Before revision: 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. 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, May's thesis directly contradicted the longstanding ecological intuition that diversity promotes stability. In economics and finance, May's work helped to consolidate growing concerns about the fragility of an increasingly interconnected global marketplace. In this Letter , we draw on recent theoretical progress in random matrix theory and statistical physics to fundamentally extend and reinterpret May's theorem.
After revision: With a brief letter to Nature in 1972, Robert May triggered a worldwide research program studying ecological communities using random matrix theory. Yet, it remains unclear if and when we can treat real communities as random ecosystems. Here , we draw on recent theoretical progress in random matrix theory and statistical physics to fundamentally extend and reinterpret May's theorem.