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About the Methods of Extracting a Biological Resource That Provide the Maximum Average Time Benefit

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Abstract

Models of structured populations consisting of individual species or divided into age groups are considered. One example is fishing for different species that compete for food or habitats. The dynamics of the population in the absence of exploitation is described by a system of differential equations; at certain points in time, part of the resource is extracted from the population. The average time benefit equal to the limit of the average cost of the resource with an unlimited increase in the moments of extraction is estimated. A method of resource extraction for the long-term collection mode is proposed which maintains the constant preservation of a certain part of the population required for its further recovery, and the maximum average time benefit is achieved. The results are illustrated by examples of models of interaction between two species, such as competition and symbiosis.

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Funding

This study was supported by the Russian Foundation for Basic Research (project no. 20-01-00293).

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Authors and Affiliations

  1. Vladimir State University, 600000, Vladimir, Russia

    M. S. Woldeab & L. I. Rodina

  2. National University of Science and Technology MISiS, 119049, Moscow, Russia

    L. I. Rodina

Authors
  1. M. S. Woldeab
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  2. L. I. Rodina
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Corresponding authors

Correspondence to M. S. Woldeab or L. I. Rodina.

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The authors declare that they have no conflicts of interest.

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Translated by M. Shmatikov

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Woldeab, M.S., Rodina, L.I. About the Methods of Extracting a Biological Resource That Provide the Maximum Average Time Benefit. Russ Math. 66, 8–18 (2022). https://doi.org/10.3103/S1066369X22010078

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  • DOI: https://doi.org/10.3103/S1066369X22010078

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