Stability of Community Interaction Matrices
We sketch a conceptual, self-contained proof (Hastings, 1982a) of R.M. May’s (1972) stability theorem for randomly assembled linear systems. Several ecological consequences follow. First, ecological constraints on interaction matrices (May, 1974; L.R. Lawlor, 1978) as well as organization into loosely coupled subsystems (cf. May, 1972) tend to enhance stability. Secondly, scaling results on interaction strength reconcile May’s stability criterion with R.H. MacArthur’s (1955) thesis that the existence of multiple energy pathways enhances stability. Finally, we analyze the effect of noise in these models.
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- BollobAs, B. (1979): Graph Theory, Graduate Texts in Math., Vol. 63, Springer, New York.Google Scholar
- Hastings, H.M. (1983): Stability of community interaction matrices, Food Web Workshop,ed. De Angelis, D.L., Post, M., and Sugihara, G., Oak Ridge National Laboratory, Technical Report (in press).Google Scholar
- May, R.M. (1974): Stability and Complexity in Model Ecosystems, Princeton U. Press, Princeton.Google Scholar
- Wigner, B. (1959): Statistical properties of real symmetric matrices with many dimensions, in Proc. Fourth Canad. Math. Cong., ed. MacPhail, M.S., U. Toronto Press, Toronto, pp. 174–184.Google Scholar