Method and device for solving equilibrium solution of scale population model based on density distribution reconstruction

Abstract

The invention discloses a method for solving a balanced solution of a scale population model based on density distribution reconstruction, and the method comprises the following steps: S1, building a population dynamics model with a scale structure according to the life cycle characteristics of a research object; s2, according to non-local boundary conditions, setting incubation growth amount and breeding circulation amount; s3, fixing the incubation growth amount, and solving the breeding circulation amount; s4, judging whether the population dynamics model is in a balance state or not according to the population number growth rate; if the state is the balance state, executing the step S5; if the state is the unbalanced state, the breeding circulation amount is used as the next incubation growth amount, and iteration is carried out until the breeding circulation amount is equal to the incubation growth amount; and S5, reconstructing population number distribution in an equilibrium solution state. According to the method, stable and unstable equilibrium solutions can be solved.

Description

Technical Field

[0001] The present invention relates to the technical field of ecology, and in particular, to a method and device for solving the equilibrium solution of a size-structured population model based on density distribution reconstruction. Background Art

[0002] In recent years, size-structured models have received increasing attention in ecology. Such models use a set of differential equations to describe the processes of individuals of different sizes over time and the resulting changes in population dynamics, aiming to characterize the size distribution, dynamic changes within the population, and the interactions with factors such as the environment and resources.

[0003] In size-structured models, the stability of the population equilibrium solution is an important issue. Stability analysis is usually judged by observing the response of the population system to small perturbations after reaching the equilibrium state. If the system can return to the original equilibrium state after sufficient time, the equilibrium solution is considered stable; otherwise, if it cannot recover, the equilibrium solution is considered unstable.

[0004] Currently, the methods for solving the population equilibrium solution usually rely on classical discretization techniques of difference equations, and judge by numerical simulation and plotting the time series of population biomass. Although the time series plot can intuitively show some equilibrium solutions that tend to be stable, there are still limitations, such as possibly missing some equilibrium solutions or being unable to accurately judge the stability of all equilibrium solutions.

[0005] Therefore, how to effectively solve the population model containing all equilibrium solutions, especially in size-structured models, has always been a challenge in ecological research. Summary of the Invention

[0006] Object of the Invention: The object of the present invention is to provide a method and device for solving the equilibrium solution of a size-structured population model based on density distribution reconstruction, which can effectively and comprehensively solve stable and unstable equilibrium solutions, breaking through the limitation that traditional time series methods can only analyze some stable equilibrium solutions, cannot effectively identify all equilibrium solutions and accurately judge their stability.

[0007] Technical Solution: A method for solving the equilibrium solution of a size-structured population model based on density distribution reconstruction includes the following steps:

[0008] S1, establish a size-structured population dynamics model according to the life cycle characteristics of the research object;

[0009] S2, set the hatching growth amount and reproductive flux according to non-local boundary conditions;

[0010] S3, fix the hatching growth amount and find the reproductive flux;

[0011] S4. Determine whether the population dynamics model is in an equilibrium state according to the population growth rate; if it is in an equilibrium state, execute step S5; if it is not in an equilibrium state, use the reproductive flux as the next hatching growth amount and perform iteration until the reproductive flux is equal to the hatching growth amount;

[0012] S5. Reconstruct the population quantity distribution in the equilibrium solution state.

[0013] Furthermore, based on the body length x, the resource biomass R, and the predator population density P, establish a population dynamics model; the population dynamics model includes the McKendrick-Von Foerster equation for consumer population dynamics, the ordinary differential equation for resource biomass dynamics, and the ordinary differential equation for predator population density dynamics;

[0014] The McKendrick-Von Foerster equation for consumer population dynamics, which is used to describe the number density dynamics of consumers and the expression of non-local boundary conditions, is as follows:

[0015]

[0016] c(t,x) represents the number density of consumers with body length x at time t; g(R,x), μ(x,R,P), and b(R,x) represent the growth rate, mortality rate, and birth rate of consumers respectively. The body length of a consumer at birth is x b , and the body length at maturity is x j , and it grows to the maximum achievable body length x when there is enough food m ;

