A method for establishing a dynamic model of feeding amount during fish adaptation period based on evolutionary game

Abstract

The application discloses a kind of based on evolution game's fish adaptive period feeding amount dynamic model establishment method, this method mainly uses evolution game related content, including the payment matrix of game subject is constructed, according to the expected income to establish replication dynamic equation, get equilibrium point by replication dynamic equation and further determine evolution stable strategy (ESS), finally draw dynamic evolution process, determine fish feeding amount in adaptive period in combination with dynamic evolution process image.The fish adaptive period feeding amount dynamic model method constructed by the application is simple and effective, can effectively reduce the uncertainty of current adaptive period feeding amount by fish total biomass combined with breeding experience, can effectively inhibit fish population size differentiation while fully meeting the energy required for fish growth in adaptive period, avoid deterioration of aquaculture water quality, improve breeding efficiency, meet the development needs of modern aquaculture.

Description

Technical Field

[0001] The present invention relates to the field of planning of fish feeding amount in aquaculture, and in particular to a method for establishing a dynamic model of fish feeding amount during the adaptation period based on evolutionary game. Background Art

[0002] With rapid economic and social development and significant improvements in people's living standards, demand for fish protein is increasing, leading to the booming development of my country's aquaculture industry. From the seedling rearing stage to the final harvest, fish cannot be kept in the same pond. Throughout the entire aquaculture process, fish will be moved at least once. After entering a new pond, the fish need time to adapt to the new environment. During this adaptation period, the fish's food intake will fluctuate. Currently, the commonly used method is to determine the feed rate based on the biomass of the fish and aquaculture experience. However, as fish continue to adapt to the new environment, their food intake fluctuates continuously, making it difficult to accurately determine the feed rate. Underfeeding can cause more adaptable individuals in the school to receive more food than others, leading to increased differentiation between large and small individuals and cannibalism. Overfeeding, on the other hand, not only increases aquaculture costs but also pollutes the aquaculture water.

[0003] The emergence of evolutionary game theory offers a possible solution to this problem. Compared to traditional game theory, evolutionary game theory no longer models game players as hyper-rational. Instead, it argues that game players typically reach equilibrium through trial and error. Evolutionary game theory doesn't require players to be completely rational, but rather views them as beings with bounded rationality, and it doesn't require perfect information.

[0004] In summary, the present invention proposes a method for establishing a dynamic model of fish feeding amounts during the adaptation period based on evolutionary game theory. Based on the theory of evolutionary game theory and combined with farming experience, a model is constructed that can reflect the continuous changes in fish food intake during the adaptation period over time and the number of feedings. This model allows real-time control of the current stage of fish food intake, providing a reference for the feed amount to be fed after fish relocation in aquaculture. This more accurate feeding method ensures fish food intake and cost control compared to relying solely on farming experience. Summary of the Invention

[0005] The purpose of this invention is to provide a method for establishing a dynamic model of feeding amount during the adaptation period of fish based on evolutionary game. In this model, each feeding game of fish can be regarded as a trial and error process for the next game. The profit of this round of game will directly lead to the change of strategy in the next round of game, which is specifically reflected in Figure 1 The results provide a reference for the feed dosage during the adaptation period of fish in aquaculture.

[0006] The above modeling method is used to establish a dynamic model of fish feeding amount during the adaptation period based on evolutionary game. The establishment method includes the following steps:

[0007] 1) Establish the payoff matrix of the game subject in a game:

[0008]

[0009] Table 1: I1 is the profit obtained by the fish (personality 1) after it has fully eaten, and a represents the insufficient feeding coefficient of the fish (personality 1). When the fish (personality 1) chooses the strategy of insufficient feeding, the profit is reduced to a*I1. At the same time, if the fish (personality 2) chooses to eat fully, in the following period, the fish that has not eaten fully will incur a certain survival cost P1 due to its reduced body size and vitality compared to the fish that has eaten fully. Similarly, I2 is the profit obtained by the fish (personality 2) after it has fully eaten, and b represents the insufficient feeding coefficient of the fish (personality 2). When the fish (personality 2) chooses the strategy of insufficient feeding, the profit is reduced to b*I2. At the same time, if the fish (personality 1) chooses to eat fully, in the following period, the fish that has not eaten fully will incur a certain survival cost P2 due to its reduced body size and vitality compared to the fish that has eaten fully. x1 and x2 are the probabilities of fish with two different personalities choosing to eat fully.

