific process is as follows:

[0075] Based on soil seed bank survey data and combined with the results of surveys on the tillering rate and seed setting rate of *Allium tuberosum* bulbs, the Natural Regeneration Recovery Potential Index (RPI) was calculated. To address the noise influence in the observation data, when each indicator has at least four observation periods and its distribution is approximately symmetrical, the mean of the multi-period data for each indicator minus one standard deviation can be used as a conservative estimate for RPI calculation. If the data distribution is significantly skewed, a logarithmic transformation can be performed before making a conservative estimate. Alternatively, the sliding window mean (i.e., the mean of the most recent three periods) or the 30th percentile (i.e., the 30th percentile in historical data) can be used as a conservative estimate.

[0076] Furthermore, in step S4, the step of classifying the update assistance level based on the conservative estimate of the Recovery Potential Index (RPI) includes: if the conservative estimate is higher than a first threshold, then a light assistance measure mainly based on protective enclosure is adopted; if the conservative estimate is between a second threshold and a first threshold, then seed rain supplementation is added on the basis of enclosure; if the conservative estimate is lower than a second threshold, then artificial reseeding of multi-spotted chive seeds is further added; wherein, the first threshold is greater than the second threshold. An optional grading example is as follows:

[0077] If the conservative RPI value is higher than 0.65, the natural regeneration capacity is strong, and mild auxiliary measures, mainly protective enclosure, should be adopted; if the conservative RPI value is between 0.35 and 0.65, the regeneration capacity is moderate, and seed rain should be added to the enclosure; if the conservative RPI value is lower than 0.35, the regeneration capacity is weak, and artificial reseeding of multi-spotted chive seeds should be further added.

[0078] S5: Spatially match and implement the current periodic measures in the optimal control measure sequence with the update assistance level. After acquiring new population state data in the next monitoring cycle, return to step S2 to update the state estimate and re-execute steps S3 and S4 to dynamically adjust subsequent control and update schemes.

[0079] Step S5 is used to achieve coordinated implementation and dynamic adjustment of control and update measures. Specifically:

[0080] The control measures output in step S3 are spatially matched with the update assistance level determined in step S4: in areas with high density of competing species, the focus is on clearing and control, while in areas with low update potential, reseeding is increased. After one cycle, new monitoring data is collected, and the state estimate and noise parameters are updated back to step S2. Steps S3 and S4 are then run again to update subsequent control and update plans. This closed-loop process of monitoring → estimation → decision-making → implementation → remonitoring runs throughout the entire remediation period.

[0081] Figure 3 This is a schematic diagram of a system for regulating the interaction between *Allium chinense* and competing species and for natural population renewal and repair, according to an embodiment of the present invention. Figure 3 As shown, a system for regulating interactions between *Allium chinense* and competing species, and for natural population regeneration and restoration, includes:

[0082] The data acquisition module 210 is used to acquire population status data of *Lepidium apetalum* and its competing species in multiple monitoring cycles;

[0083] The model building module 220 is used to establish an improved dynamic model describing the density changes of the multi-star chives and competing species;

[0084] The state estimation module 230 is used to express the improved dynamic model as a stochastic form containing process noise and observation noise, and to use a filtering algorithm to estimate the population state online, and output the state estimate and its uncertainty measure.

[0085] The rolling optimization module 240 is used to generate multiple scenarios for simulating future population evolution based on the state estimate and its uncertainty measure, construct an objective function to balance degradation risk and regulation cost based on the scenarios, and search for the optimal sequence of regulation measures through an optimization algorithm; the regulation measures include the intensity of elimination of competing species and indications of enclosure measures;

[0086] The updated assessment module 250 is used to calculate the natural regeneration recovery potential index of the population based on soil seed bank survey data and the reproductive index of *Leekia spicata*, and to classify the regeneration auxiliary level according to the conservative estimate of the recovery potential index.

[0087] The collaborative execution module 260 is used to spatially match and implement the current periodic measures in the optimal control measure sequence with the update assistance level, and after acquiring new population state data in the next monitoring cycle, it triggers the state estimation module, rolling optimization module and update evaluation module to update, so as to dynamically adjust the subsequent control and update schemes.

