A method for calculating reasonable aquaculture density in aquaculture water bodies

Abstract

The present invention provides a method for calculating the reasonable aquaculture density of aquaculture water bodies, which relates to the technical field of aquaculture. The method comprises the following steps: constructing a bioaccumulation model of aquaculture objects in a limited space, conducting a density gradient aquaculture test, obtaining biomass accumulation parameters of the test group, and solving the limit yield k of each density gradient test group. i , solve the aquaculture capacity of the target aquaculture water body and find the approximate solution K m , calculating the appropriate stocking density N. The beneficial effects of the present invention are as follows: This method obtains actual aquaculture data of biomass accumulation parameters for the experimental group through density gradient aquaculture experiments, and calculates an approximate solution for aquaculture capacity based on the constructed model and aquaculture data. The obtained approximate solution is then verified, ultimately providing a basis for calculating the appropriate stocking density. This calculation method combines theoretical calculations with actual aquaculture experiments to quickly and efficiently determine the appropriate stocking density for intensive aquaculture water bodies, with reliable results and strong guidance for aquaculture production.

Description

Technical Field

[0001] The present invention relates to the technical field of aquaculture, and in particular to a method for calculating a reasonable aquaculture density of an aquaculture water body. Background Art

[0002] Stocking density is the most critical technical parameter in aquaculture production. A reasonable stocking density is the prerequisite and foundation for efficient and healthy aquaculture. Until now, due to a lack of a calculation basis, stocking density in intensive aquaculture waters has been difficult to accurately calculate. Instead, it has been determined by farmers through trial and error based on their production experience, lacking rationality and scientific basis. Driven by the pursuit of high yields, stocking densities are often excessive, leading to a series of bottlenecks that hinder the sustainable development of green, high-quality aquaculture, such as deteriorating water quality, frequent disease outbreaks, and low-quality aquaculture products. Therefore, establishing a precise method for calculating the appropriate stocking density in intensive aquaculture waters is urgent and crucial. Summary of the Invention

[0003] In view of this, in order to accurately obtain the reasonable stocking density of aquaculture, improve aquaculture production, and enhance the economic benefits of aquaculture, the present invention provides a method for calculating the reasonable stocking density of aquaculture water, comprising the following steps:

[0004] S1: Construct a bioaccumulation model for confined space aquaculture objects;

[0005] S2: Conduct density gradient aquaculture experiments: Select target aquaculture water bodies and aquaculture objects, divide the aquaculture objects into multiple density gradient groups within the aquaculture water bodies for aquaculture experiments, and conduct multi-gradient stocking density aquaculture experiments; obtain biomass accumulation parameters for multiple density gradient test groups until the end of the specified aquaculture cycle;

[0006] S3: Using the bioaccumulation model of the confined space aquaculture object constructed in step S1, analyze the limit yield of each density gradient test group in step S2 ( k 1, k 2,…, k n );

[0007] S4: Test the limit yield of each density gradient experimental group in step S3 and find the approximate solution of the aquaculture capacity of the target aquaculture water body K m ;

[0008] In step S4, the aquaculture capacity of the target aquaculture water body is used to obtain an approximate solution. K m The process is:

[0009] S41: Take the limit yield of each density gradient experimental group as the research object, and verify that when the limit yield ( k 1, k2,…, k n ) is the stocking rate, whether the instantaneous growth rate of biomass is close to 0; the limit yield of the experimental group in which the instantaneous growth rate of biomass is close to 0 is selected as the target value for the next test k i ;

[0010] S42: Based on the maximum yield of the experimental group that meets the requirements in the previous step, the biomass of the aquaculture system is inspected to reach 1 / 2 k i Changes in instantaneous growth rate before and after the test, when biomass = 1 / 2 k i When the instantaneous biomass growth rate is the maximum value, select 1 / 2 k i The maximum yield of the experimental group is the inflection point of the instantaneous biomass growth rate k i ;

[0011] S43: Perform productivity verification on the experimental group limit yield obtained in step S42, and the experimental group limit yield that passes the productivity verification k i This is the optimal approximate solution for the aquaculture capacity of the target aquaculture water body. K m ;

[0012] S5: Based on the premise of maintaining the high growth rate of the breeding system, the reasonable breeding density is calculated by the following formula N :

[0013]

[0014] Where: N is the stocking density, K m is the approximate solution for the breeding capacity, A is the breeding specification, and P is the breeding survival rate.

