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.
KeywordsInteraction Strength Interaction Matrice Stability Theorem Underlying Graph Ecological Constraint
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