Optimal Harvest Problem for Fish Population—Structural Stabilization
The influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is investigat...
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| Format: | Article |
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/6/986 |
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| author | Aleksandr Abakumov Yuri Izrailsky |
| author_facet | Aleksandr Abakumov Yuri Izrailsky |
| author_sort | Aleksandr Abakumov |
| collection | DOAJ |
| description | The influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is investigated and an optimality system to the problem research is constructed. The solutions properties in various cases have also been investigated. Environmental conditions influence the fish population through recruitment. Modelling of recruitment rate is made by using a stochastic imitation of environmental conditions. In the case of stationary environment, a population model admits nontrivial equilibrium state. The parameters of fish population are obtained from this equilibrium condition. The variability of environment leads to large oscillations of generation size. The fluctuations of the fish population density follow the dynamics of recruitment rate fluctuations but have smaller gradients than recruitment. The dynamics of the optimal fishing effort is characterized by high variability. The population and the average size of individuals decrease under the influence of fishery. In general, the results of computer calculations indicate the stabilization of the population dynamics under influence of size structure. Optimal harvesting also contributes to stabilization. |
| first_indexed | 2024-03-09T13:25:24Z |
| format | Article |
| id | doaj.art-7c59ce38e93b4349a706fc0ad91ec11b |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T13:25:24Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7c59ce38e93b4349a706fc0ad91ec11b2023-11-30T21:25:04ZengMDPI AGMathematics2227-73902022-03-0110698610.3390/math10060986Optimal Harvest Problem for Fish Population—Structural StabilizationAleksandr Abakumov0Yuri Izrailsky1Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, 5 Radio Street, 690041 Vladivostok, RussiaInstitute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, 5 Radio Street, 690041 Vladivostok, RussiaThe influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is investigated and an optimality system to the problem research is constructed. The solutions properties in various cases have also been investigated. Environmental conditions influence the fish population through recruitment. Modelling of recruitment rate is made by using a stochastic imitation of environmental conditions. In the case of stationary environment, a population model admits nontrivial equilibrium state. The parameters of fish population are obtained from this equilibrium condition. The variability of environment leads to large oscillations of generation size. The fluctuations of the fish population density follow the dynamics of recruitment rate fluctuations but have smaller gradients than recruitment. The dynamics of the optimal fishing effort is characterized by high variability. The population and the average size of individuals decrease under the influence of fishery. In general, the results of computer calculations indicate the stabilization of the population dynamics under influence of size structure. Optimal harvesting also contributes to stabilization.https://www.mdpi.com/2227-7390/10/6/986mathematical modelharvestpopulation dynamicsoptimal controlenvironment |
| spellingShingle | Aleksandr Abakumov Yuri Izrailsky Optimal Harvest Problem for Fish Population—Structural Stabilization Mathematics mathematical model harvest population dynamics optimal control environment |
| title | Optimal Harvest Problem for Fish Population—Structural Stabilization |
| title_full | Optimal Harvest Problem for Fish Population—Structural Stabilization |
| title_fullStr | Optimal Harvest Problem for Fish Population—Structural Stabilization |
| title_full_unstemmed | Optimal Harvest Problem for Fish Population—Structural Stabilization |
| title_short | Optimal Harvest Problem for Fish Population—Structural Stabilization |
| title_sort | optimal harvest problem for fish population structural stabilization |
| topic | mathematical model harvest population dynamics optimal control environment |
| url | https://www.mdpi.com/2227-7390/10/6/986 |
| work_keys_str_mv | AT aleksandrabakumov optimalharvestproblemforfishpopulationstructuralstabilization AT yuriizrailsky optimalharvestproblemforfishpopulationstructuralstabilization |