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Ecological and Lyapunov Stability

Published online by Cambridge University Press:  01 January 2022

James Justus
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Abstract

Ecologists have proposed several incompatible definitions of ecological stability. Emulating physicists, mathematical ecologists commonly define it as Lyapunov stability. This formalizes the problematic concept by integrating it into a well-developed mathematical theory. The formalization also seems to capture the intuition that ecological stability depends on how ecological systems respond to perturbation. Despite these advantages, this definition is flawed. Although Lyapunov stability adequately characterizes perturbation responses of many systems studied in physics, it does not for ecological systems. This failure reveals a limitation of its underlying mathematical theory, and an important difference between dynamic systems modeling in physics and ecology.

Type
Research Article
Information
Philosophy of Science , Volume 75 , Issue 4 , October 2008 , pp. 421 - 436
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

A Josephine De Kármán fellowship supported this research. For helpful comments and discussions, thanks to Mark Colyvan, Simon Huttegger, Greg Mikkelson, Alexander Moffett, Samir Okasha, Eric Pianka, Mark Sainsbury, Carl Salk, Sahotra Sarkar, and audience members at the University of Wisconsin at Madison, where an early version of this paper was presented.

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