[0088] Example 2:

[0089] The following example, a 5.2-hectare degraded *Leonurus japonicus* plot in the Jiucaiping Scenic Area, illustrates the implementation process of this invention. This plot is located in the mid-altitude region of the scenic area, with the main competing species being *Phyllostachys shuichengensis* and *Dipsacus asper*. Before implementation, the average density of *Leonurus japonicus* was approximately 31 plants / m² (based on the mean of 15 1m×1m quadrats within the plot, with a standard deviation of ±7 plants / m²), and the humus layer thickness was less than 1cm.

[0090] (I) Monitoring quadrat layout and model construction (step S1):

[0091] Fifteen fixed quadrats (1m×1m) were established within the sample plots according to the density gradient of competing species. Surveys were conducted annually during the peak growth period of *Leekia scabra* and the post-fruiting nutrient stage, corresponding to two monitoring cycles per calendar year. Continuous surveys were conducted for several years, yielding 12 valid data points. Survey indicators included the aboveground density and humus layer thickness of *Leekia scabra*, *Phyllostachys edulis*, and *Dipsacus asper*. Simultaneously, annual precipitation and visitor volume data for the scenic area during the same period were compiled, and the precipitation anomaly and visitor volume were normalized separately before being weighted to synthesize an environmental stress index. Each has a weight of 0.5.

[0092] The model parameters were fitted using data from the first 10 periods, with the last 2 periods reserved for validation. The parameter search space was set as follows: , , , , Eight initial values ​​were uniformly selected in the parameter space using Latin hypercube sampling, and Nelder-Mead optimization was run on each. The result with the smallest fitting error was selected. The following was identified: , , Water City Jade Mountain Bamboo , , Cycle; Sichuan distiller's , , cycle; The difference in MAPE between the best and second-best results in the eight sets of results was less than 0.5%, indicating that the parameter identification results were relatively robust. Prediction results for the subsequent two validation periods showed that the improved model had a MAPE of 16.0%, while the classic LV model in the same period had a MAPE of 18.3%, indicating improved prediction accuracy in this case.

[0093] Figure 4 To improve the fitting results of the competitive dynamics model and the classic Lotka-Volterra model on the density changes of multiple stars, this study aims to improve the fitting results of the competitive dynamics model and the classic Lotka-Volterra model on the density changes of multiple stars. Figure 4It is evident that both models can reflect the overall recovery trend of *Allium chinense* populations. However, the classic LV model exhibits a certain degree of systematic overestimation in the mid-to-late stages, while the improved model proposed in this invention is closer to the measured density in each monitoring period. This is because the improved model introduces a non-integer time lag term and a nonlinear competition index, which better describes the delayed inhibitory effect of competing species on *Allium chinense* growth and the nonlinear characteristics of competition intensity changing with density, thus achieving higher fitting accuracy and ecological adaptability.

[0094] (II) State estimation and rolling optimization (steps S2-S3):

[0095] Using the model fitting residual covariance as The initial values ​​of the matrix are the variance of repeated measures within the sample plots. Initialize the matrix and establish an unscented Kalman filter. In the first monitoring cycle after model fitting, initialize the state estimate and run rolling optimization. Optimization parameters are set as follows: number of scenes. Predicting the time domain The competitive species elimination intensity is set at 5% intervals within each period, ranging from 0% (no elimination) to 70%. The minimum viable density threshold is set at 25 plants. The requirement is that the proportion of scenarios meeting this threshold among 200 scenarios is not less than [a certain percentage]. The CMA-ES population size is set to 50, the maximum number of iterations is 200, and the objective function change is less than [missing value]. The process stops at a certain point. In this embodiment, scene weights are constructed using the differences in magnitude and direction of gradients for each scene. The optimization algorithm converges after approximately 150 iterations, outputting the optimal control sequence. Figure 5 This is a schematic diagram of the optimization decision-making process based on state estimation and scenario generation.

[0096] (III) Update Assessment and Closed-Loop Implementation (Steps S4-S5):

[0097] Based on the seed bank and plant propagation index survey data from the first monitoring period, each index has been observed for four periods and is basically symmetrically distributed. The conservative value after subtracting the standard deviation from the mean of each index is used to participate in the RPI calculation. The conservative RPI value is approximately between 0.26 and 0.34. If it is below 0.35, it is classified as a level with weak regeneration capacity, and artificial reseeding intensity is provided as an auxiliary measure.

