Combined harvesting of a stage structured prey-predator model incorporating cannibalism in competitive environment

SUSTAINABLE DEVELOPMENT OF EUROPEAN HAKE RESOURCE: BIOECONOMIC PERSPECTIVE

This paper deals with the surplus production models of Verhulst-Schaefer and Gompertz-Fox that are applied to the European Hake fishery to develop static as well as dynamic frameworks to investigate the sustainability properties of the stock, optimal utilization of the resource and the management of the fishery. To illustrate the approach through which long-run sustainability can achieve an optimum exploitation of the fishery, a conventional economic model is combined with a biological population growth model to develop a deterministic bioeconomic model. The parameters of the bioeconomic model are estimated using empirical data of catch and effort of the European Hake fishery. Standard reference points are analyzed and tax policies are introduced to attain the standard reference points. In order to achieve maximum profit from the fishery, optimal steady state solutions are determined for separate discount rates.

Biological conservation of a prey-predator system incorporating constant prey refuge through provision of alternative food to predators: a theoretical study

We describe a prey-predator system incorporating constant prey refuge through provision of alternative food to predators. The proposed model deals with a problem of non-selective harvesting of a prey-predator system in which both the prey and the predator species obey logistic law of growth. The long-run sustainability of an exploited system is discussed through provision of alternative food to predators. We have analyzed the variability of the system in presence of constant prey refuge and examined the stabilizing effect on predator-prey system. The steady states of the system are derived and dynamical behavior of the system is extensively analyzed around steady states. The optimal harvesting policy is formulated and solved with the help of Pontryagin's maximal principle. Our objective is to maximize the monetary social benefit through protecting the predator species from extinction, keeping the ecological balance. Results finally illustrated with the help of numerical examples.

An ecological perspective on marine reserves in prey-predator dynamics

This paper describes a prey-predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge-Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.