The may-wigner stability theorem

Abstract We provide heuristic arguments and a simple, self-contained proof of May's (1972) stability theorem for randomly assembled linear systems. See also Gardner & Ashby's (1970) simulation results. Our argument is easily modified to handle typical ecological constraints (May, 1974; Lawlor, 1978) on community interaction matrices. In complex systems, our argument suggests that weak interactions with many species (high C , low α) are favored over strong interactions with few species (low C , high α). This partially resolves the “rocky intertidal paradox” (May, 1979; Murdock, 1979) by explaining overall structure in this intensely competitive community.

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