River-tracing spawning migration fish resource simulation analysis method based on age structure

Abstract

The invention discloses a river-tracing spawning migration fish resource simulation analysis method based on an age structure. The method comprises the following steps: constructing population vectors in a target lake and a river; calculating the population number of lakes and rivers every year; constructing an age structure function of a population migration breeding population in the river; calculating a repeated propagation coefficient; calculating the quantity of lake supplementary populations; and updating the future lake population vector and the total resource quantity based on the lake supplementary population quantity. According to the method, through population vector construction, age structure analysis, propagation coefficient calculation, supplementary population quantification and population iteration updating, annual iteration of population quantity is realized, and population age structure change, supplementary population fluctuation and total resource quantity evolution trend of many years can be continuously tracked. Compared with a static evaluation model, the method can quantify long-term effects of measures such as reproduction protection and migration channel improvement.

Description

Technical Field

[0001] This invention belongs to the field of fishery resource assessment technology, specifically relating to a dynamic simulation analysis method for anadromous fish resources, particularly a refined simulation assessment method that integrates age structure, sex ratio, and environmental drivers. Background Technology

[0002] Anadromous fish (such as the Qinghai Lake naked carp) are fish resources of significant ecological and economic value. Their life cycle is complex, involving birth in rivers, growth in lakes or oceans, and then migrating upstream to spawning grounds. This characteristic makes their populations susceptible to multiple factors, including fishing pressure, habitat changes, and the connectivity of migration routes, making resource assessment and conservation management very challenging. Currently, the assessment of dynamic changes in anadromous fish populations mainly employs resource assessment models based on fishing statistics and underwater acoustic detection methods in lake areas.

[0003] Resource assessment models based on fishing statistics primarily infer resource levels by collecting parameters such as historical and current fishery catches and efforts, combined with statistical models. The accuracy of this method is highly dependent on the continuity and authenticity of the fishing data. In reality, varying fisherman experience, illegal fishing, and false or missed reporting are difficult to eliminate, resulting in weak reliability of the basic data. Furthermore, this method is essentially a "black box" or "grey box" inversion based on historical data, making it difficult to analyze the internal structure of the population or quantify the direct impact of environmental factors on each stage of the population's life history. Therefore, it cannot predict the dynamic response and succession process of the population under future environmental changes. In contrast, underwater acoustic detection methods in lake areas utilize acoustic equipment to directly detect fish resources in the water, obtaining the resource density distribution at a specific time point. However, this assessment method is affected by factors such as the "driving coefficient" value of the equipment carried by the instrument, resulting in significant errors in the assessment results. Furthermore, this method is only a static "snapshot" assessment, which cannot reveal the dynamic change mechanism of resources. It cannot trace the age structure evolution of historical populations, nor can it predict future resource development trends. Underwater acoustic detection also suffers from problems such as high cost and difficulty in sustainable and large-scale application.

[0004] It is evident that existing technologies have shortcomings in terms of accuracy in resource assessment, ability to analyze population structure, and dynamic prediction of population changes, making it difficult for managers to formulate forward-looking, ecologically process-based conservation and restoration strategies. Therefore, there is an urgent need for an analytical method that can overcome these deficiencies and accurately simulate and predict the dynamic changes in anadromous fish resources. Summary of the Invention

[0005] The purpose of this invention is to address the aforementioned shortcomings in the prior art by providing a method for simulating and analyzing anadromous fish resources based on age structure, thereby solving the problems of low accuracy and significant limitations in existing age-structure-based simulation results of anadromous fish resources.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for simulating and analyzing migratory fish resources based on age structure includes the following steps: S1. Construct population vectors for female and male fish in the target lake; S2. Construct population vectors for female and male fish in the migratory breeding population of the target river; S3. Calculate the annual population size of lakes and rivers based on the population vectors of female and male fish in lakes and rivers. S4. Based on the population vectors of female and male fish in the river and the population size of the river, construct the age structure function of the migratory breeding population in the river; S5. Convert the age structure function into a function that follows a normal distribution; S6. Calculate the repeat reproduction coefficient based on the river breeding population and the lake population; S7. Based on the repeat reproduction coefficient, establish the relationship between the migratory river population and the replenished lake population; S8. Calculate the replenishment population size in lakes based on the repeat reproduction coefficient and the river reproduction population size; S9. Update the future lake population vector and total resource quantity based on the lake replenishment population quantity.