[0015] Furthermore, the bioaccumulation model of the confined space aquaculture object constructed in step S1 is

[0016]

[0017] Where: d B / d t is the instantaneous accumulation rate of the total biomass of the cultured objects in the limited culture space, r m is the intrinsic weight gain rate of the cultured object, and B is the existing biomass of the cultured object; k It is the environmental carrying capacity of limited breeding space.

[0018] Furthermore, in step S2, the number of gradient culture density test groups is at least three, and each gradient culture density test group includes at least three parallel groups.

[0019] Furthermore, the process of obtaining the biomass accumulation parameter of the experimental group in step S2 is: regularly fishing the aquaculture objects at equal time intervals and measuring the weight of the aquaculture objects, wherein the biomass accumulation parameter obtained is ( t n , B n ),in t n For fishing time, B n is the average weight of the aquacultured animals at the corresponding harvest time.

[0020] Furthermore, in step S2, the three-point method, the four-point method or the inflection point method is used to analyze the limit yield of each density gradient test group in step S2.

[0021] Furthermore, the process of analyzing the limit yield of each density gradient test group in step S2 using the three-point method is as follows: select three measured data sequences ( t 11 , B 11 )、( t 12 , B 12 )、( t 13 , B 13 ), where 2 t 12 = t 11 + t 13 ; Calculate the limit yield K by the following formula:

[0022] .

[0023] Furthermore, the process of analyzing the limit yield of each density gradient test group in step S2 using the four-point method is as follows: select 4 measured data sequences ( t 1, B 1) ( t 2, B 2) ( t 3. B 3) ( t 4. B 4), where t 2+ t 3= t 1+t4,

[0024] The limiting yield K is calculated by the following formula

[0025] .

[0026] The beneficial effect of the method for calculating the reasonable aquaculture density of aquaculture water bodies of the present invention is as follows: the method comprises the following steps: constructing a bioaccumulation model of aquaculture objects in a limited space, conducting a density gradient aquaculture test, obtaining biomass accumulation parameters of the test group, solving the limit yield K of each density gradient test group, and finding an approximate solution for the aquaculture capacity K of the target aquaculture water body. K m , calculate reasonable breeding density N In the above steps, the actual breeding data of the biomass accumulation parameters of the experimental group are obtained through the density gradient breeding test, and the approximate solution of the breeding capacity is calculated by combining the component model and the breeding data. The obtained approximate solution is verified and the approximate solution is verified again through production. This calculation method combines theoretical calculations and actual breeding tests to quickly and efficiently determine the reasonable stocking density of intensive breeding water bodies, and the results are reliable and have strong guidance for breeding production. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 The present invention is a flowchart of a method for calculating a reasonable aquaculture density in an aquaculture water body according to an embodiment of the present invention. DETAILED DESCRIPTION

[0028] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0029] Please refer to Figure 1 , Figure 1 This is a flow chart of a method for calculating the reasonable stocking density of aquaculture water bodies invented by the present invention. The purpose of the present invention is to solve the technical problems raised by the background technology and provide an accurate calculation method for the stocking density of intensive aquaculture water bodies.

[0030] The purpose of the present invention is achieved through the following technical solutions:

[0031] The first step is to construct a bioaccumulation model for confined space aquaculture objects.

