Modeling multi-trophic ecosystems with consumer resource model

MacArthur's consumer-resource model describes the ecological dynamics of a simple two trophic-layer ecosystem where consumers compete for a pool of resources (e.g herbivores compete for plants). However, real ecosystems often possess multiple trophic layers (e.g. carnivores, herbivores, plants) that all interact to determine ecosystem dynamics. Inspired by this observation, we analyze a generalization of MacArthur's consumer model with multiple trophic layers using methods from statistical physics. For the three-layer model, we discuss the new properties of the model, connection with constrained optimization, and present a mean-field solution for the multi-trophic layer model using the cavity method. We show that the introduction of additional trophic layers into an ecosystem can result in both quantitative and qualitative changes in ecosystem-level properties.