[0017] The ordinary differential equation for resource biomass dynamics, which is used to describe resource biomass dynamics, follows semi-steady-state growth and is preyed upon by consumers of all body lengths. The expression is as follows:

[0018]

[0019] K is the resource carrying capacity; A(x) is the predation rate function of consumers on resources; H(x) is the handling time function; τ represents "activity change", and its value range is from 0 to 1;

[0020] The ordinary differential equation for predator population density dynamics, which is used to describe the density dynamics of Lotka-Volterra type predators, is as follows:

[0021]

[0022] The predator preys on the biomass B of consumers with body length between x b and x v . The expression of the biomass B is as follows:

[0023]

[0024] w(x) = βx 3

[0025] where w(x) represents the consumer quality function with body length x, and β is the proportionality coefficient of body length to body weight; x v is the maximum body length that can be preyed upon; a is the consumer attack rate, T h is the predator's prey handling time, ε is the predator's conversion efficiency of food, and δ is the predator's natural mortality rate.

[0026] Furthermore, when the population reaches the equilibrium state, the overall growth rate of the population is zero; based on this equilibrium condition, one side of the non-local boundary condition equation is the hatching growth amount, and the other side is the reproductive flux.

[0027] Furthermore, in step S3, is the non-local boundary condition, where the left side of the equation is the hatching growth amount of the population, and the right side of the equation is the reproductive flux;

[0028] Fix the hatching growth amount, let: g(R, x b )c(t, x b ) = R flx

[0029] The reproductive flux is expressed as:

[0030] Substitute the value of the hatching growth amount R fix into the population dynamics model. After a period of time, the population will reach a stable state or an unstable state. The reproductive flux R flux will stably tend to a fixed value over time, and is denoted as R flux_end ;

[0031] The hatching growth amount represents the biomass of hatched eggs growing into juvenile consumers, and the reproductive flux represents the biomass consumed by adult consumers laying eggs.

[0032] Furthermore, when R fix = R flux_end , the population growth rate is 0, which is the equilibrium solution state of the model;

[0033] When R fix < R flux_end , the population growth rate is greater than 0, and the biomass will continue to increase; similarly, when R fix > R flux_end , the population growth rate is less than 0, and the biomass will continue to decrease; in both of the above cases, the equilibrium solution state is not reached. Take the current R flux_end as the next R fixThe input value is continuously iterated until R fix = R flux_end .

[0034] Furthermore, in step S5, the numerical integration method is used to solve the population quantity at each body length x, and the stable distribution of the entire consumer population in the equilibrium state is obtained.

[0035] A device for solving the equilibrium solution of a population model with scale based on density distribution reconstruction, which executes any of the above methods through a processor, includes:

[0036] The population dynamics model module is mainly responsible for constructing a population dynamics model with scale structure, depicting the change of population quantity over time and the change of individual size distribution according to the population life history parameters;

[0037] The non-local boundary condition setting hatching growth quantity and reproduction flux module sets the hatching growth quantity and reproduction flux according to the non-local boundary condition;

[0038] The module for fixing the hatching growth quantity and calculating the reproduction flux fixes the hatching growth quantity according to the population dynamics model module and the non-local boundary condition setting hatching growth quantity and reproduction flux module, calculates the change of the reproduction flux, and records the reproduction flux at the end time;

[0039] The module for judging whether it is an equilibrium point judges whether the equilibrium point is reached according to the calculation result of the module for fixing the hatching growth quantity and calculating the reproduction flux; it is judged by evaluating whether the fixed hatching growth quantity of the system is equal to the reproduction flux at the end time. If they are equal, it is an equilibrium point;

[0040] The module for reconstructing the population quantity distribution in the equilibrium solution state uses the numerical integration method to reconstruct the population quantity at each body length in the equilibrium solution state, and obtains the stable distribution of the entire consumer population in the equilibrium state, reflecting the final scale and structure of the population.

