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 scalefree 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 powerspectrum. * sumithras@iisc.ac.in 1 All rights reserved. No reuse allowed without permission.(which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.

Easy, fast and reproducible Stochastic Cellular Automata with chouca

“…The sizes and numbers of those patches can be readily quantified from remote-sensing images, and such patterns can be used to infer whether facilitation occurs between plants (Chen et al 2022;Xu et al 2015). This is traditionally done by summarizing the spatial structure into spatial statistics, such as spatial autocorrelation (Sankaran et al 2017) or type of patch size distribution (Kéfi et al 2011;Siteur et al 2023), and linking the observed changes in those metrics to theoretical results (Kéfi et al 2011;Scanlon et al 2007). However, such qualitative comparison logically results in a qualitative and corroborative result, i.e.…”

“…2015). This is traditionally done by summarizing the spatial structure into spatial statistics, such as spatial autocorrelation (Sankaran et al . 2017) or type of patch size distribution (Kéfi et al .…”

Monitoring ecosystem degradation using spatial data and the R package spatialwarnings

“…a spanning cluster. As density decreases, this spanning cluster breaks down into smaller ones until a barren ecosystem state is reached (Corrado, Cherubini, & Pennetta, ; Kéfi et al., ; Sankaran, Majumder, Viswanathan, & Guttal, ; Van Den Berg, ). When using spatio‐temporal data, this sequential process is reflected in changes of the patch size distribution (PSD) (Kéfi et al., ).…”

“…(4) In the final stages before reaching a fully empty state, only small patches persist and the patch size distribution is best‐described by an exponential distribution ( e − βx ) with presence of a spanning cluster of empty cells. Identifying where in these four phases an ecological system lies could thus constitute an indicator of degradation level (Kéfi et al., , but see Sankaran, Majumder, Viswanathan, et al., ; Schneider & Kéfi, ).…”