[Pre-print] Harvesting fisheries management strategies with modified effort function

Abstract

In traditional harvesting model, a fishing effort, E, is defined by the fishing intensity and does not address the inverse effect of fish abundance on the fishing effort. In this paper, based on a canonical differential equation model, we developed a new fishing effort model which relies on the density effect of fish population. We obtained new differential equations to describe certain standard Fisheries management strategies. This study concludes that a control parameter β( the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values. To examine systematically the consequences of different harvesting strategies, we used numerical simulations and qualitative analysis of six fishery strategies, e.g., proportional harvesting, threshold harvesting, proportional threshold harvesting, and seasonal and rotational harvesting.