Modeling ecological issues in fish dynamics: Competing predators, invasiveness, and over-harvesting

Abstract

A mathematical model of a three-species dynamical system is employed to analyze some ecological issues in fish dynamics, namely, competition between predators, effect of an invasive species, and over-harvesting of either the prey or one of the predators. To address the issue of competition between predators, we assume that one of the predators is a specialist predator using a Holling Type II response while the other one is a generalist predator using a Holling Type III response. The latter assumption is also used to analyze the effect of having an invasive species as a second predator. We use an analytical approach to compute the equilibria and investigate the linear stability of each point. We also compute the bionomic equilibria and find conditions for their existence. We use a numerical approach to analyze the effects of harvesting efforts on the prey and on one of the predators. The proposed dynamical system may be used to analyze special fish dynamics in the Chesapeake Bay with the Atlantic menhaden as prey as well as striped bass and catfish as competing predators. In particular, we address a recent policy on eating-the-invaders as a way to control the growth of the catfish as an invasive species in the Chesapeake Bay.