Nestedness Promotes Stability in Maximum-Entropy Bipartite Food Webs

Abstract: Food web topology and energy flow rates across food web linkages can influence ecosystem properties such as stability. Stability predictions from current models of energy flow are often sensitive to details in their formulation, and their complexity makes it difficult to elucidate underlying mechanisms of general phenomena. Here, within the maximum information entropy inference framework (MaxEnt), we derive a simple formula for the energy flow carried by each linkage between two adjacent trophic layers. Inputs to the model are the topological structure of the food web and aggregate energy fluxes entering or exiting each species node. For ecosystems with interactions dominated by consumer-resource interactions between two trophic layers, we construct a model of species dynamics based on the energy flow predictions from the MaxEnt model. Mathematical analyses and simulations of the model show that a food web topology with a higher matrix dipole moment promotes stability against small perturbations in population sizes, where the \textit{matrix dipole moment} is a simple nestedness metric that we introduce. Since nested bipartite subnetworks arise naturally in food webs, our result provides an explanation for the stability of natural communities.