A technique for estimating maximum harvesting effort in a stochastic fishery model
Exploitation of biological resources and the harvest of population species are commonly practiced in fisheries, forestry and wild life management. Estimation of maximum harvesting effort has a great impact on the economics of fisheries and other bio-resources. The present paper deals with the problem of a bioeconomic fishery model under environmental variability. A technique for finding the maximum harvesting effort in fluctuating environment has been developed in a two-species competitive system, which shows that under realistic environmental variability the maximum harvesting effort is less than what is estimated in the deterministic model. This method also enables us to find out the safe regions in the parametric space for which the chance of extinction of the species is minimized. A real life fishery problem has been considered to obtain the inaccessible parameters of the system in a systematic way. Such studies may help resource managers to get an idea for controlling the system.
KeywordsColour noise harvested competitive system maximum harvesting parametric safe zone solution of stochastic differential equation spectral density Tchebycheff’ s inequality
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- Clark C W 1990Mathematical bioeconomics: The optimal management of renewable resources (New York: John Wiley)Google Scholar
- Danilina N I, Dubrovskaya N S, Kvasha O P and Smirnov G L 1988Computational mathematics (Moskow: Mir Publishers)Google Scholar
- Dimentberg M F 1988 Statistical dynamics of nonlinear and time varying systems (New York: John Wiley)Google Scholar
- Gause G F 1935La Théorie Mathématique de la Lutte pour la Vie (Paris: Harmann)Google Scholar
- Hoel P G, Port S C and Stone C J 1993Introduction to stochastic process (Boston: Houghton Mifflin Company)Google Scholar
- Horsthemke W and Lefever R 1983Noise induced transitions (Berlin: Springer-Verlag)Google Scholar
- Laloe F and Samba A 1991 A simulation model of artisanal fisheries of Senegal;ICES Mar. Sci. Symp. 193 281–286Google Scholar
- May R M 1975Stability and complexity in model ecosystems (Princeton: Princeton University Press)Google Scholar
- Pella J J and Tomlinson P K 1969A generalized stock production model;Bull. IATTC 13 419–496Google Scholar
- Schaefer M B 1957 A study of the dynamics of the fishery for yellowfin tuna in the Eastern Tropical Pacific Ocean;Bull. IATTC 2 247–285Google Scholar
- Uhlenbeck G E and Ornstein L S 1954 On the theory of Brownian motion; inSelected papers on noise and stochastic process (ed.) N Wax (New York: Dover)Google Scholar