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1-137-SheepGraze-ModelingScenario

Author(s): Mary Vanderschoot

Keywords: herbivore plant phase lines bifurcation overexploitation sheep graze

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Abstract

Resource Image In this activity, students will apply graphical analysis (such as phase lines) to determine the long-term predictions of a differential equation model for pasture grass using two different formulas for the herbivore consumption rate.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

One of the most well-known mathematical models in ecology is the Lotka-Volterra predator-prey system of differential equations. Initially, this model was used to analyze interactions between two animal populations. But ecologists discovered that it could also be applied to plant (`prey') and herbivore (`predator') interactions. A grazing system (such as sheep in a pasture) is a special type of plant-herbivore system in which the herbivore population is controlled by humans. Because the number of herbivores does not change, the model consists of a single differential equation for the vegetation.

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Authors

Author(s): Mary Vanderschoot

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