Existence of Hydra Effect in a Three‐Species Food Chain Mathematical Model With General Holling Type Response Functions

Abstract

ABSTRACT This study explores existence of hydra effect and sustainable harvesting strategies in three species food chain system with all‐purpose Holling type response functions (HT‐I, II, III, and IV). The hydra effect (as mentioned in Sieber and Hilker 2012) is superficially ecological paradox which refers to an increase of a species population size in response to an increase in its mortality rate. Assuming the interior equilibrium point of the model exists under certain conditions and its stability, the stock‐level variation of species biomass under choosy harvesting efforts of the model is measured in terms of hydra effect, maximum sustainable total yield (MSTY), the bionomic equilibrium point, and optimum level of harvesting. In this food chain model, we verified: prey species harvesting demonstrate hydra effect but not the MSY whenever the intermediate predator response function increases. However, the MSY is conditionally attained for the rest Holling type response functions; a top‐predator harvesting produce hydra effect but not MSY for Holling type combinations HT‐I–HT‐III and HT‐II–HT‐III; the global MSTY is reached due to combined and integrated harvesting policy for certain preconditions and an optimal stock level maximizes the net revenue whenever an optimal effort is applied. The analytical and qualitative results are also supported and verified by numerical simulations.