[0007] Furthermore, in S1, the population vectors of female and male fish in the lake are represented as follows:

[0008] In the formula, For the first Annual lake female fish population vector; For the first Annual population vector of male fish in lakes; For the first Lake Number of female fish of the same age; For the first Lake Number of male fish of the appropriate age; , These are the maximum ages of the female and male fish, respectively, expressed in years (a). This represents the transpose of a vector.

[0009] Furthermore, in S2, the population vectors of female and male fish in the migratory breeding population in the river are represented as follows:

[0010] In the formula, For the first Annual river female fish breeding population vector; For the first Annual river male fish breeding population vector; , These represent the minimum and maximum reproductive ages of the female fish, respectively. , These represent the minimum and maximum reproductive ages of male fish, respectively.

[0011] Furthermore, in S3, the annual population size of lakes and rivers is calculated; The lake population size is as follows:

[0012] In the formula, For the first Total number of female fish in lakes in a given year; For the first Total number of male fish in lakes in a given year; For the first Year Lake Total number of fish of all ages; For the first Total annual lake resources; The river breeding population size is:

[0013] In the formula, For the first Total number of female fish breeding populations in rivers in a given year; For the first Total number of male fish breeding populations in rivers each year; For the first Total annual river breeding population.

[0014] Furthermore, in S4, the age structure function of the migratory breeding population in the river is expressed as:

[0015] In the formula, This refers to a breeding population (female + male) in a river. Age structure function of fish; For breeding groups of female fish in rivers Age structure function of fish; For the breeding population of male fish in the river The age structure function of fish.

[0016] Furthermore, in step S5, the age structure function is converted into a function that follows a normal distribution, which is expressed as:

[0017]

[0018]

[0019] In the formula, The average age of the mixed group; The standard deviation of the age distribution; This is the peak reproductive age for female fish; This is the peak reproductive age for male fish; , These represent the standard deviations of the age distribution for female and male fish, respectively.

[0020] Furthermore, in S6, the repeatability coefficient is expressed as:

[0021] In the formula, This is the repeatability coefficient for female fish, which is the number of times a parent fish enters the river to participate in reproduction during its lifetime; The repeatability coefficient for male fish; This is to allow for repeated reproduction time differences.

[0022] Furthermore, in S7, the relationship between the river migratory population and the lake replenishment population is expressed as follows: .

[0023] Furthermore, in S8, the replenishment population size of the lake is calculated, which is expressed as:

[0024]

[0025]

[0026] In the formula, The total population replenished to the lake in year t is the total number of juvenile fish that hatched and survived to enter the lake population that year. The breeding success rate represents the proportion of surviving juveniles successfully produced by each unit of river breeding population in one breeding cycle, with a value range of [0,1], and is affected by water temperature and spawning ground environmental factors; To replenish the number of female fish in the population in year t; The number of male fish in the population is replenished in year t.

[0027] Furthermore, in S9, the future lake population vector and total resource quantity are updated based on the replenished lake population quantity, which is expressed as: The female fish population vector update is represented as:

[0028] Male fish population vector update:

[0029] Total predicted lake resources

[0030] In the formula, Let i be the number of female fish of age i in the lake in year t+1. Let i be the number of male fish of age i in the lake in year t+1. The survival rate of fish from age i-1 to age i represents the proportion of individuals from age i-1 who successfully survive to age i. The value ranges from [0,1] and decreases with age. The number of i-1-year-old female fish from the lake that migrate to the river in year t; The number of i-1-year-old male fish that migrated from the lake to the river in year t; This represents the total lake resources in year t+1.

[0031] The method for simulating and analyzing anadromous fish resources based on age structure provided by this invention has the following beneficial effects: 1. This invention integrates the river breeding population size with the repeated reproduction coefficient, combines the parent fish's reproductive capacity with the breeding success rate to calculate the replenishment population, and then uses the population age structure of the associated migration vector and the newly added survival rate parameter to completely connect the entire life cycle process of "migration reproduction - replenishment population - lake population renewal". This design avoids the problem of isolated data in each link in traditional models, accurately restores the ecological characteristics of migratory fish "lake habitat - river reproduction - juvenile fish returning to lake", and makes the simulation results more consistent with the actual change law of natural populations.

