Patchiness and scale-free correlations: characterising criticality in ecosystems.

Abstract

A variety of ecosystems exhibit spatial clustering devoid of characteristic sizes, also known as scale-free clustering. In physics, scale-free behaviour is known to arise when a system is at a critical point, which occurs at the edge of two phases of matter. Scale-free clustering in physics therefore indicates that a system is not resilient. Spatial ecological studies, however, posit that scale-free clustering arises away from critical points and is therefore an indicator of robustness. This inconsistency is troubling. Here, we synthesize the literature on cluster-size distributions together with analyses of a spatial ecological model that incorporates local birth, death and positive feedbacks. We argue that scale-free clustering in real ecological systems is driven by strong positive feedbacks. Using the model, we demonstrate that power-law relations may occur far away from, near or at the critical point of ecosystem collapse depending on the strength of local positive feedbacks. We therefore infer that clustering patterns are unrelated to critical points of ecosystem collapse. Power-law clustering, instead, indicates a different critical point, called a percolation point, that signifies the onset of spanning clusters in a landscape. Finally, we show that a collapse or a regime shift in an ecosystem is characterized by the emergence of scale-free spatial correlations in the system, reflected in a scale-free power-spectrum.