[0032] Intensive aquaculture is essentially the accumulation of biomass in aquaculture animals, with the goal of harvesting aquatic products. As aquaculture animals grow (accumulate biomass), their demands for aquaculture environment, such as water space, nutrients, and dissolved oxygen, gradually increase. However, within a specific aquaculture system, such as a pond or a facility-based aquaculture system, the intensive aquaculture water body is bounded and can be considered a finite aquaculture space. Within this limited aquaculture space, environmental factors that influence aquaculture, such as water space, dissolved oxygen, and the water's self-purification capacity, all have upper limits. Feed is a special input that can be continuously replenished according to the needs of the aquaculture animals. This means that nutrient input is considered unlimited and is not limited by aquaculture space. However, other environmental factors besides feed, such as oxygenation and water conditioners, can improve the environment to a certain extent. However, due to the limited power of the aeration equipment and the oxygenation efficiency per unit time, there is also a limit to the dissolved oxygen content. The water quality improvement effect of inputs such as water conditioners is also limited and cannot be unlimited. Therefore, when aquaculture is carried out within a confined space, as the aquacultured animals grow (accumulating biomass), the water within the aquaculture space becomes increasingly congested, and dissolved oxygen becomes increasingly scarce. Simultaneously, toxic and harmful substances such as ammonia nitrogen and nitrite excreted by the aquacultured animals gradually accumulate. These, along with other environmental factors such as limited dissolved oxygen and water space, act as environmental resistance to the accumulation of aquacultured biomass. Furthermore, as the aquacultured animals continue to grow, the remaining space available for growth within the confined aquaculture space becomes increasingly smaller, manifesting as increasing environmental resistance. In other words, as individuals grow, the environmental resistance of the aquaculture system increases, resulting in slower growth. Therefore, within a given aquaculture water body (aquaculture space), the instantaneous rate of total biomass accumulation of aquacultured animals is proportional to the intrinsic weight gain rate of the individual aquacultured animals (i.e., the inherent weight gain rate of the aquacultured animals), the existing biomass of the aquacultured animals, and the remaining aquaculture space. Therefore, a differential equation for the accumulation of biomass of aquacultured animals within a confined space can be constructed:

[0033]

[0034] In the formula: (dB / dt) is the instantaneous accumulation rate of the total biomass of the cultured objects in the limited culture space; t is the time; (rm) is the intrinsic weight gain rate of the cultured objects; B is the existing biomass of the cultured objects; (1-B / K) is the remaining space; K is the environmental carrying capacity of the limited culture space.

[0035] The second step is to conduct density gradient culture experiments.

[0036] In the target aquaculture water body, with specific aquaculture objects as the test objects, three or more gradient stocking densities are designed simultaneously (if conditions permit, at least three parallel designs are made for each gradient aquaculture density test group). The aquaculture test is carried out according to normal aquaculture management methods, and the weight of the aquaculture objects is regularly sampled and monitored at equal time intervals to obtain necessary parameters such as biomass accumulation of the test group (t1, B1), (t2, B2), (t3, B3)... until the end of the specified aquaculture cycle.

[0037] The third step is to analyze the limiting yield of each density gradient test group in step S2

[0038] The differential equation for biomass accumulation in confined space aquaculture constructed in the first step conforms to the logistic equation. Common methods for solving key parameters include the three-point method, the four-point method, the inflection point method, and the regression method.

[0039] Among them, the three-point method is to use three measured data series ( t 11 , B 11 )、( t 12 , B 12 )、( t 13 , B 13 ) can calculate the K value. The formula is as follows:

[0040]

[0041] It should be noted that the three points should be at the same time interval, that is: 2 t 12 = t 11 + t 13 .

[0042] In addition, similar to the three-point method, a four-point method is proposed on its basis:

[0043]

[0044] Similarly, the time should satisfy t2+ t3=t1+t4.

[0045] The three-point method and the four-point method share the same principles, but because the four-point method adds an additional observation, its accuracy is slightly higher than the three-point method. Furthermore, the three-point method is more suitable for situations where there is an odd number of measured points, while the four-point method has no restrictions.

