Diverse communities behave like typical random ecosystems

Abstract

With a brief letter to Nature in 1972, Robert May triggered a worldwide research program in theoretical ecology and complex systems that continues to this day[1]. Building on powerful mathematical results about large random matrices, he argued that systems with sufficiently large numbers of interacting components are generically unstable. In the ecological context, Mays thesis directly contradicted the longstanding ecological intuition that diversity promotes stability[2-4]. In economics and finance, Mays work helped to consolidate growing concerns about the fragility of an increasingly interconnected global marketplace[5-7]. In this Letter, we draw on recent theoretical progress in random matrix theory and statistical physics to fundamentally extend and reinterpret Mays theorem. We confirm that a wide range of ecological models become unstable at the point predicted by May, even when the models do not strictly follow his assumptions. Surprisingly, increasing the interaction strength or diversity beyond the May threshold results in a reorganization of the ecosystem - through extinction of a fixed fraction of species - into a new stable state whose properties are well described by purely random interactions. This self-organized state remains stable for arbitrarily large ecosystem and suggests a new interpretation of Mays original conclusions: when interacting complex systems with many components become sufficiently large, they will generically undergo a transition to a \"typical\" self-organized, stable state.