[0041] Compared with the prior art, the remarkable effects of the present invention are as follows:

[0042] 1. The method of the present invention adopts the method based on density distribution reconstruction, which can comprehensively identify all equilibrium solutions in the population model, including stable solutions and unstable solutions, solves the limitation that the traditional method can only identify some stable equilibrium solutions; and can provide more comprehensive and accurate equilibrium solution information for ecological research, avoiding missing potential important equilibrium solutions;

[0043] 2. In the method of the present invention, by fixing the population growth rate, the stability of the equilibrium solution can be accurately judged; the traditional stability analysis method often relies on time series and qualitative judgment, with certain errors and uncertainties. The present invention solves the problem that it is difficult to accurately judge the stability of the equilibrium solution by the existing methods;

[0044] 3. The density distribution reconstruction method of the present invention has higher computational efficiency, can quickly solve the equilibrium solution, is especially suitable for high-dimensional complex population models, can effectively save computational time and resources, and improves the operability and practicality of ecological models. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 is the basic flowchart of the present invention;

[0046] Figure 2 is the schematic diagram of the ecological significance of the present invention, showing the life cycle of the Rutilus rutilus population, including birth, growth, maturity, and reproduction stages;

[0047] Figure 3 is the reproduction flux R flux changing with time graph;

[0048] Figure 4 is R flux_end -R fix relationship graph, points A and C represent stable equilibrium solutions, point B represents an unstable equilibrium solution, and at points A, B, and C, R fix = R flux_end , the population reaches the equilibrium solution state, and points P and Q are random points on the curve of R flux_end -R fix in the graph;

[0049] Figure 5 is the time series graph of the population biomass under the equilibrium solution state, and curve e represents Figure 4 the stable equilibrium solution situations of points A and C in Figure 4 , and curve f represents

[0050] Figure 6 is the distribution graph of the population biomass under the equilibrium solution, and the three curves respectively correspond to Figure 4 the equilibrium solutions A, B, and C in

[0051] Figure 7 is the device architecture diagram of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0052] The present invention will be further described in detail below in conjunction with the accompanying drawings of the specification and the specific embodiments.

[0053] The present invention proposes a method for solving the equilibrium solution of a scale population model based on density distribution reconstruction. This method breaks through the limitations of traditional time series methods and can obtain all the equilibrium solutions in the model, including stable and unstable ones, so as to comprehensively depict the quantity distribution of the population in the equilibrium state and its ecological interaction process.

[0054] AsFigure 1 The figure shows a flowchart of a method for reconstructing and solving the equilibrium solution of a size-structured population model based on density distribution, including the following steps:

[0055] Step 1, establish a size-structured population dynamics model;

[0056] Preferably, according to the life cycle characteristics of the research object, establish a population dynamics model based on body length x, resource biomass R, and predator population density P. This model consists of a set of differential equations, which are used to describe the dynamic changes of the number density of size-structured consumers and their population fluxes, and at the same time reflect the changes of resources and predators. The model comprehensively covers the whole process of consumers from birth, growth, maturity to reproduction, and accurately depicts the biological behaviors of individuals at different body length stages and their impacts on population dynamics.

[0057] Preferably, this set of differential equations specifically includes: the McKendrick-Von Foerster equation for consumer population dynamics (including a partial differential equation and a non-local boundary condition), an ordinary differential equation for resource biomass dynamics, and an ordinary differential equation for predator population density dynamics.

[0058] Step 2, set the hatching growth amount and reproductive flux according to the non-local boundary condition;

[0059] Preferably, when the population reaches the equilibrium state, the overall growth rate of the population is zero, that is, for size-structured consumers, the biomass of eggs hatching into juveniles (hatching growth amount +) and the biomass consumed by adult fish spawning (reproductive flux -) respectively play a promoting and reducing role in the biomass of the whole population. In the process of mutual offset, this effect will reach a state of neither increasing nor decreasing, that is, the effect of 0. Based on this equilibrium condition, one side of the non-local boundary condition equation is the hatching growth amount, and the other side is the reproductive flux;

[0060] Step 3, fix the hatching growth amount and find the reproductive flux;

[0061] Preferably, substitute the value of the hatching growth amount R fix into the size-structured population dynamics model. After a period of time, the population will reach a stable state or an unstable state. The reproductive flux R flux will stably tend to a fixed value over time, and is denoted as R flux_end .