[0046] The inflection point method relies on the logistic equation's characteristic of maximum growth rate at B = ½K. It approximates the K value by solving and comparing the slopes at each point. However, this method is difficult to implement. In practice, only when |Δt| is very small can the corresponding ΔB / Δt be used to estimate the instantaneous growth rate at each time point. The maximum ΔB / Δt value corresponds to a B value of ½K.

[0047] The above three methods can quickly and easily determine the K value, but due to limited measured data and simplified calculation methods, they suffer from poor fitting accuracy. In particular, the inflection point method requires a small |Δt| value, making it difficult to determine ΔN / Δt during actual monitoring. Therefore, the above three methods are only suitable for rough calculations and have relatively low fitting accuracy.

[0048] With the rapid development of machine computing power, there are currently a variety of high-precision computing tools that can be applied to data fitting, such as the currently commonly used IBM SPSS Statistics, OriginLab Origin, Python and R software and programming languages. Through the above software, it is relatively simple to perform linear regression and nonlinear regression on the measured data. When performing linear regression on Logistic, the equation model can first be converted into a linear function, and then the parameters are obtained by the least squares method, and the regression curve is obtained after appropriate changes. In nonlinear regression, the least squares unbiased estimation of the parameters is performed by the Levenberg-Marquardt iteration method, which can be iterated quickly multiple times. This method can obtain a higher correlation coefficient R2, that is, the fitting accuracy is higher. In the present invention, the R language is selected to perform nonlinear regression fitting. The specific method is as follows:

[0049] Logistic fitting and graph generation mainly require the download and use of two R software packages.

[0050] First is ggplot2, the most widely used image production package in R. This package is mainly used to generate images after function fitting.

[0051] The second is the deSolve package, which is primarily used for the numerical treatment of systems of differential equations. The package contains functions for solving initial value problems for systems of first-order ordinary differential equations (ODEs), partial differential equations (PDEs), differential algebraic equations (DAEs), and delay differential equations (DDEs). These functions provide interfaces to the FORTRAN functions lsoda, lsodar, lsode, lsodes from the ODEPACK collection, as well as the FORTRAN functions dvode, zcode, daspk, and radau5, and C implementations of the Runge-Kutta family of solvers with fixed or variable time steps. The package also contains routines for solving ordinary differential equations arising from one-, two-, and three-dimensional partial differential equations (PDEs) that have been converted to ordinary differential equations by numerical differentiation.

[0052] The specific code and operation are as follows:

[0053] x<-c(t1,t2,t3,t4)

[0054] y<-c(B1,B2,B3,B4)

[0055] # Input the fitting data collected during the breeding process, t value is the sampling time, and B value is the total biomass of fish at the corresponding time.

[0056] #Assign t and B to x and y respectively.

[0057] The t and B value data set should contain at least three elements. The more data elements, the greater the difference in t values, and the more accurate the fit.

[0058] df<-as.data.frame(cbind(x,y))

[0059] #Merge x and y and convert them into data frame.

[0060] install.packages('deSolve')

[0061] #Download and install the deSolve software package.

[0062] library(deSolve)

[0063] #Import and load the deSolve software package.

[0064] SS<-getInitial(n~SSlogis(m,alpha,xmid,scale),data=df)

[0065] # Use the getInitial function to make a preliminary estimate of the model parameters based on the data. Then pass the output of this function as a vectorized parameter to the self-starting function (SSlogis), and also assign the three unquoted parameter names (i.e., alpha, xmid, and scale) to the logistic equation.

[0066] K_start<-SS["alpha"]

[0067] R_start<-1 / SS["scale"]

[0068] N0_start<-SS["alpha"] / (exp(SS["xmid"] / SS["scale"])+1)

[0069] #Modify the parameter form. Since the parameter settings of SSlogis are slightly different, the output value of SSlogis needs to be processed to make it consistent with the form of the logistic equation.

