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Using Harvesting Models to Teach Modeling with Differential Equations

Abstract: Harvesting models based on ordinary differential equations are commonly used in the fishery industry and wildlife management to model the evolution of a population depleted by harvest mortality. We present a project consisting of a series of scenarios based on fishery harvesting models to teach the application of theoretical concepts learned in a differential equations course to scenarios encountered in real fisheries. These projects require a thorough understanding of simplifying assumptions inherent in various models, as well as a qualitative analysis of phase portraits, bifurcations, and stability of steady states. Parameters are estimated and equations are sometimes solved both analytically and numerically. Students learn to respond to a professional request from a fishery in the form of a scientific report, which requires organizing and communicating assumptions, models, solution methods, results, and a final recommendation with clarity and professionalism.