Maximum entropy networks predict fluctuations and stability of food web energetics
A central goal of ecology is understanding how the architecture of food webs, which represent the structural backbone of ecosystems, affects their stability. The analysis of stability in the classical sense of population dynamics (i.e. return to equilibrium) can be successful for a single instance of an empirical food web but ignores the multiplicity of alternative states in which the system could be found as a result of intrinsic variability and fluctuations. Here we propose and test a new methodology to reconstruct, from single empirical observations of a food web, the viable ensemble of alternative realizations respecting the observed resource-consumer linkages and empirical ener-getics. The reconstruction can be handled analytically within a maximum-entropy framework which predicts how empirical food webs access a multitude of alternative states with comparable stability and reactivity. The (measurable) entropy of the reconstructed ensemble directly quantifies this multiplicity and serves as a novel proxy of system resilience, that is the rate of return to equilibrium in response to an external perturbation. We show that the associated ensemble fluctuations provide explicit predictions for the expected response of food webs to external perturbations, such as anthropogenic or climate-induced stresses. We do that by validating the proposed fluctuation-response relation on empirical soil food webs subjected to experimentally controlled perturbations, confirming that intrinsic fluctuations in the unperturbed state predict responses to subsequent stresses. The perturbed states are associated with higher entropy, indicating less likely spontaneous recovery.