Impact of overfishing of large predatory fish on algal blooms: a mathematical study

Abstract

Algal blooms are a sudden increase in the population of algae in aquatic eco-system. The harmful algal blooms can make water toxic and hence can cause sufferings to humans and fish populations. So the control of algal bloom is very much desirable. In this paper, a four-species food-chain model for the biological control of algal bloom is proposed and analyzed. Here we consider algae population, zooplankton, small fish and large fish linked as a food chain. The large fish acts as a top predator and small fish & zooplankton as middle predator. The algae population is serving as prey. The formulation of this mathematical model is based on the assumption that fish population is very much effective in regulating the dynamics of algal bloom and the harvesting of large predatory fish is linked with the growth of algae population. The equilibria of the proposed model are found and local stability of these equilibria are discussed in detail. Numerical simulation is performed to visualize the impact of harvesting rate constant of the large predatory fish and carrying capacity of algae population on algal blooms.