Stability in Models of Mutualism

A simple test for global stability in a large class of nonlinear models of mutualism is derived. In Lotka-Volterra models of mutualism, local stability implies global stability. In the space of the interaction parameters, the continuum of stable Lotka-Volterra models of two-species mutualism is equa...

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Bibliographic Details
Published in:The American naturalist 1979-02, Vol.113 (2), p.261-275
Main Author: Goh, B. S.
Format: Article
Language:English
Subjects:
Ecological balance
Ecological competition
Ecological modeling
Ecology
Ecosystem models
Ecosystems
Mathematical models
Mutualism
Population ecology
Species
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Summary:A simple test for global stability in a large class of nonlinear models of mutualism is derived. In Lotka-Volterra models of mutualism, local stability implies global stability. In the space of the interaction parameters, the continuum of stable Lotka-Volterra models of two-species mutualism is equal to the continuum of stable Lotka-Volterra models of competition, but it is smaller than the continuum of stable Lotka-Volterra models of a single-prey and a single-predator interaction. For three or more species the continuum of globally stable Lotka-Volterra models of mutualism is smaller than the continuum of globally stable Lotka-Volterra models of competition or prey-predator interactions. This mathematical result suggests that in nature mutualism is less common than competition and predation.
ISSN:0003-0147
1537-5323
DOI:10.1086/283384