Ecological chaos and the choice of optimal harvesting policy

Harvested populations fluctuate because of two primary reasons: the inherent nonlinearity contained in the interactions among the constituent species and the forces of harvesting acting on the oscillatory dynamics resulting from species interactions. During the course of these fluctuations, population densities make excursions to low densities. When the ecological system executes chaotic motion, extinction-sized densities are common. Thus, it is imperative to design harvesting strategies which aim at maximizing economic gains giving due consideration to the ecological health of the concerned ecological system. The present study was designed and performed to figure out how to set harvesting strategies which optimize the economic gain. The choice of optimal harvesting policy can be made only if dynamical features of the concerned ecological system are well understood. In this paper, we have consider the temporal and spatiotemporal interactions among phytoplankton, zooplankton and fish population with Holling type II and Holling type III functional responses. We have calculated stability analysis of the model system and performed the numerical simulations for both non-spatial and spatial models to figure out the parameters that are responsible for chaotic dynamics of the model system. The temporal model system shows rich dynamics including limit cycles and chaos whereas spatial model shows different types of patterns for population distribution. In this work, we have taken the case study of Sundarban wetland ecosystem. We have carried out the analysis of maximum sustainable yield and identified the parameters that are responsible for good health of wetland ecosystem through numerical simulation results.