[0032] 2. This invention achieves annual iteration of population size through population vector construction, age structure analysis, reproduction coefficient calculation, supplementary population quantification, and iterative population updates. It can continuously track changes in population age structure, fluctuations in supplementary populations, and the evolution trend of total resource quantity over multiple years. Compared to static assessment models, it can quantify the long-term effects of measures such as reproductive protection and migration channel improvement. Attached Figure Description

[0033] Figure 1 This is a flowchart illustrating an example of a simulation analysis method for anadromous fish resources based on age structure. Detailed Implementation

[0034] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0035] The life history of fish is a process from birth to death. For anadromous fish, migrating to rivers to spawn and reproduce is a crucial process in their life history. Changes in fish populations are the result of generational evolution across different age groups. Different age groups exhibit different natural mortality rates, with the natural mortality rates of fry and young fish being significantly higher than those of subadults and adults. The catch mortality rate of subadults and adults is higher than that of fry and young fish. Furthermore, the gonadal development of females and males differs, with females typically maturing later than males. The reproductive populations of females and males exhibit age structure differences, which can be represented by an age structure function. Therefore, subdividing the population into age-specific stocks, tracking the dynamic changes of each age group, and establishing an age-structured population model are important methods for calculating interannual variations in fish populations. Based on this, this embodiment provides a method for simulating and analyzing migratory fish resources based on age structure, referencing... Figure 1 Specifically, it includes the following: S1. Construct the population vectors of female and male naked carp in the target lake, which are represented as follows:

[0036] In the formula, For the first Annual lake female fish population vector; For the first Annual population vector of male fish in lakes; For the first Lake Number of female fish of the same age; For the first Lake Number of male fish of the appropriate age; , These are the maximum ages of the female and male fish, respectively, expressed in years (a). This represents the transpose of a vector.

[0037] S2. Construct the population vectors of female and male naked carp in the target river's migratory breeding population; their representation is:

[0038] In the formula, For the first Annual river female fish breeding population vector; For the first Annual river male fish breeding population vector; , These represent the minimum and maximum reproductive ages of the female fish, respectively. , These represent the minimum and maximum breeding ages of the male fish, respectively. S3. Calculate the annual population size of lakes and rivers based on the population vectors of female and male fish in lakes and rivers; in S3, the annual population size of lakes and rivers is calculated. The lake population size is as follows:

[0039] In the formula, For the first Total number of female fish in lakes in a given year; For the first Total number of male fish in lakes in a given year; For the first Year Lake Total number of fish of all ages; For the first Total annual population of naked carp in lakes; The river breeding population size is:

[0040] In the formula, For the first Total number of female fish breeding populations in rivers in a given year; For the first Total number of male fish breeding populations in rivers each year; For the first Annual breeding population of naked carp in rivers S4. Based on the population vectors of female and male fish in the river and the population size of the river, construct the age structure function of the migratory breeding population of naked carp in the river, which is expressed as:

[0041] In the formula, This refers to a breeding population of naked carp (female + male) in a river. Age structure function of fish; For breeding groups of female fish in rivers Age structure function of fish; For the breeding population of male fish in the river The age structure function of fish.

[0042] S5. Transform the age structure function into a function that follows a normal distribution, as follows:

[0043]

[0044]

[0045] In the formula, The average age of the mixed group; The standard deviation of the age distribution; This is the peak reproductive age for female fish; This is the peak reproductive age for male fish; , These represent the standard deviations of the age distribution for female and male fish, respectively.

[0046] S6. Calculate the repeatability coefficient based on the river and lake population sizes; the repeatability coefficient in S6 is expressed as:

[0047] In the formula, This is the repeatability coefficient for female fish, which is the number of times a parent fish enters the river to participate in reproduction during its lifetime; The repeatability coefficient for male fish; This is to allow for repeated reproduction time differences.

