Stability of Community Interaction Matrices

  • Harold M. Hastings
Conference paper
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 52)


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.


Interaction Strength Interaction Matrice Stability Theorem Underlying Graph Ecological Constraint 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Harold M. Hastings

There are no affiliations available

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