Will a Large Complex System be Stable? Revisited

TL;DR

This paper revisits the complexity-stability debate in ecological systems, offering a new mathematical approach to better understand stability mechanisms beyond random matrix theory.

Contribution

It introduces a novel mathematical framework that clarifies stability mechanisms in large ecological systems, challenging previous broad conclusions.

Findings

Revisits May's stability analysis with new mathematical tools

Provides detailed insights into stability mechanisms in complex systems

Counteracts the broad conclusion that larger systems are inherently less stable

Abstract

Over fifty years ago, Robert May applied random matrix theory to show that as ecological systems grow in size, stability decreases. What emerged from this and the critique that followed was decades of what has been called the complexity-stability debate. However, decades of critique over the assumptions that Robert May applied in carrying out his analysis have not been enough to fully dispel the strength of his conclusion and close the debate. Drawing on a mathematical approach that had not yet been fully developed in the early 70s, it is possible to revisit the argument without the use of random matrix techniques, and provide more detailed understanding of the mechanisms that play a deciding role in stability of ecological systems, countering the broad conclusion that led to the complexity-stability debate.