[0062] Step 4, determine whether the population dynamics model is in the equilibrium state;

[0063] Preferably, when R fix = R flux_end , the population growth rate is 0, and this is the equilibrium solution state of the model at this time. When R fix < Rflux_end When the population growth rate is greater than 0, the biomass will continue to increase; similarly, when R fix >R flux_end , the population growth rate is less than 0, and the biomass will continue to decrease. In the latter two cases, the equilibrium solution state is not reached. For these two unbalanced states, the current R flux_end is used as the input value of the next R fix , and it is continuously iterated until R fix =R flux_end ;

[0064] Step 5, reconstruct the population quantity distribution under the equilibrium solution state;

[0065] Preferably, the numerical integration method is used to solve the population quantity at each body length x to obtain the stable distribution of the entire consumer population in the equilibrium state.

[0066] The present invention also provides a computer program device, as Figure 7 shown, including:

[0067] A computer program that executes a method for reconstructing and solving the equilibrium solution of a population model with scale based on density distribution through a processor.

[0068] The population dynamics model module is mainly responsible for constructing a population dynamics model with scale structure, depicting the change of population quantity over time and the change of individual size distribution according to the population life history parameters.

[0069] The non-local boundary condition setting hatching growth amount and reproduction flux module sets the hatching growth amount and reproduction flux according to the non-local boundary condition.

[0070] The fixed hatching growth amount and calculate reproduction flux module fixes the hatching growth amount R fix , calculates the change of the reproduction flux R flux , and records the reproduction flux R flux_end at the end time.

[0071] The judging whether it is an equilibrium point module judges whether the equilibrium point is reached (that is, the population dynamics model is in the equilibrium state) according to the calculation result of the fixed hatching growth amount and calculate reproduction flux module. Judging the equilibrium point is by evaluating whether the fixed hatching growth amount R fix of the system and the reproduction flux R flux_end at the end time are equal. If they are equal, it is the equilibrium solution state of the model at this time.

[0072] The module for reconstructing the population quantity distribution in the equilibrium solution state uses numerical integration methods to reconstruct the population quantity at each body length in the equilibrium solution state, so as to obtain the stable distribution of the entire consumer population in the equilibrium state, reflecting the final scale and structure of the population.

[0073] In this embodiment, by fixing the population growth rate, all equilibrium solutions in the model can be obtained, including stable and unstable solutions. And through transformation and integration, the population quantity distribution in the equilibrium solution state is obtained.

[0074] In this embodiment, a perch - roach - zooplankton food chain model verified by experimental data is used, and the main research object is the roach with size structure. This population experiences the entire growth process from birth to maturity and then to the maximum size as Figure 2 shown. Among them, the maximum prey body length is included between the birth length and the mature length. Roaches with body lengths between the birth length and the maximum prey body length all have the probability of being preyed on by perch, while roaches with other body lengths will not be preyed on. The life cycle of this population includes the growth and development of juvenile fish, the maturity and reproduction of adult fish, and the process of eggs hatching into juvenile fish, forming a complete biological cycle.

[0075] The population modeling of the specific example describes the life history of roach individuals with foraging, growth, reproduction, and mortality as indicators, which are mainly determined by body length x, resource biomass R, and predator population density P. The population dynamics model is described by the following differential equations:

[0076]

[0077]

[0078] Among them, c(t, x) represents the consumer number density at body length x at time t, and g(R, x), μ(x, R, P), and b(R, x) represent the consumer growth rate, mortality rate, and birth rate respectively; the body length of the consumer individual at birth is x b , and the body length at maturity is x j , and it grows to the maximum achievable body length x m under the condition of sufficient food; K is the resource carrying capacity.

[0079] Formulas (1) and (2) describe the consumer number density dynamics and non - local boundary conditions, which are also called the McKendrick - Von Foerster equations;

[0080] Formula (3) describes the resource biomass dynamics, which follows semi - chemostat growth and is preyed on by consumers of all body lengths.

