Search Site



Advanced Search


 
Product No. 99776 Supplementary Print Price: FREE with membership
 

Small Mammal Dispersion (UMAP)

Ray Huffaker, Kevin Cooper, Thomas Lofaro


Mathematics Topic:
Differential Equations
Application Areas:
Biology, ecology
Prerequisites:
Introduction to ordinary differential equations covering phase-plane solutions.

| ©2000 by COMAP, Inc. | Tools for Teaching 1999 | 19 pages |


This module introdcues students to the social fence hypothesis explaining small mammal migration between adjacent land areas. Students are shown how the hypothesis is formulated in the population ecology literature as a pair of autonomous differential equations, and then they are directed toward a modified version of the standard formulation leading to increased realism. The modified version is solved qualitatively with phase diagrams for a range of ecological circumstances. Students also gain experience working with the numerical phase-plane plotter Dynasys, which can be downloaded from the World Wide Web. The social fence hypothesis is presented within the real-world context of controlling beaver-related damage in a given area by trapping.

Table of Contents:

INTRODUCTION

MATHEMATICAL FORMULATION OF THE SOCIAL FENCE HYPOTHESIS

THE SOCIAL FENCE FORMULATION WITH TRAPPING

DIMENSIONS RATE EQUATIONS

ZERO-TRAPPING DYNAMICS

POSITIVE TRAPPING DYNAMICS

DISCUSSION

SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHORS