Modeling the Ecological Dynamics of a Three-Species Fish Population in the Chesapeake Bay

Abstract

We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based on some simplifying assumptions to demonstrate the application of theoretical concepts to actual fisheries in the Chesapeake Bay. Analysis involves elementary skills such as finding the roots of polynomial equations, computing eigenvalues and eigenvectors, and some advanced topics such as Routh-Hurwitz criteria and the Hartman-Grobman Theorem. Numerical simulations via MATLAB are utilized to produce graphical simulations and analyze long-time behaviors. Our model predicts that if no serious measures are taken to prevent the spread of the invasive blue catfish, the native predator species will be seriously affected and may even become extinct. The model also shows that linear harvesting is sufficient to limit the growth of the invasive catfish population; however, it is not sufficient to save the striped bass from becoming extinct. The results of this study illustrate the fundamental ecological principle of competitive exclusion, according to which two competing species that attempt to occupy the same niche in an ecosystem cannot co-exist indefinitely and one of the two populations will either go extinct or will adapt to fill a different niche.