Abstract
There exists a vast number of mathematical models dealing with problems of optimal exploitation of biological resources [1–5]. There appear different types of models. This is due to the fact that people pursue different aims and objects by using mathematical models. The purpose of the paper in hand is to find some general trends for some ecological problems which arise in the exploitation of populations. Therefore simple models of population dynamics are used. Because of their abstractions and idealisations they reveal qualitative results which can be generalized. However they are not suitable to make quantitatively correct predictions for a specific situation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Clark, C.W. 1976, Mathematical Bioeconomics. Wiley, New York.
Vincent, T.T. and Skowronski, J.M. (Editors), 1981. Renewable Resource Management. Lecture Notes in Biomathematics, Vol.40, Springer, Berlin.
May, R.M.(Ed.), (1984). Exploitation of Marine Communities, Report of the Dahlem Workshop 1984, Springer, Berlin.
Clark, C.W. (1985). Bioeconomic. Modelling and Fisheries Management. Wiley, New York.
Goh, B.S., 1980. Management and analysis of biological populations. Elsevier, Amsterdam.
May, R.M., Beddington, J.R., Horwood, J.W. and Shepherd, J.G., 1978. Exploiting natural populations in an uncertain world. Math.Biosci., 42: 219–252.
Kirkwood, G.P., 1981. Allowing for risk in setting catch limits based on MSY. Math.Biosci., 53: 119–129.
Ludwig, D., 1981. Harvesting strategies for a randomly fluctuating resource. SIAM J.Appl.Math., 37: 116–174.
Silvert, W., (1977). The economics of over-fishing. Trans. Amer. Fish. Soc. 106, 121–130.
Goel, N.S. and Richter-Dyn, N., 1974. Stochastics models in biology, Academic Press, London.
Kleiding, N., 1975. Extinction and growth in random environments., Theor.Pop.Biol., 8: 49–63.
Turelli, M., 1977. Random environments and stochastic calculus., Theor.Pop.Biol., 12: 140–178.
Tuckwell, H.C., 1974. A study of some diffusion models of population growth., Theor.Pop.Biol., 5: 345–357.
Capocelli, R.M. and Ricciardi, L.M., 1971. A diffusion model for population growth in random environment., Theor. Pop. Biol., 5: 28–41.
Gardiner, C.W., 1983. Handbook of stochastic methods., Springer, New York.
Jacobs, J., 1984. Cooperation, optimal density and low density thresholds: yet another modification of the logistic model, Oecologia, 64: 389–395.
Pierre, D., 1969. Optimization theory with applications., Wiley, New York.
Fleming, W.H. and Rishel, R.W., 1975. Deterministic and stochastic optimal control. Springer, New York.
Lee, E.B. and Markus, L., 1967. Foundations of optimal control theory. MacGraw Hill, New York.
Nisbet, R.M. and Gurney, W.S.C., 1982. Modelling fluctuating populations. Wiley, New York.
Hutchinson, C.E. and Fischer, T.R., 1979. Stochastic control theory applied to fishery management. IEEE Trans. Sys. Man and Cybern. SMC-9, 5: 253–259.
Wissel, C., 1985. Solution of the master equation of a bistable reaction system. Physica 128 A, 150–163.
Haken, H., 1983. Synergetics. An introduction. Springer, Berlin.
Wilkinson, J.H., 1965. The algebraic eigenvalue problem. Clarendon Press, Oxford.
Wissel, C., and Schmitt, T., (1987). How to avoid extinction of populations optimally exploited. Math.Biosci. 84, 127–138
Schmitt, T. and Wissel, C., 1985. Interdependence of ecological risk and economic profit in the exploitation of renewable resources. Ecol.Mod. 28: 201–215
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wissel, C. (1988). Avoidance of Ecological Risk in Optimal Exploitation of Biological Resources. In: Wolff, W., Soeder, CJ., Drepper, F.R. (eds) Ecodynamics. Research Reports in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73953-8_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-73953-8_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-73955-2
Online ISBN: 978-3-642-73953-8
eBook Packages: Springer Book Archive