Pustaka Ilmiah Universitas Padjadjaran

Abstrak

A Mathematical Model For Optimal Exploitation Of Bio-geographically Interconnected Natural Resources

The exploitation of multi-species fisheries, such as fisheries which have biological interactions between species (population) or fisheries incorporating geographically interconnected species, is not well understood (Hilborn and Walters, 1992). Many scientists point out that appropriate policies for fisheries management are only possible if we have a comprehensive understanding of the underlying systems which are exploited (Yodzis, 1994; Botsford et al., 1997). They also argue that management practices could be improved if we include interactions between species in developing multi-species models (Hall, 1998).

In this paper we discuss a continuous mathematical model for the exploitation of a biogeographically- interconnected populations. Biologically the population has a predator-prey interaction and geographically it has a metapopulation structure. The model here modifies Clark (1976) model for selective and explicit inshore-offshore model with the inclusion of two species interaction within two patches of habitat. These two patches are connected by the diffusion of the prey and the predator. The rates of the diffusion are assumed to be proportional to the differences of the population size between the two patches. It is assumed that individuals flow from the larger population size to the smaller.