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Computer Research and Modeling, 2019, Volume 11, Issue 5, Pages 879–893
DOI: https://doi.org/10.20537/2076-7633-2019-11-5-879-893
(Mi crm748)
 

This article is cited in 1 scientific paper (total in 1 paper)

ANALYSIS AND MODELING OF COMPLEX LIVING SYSTEMS

Optimal fishing and evolution of fish migration routes

V. G. Ilichev, L. Dashkevich

Federal Research Centre The Southern Scientific Centre of the Russian Academy of Sciences, 41 Chekhov st., Rostov-on-Don, 344006, Russia
Full-text PDF (411 kB) Citations (1)
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Abstract: A new discrete ecological-evolutionary mathematical model is presented, in which the search mechanisms for evolutionarily stable migration routes of fish populations are implemented. The proposed adaptive designs have a small dimension, and therefore have high speed. This allows carrying out calculations on long-term perspective for an acceptable machine time. Both geometric approaches of nonlinear analysis and computer “asymptotic” methods were used in the study of stability. The migration dynamics of the fish population is described by a certain Markov matrix, which can change during evolution. The “basis” matrices are selected in the family of Markov matrices (of fixed dimension), which are used to generate migration routes of mutant. A promising direction of the evolution of the spatial behavior of fish is revealed for a given fishery and food supply, as a result of competition of the initial population with mutants. This model was applied to solve the problem of optimal catch for the long term, provided that the reservoir is divided into two parts, each of which has its own owner. Dynamic programming is used, based on the construction of the Bellman function, when solving optimization problems. A paradoxical strategy of “luring” was discovered, when one of the participants in the fishery temporarily reduces the catch in its water area. In this case, the migrating fish spends more time in this area (on condition of equal food supply). This route is evolutionarily fixes and does not change even after the resumption of fishing in the area. The second participant in the fishery can restore the status quo by applying “luring” to its part of the water area. Endless sequence of “luring” arises as a kind of game “giveaway”. A new effective concept has been introduced - the internal price of the fish population, depending on the zone of the reservoir. In fact, these prices are Bellman's private derivatives, and can be used as a tax on caught fish. In this case, the problem of long-term fishing is reduced to solving the problem of one-year optimization.
Keywords: long-term fishing, optimization, spatial adaptation, strategy of luring, internal prices.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation AAAA-A18-118122790121-5
Russian Foundation for Basic Research 18-01-00453
The research is carried out in the frame of government task of SSC RAS under project (state registration No. AAAA-A18- 118122790121-5) and grant RFBR No. 18-01-00453.
Received: 13.08.2019
Revised: 11.09.2019
Accepted: 11.09.2019
Document Type: Article
UDC: 577.38:574.62
Language: Russian
Citation: V. G. Ilichev, L. Dashkevich, “Optimal fishing and evolution of fish migration routes”, Computer Research and Modeling, 11:5 (2019), 879–893
Citation in format AMSBIB
\Bibitem{IliDas19}
\by V.~G.~Ilichev, L.~Dashkevich
\paper Optimal fishing and evolution of fish migration routes
\jour Computer Research and Modeling
\yr 2019
\vol 11
\issue 5
\pages 879--893
\mathnet{http://mi.mathnet.ru/crm748}
\crossref{https://doi.org/10.20537/2076-7633-2019-11-5-879-893}
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  • https://www.mathnet.ru/eng/crm748
  • https://www.mathnet.ru/eng/crm/v11/i5/p879
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Computer Research and Modeling
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    Abstract page:592
    Full-text PDF :69
    References:39
     
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