Random interactions and high-dimensionality in ecology

Natural ecosystems exhibit astounding richness. This suggests that we treat them as many-variable interacting systems, but is there evidence to support this perspective? I will discuss possible footprints of high-dimensionality, including phase-transitions, and “thermodynamic” variables which determine the system’s large-scale behavior. We show that the latter are found in a wide range of accepted models in the field. Then, I’ll present a theory for how interactions organize to allow many species to coexist. Data from plant-competition experiments confirms the theoretical predictions, providing evidence for high-dimensionality in that ecosystem.