[0081] The rate at which consumers obtain energy from resources is:

[0082]

[0083] ε R represents the consumer's food conversion efficiency, τ represents the behavioral characteristic of "activity change", and its value range is 0 to 1. The higher the value, the higher the behavioral activity. This parameter will be greatly affected by human behavior; A(x) is the consumer's predation rate function on resources, which depends on the individual size of the consumer, and its expression is as follows:

[0084]

[0085] is the dome shape function, when the individual weight is w opt The maximum attack rate reaches A max , where α is an exponential constant; w opt is the weight of the consumer when the maximum attack rate is reached. w(x) represents the mass function of the consumer with a body length of x, which is proportional to the cube of the consumer's body length.

[0086] H(x) is a processing time function, which is limited by the ability of the intestine to digest food and is proportional to the power function of body weight. Its expression is as follows:

[0087]

[0088] Among them, ξ 1 is the proportionality constant, ξ 2 is an exponential constant.

[0089] The food digested by consumers is converted into R Assimilation is carried out, and the assimilated energy is used for maintenance, growth and reproduction, of which a proportion of κ is allocated to the metabolism of growth and life maintenance activities, and the rest is used for the development of sexual organs of immature individuals or the reproduction of offspring of mature individuals.

[0090] The metabolism that maintains life activities takes precedence over growth, including basal metabolism and activity metabolism

[0091]

[0092] They have similar forms proportional to the power function of body weight. The remaining energy used for metabolism is used for individual growth, and the expression of consumer growth rate is as follows:

[0093]

[0094] Among them, κ represents the energy distribution ratio; β is the ratio coefficient of body length to body weight;

[0095] But if all that energy isn't enough to sustain metabolism, growth stops.

[0096] With c r Efficient mature individuals reproduce, and the birth rate of reproduction is obtained by calculating the energy consumption per egg, and the expression is as follows:

[0097]

[0098] The expression of the mortality rate is as follows:

[0099] μ(x,R,P) = μ 0 + μ s + μ p (10)

[0100] Where μ 0 is the natural mortality rate, μ s is the starvation mortality rate, and μ p is the predation mortality rate. All consumer individuals have a natural mortality rate independent of size, and when the energy is insufficient to meet the metabolic consumption, they may further experience the starvation mortality rate. The starvation mortality rate function μ s (x,R) has the following expression:

[0101]

[0102] Where s is the starvation mortality rate proportionality constant and κ is the energy allocation ratio.

[0103] At the same time, only individuals with body lengths between x b and x v have the risk of being preyed upon, and the predation mortality rate is:

[0104]

[0105] Formula (4) describes the density dynamics of Lotka-Volterra type predators. The predators feed on the biomass B of consumers with body lengths between x b and x v . The description of B is as follows:

[0106]

[0107] w(x) = βx 3 (14)

[0108] Where w(x) represents the mass of roach with body length x, which is proportional to the cube of its body length.

[0109] The foraging of perch follows the Holling-II type functional response function. The consumer attack rate is a, the handling time for a single predation by the consumer is T h , the conversion efficiency of food is ε, and the natural mortality rate is δ.

[0110] Table 1 lists the specific example model variables and parameters.

[0111] Table 1 Empirical parameters of the perch-roach system

[0112]

[0113] In this specific example, only mature fish (adult stage) can reproduce and lay eggs, and the fish eggs hatch into juveniles after hatching. The biomass of this part that has reproduced and laid eggs participates in the population growth cycle, which the present invention calls the reproductive flux. The processes of population reproduction, egg-laying, and hatching are the breakthrough points for solving the equilibrium solution based on density distribution reconstruction. The biomass of hatched juveniles (hatching growth +), and the biomass of adult fish consumed by egg-laying (reproductive flux -) respectively play a promoting and reducing role in the biomass contribution of the entire population. In the process of mutual cancellation, this effect will reach a state of neither increasing nor decreasing, that is, an effect of 0. At this time, the ecological structure of the population is a balanced state (as Figure 3 shown). In the population dynamics model, is called a non-local boundary condition, where the left side of the equation is the hatching growth of the population, and the right side of the equation is the reproductive flux.

