Statistical Mechanics of Large and Complex Ecosystems

Our intuition for ecological and evolutionary dynamics comes from simple models representing the interactions among two or three distinct kinds of organisms. But real ecosystems contain large numbers of distinct kinds of individuals, and the high dimensionality of the resulting state space can invalidate low-dimensional insights. The cavity method from spin glass physics has recently emerged as a powerful tool for exploring the opposite limit, with approximations that become more accurate as the dimensionality grows. I will present some results I have recently obtained using this approach, which shed new light on classic ecological observations and suggest intriguing avenues for further investigation.