Clustering and correlations: Inferring resilience from spatial patterns in ecosystems

In diverse ecosystems, organisms cluster together in such a manner that the frequency distribution of cluster sizes is a power law function. Spatially explicit computational models of ecosystems suggest that a loss of such power law clustering may indicate a loss of ecosystem resilience; the empirical evidence in support for this hypothesis has been mixed. On the other hand, a well-known dynamical feature of systems with reduced resilience is the slower recovery from perturbations, a phenomenon known as critical slowing down (CSD). Here, we examine the relationship between spatial clustering and CSD to better understand the use of cluster size distributions as indicators of ecosystem resilience. Local positive feedback is an important driver of spatial clustering, while also affecting the dynamics of the ecosystem: Studies have demonstrated that positive feedback promotes abrupt regime shifts. Here, we analyse a spatial model of ecosystem transitions that enables us to disentangle the roles of local positive feedback and environmental stress on spatial patterns and ecosystem resilience. We demonstrate that, depending on the strength of positive feedback, 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 feedback, which are more likely to exhibit abrupt transitions, there may be no loss of power law clustering prior to critical thresholds. Our analyses show that cluster size distributions are unrelated to the phenomenon of CSD and that loss of power law clustering is not a generic indicator of ecosystem resilience. Further, due to CSD, a power law feature does occur near critical thresholds but in a different quantity; specifically, a power law decay of spatial covariance of ecosystem state. Our work highlights the importance of links between local positive feedback, emergent spatial properties and how they may be used to interpret ecosystem resilience.