A Bioeconomic Model of a Multi-site Fishery with Nonlinear Demand Function: Number of Sites Optimizing the Total Catch
- PDF / 472,130 Bytes
- 14 Pages / 439.37 x 666.142 pts Page_size
- 69 Downloads / 143 Views
A Bioeconomic Model of a Multi-site Fishery with Nonlinear Demand Function: Number of Sites Optimizing the Total Catch Sidy Ly • Pierre Auger • Moussa Balde
Received: 12 November 2013 / Accepted: 12 May 2014 Springer Science+Business Media Dordrecht 2014
Abstract We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to overexploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery. Keywords Multi-site fishery Variable price Nonlinear demand function Aggregation of variables Optimum catch.
S. Ly (&) P. Auger M. Balde Laboratory of Geometry and Application (LGA), Universite´ Cheikh-Anta-Diop, Dakar, Senegal e-mail: [email protected] P. Auger e-mail: [email protected] M. Balde e-mail: [email protected] S. Ly P. Auger M. Balde IRD UMI 209, UMMISCO, 32 av. Henri Varagnat, 93140 Bondy Cedex, France
123
S. Ly et al.
1 Introduction There is an important need to develop mathematical models as tools for a better management of renewable resources in particular in the field of fisheries. Bioeconomic models have been developed since many years. The originality of bioeconomic models is to take into account biological aspects as well as economic ones and we refer to classical major contributions by Clark (1990) and more recently by de Lara and Doyen (2008). In such bio-economic models, (usually a set of coupled ODEs), a first equation describes the time variation of the resource, In our case, the fish is assumed to grow logistically and is harvested by a fishing fleet. The catch is usually considered as a Schaefer function (Schaefer 1957), which is similar to a type I or Lotka-Volterra functional response. In many models, a second equation describes the time variation of the fishing effort with respect to time t (Smith 1968, 1969; Barbier et al. 2002). It is rather usual to consider that the fishing effort varies according to the difference between the benefice, i.e. the catch multiplied by the market price of the fish, and the costs of the fishery such as fishermen wages, fuel, taxes… In many models, the m
Data Loading...
