Harvesting and predator-prey interaction in a Georges Bank food chain

Shari Wiley
Mathematics Department, Howard University

(June 9, 2011 10:30 AM - 11:30 AM)

Harvesting and predator-prey interaction in a Georges Bank food chain

Abstract

In this talk, we use a generalized age-structured model to discuss the role that both compensatory (non-oscillatory) and overcompensatory (oscillatory) dynamics play in the long term dynamics of exploited fisheries. When each species is governed by compensatory dynamics via the Beverton-Holt model and the predator's response to species interaction is modeled using a linear function, we show that the predator-prey model exhibits a globally stable positive fixed point. In stark contrast, we show that when each species is governed by compensatory dynamics via the Beverton-Holt model and the predator response function is exponential, then the predator-prey model exhibits population oscillations.