Hydra Effect and Harvesting Optimal Policy in a Generalist Predator Prey Model With General Holling Type Response Functions

This study illustrates selective and combined harvesting efforts to examine the existence of hydra effect and global MSTY (maximum sustainable total yield) in a generalist predator–prey mathematical model with general Holling type response functions. The hydra effect is an ecological paradox in which a species’ population size increases in response to an increase in its mortality rate. Existence of unique solution, positivity, and boundedness of solution of the mathematical model are verified. The equilibrium points and their stability are discussed. MSTY, the bionomic equilibrium point, and optimum level of harvesting are explained. Mainly, in this stable species interaction model, we showed (i) predator harvesting establishes hydra effect in a generalist predator–prey model; (ii) the global MSTY exists in a generalist prey–predator system for Holling Type I (HT-I) functional response for some conditions; and (iii) an optimal stock level maximizes the net revenue applying an optimal harvesting effort. However, inducing harvesting efforts greater than the optimal level causes a reduction in species density, leading to extinction. Moreover, net revenue declines. The analytical results are also supported and verified by numerical simulations.