How Should Ecological Stability be Defined?

James Justus, Philosophy; University of Texas, Austin

Abstract
Ecologists have proposed several incompatible definitions of ecological stability. One commonly cited definition equates ecological stability with Lyapunov stability. This definition has some obvious advantages. Unlike all other proposed definitions, it integrates ecological stability into a thoroughly studied mathematical theory that has proved fruitful in many other sciences, especially physics. This theory also seems to provide a formally precise characterization of the intuition that ecological stability depends on how an ecological system responds to disturbance, which is absent or imprecisely captured by other definitions. Despite these advantages, I argue ecological stability should not be defined as Lyapunov stability, for two reasons. First, as a description of the behavior of an ecological system, Lyapunov stability does not have a realistic biological interpretation. Second, analysis of different criteria for Lyapunov stability demonstrates that the conditions an ecological system must satisfy to be Lyapunov stable are biologically unrealistic. This shows that scientific definitions that make an initially vague concept precise by integrating it into a thoroughly studied mathematical theory, even one fruitfully utilized in other sciences, are not always satisfactory. The mathematical theory must also adequately represent the domain of application of the defined concept. A close correspondence between the mathematical theory of Lyapunov stability and well-confirmed theoretical principles ensures this in physics, but the lack of the latter within ecology precludes Lyapunov stability from playing a similarly fruitful role.

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