[0048] The Qinghai Lake naked carp is a repeat-spawning species with reproductive intervals, spawning synchronously in batches. The majority of breeding populations are 4-5 years old, with individuals over 8 years old being a minority. Separately, the youngest breeding age for males is 3 years, and for females, it is 4 years. After spawning, the gonads of the Qinghai Lake naked carp regress to stage II, and they quickly return to the lake to feed and grow. Therefore, after spawning, the parent fish need to complete gonad development from stage II to stage IV in Qinghai Lake before returning to rivers to reproduce. Qinghai Lake is an oligotrophic lake, and the low temperature environment slows down the gonad and growth development of the naked carp. It takes at least one year for gonad development from stage II to the end of stage III. According to current research, stage IV gonad development in the lake requires a year from the initial to the final stage. Therefore, it takes approximately 2-3 years for the Qinghai Lake naked carp to develop from stage II gonads to stage IV gonads, which are suitable for migratory reproduction. The male's repeat reproductive coefficient should be 2-3 times, with a maximum of 4 times. Considering that the female's ovary development requires more resources, the female will reproduce 1-2 times in her lifetime, with a maximum of 3 times. Therefore, theoretically, the average range of the repeat reproductive coefficients for both male and female fish is:

[0049]

[0050] S7. Based on the repeat reproduction coefficient, establish the relationship between the migratory river population and the replenished lake population; the relationship between the migratory river population and the replenished lake population in S7 is expressed as follows:

[0051] S8. Based on the repeat reproduction coefficient and the river breeding population size, calculate the replenishment population size of naked carp in lakes, expressed as follows:

[0052]

[0053]

[0054] In the formula, The total population of naked carp in lakes in year t is the total number of juvenile fish that hatch and survive to enter the lake population in that year. The reproductive success rate represents the proportion of surviving juveniles successfully produced by each unit of river breeding population in one breeding cycle, with a value range of [0,1]. It is affected by water temperature and spawning ground environmental factors. The reproductive success rate parameter is introduced to quantify the contribution of parent fish reproductive behavior to the number of newly added juveniles in the lake. To replenish the number of female fish in the population in year t; The number of male fish in the population is replenished in year t.

[0055] S9. Update the future lake naked carp population vector and total resource quantity based on the replenishment population size, which is expressed as follows: The female fish population vector update is represented as:

[0056] Male fish population vector update:

[0057] Total predicted lake resources:

[0058] In the formula, Let i be the number of female fish of age i in the lake in year t+1. Let i be the number of male fish of age i in the lake in year t+1. The survival rate of fish from age i-1 to age i represents the proportion of individuals from age i-1 who successfully survive to age i. The value ranges from [0,1] and decreases with age. The number of i-1-year-old female fish from the lake that migrate to the river in year t; The number of i-1-year-old male fish that migrated from the lake to the river in year t; This represents the total population of naked carp in the lake in year t+1.

[0059] This embodiment defines the repeatability coefficient of male and female parent fish, which refers to the average number of times a parent fish participates in reproduction throughout its lifetime. This is an important parameter in naked carp population models. The repeatability coefficient of male and female fish can be estimated through cage culture experiments of post-spawning parent fish. In specific sampling, since the specific sex ratio varies considerably, mainly affected by sampling location, time, and sample size, the sample survey area can be expanded and the field sampling intensity of lakes and rivers increased to obtain more accurate and representative sex ratio values ​​for lakes and rivers.

[0060] This embodiment quantitatively elucidates the impact of changes in the population size and sex ratio of *Naked Carp* in Qinghai Lake, addressing a crucial scientific issue for its conservation. Currently, the dynamic changes in *Naked Carp* population size in Qinghai Lake are primarily assessed using resource evaluation models based on fishing parameters and underwater acoustic detection methods. These methods cannot evaluate the impact of sex ratio and environmental changes. This project proposes constructing a mathematical model of the *Naked Carp* population in Qinghai Lake based on age structure, which can assess the impact of sex ratio and environmental changes on population size and estimate the generational succession process of the *Naked Carp* population in Qinghai Lake.