[0114] Fix the hatching growth, let:

[0115] g(R,x b )c(t,x b )=R flx (15)

[0116] The reproductive flux can be expressed as:

[0117]

[0118] Fix the value of the hatching growth R fix , substitute the hatching growth R fix into the kinetic equation, and after a period of time, the population will reach a stable state or an unstable state. The reproductive flux R flux will stably tend to a fixed value over time, and is denoted as R flux_end . Traverse the values of R fix and calculate the corresponding R flux_end .

[0119] When R fix =R flux_end , the population growth rate is 0, and this is the equilibrium solution state of the model. When R fix <R flux_end , the population growth rate is greater than 0, and the biomass will continue to increase; similarly, when R fix >R flux_endWhen the population growth rate is less than 0, the biomass will continue to decrease. In the latter two cases, the equilibrium solution state is not reached. For these two unbalanced states, the R at this time flux_end is used as the input value for the next R fix , and it is continuously iterated until R fix = R flux_end .

[0120] Figure 4 is the R of this specific example flux_end -R fix relationship diagram. Points A and C represent stable equilibrium solutions, and point C represents an unstable equilibrium solution. At points A, B, and C, R fix = R flux_end , and the population reaches the equilibrium solution state. Points P and Q are random points on the curve in the R flux_end -R fix diagram.

[0121] Figure 5 is the time series diagram of the population biomass in the equilibrium solution state of this specific example. Curve e represents Figure 4 the stable equilibrium solution cases of points A and C in

[0122] Analyzing this specific example, taking point C in Figure 4 as an example, when the population is in the unbalanced state at point P (near the left end of point C, where R fix < R flux_end ), the population growth rate is greater than 0, and the biomass will continue to increase. Taking the R flux_end at this time as the input value for the next R fix , then as the R fix value increases, the corresponding R flux_end also increases and gets closer to point C. This process continues until point P is infinitely close to point C and coincides, that is, the equilibrium state.

[0123] Next, calculate the population quantity distribution in the equilibrium solution state of this example. Since the population growth rate is 0 in the equilibrium solution state, therefore, there is:

[0124]

[0125] It can be expressed as:

[0126]

[0127] Thus, there is:

[0128]

[0129] By transformation and integration, the population quantity distribution in the equilibrium solution state can be obtained as:

[0130]

[0131] The population biomass distribution solved based on density distribution reconstruction in this example is as Figure 6 shown, and the three curves respectively correspond to Figure 4 the equilibrium solutions A, B, and C in

[0132] Based on the above invention content, those skilled in the art can further understand the specific implementation manners of the present invention. Specific claims will be prepared according to the technical solutions and embodiments of the present invention to cover all innovative points and protection scopes. Any technical solution, embodiment, or feature combination described in the present invention should be regarded as being included in the protection scope of the present invention. Any equivalent transformation or modification of the spirit of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for reconstructing a scaled population model based on density distribution, characterized in that: The steps include: S1, establish a population dynamics model with scale structure according to the life cycle characteristics of the research object; S2, setting the hatching growth and reproductive flux according to the nonlocal boundary conditions; S3, fix the hatching growth, find the reproductive flow; S4, judging whether the population dynamics model is in a balanced state according to the population growth rate; if it is in a balanced state, executing step S5; if it is in an unbalanced state, taking the reproductive flow as the next hatching growth amount, and iterating until the reproductive flow is equal to the hatching growth amount; S5, reconstruct the population size distribution under the equilibrium solution state.