[0010] 2) Calculate the expected returns of all parties involved in the game and replicate the dynamic equation:

[0011] The expected benefits of the game players:

[0012] Fish (Personality 1): Fully fed benefit: U 11 =I1; Insufficient eating benefit: U 12 =a×I1-x2×P1; Current game payoff: U1=x1×U 11 +(1-x1)×U 12

[0013] Fish (Personality 2): Fully fed benefit: U 21 =I2; Insufficient eating benefit: U 22 =b×I2-x1×P2; Current game payoff: U2=x2×U 21 +(1-x2)×U 22

[0014] Copy the dynamic equations:

[0015] F(x1)=dx1 / dt=x1×(U 11 -U1)=x1×(1-x1)×[(1+a)×I1-x2×P1]

[0016] F(x2)=dx2 / dt=x2×(U21 -U2)=x2×(1-x2)×[(1+b)×I2-x1×P2]

[0017] 3) Let the replicated dynamic equation be 0 to obtain the equilibrium point:

[0018] A(0,1);B(0,0);C(1;0);D(1,1);E((1+b)*I2 / P2,(1+a)*I1 / P1)

[0019] 4) Construct the Jacobian matrix to determine which equilibrium points of the replicated dynamic equations are evolutionarily stable strategies (ESS):

[0020]

[0021] The equilibrium point of the replication dynamic equation is an evolutionarily stable strategy if the following two conditions are met at the same time:

[0022] det J=a 11 ×a 22 -a 12 ×a 21 >0

[0023] tr J=a 11 +a 22 <0

[0024] Since x1 and x2 need to take values ​​in the range [0,1], it can be seen that the equilibrium point E cannot actually meet this condition and can be directly discarded.

[0025] 5) Combine software (MATLAB) to draw the dynamic evolution process;

[0026] 6) Determine the current feeding amount for the fish school based on the current game strategy point corresponding to the dynamic evolution process:

[0027]

[0028] Among them: F C Represents the feeding amount at the current stage, F O represents the normal feeding amount of the fish group, P i represents the current strategy point, and ESS represents the evolutionary stable strategy point.

[0029] The present invention successfully constructs a model that can reflect the continuous changes in the food intake of fish during the adaptation period with time and feeding times. It is a more accurate and reliable feeding method compared to relying solely on breeding experience. It not only ensures the food intake of fish but also is more conducive to cost control. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1is the dynamic evolution process graph drawn by using software (MATLAB) after combining the payment matrix and the replicator dynamic equation.

[0031] In the figure: let I1=I2=1, a=0.8, b=0.6, P1=0.1, P2=0.2; after 57 times of dynamic evolution, the infinite approximation evolution stable strategy (ESS) is approached. DETAILED DESCRIPTION

[0032] The application will be further described below in combination with the game matrix and the dynamic evolution process graph.

[0033] The "individuality" of the fish in the application refers to that under the same feeding condition, different feeding strategies (i.e. individuality 1 corresponds to feeding strategy 1), different kinds of fish and different individuals of the same kind of fish can adopt different feeding strategies.

[0034] The modeling method is applied to establish a dynamic model of fish feeding amount in the adaptation period based on evolutionary game, and the establishment method comprises the following steps:

[0035] 1) establishing the payment matrix of the game subject in one game:

[0036]

[0037] In Table 1, I1 is the income of the fish (individuality 1) after sufficient feeding, a represents the insufficient feeding coefficient of the fish (individuality 1), when the fish (individuality 1) selects the insufficient feeding strategy, the income is reduced to a*I1, and meanwhile, if the fish (individuality 2) selects sufficient feeding, the insufficient feeding fish will pay a certain survival cost P1 due to the reduction of the body type and activity relative to the sufficient feeding fish in the next time; similarly, I2 is the income of the fish (individuality 2) after sufficient feeding, b represents the insufficient feeding coefficient of the fish (individuality 2), when the fish (individuality 2) selects the insufficient feeding strategy, the income is reduced to b*I2, and meanwhile, if the fish (individuality 1) selects sufficient feeding, the insufficient feeding fish will pay a certain survival cost P2 due to the reduction of the body type and activity relative to the sufficient feeding fish in the next time; x1 and x2 are the probabilities of the fish of two different individualities selecting sufficient feeding respectively.

[0038] 2) calculating the expected income of each game subject and the replicator dynamic equation:

[0039] The expected income of the game subject:

[0040] The fish (individuality 1): sufficient feeding income: U 11 =I1; insufficient feeding income: U 12 =a×I1-x2×P1; current game income: U1=x1×U 11+ (1 - x1) x U 12

[0041] Fish (Personality 2): Fully fed payoff: U 21 = I2; underfed payoff: U 22 = b x I2 - x1 x P2; current game payoff: U2 = x2 x U 21 + (1 - x2) x U 22

[0042] Replicator dynamic equations:

[0043] F(x1) = dx1 / dt = x1 x (U 11 - U1) = x1 x (1 - x1) x [(1 + a) x I1 - x2 x P1]

[0044] F(x2) = dx2 / dt = x2 x (U 21 - U2) = x2 x (1 - x2) x [(1 + b) x I2 - x1 x P2]

[0045] 3) Set the replicator dynamic equations to 0 to get equilibrium points:

[0046] A (0, 1); B (0, 0); C (1; 0); D (1, 1); E ((1 + b) * I2 / P2, (1 + a) * I1 / P1)

[0047] 4) Construct the Jacobian matrix to determine which equilibrium points of the replicator dynamic equations are evolutionarily stable strategies (ESS):

[0048]

[0049] An equilibrium point of the replicator dynamic equations is an evolutionarily stable strategy if it satisfies the following two conditions:

[0050] det J = a 11 x a 22 - a 12 x a 21 > 0

[0051] tr J = a 11 + a 22 < 0

[0052] (For example, in this example, let I1 = I2 = 1, a = 0.8, b = 0.6, P1 = 0.1, P2 = 0.2) At this time, E (8, 18) (x1, x2 needs to take the value range [0, 1]), discard.