[0070] log_formula<-formula(n~K*N0*exp(R*m) / (K+N0*(exp(R*m)-1)))

[0071] #Build the formula of the model.

[0072] formu<-nls(log_formula,start=list(K=K_start,R=R_start,N0=N0_start))

[0073] #Fit the model.

[0074] summary(formu)

[0075] # Estimate parameters.

[0076] install.packages('ggplot2')

[0077] #Download and install the deSolve software package.

[0078] library(ggplot2)

[0079] #Import and load the deSolve software package.

[0080] ggplot(df,aes(m,predict(formu)))+geom_line()+geom_point(aes(y=n))+theme_bw()+theme(panel.grid.minor = element_blank(),panel.grid.major =element_blank()) +scale_x_ discrete(limits=c(t1,t2,t3,t4))+xlab("Days")+ylab("Biomass")

[0081] #Use ggplot2 to plot the above Logistic function and set the graphic parameters.

[0082] The fourth step is to find the optimal approximate solution for the aquaculture capacity of the target aquaculture water body. K m

[0083] An approximate solution is obtained based on two inferences of the Logistic model: ① When the biomass approaches the environmental carrying capacity (K), the instantaneous biomass growth rate approaches 0; ② the maximum instantaneous biomass growth rate (inflection point) occurs at ½K.

[0084] Step 1: Take the limit yield of each density gradient experimental group as the research object, and verify whether the instantaneous growth rate of biomass is close to 0 when the limit yield (k1, k2, ..., kn) is used as the stocking rate. If the instantaneous growth rate is close to 0, it means that the limit yield of this density experimental group ( K m ) has approached the breeding capacity. K m ≈K.

[0085] Step 2: Approximate the value of K found in the previous step ( K m ) based on the study of the changes in the instantaneous growth rate of the aquaculture system before and after the biomass reaches ½ km, and to test the effect of biomass = ½ km K m Is the instantaneous growth rate of biomass the maximum when K m When the instantaneous speed increases gradually, it reaches the maximum and then gradually decreases. If the support test results are still obtained in this step, it can be further proved that the above K m The conclusion that ≈K is reliable.

[0086] After the above two steps of testing, the breeding capacity K that meets the requirements can be approximately solved.

[0087] Step 3: Perform production verification on all aquaculture capacities K to obtain the optimal approximate solution for the optimal aquaculture capacity. K m .

[0088] Step 5: Calculate the reasonable breeding density

[0089] Theoretically, the instantaneous biomass accumulation rate reaches its maximum when the biomass of the aquaculture system accumulates to ½K. If maintaining a high-speed growth of the aquaculture system (i.e., pursuing high-efficiency aquaculture) is the premise, the present invention proposes the following formula to calculate the appropriate stocking density (N, tails) based on the growout specification (kg / tail):

[0090]

[0091] Where: N is the stocking density, K m is the approximate solution for the breeding capacity, A is the breeding specification, and P is the breeding survival rate.

[0092] In this document, directional terms such as front, back, top, and bottom are defined based on the positions of components in the accompanying drawings and relative to each other, and are intended only for clarity and convenience in describing the technical solution. It should be understood that the use of these directional terms should not limit the scope of protection claimed in this application.

[0093] In the absence of conflict, the above embodiments and features in the embodiments may be combined with each other.

[0094] The above description is only a preferred embodiment of the present invention and 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 in the scope of protection of the present invention.