[0061] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A method for simulating and analyzing anadromous fish resources based on age structure, characterized in that, Includes the following steps: S1. Construct population vectors for female and male migratory fish in the target lake; S2. Construct population vectors for female and male fish in the migratory breeding population of migratory fish in the target river; S3. Calculate the annual population size of lakes and rivers based on the population vectors of female and male fish in lakes and rivers. S4. Based on the population vectors of female and male fish in the river and the population size of the river, construct the age structure function of the migratory breeding population in the river; S5. Convert the age structure function into a function that follows a normal distribution; S6. Calculate the repeat reproduction coefficient based on the river breeding population and the lake population; S7. Based on the repeat reproduction coefficient, establish the relationship between the migratory river population and the replenished lake population; S8. Calculate the replenishment population size in lakes based on the repeat reproduction coefficient and the river reproduction population size; S9. Update the future lake population vector and total resource quantity based on the lake replenishment population quantity.

2. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 1, characterized in that, In S1, the population vectors of female and male fish in the lake are represented as follows: In the formula, For the first Annual lake female fish population vector; For the first Annual population vector of male fish in lakes; For the first Lake Number of female fish of the same age; For the first Lake Number of male fish of the appropriate age; , These are the maximum ages of the female and male fish, respectively, expressed in years (a). This represents the transpose of a vector.

3. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 2, characterized in that, In S2, the population vectors of female and male fish in the migratory breeding population in the river are represented as follows: In the formula, For the first Annual river female fish breeding population vector; For the first Annual river male fish breeding population vector; , These represent the minimum and maximum reproductive ages of the female fish, respectively. , These represent the minimum and maximum reproductive ages of male fish, respectively.

4. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 3, characterized in that, In S3, the annual population size of lakes and rivers is calculated; The lake population size is as follows: In the formula, For the first Total number of female fish in lakes in a given year; For the first Total number of male fish in lakes in a given year; For the first Year Lake Total number of fish of all ages; For the first Total annual lake migratory fish population; The river breeding population size is: In the formula, For the first Total number of female fish breeding populations in rivers in a given year; For the first Total number of male fish breeding populations in rivers each year; For the first Total annual river breeding population.

5. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 4, characterized in that, In S4, the age structure function of the migratory breeding population in the river is expressed as: In the formula, This refers to a breeding population (female + male) in the river. Age structure function of fish; For breeding groups of female fish in rivers Age structure function of fish; For the breeding population of male fish in the river The age structure function of fish.

6. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 5, characterized in that, In step S5, the age structure function is transformed into a function that follows a normal distribution, which is expressed as: In the formula, The average age of the mixed group; The standard deviation of the age distribution; This is the peak reproductive age for female fish; This is the peak reproductive age for male fish; , These represent the standard deviations of the age distribution for female and male fish, respectively.

7. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 6, characterized in that, In S6, the repeatability coefficient is expressed as follows: In the formula, This is the repeatability coefficient for female fish, which is the number of times a parent fish enters the river to participate in reproduction during its lifetime; The repeatability coefficient for male fish; This is to allow for repeated reproduction time differences.

8. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 7, characterized in that, In S7, the relationship between the riverine migratory population and the lacustrine replenishment population is expressed as follows: 。 9. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 7, characterized in that, In S8, the number of replenished populations in the lake is calculated, which is expressed as: In the formula, The total population replenished to the lake in year t is the total number of juvenile fish that hatched and survived to enter the lake population that year. The breeding success rate represents the proportion of surviving juveniles successfully produced by each unit of river breeding population in one breeding cycle, with a value range of [0,1], and is affected by water temperature and spawning ground environmental factors; To replenish the number of female fish in the population in year t; The number of male fish in the population is replenished in year t.

10. The method for simulating and analyzing anadromous fish resources based on age structure according to claim 9, characterized in that, In S9, the future lake population vector and total resource quantity are updated based on the replenished lake population quantity, which is expressed as follows: The female fish population vector update is represented as: Male fish population vector update: Total predicted lake resources: In the formula, Let i be the number of female fish of age i in the lake in year t+1. Let i be the number of male fish of age i in the lake in year t+1. The survival rate of fish from age i-1 to age i represents the proportion of individuals from age i-1 who successfully survive to age i. The value ranges from [0,1] and decreases with age. The number of i-1-year-old female fish from the lake that migrate to the river in year t; The number of i-1-year-old male fish that migrated from the lake to the river in year t; This represents the total lake resources in year t+1.

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