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Optimal Harvest Problem for Fish Population—Structural Stabilization

Author

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  • Aleksandr Abakumov

    (Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, 5 Radio Street, 690041 Vladivostok, Russia)

  • Yuri Izrailsky

    (Institute of Automation and Control Processes, Far Eastern Branch of the Russian Academy of Sciences, 5 Radio Street, 690041 Vladivostok, Russia)

Abstract

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.

Suggested Citation

  • Aleksandr Abakumov & Yuri Izrailsky, 2022. "Optimal Harvest Problem for Fish Population—Structural Stabilization," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:986-:d:774771
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    References listed on IDEAS

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    1. Vincent Martinet & Julio Peña-Torres & Michel Lara & Hector Ramírez C., 2016. "Risk and Sustainability: Assessing Fishery Management Strategies," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 64(4), pages 683-707, August.
    2. Kar, T.K. & Ghosh, Bapan, 2013. "Impacts of maximum sustainable yield policy to prey–predator systems," Ecological Modelling, Elsevier, vol. 250(C), pages 134-142.
    3. Perissi, Ilaria & Bardi, Ugo & El Asmar, Toufic & Lavacchi, Alessandro, 2017. "Dynamic patterns of overexploitation in fisheries," Ecological Modelling, Elsevier, vol. 359(C), pages 285-292.
    4. Richard Carson & Clive Granger & Jeremy Jackson & Wolfram Schlenker, 2009. "Fisheries Management Under Cyclical Population Dynamics," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 42(3), pages 379-410, March.
    5. Ola Flaaten, 1983. "The Optimal Harvesting of a Natural Resource with Seasonal Growth," Canadian Journal of Economics, Canadian Economics Association, vol. 16(3), pages 447-462, August.
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