Claims

1. A method for calculating a reasonable aquaculture density in an aquaculture water body, characterized by: The steps include: S1: Construct a bioaccumulation model for confined space aquaculture objects; S2: Conduct density gradient aquaculture experiments: Select target aquaculture water bodies and aquaculture objects, divide the aquaculture objects into multiple density gradient groups within the aquaculture water bodies for aquaculture experiments, and conduct multi-gradient stocking density aquaculture experiments; obtain biomass accumulation parameters for multiple density gradient test groups until the end of the specified aquaculture cycle; S3: Using the bioaccumulation model of the confined space aquaculture object constructed in step S1, analyze the limit yield of each density gradient test group in step S2 ( k 1, k 2,…, k n ); S4: Test the limit yield of each density gradient experimental group in step S3 to find the optimal approximate solution for the aquaculture capacity of the target aquaculture water body K m ; In step S3, the limit yield is used to solve the approximate solution of the aquaculture capacity of the target aquaculture water body. K m The process is: S41: Take the limit yield of each density gradient experimental group as the investigation object, and verify that when the limit yield ( k 1, k 2,…, k n ) is the stocking rate, whether the instantaneous growth rate of biomass is close to 0; the limit yield of the experimental group in which the instantaneous growth rate of biomass is close to 0 is selected as the target value for the next test k i ; S42: Based on the maximum yield of the experimental group that meets the requirements in the previous step, the biomass of the aquaculture system is inspected to reach 1 / 2 k i Changes in instantaneous growth rate before and after the test, when biomass = 1 / 2 k i When the instantaneous biomass growth rate is the maximum value, select 1 / 2 k i The maximum yield of the experimental group is the inflection point of the instantaneous biomass growth rate k i ; S43: Perform productivity verification on the experimental group limit yield obtained in step S42, and the experimental group limit yield that passes the productivity verification k i That is the optimal approximate solution for the aquaculture capacity of the target aquaculture water body K m ; S5: Based on the premise of maintaining the high growth rate of the breeding system, the reasonable breeding density is calculated by the following formula N : Where: N is the stocking density, K m is the approximate solution for the breeding capacity, A is the breeding specification, and P is the breeding survival rate.

2. The method for calculating a reasonable aquaculture density of an aquaculture water body according to claim 1, wherein: The bioaccumulation model of the confined space aquaculture object constructed in step S1 is: Where: d B / d t It is the instantaneous accumulation rate of the total biomass of the cultured objects in the limited culture space; r m is the intrinsic weight gain rate of the cultured object; B is the existing biomass of the cultured object; k It is the environmental carrying capacity of limited breeding space.

3. The method for calculating a reasonable aquaculture density of an aquaculture water body according to claim 1, wherein: In step S2, the number of gradient culture density test groups is at least three, and each gradient culture density test group includes at least three parallel groups.

4. The method for calculating a reasonable aquaculture density of an aquaculture water body according to claim 3, wherein: The process of obtaining the biomass accumulation parameter of the experimental group in step S2 is: regularly fishing the aquaculture objects at equal time intervals and measuring the weight of the aquaculture objects, wherein the biomass accumulation parameter obtained is ( t n , B n ),in t n For fishing time, B n is the average weight of the aquacultured animals at the corresponding harvest time.

5. The method for calculating a reasonable aquaculture density of an aquaculture water body according to claim 1, wherein: In step S2, the three-point method, the four-point method or the inflection point method is used to analyze the limit yield of each density gradient test group in step S2.

6. The method for calculating a reasonable aquaculture density of an aquaculture water body according to claim 1, wherein: The process of analyzing the limit yield of each density gradient test group in step S2 using the three-point method is as follows: select three measured data sequences ( t 11 , B 11 )、( t 12 , B 12 )、( t 13 , B 13 ), where 2 t 12 = t 11 + t 13 ; Calculate the limit yield K by the following formula: 。 7. The method for calculating a reasonable aquaculture density of an aquaculture water body according to claim 3, wherein: The process of analyzing the limit yield of each density gradient test group in step S2 using the four-point method is as follows: select 4 measured data sequences ( t 1, B 1) ( t 2, B 2) ( t 3. B 3) ( t 4. B 4), where t 2+ t 3= t 1+t4, The limiting yield K is calculated by the following formula 。

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