2. The method for reconstructing a scaled population model based on density distribution according to claim 1, characterized in that: A population dynamics model is established based on body length x, resource biomass R and predator population density P; the population dynamics model includes the McKendrick-Von Foerster equation for consumer population dynamics, the ordinary differential equation for resource biomass dynamics and the ordinary differential equation for predator population density dynamics; The McKendrick-Von Foerster equation for consumer population dynamics, which is used to describe the number density dynamics of consumers and non-local boundary conditions, is given by: c(t,x) represents the number density of consumers with body length x at time t; g(R,x), μ(x,R,P), b(R,x) represent the consumer growth rate, mortality rate and birth rate respectively. The body length of a consumer at birth is x. b , body length at maturity is x j , and grow to its maximum attainable length x if there is enough food m ; The ordinary differential equation for the dynamics of resource biomass, which follows semi-steady growth and is preyed upon by consumers of all body lengths, is given by: K is the resource carrying capacity; A(x) is the consumer predation rate function on resources; H(x) is the processing time function; τ represents "activity change" and ranges from 0 to 1; The ordinary differential equation for the density dynamics of the predator population is as follows: Predators with a body length between x b and x v The biomass B of the consumers is food, and the expression of biomass B is as follows: w(x)=βx 3 Where w(x) represents the mass function of a consumer with a body length of x, β is the coefficient of the ratio of body length to body weight; x v is the maximum body length of the prey; a is the consumer attack rate, T h is the predator’s predation processing time, ε is the predator’s food conversion efficiency, and δ is the predator’s natural mortality rate.

3. The method for reconstructing the equilibrium solution of a scaled population model based on density distribution according to claim 2, characterized in that: When the population reaches equilibrium, the overall growth rate of the population is zero; based on this equilibrium condition, one side of the non-local boundary condition equation is the hatching growth, and the other side is the reproductive flow.

4. The method for reconstructing a scaled population model based on density distribution according to claim 3, characterized in that: In step S3, is a non-local boundary condition, where the left side of the equation is the hatching growth of the population, and the right side of the equation is the reproductive flux; Fixed incubation growth, let: g(R,x b )c(t,x b )=R flx The reproductive flux is expressed as: The hatching growth R fix The value of is brought into the population dynamics model. After a period of time, the population will reach a stable or unstable state. The reproductive flow R flux As time goes by, it tends to a fixed value and is recorded as R flux_end ; The hatchery growth represents the biomass grown from hatched eggs into young consumers, and the reproductive flux represents the biomass consumed by adult consumers in laying eggs.

5. The method for reconstructing the equilibrium solution of a scaled population model based on density distribution according to claim 4, characterized in that: When R fix =R flux_end When , the population growth rate is 0, which is the equilibrium solution state of the model; When R fix <R flux_end When the population growth rate is greater than 0, the biomass will continue to increase; similarly, when R fix >R flux_end When the population growth rate is less than 0, the biomass will continue to decrease; neither of the above two situations has reached the equilibrium solution state. flux_end As the next R fix The input value is iterated continuously until R fix =R flux_end .

6. The method for reconstructing a scaled population model based on density distribution according to claim 2, characterized in that: In step S5, the numerical integration method is used to solve the population size under each body length x, and the stable distribution of the entire consumer population in the equilibrium state is obtained.

7. A device for reconstructing a scaled population model based on density distribution, characterized in that: Executing, by a processor, the method according to any one of claims 1 to 6, comprising: The population dynamics model module is mainly responsible for constructing a population dynamics model with scale structure, describing the changes of population size over time and the changes of individual size distribution according to population life history parameters; The hatching growth and reproduction flow modules are set according to the non-local boundary conditions. The hatching growth volume is fixed and the reproductive circulation volume is calculated. The hatching growth volume and the reproductive circulation volume are set according to the population dynamics model module and the non-local boundary conditions. The hatching growth volume is fixed, the change of the reproductive circulation volume is calculated, and the reproductive circulation volume at the last moment is recorded. The module for judging whether it is a balance point is used to judge whether the balance point has been reached according to the calculation results of the module for fixing the hatching growth and calculating the reproductive flow. The module is judged by evaluating whether the fixed hatching growth of the system and the reproductive flow at the last moment are equal. If they are equal, it is a balance point. The module for reconstructing the population distribution under the equilibrium solution state uses the numerical integration method to reconstruct the population quantity at each body length under the equilibrium solution state, and obtains the stable distribution of the entire consumer population under the equilibrium state, reflecting the final size and structure of the population.

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