Bapan Ghosh

Sustainability and optimal control of an exploited prey predator system through provision of alternative food to predator.

In the present paper, we develop a simple two species prey-predator model in which the predator is partially coupled with alternative prey. The aim is to study the consequences of providing additional food to the predator as well as the effects of harvesting efforts applied to both the species. It is observed that the provision of alternative food to predator is not always beneficial to the system. A complete picture of the long run dynamics of the system is discussed based on the effort pair as control parameters. Optimal augmentations of prey and predator biomass at final time have been investigated by optimal control theory. Also the short and large time effects of the application of optimal control have been discussed. Finally, some numerical illustrations are given to verify our analytical results with the help of different sets of parameters.

Possible ecosystem impacts of applying maximum sustainable yield policy in food chain models.

This paper describes the possible impacts of maximum sustainable yield (MSY) and maximum sustainable total yield (MSTY) policy in ecosystems. In general it is observed that exploitation at MSY (of single species) or MSTY (of multispecies) level may cause the extinction of several species. In particular, for traditional prey-predator system, fishing under combined harvesting effort at MSTY (if it exists) level may be a sustainable policy, but if MSTY does not exist then it is due to the extinction of the predator species only. In generalist prey-predator system, harvesting of any one of the species at MSY level is always a sustainable policy, but harvesting of both the species at MSTY level may or may not be a sustainable policy. In addition, we have also investigated the MSY and MSTY policy in a traditional tri-trophic and four trophic food chain models.

Sustainability and economic consequences of creating marine protected areas in multispecies multiactivity context

The present study deals with harvesting of prey species in the presence of predator in a multispecies marine fishery. The total habitat is divided into two patches: one is reserve area where fishing is completely banned and other zone is called fishing area where only prey is exploited. We assume that the prey fish possesses heterogeneous intrinsic growth rate with uniform carrying capacity where as predator has constant intrinsic growth rate with prey dependent carrying capacity. The analytical conditions are derived to prevent the species extinction for larger employed effort in single (only prey) species fishery. Optimal equilibrium premium are presented for both monospecies and multispecies fishery for all degree of protection. Increasing standing stock (ISS) and protected standing stock (PSS) are measured in the presence of prey-predator interaction.

Maximum sustainable yield and species extinction in a prey-predator system: some new results.

Though the maximum sustainable yield (MSY) approach has been legally adopted for the management of world fisheries, it does not provide any guarantee against from species extinction in multispecies communities. In the present article, we describe the appropriateness of the MSY policy in a Holling–Tanner prey–predator system with different types of functional responses. It is observed that for both type I and type II functional responses, harvesting of either prey or predator species at the MSY level is a sustainable fishing policy. In the case of combined harvesting, both the species coexist at the maximum sustainable total yield (MSTY) level if the biotic potential of the prey species is greater than a threshold value. Further, increase of the biotic potential beyond the threshold value affects the persistence of the system.

Relationship between exploitation, oscillation, MSY and extinction

We give answers to two important problems arising in current fisheries: (i) how maximum sustainable yield (MSY) policy is influenced by the initial population level, and (ii) how harvesting, oscillation and MSY are related to each other in prey-predator systems. To examine the impact of initial population on exploitation, we analyze a single species model with strong Allee effect. It is found that even when the MSY exists, the dynamic solution may not converge to the equilibrium stock if the initial population level is higher but near the critical threshold level. In a prey-predator system with Allee effect in the prey species, the initial population does not have such important impact neither on MSY nor on maximum sustainable total yield (MSTY). However, harvesting the top predator may cause extinction of all species if odd number of trophic levels exist in the ecosystem. With regard to the second problem, we study two prey-predator models and establish that increasing harvesting effort either on prey, predator or both prey and predator destroys previously existing oscillation. Moreover, equilibrium stock both at MSY and MSTY level is stable. We also discuss the validity of found results to other prey-predator systems.

Biological conservation through marine protected areas in the presence of alternative stable states

This article addresses how depleted stock can be restored by creation of marine reserve and species mobility when alternative stable states persist in a marine ecosystem. To understand the role of a marine protected area, we develop a two-patch version of an originally single-patch model. In the two-patch model, we prove that some of the locally stable equilibria are not stable equilibria from an ecological viewpoint. Similarly, some unstable equilibria determined classically from the mathematical model are no longer equilibria. It is shown that increasing reserve size may produce three alternative stable states in the presence of harvesting. Dynamic solutions have a tendency to reach an upper stable state from a lower stable state when reserve size is increased, but the opposite phenomenon (i.e., shifting to a lower stable state from an upper one) never occurs. This suggests that MPAs always have a positive effect in stock conservation even when alternative stable states inherently persist in marine ecosystems.

Sustainability of exploited ecologically interdependent species

This paper examines the application of maximum sustainable yield (MSY) policy in ecosystem and indicates when the ecosystem based fisheries management approach is required for conservation purpose. To describe the possible impacts of applying global MSY policy in an ecosystem, we have considered both specialist and generalist prey–predator models with different fishing efforts. It is found that harvesting both prey and predator species in specialist prey–predator systems, to achieve global maximum sustainable total yield (MSTY) under independent efforts, will cause the extinction of the predator species. In contrast, the global MSTY may exist in a generalist prey–predator system. If global MSTY does not exist, then it is due to the extinction of predator species. Hence, the prey species never goes to extinction under independent efforts and this scenario is quite different from the one found under combined harvesting effort.

Harvesting induced stability and instability in a tri-trophic food chain

Non-equilibrium dynamics in the form of oscillations or chaos is often found to be a natural phenomenon in complex ecological systems. In this paper, we first analyze a tri-trophic food chain, which is an extension of the Rosenzweig-MacArthur di-trophic food chain. We then explore the impact of harvesting individual trophic levels to answer the following questions : a) when a non-equilibrium dynamics persists, b) whether it can locally be stabilized to a steady state, c) when the system switches from a stable steady state to a non-equilibrium dynamics and d) whether the Maximum Sustainable Yield (MSY) always exists when the top predator is harvested. It is shown that searching for a general theory to unify the harvesting induced stability must take into account the number of trophic levels and the degree of species enrichment, the outcomes that cannot be obtained from the earlier reports on prey-predator models. We also identify the situation where harvesting induces instability switching: the non-equilibrium state enters into a stable steady-state and then, upon more intensive harvesting, the steady-state again loses its stability. One of the new and important results is also that the MSY may not exist for harvesting the top predator. In general, our results contribute to biological conservation theory, fishery and ecosystem biodiversity management.