[0098] Following the optimized plan, competing species were removed in the next monitoring cycle (optimized output intensity was approximately 40%–55% of the existing density, varying slightly between different zones) and artificial reseeding was implemented, along with protective enclosure of marginal areas. After new monitoring data returned in subsequent years, filtering and optimization were re-run, with fine-tuning of the subsequent removal intensity. Approximately two years after implementation (i.e., after four more monitoring cycles), the average density of *Allium macrostemon* in the sample plots recovered to 57–65 plants / m² (15 quadrats, 95% confidence interval). As a reference, three control plots (each containing five 1m × 1m quadrats) were set up in non-degraded areas adjacent to the remediation plots at the same altitude and slope aspect, with a humus layer thickness greater than 3cm. The *Allium macrostemon* densities in these control plots were 69, 73, and 74 plants / m², respectively, with a total mean of 72 plants / m² and a standard deviation of ±2.6 plants / m². The density difference between the remediation and control plots was significantly reduced. These results demonstrate that the method of this invention effectively promoted the recovery of *Allium macrostemon* populations in the demonstration plots.

[0099] The above description is only a preferred embodiment of the present invention and is used only to explain the present invention. It is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0100] It should also be noted that, in the embodiments of this application, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0101] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined in the embodiments of this application may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown in this application, but is to be accorded the widest scope consistent with the principles and novel features disclosed in the embodiments of this application.

Claims

1. A method for regulating the interaction between *Allium chinense* and competing species and for the natural regeneration and restoration of its population, characterized in that, Includes the following steps: S1: Acquire population status data of *Lepidium apetalum* and its competing species in multiple monitoring periods, and establish an improved dynamic model describing the density changes of *Lepidium apetalum* and its competing species. S2: The improved dynamic model is expressed as a stochastic form containing process noise and observation noise, and a filtering algorithm is used to estimate the population state online, outputting the state estimate and its uncertainty measure; S3: Based on the state estimate and its uncertainty measure, generate multiple scenarios for simulating future population evolution, construct an objective function to balance degradation risk and regulation cost based on the scenarios, and search for the optimal sequence of regulation measures through an optimization algorithm; the regulation measures include the intensity of elimination of competing species and indications of enclosure measures; S4: Based on soil seed bank survey data and the reproductive index of *Leekia spicata*, calculate the natural regeneration recovery potential index of the population, and classify the regeneration auxiliary level according to the conservative estimate of the recovery potential index. S5: Spatially match and implement the current periodic measures in the optimal control measure sequence with the update assistance level. After acquiring new population state data in the next monitoring cycle, return to step S2 to update the state estimate and re-execute steps S3 and S4 to dynamically adjust subsequent control and update schemes.

2. The method according to claim 1, characterized in that, In step S1, the improved dynamic model includes a first nonlinear exponent characterizing the intraspecific nonlinear effect of competition, a second nonlinear exponent characterizing the interspecific nonlinear effect of competition, and a time delay term characterizing the delayed characteristics of the competition effect. The discrete form of the improved dynamic model is as follows: ； in, The monitoring period number is 'm', where 'm' represents *Allium chinense* and 'j' represents the code for competing species. For multi-star chive density, For the density of competing species j, The intrinsic growth rate For environmental carrying capacity, It is an intraspecific nonlinear density index. and These are the nonlinear competition index and competition coefficient of competing species j against multiple species of chives, respectively. The number of delay periods for the competition effect. The environmental stress index. The stress response coefficient; The population density of *Leekia multiflora* during the kth monitoring period; For the first The predicted population density of *Leekia scabra* over a monitoring period.

3. The method according to claim 2, characterized in that, In step S1, when estimating the model parameters, a multi-initialization local optimization strategy is adopted: multiple initial values ​​are selected within a reasonable parameter range, and the error between the model prediction value and the measured value is minimized by the optimization algorithm. The parameter combination with the smallest error is taken as the estimated value.

