Stock estimation, environmental monitoring and equilibrium control of a fish population with reserve area
- 210 Downloads
For sustainable exploitation of renewable resources, the separation of a reserve area is a natural idea. In particular, in fishery management of such systems, dynamic modelling, monitoring and control has gained major attention in recent years. In this paper, based on the known dynamic model of a fish population with reserve area, the methodology of mathematical systems theory and optimal control is applied. In most cases, the control variable is fishing effort in the unreserved area. Working with illustrative data, first a deterministic stock estimation is proposed using an observer design method. A similar approach is also applied to the estimation of the effect of an unknown environmental change. Then it is shown how the system can be steered to equilibrium in given time, using fishing effort as an open-loop control. Furthermore, a corresponding optimal control problem is also solved, maximizing the harvested biomass while controlling the system into equilibrium. Finally, a closed-loop control model is applied to asymptotically control the system into a desired equilibrium, intervening this time in the reserve area.
KeywordsStock estimation Fishery resource management Reserve area Observer system Ecosystem monitoring Ecosystem control
The research has been supported by the Hungarian Scientific Research Fund OTKA (K81279). The valuable comments of the anonymous referees are acknowledged.
- Agardy TS (1997) Marine protected areas and ocean conservation. R.G Landes Co, Academic Press, CaliforniaGoogle Scholar
- Banga JR, Balsa-Canto E, Moles CG, Alonso AA (2005) Dynamic optimization of bioprocesses: efficient and robust numerical strategies. J Biothecnol 117:407–419Google Scholar
- Cadrin SX, Friedland KD, Waldman JR (eds) (2005) Stock identification methods: applications in fishery science. Academic Press, New YorkGoogle Scholar
- Chakraborty K, Das S, Kar TK (2011) Optimal control of effort of a stage structured prey-predator fishery model with harvesting. Nonlinear Analysis: Real World Appl (in press). doi: 10.1016/j.nonrwa.2011.06.007
- Clark CW (1976) Mathematical bioeconomics: the optimal management of renewable resources, 2nd edition. Wiley, New YorkGoogle Scholar
- Clark CW (2010) Mathematical bioeconomics: the mathematics of conservation, 3rd edition. Wiley, HobokenGoogle Scholar
- Gámez M, López I, Garay J, Varga Z (2011) Monitoring and control in a spatially structured population model. In: Murgante B, Gervasi O, Iglesias A, Taniar D, Apduhan BO (eds) Computational science and its applications, vol V, pp 511–520, “Lecture Notes in Computer Science” 6786. Springer-Verlag Berlin, HeidelbergGoogle Scholar
- Goh BS (1980) Management and analysis of biological populations. Elsevier, AmsterdamGoogle Scholar
- Kar TK, Chaudhuri KS (2004) Harvesting in a two prey one predator fishery: a bioeconomic model. ANZIAM J 45(3):443–456 (Australian Mathematical Society)Google Scholar
- Lee EB, Markus L (1971) Foundations of optimal control theory. Wiley, New YorkGoogle Scholar