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.