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Some strategies for harvesting a single species

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Abstract

Then-stage harvesting strategy of Elizarov and Svirezhev is examined. As a result, some important new features appear. A discussion is presented on whether or not one should harvest a species at one time stage or wait until a later time. The paper is concerned with contributions which are primarily mathematical formulations and results for continuous, as well as discrete time, logistic growth of a single species being harvested. Age class structure is ignored.

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Literature

  • Ayala, F. J., M. E. Gilpin and J. G. Ehrenfeld. 1973. “Competition Between Species: Theoretical Models and Experimental Tests.”Theo. Pop. Biol.,4, 331–356.

    Article  MathSciNet  Google Scholar 

  • Becker, N. G. 1970. “Control of a Pest Population.”Biometrics,26, 365–375.

    Article  Google Scholar 

  • Bellman, R. E. 1957.Dynamic Programming. Princeton: Princeton University Press.

    Google Scholar 

  • — and R. Kalaba. 1960. “Some Mathematical Aspects of Optimal Predation in Ecology and Boviculture.”Proc. Natn. Acad. Sci. U.S.A.,46, 718–720.

    Article  MATH  MathSciNet  Google Scholar 

  • Cherniavsky, E. A. and H. M. Taylor. 1972. “Control of a General Lethal Growth Process.”Math. Biosci.,13, 235–252.

    Article  MATH  MathSciNet  Google Scholar 

  • Clark, C. W. 1973. “The Economics of Overexploitation.”Science,181, 630–634.

    Google Scholar 

  • D'an, G., P. Kokotović and D. Gottlieb. 1971. “Time-Optimal Control for a Model of Bacterial Growth.”J. Optimization Theory Appl.,7, 61–69.

    Article  Google Scholar 

  • Elizarov, E. Ya. and A. Rybalko. 1970. “Maximal Productivity in Homogeneous Population.”Studia Biophysica (Berlin), No. 23, 43–50.

    Google Scholar 

  • — and Yu. M. Svirezhev. 1972. “The Optimal Productivity of Biogeocenoses.”Systems Theory Res.,22, 193–204.

    Google Scholar 

  • — and —. 1972a. “On Optimal Productivity of Biosystems.”Zhurnal Obshchey Biologii.,33, 251–260.

    Google Scholar 

  • Gilpin, M. E. and F. J. Ayala. 1973. “Global Models of Growth and Competition.”Proc. Natn. Acad. Sci. U.S.A.,70, 3590–3593.

    Article  MATH  Google Scholar 

  • Goh, B. S. 1969/1970. “Optimal Control of a Fish Resource.”Malayan Scientist,5, 65–70.

    Google Scholar 

  • Gompertz, B. 1825. “On the Nature of the Function Expressive of the Law of Human Mortality and on a New Model of Determining Life Contingencies.”Phil. Trans. Roy. Soc. (Lond.),115, 513–585.

    Google Scholar 

  • Gottfried, B. S. and J. Weisman. 1973.Introduction to Optimization Theory. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Jaquette, D. L. 1972. “Mathematical Models for the Control of Growing Biological Populations.”Operations Res.,20, 1142–1151.

    Article  MATH  Google Scholar 

  • Laird, A. K. 1964. “Dynamics of Tumor Growth.”Br. J. Cancer,18, 490–502.

    Google Scholar 

  • Miller, R. S. and D. B. Botkin. 1974. “Endangered Species: Models and Predictions.”Am. Sci.,62, 172–181.

    Google Scholar 

  • Pearl, R. 1924.Studies in Human Biology. New York: Williams & Wilkins.

    Google Scholar 

  • Shoemaker, C. A. 1973. “Optimization of Agricultural Pest Management III. Results and Extensions of a Model.”Math. Biosci.,18, 1–22.

    Article  MATH  Google Scholar 

  • Svirezhev, Yu. M. and E. Ya. Elizarov. 1972. “Mathematical Modeling of Biological Systems.” InProblems of Space Biology, Vol. 20. Moscow: Nauka.

    Google Scholar 

  • Verhulst, P. F. 1845. “Recherches Mathématiques sur la loi d'Acroissement de la Population.”Mem. Acad. Roy. Bruxelles,18, 1.

    Google Scholar 

  • — 1847. “Recherches Mathématiques sur la loi d'Acroissement de la Population.”Mem. Acad. Roy. Bruxelles,20, 1.

    Google Scholar 

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Swan, G.W. Some strategies for harvesting a single species. Bltn Mathcal Biology 37, 659–673 (1975). https://doi.org/10.1007/BF02459529

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  • DOI: https://doi.org/10.1007/BF02459529

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