Stability in Models of Mutualism
- 1 February 1979
- journal article
- research article
- Published by University of Chicago Press in The American Naturalist
- Vol. 113 (2) , 261-275
- https://doi.org/10.1086/283384
Abstract
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 2 spp. 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 3 or more spp. 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.This publication has 3 references indexed in Scilit:
- Global Stability in Many-Species SystemsThe American Naturalist, 1977
- Nonvulnerability of ecosystems in unpredictable environmentsTheoretical Population Biology, 1976
- On matrices with non-positive off-diagonal elements and positive principal minorsCzechoslovak Mathematical Journal, 1962