4. The method according to claim 2, characterized in that, Step S2 specifically includes: The improved dynamic model is expressed as a stochastic form containing process noise and observation noise as follows: ； in, : No. Predicted state vector for each monitoring cycle; Let be the state vector consisting of multi-star chives and the densities of each competing species; The set of historical state vectors considering time delay effects, containing all time delays. Species density; This is a vector of regulatory measures that includes indicators of the intensity of competing species removal and enclosure measures; For the improved dynamic model, is the vector-valued function; To characterize the process noise vector that the model fails to capture random fluctuations; This represents the actual observation vector for the kth monitoring period; The observation noise vector characterizing sampling and measurement errors; The unscented Kalman filter algorithm is used for online estimation of the population state, including: Sigma points are generated through an unscented transformation, and then processed by the vector-valued function. After propagation, the state mean and covariance matrix are reconstructed, and new observations are obtained in each monitoring period. Then, a measurement update is performed, and the state estimate is output. and its state estimation error covariance matrix , respectively, serve as the state estimate and its uncertainty measure; The initial values ​​of the process noise covariance matrix and the observation noise covariance matrix of the unscented Kalman filter algorithm are estimated by the model fitting residual covariance and the intra-sample repeated measurement variance, respectively, and are updated using a sliding window during operation.

5. The method according to claim 1, characterized in that, Step S3, which involves constructing an objective function based on the scenario to balance degradation risk and control costs, specifically includes: Based on the state estimate and uncertainty measure of the current period, multiple scenarios with noise disturbances are generated to simulate future population evolution. For each scenario, the trajectory of the change in the density of multiple stars during the prediction period is simulated. The proportion of scenarios with the density of multiple stars below the preset threshold during the prediction period is used as the degradation risk indicator, and the cost of control measures is calculated. Different scenario weights are assigned to each scenario, with scenarios having higher prediction uncertainty receiving higher weights. A weighted objective function is then constructed based on the degradation risk index, control costs, and scenario weights.

6. The method according to claim 5, characterized in that, The method for assigning different scenario weights to each scenario is as follows: Calculate the gradient vector of the objective function with respect to the control variable for each scenario, and set the weights according to the magnitude of the gradient vector and the angle between it and the average gradient direction, so that scenarios with larger magnitudes or larger angles with the average gradient direction receive higher weights. Alternatively, principal component analysis can be used to calculate the score of each scenario on the first principal component, and the normalized value of the absolute deviation of the score from the mean can be used as the weight.

7. The method according to claim 1, characterized in that, In step S3, the optimization algorithm is an adaptive evolution strategy for the covariance matrix.

8. The method according to claim 1, characterized in that, In step S4, when calculating the conservative estimate of the population natural regeneration recovery potential index, if each basic indicator has at least 4 periods of historical observation data and the distribution is approximately symmetrical, the mean of the data of each indicator over multiple periods is taken minus one standard deviation; if the data distribution is skewed, a logarithmic transformation is performed first before calculating the conservative estimate.

9. The method according to claim 1 or 8, characterized in that, In step S4, the step of classifying the updated assistance level based on the conservative estimate of the recovery potential index includes: If the conservative estimate is higher than the first threshold, then mild auxiliary measures, mainly protective enclosure, will be adopted. If the conservative estimate is between the second threshold and the first threshold, then seed rain will be added to supplement the enclosure. If the conservative estimate is lower than the second threshold, then further measures such as artificial reseeding of multi-spotted leek seeds will be taken. Wherein, the first threshold is greater than the second threshold.

10. A system for regulating interactions between *Allium chinense* and competing species and for natural population regeneration and restoration, characterized in that: include: The data acquisition module is used to acquire population status data of *Lepidium apetalum* and its competing species over multiple monitoring periods; The model building module is used to establish an improved dynamic model describing the density changes of the multi-star chives and competing species; The state estimation module is used to express the improved dynamic model as a stochastic form containing process noise and observation noise, and to use a filtering algorithm to estimate the population state online, outputting the state estimate and its uncertainty measure. The rolling optimization module is used to generate multiple scenarios for simulating future population evolution based on the state estimate and its uncertainty measure, construct an objective function to balance degradation risk and regulation cost based on the scenarios, and search for the optimal sequence of regulation measures through an optimization algorithm; the regulation measures include the intensity of elimination of competing species and indications of enclosure measures; The updated assessment module is used to calculate the natural regeneration recovery potential index of the population based on soil seed bank survey data and the reproductive indicators of *Leekia spicata*, and to classify the regeneration auxiliary level according to the conservative estimate of the recovery potential index. The collaborative execution module is used to spatially match and implement the current periodic measures in the optimal control measure sequence with the update assistance level, and after acquiring new population state data in the next monitoring cycle, it triggers the state estimation module, rolling optimization module and update evaluation module to update, so as to dynamically adjust the subsequent control and update schemes.

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