In a recent study of plants and herbivores on an island in the North Sea, ecologists made a surprising observation: Instead of more vegetation resulting in more grazers, more vegetation resulted in fewer grazers. Consequently, the ecologists hypothesized that, as the vegetation grew more dense, it became increasingly difficult for herbivores to reach and/or to digest the vegetation. Eventually, the vegetation might grow so dense as to be unsuitable for the herbivores. In this activity, students will apply a variety of techniques for analyzing nonlinear systems (e.g., nullclines, linearization, and technologies for drawing phase portraits) to study plant-herbivore models. In the final section, students will determine the long-term predictions of two mathematical models used in the North Sea study.
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