The cavity method for community ecology

This article is addressed to researchers and students in theoretical ecology, as an introduction to \"disordered systems\" approaches from statistical physics, and how they can help understand large ecological communities. We discuss the relevance of these approaches, and how they fit within the broader landscape of models in community ecology. We focus on a remarkably simple technique, the cavity method, which allows to derive the equilibrium properties of Lotka-Volterra systems. We present its predictions, the new intuitions it suggests, and its technical underpinnings. We also discuss a number of new results concerning possible extensions, including different functional responses and community structures.