[0053]

[0054] 5) Use software (MATLAB) to draw the dynamic evolution process (where I1 = I2 = 1, a = 0.8, b = 0.6, P1 = 0.1, P2 = 0.2). Figure 1 The dynamic evolution process with different initial values ​​is given.

[0055] 6) Determine the current feeding amount for the fish school based on the current game strategy point corresponding to the dynamic evolution process:

[0056]

[0057] Among them: F C Represents the feeding amount at the current stage, F O represents the normal feeding amount of the fish group, P i represents the current game strategy point, and ESS represents the evolutionary stable strategy point.

[0058] It can be seen that the present invention is based on the theory of evolutionary game theory and combined with breeding experience to successfully construct a model that can reflect the continuous changes in the food intake of fish during the adaptation period with time and feeding times. It can control the food intake of fish in the current stage in real time, provide a reference for the amount of feed fed after fish transplantation in aquaculture, and accurately control feeding to ensure fish feeding and cost control.

Claims

1. A method for establishing a dynamic model of feeding amount during the fish adaptation period based on evolutionary game theory, characterized in that: The method includes: constructing a payoff matrix of a game subject based on the benefits corresponding to full feeding or insufficient feeding selected by different fish species; establishing a replication dynamic equation based on the expected benefits; obtaining an equilibrium point through the replication dynamic equation and further determining an evolutionary stable strategy (ESS); drawing a dynamic evolution process based on the established replication dynamic equation; and determining a feeding amount for the fish during the adaptation period by combining the dynamic evolution process image and the evolutionary stable strategy (ESS); The construction of the payoff matrix of the game subject in a game is specifically as follows: x1 and x2 are the probabilities of two fish with different personalities: the probability of fish with personality 1 and fish with personality 2 choosing to eat fully, and the corresponding probabilities of not eating fully are 1-x1 and 1-x2, I1 is the profit obtained by fish with personality 1 after eating fully, a represents the inadequate eating coefficient of fish with personality 1. When fish with personality 1 choose the strategy of not eating fully, the profit is reduced to a*I1. At the same time, if fish with personality 2 choose to eat fully, in the following time, the fish that do not eat fully will also lose more due to the decrease in body size and vitality compared to the fish that eat fully. Spending a certain survival cost P1, that is, the income of the fish with personality 1 is a*I1-P1; similarly, I2 is the income obtained by the fish with personality 2 after fully eating, and b represents the insufficient feeding coefficient of the fish with personality 2. When the fish with personality 2 chooses the strategy of insufficient feeding, the income decreases to b*I2. At the same time, if the fish with personality 1 chooses to fully eat, in the following period, the fish that do not eat fully will spend a certain survival cost P2 because of the smaller body size and vitality compared to the fish that eat fully. That is, the income of the fish with personality 2 is b*I2-P2. Calculate the expected benefits of each game player and the replication dynamic equation: The expected benefits of the game players: Fish with personality 1: Benefits of adequate eating: ; Benefits of Insufficient Eating: ; Current gaming revenue: ; Fish with personality 2: Benefits of adequate eating: ; Benefits of Insufficient Eating: ; Current gaming revenue: ; Then, the corresponding replication dynamic equation is: ; ; Let the replica dynamic equation be 0 to obtain the equilibrium point: A(0,1); B(0,0); C(1;0); D(1,1); E((1+b)*I2 / P2,(1+a)*I1 / P1); Construct the Jacobian matrix to determine which equilibrium points of the replicated dynamic equations are evolutionary stable strategies ESS: ; The equilibrium point of the replication dynamic equation is an evolutionarily stable strategy if the following two conditions are met at the same time: ; ; in, 、 、 、 is the element at the corresponding position in the Jacobian matrix.

2. The method for establishing a dynamic model of feeding amount for fish during the adaptation period based on evolutionary game according to claim 1, characterized in that: Combining the dynamic evolution process image and the evolutionary stable strategy ESS, the feeding amount of the fish school at the current stage is determined according to the current game strategy point corresponding to the dynamic evolution process: ; in: Represents the feeding amount at the current stage, Represents the normal feeding amount of the fish group. Represents the current game strategy point, Represents the evolutionary stable strategy point.

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