Patchiness and scale-free correlations: characterising criticality in ecosystems.
I.O_LIIn diverse ecosystems, organisms cluster together in such a manner that the frequency distribution of cluster sizes is a power-law function. Spatially-explicit models of ecosystems suggest that loss of such power-law clustering may indicate loss of ecosystem resilience. Hence, it is hypothesised that spatial clustering properties in ecosystems - which can be readily measured using remotely-sensed high-resolution data - can help infer proximity to ecosystem thresholds and may even provide early warning signals of ecosystem collapse. Recent empirical and simulation studies, however, dont find consistent relationships between spatial clustering and ecosystem resilience. Furthermore, how spatial clustering metrics relate to other well-known early warning signals of ecosystems collapse, specifically the phenomenon of critical slowing down (CSD), remains unclear. C_LIO_LIWe synthesize the literature on cluster sizes in empirical and theoretical studies that show how local interactions (especially, positive feedback) among organisms can cause power-law clustering. In addition, we analyse a minimal spatial model of ecosystem transitions that allows us to disentangle the role of environmental stressor and positive feedback on spatial patterns and ecosystem resilience. C_LIO_LIOur literature synthesis reveals that empirically observed power-law clustering in ecosystems is parsimoniously explained by local positive feedback. Our synthesis together with model analysis demonstrates that, depending on the strength of positive feedback, emergence of power-law clustering can occur at any distance from the critical threshold of ecosystem collapse. In fact, we find that for systems with strong positive feedbacks, which are most likely to exhibit abrupt transitions, loss of power-law clustering may not even occur prior to ecosystem thresholds. We also argue that cluster-size distributions are unrelated to the phenomenon of CSD. C_LIO_LIWe demonstrate that, due to CSD, a power-law feature does occur near critical thresholds but in a different quantity; specifically, a power-law decay of spatial correlations of ecosystem state. C_LIO_LIWe conclude that loss of power-law clustering cannot be used as a reliable indicator of ecosystem resilience. Our synthesis and model analyses highlights links between local positive feedback, emergent spatial properties and how they may be used to interpret ecosystem resilience. C_LI