Automated Techniques for the Qualitative Analysis of Ecological Models: Continuous Models

Lynn van Coller, UBC

DOI: http://dx.doi.org/10.5751/ES-00017-010105

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Abstract

The mathematics required for a detailed analysis of the behavior of a model can be formidable. In this paper, I demonstrate how various computer packages can aid qualitative analyses by implementing techniques from dynamical systems theory. Because computer software is used to obtain the results, the techniques can be used by nonmathematicians as well as mathematicians. In-depth analyses of complicated models that were previously very difficult to study can now be done. Because the paper is intended as an introduction to applying the techniques to ecological models, I have included an appendix describing some of the ideas and terminology. A second appendix shows how the techniques can be applied to a fairly simple predator-prey model and establishes the reliability of the computer software. The main body of the paper discusses a ratio-dependent model. The new techniques highlight some limitations of isocline analyses in this three-dimensional setting and show that the model is structurally unstable. Another appendix describes a larger model of a sheep-pasture-hyrax-lynx system. Dynamical systems techniques are compared with a traditional sensitivity analysis and are found to give more information. As a result, an incomplete relationship in the model is highlighted. I also discuss the resilience of these models to both parameter and population perturbations.

Key words

bifurcation; computer analysis; dynamical systems; ecological models; qualitative analysis; ratio-dependent model; XPPAUT.

Copyright © 1997 by the author(s). Published here under license by The Resilience Alliance. This article is under a Creative Commons Attribution-NonCommercial 4.0 International License. You may share and adapt the work for noncommercial purposes provided the original author and source are credited, you indicate whether any changes were made, and you include a link to the license.