Patchiness and scale-free correlations: characterising criticality in ecosystems

Diverse ecosystems exhibit clusters that follow scale-free size distributions and lack a characteristic scale. In phase-transition theory, it is well known that scale-free behaviours arise at critical points. Scale-free behaviours, therefore, typically indicate a lack of resilience. Yet, many ecological studies associate loss of scale-free clustering with reduced resilience, presenting an intriguing inconsistency with the physics literature. Our synthesis of literature on cluster sizes in physics and ecology reveals that empirically observed scale-free clustering in ecosystems can be parsi-moniously explained by facilitative interactions. Our synthesis of theory, aided by analyses of a minimal spatial model, shows that scale-free clustering may occur far away from, near or at the critical point of ecosystem collapse depending on the strength of local facilitation. Thus, contrary to current thinking in the literature, we conclude that clustering patterns are unrelated to critical points of ecosystem collapse. Scale-free clustering, instead, indicates a different threshold called a percolation point, which signifies the onset of spanning clusters in the landscape. Finally, we suggest that ecosystem criticality can be characterized by scale-free spatial correlations in the system. Our synthesis resolves subtle links between local facilitative interactions and macroscopic patterns of scale-free clustering, scale-free correlations and ecosystem resilience, and offers future directions to investigate these phenomena.