General statistical scaling laws for stability in ecological systems
Adam Thomas Clark, Jean‐François Arnoldi, Yuval R. Zelnik, György Barabás, Dorothee Hodapp, Canan Karakoç, Sara König, Viktoriia Radchuk, Ian Donohue, Andreas Huth, Claire Jacquet, Claire de Mazancourt, Andrea Mentges, Dorian Nothaaß, Lauren G. Shoemaker, Franziska Taubert, Thorsten Wiegand, Shaopeng Wang, Jonathan M. Chase, Michel Loreau, W. Stanley Harpole
Abstract
Ecological stability refers to a family of concepts used to describe how systems of interacting species vary through time and respond to disturbances. Because observed ecological stability depends on sampling scales and environmental context, it is notoriously difficult to compare measurements across sites and systems. Here, we apply stochastic dynamical systems theory to derive general statistical scaling relationships across time, space, and ecological level of organisation for three fundamental stability aspects: resilience, resistance, and invariance. These relationships can be calibrated using random or representative samples measured at individual scales, and projected to predict average stability at other scales across a wide range of contexts. Moreover deviations between observed vs. extrapolated scaling relationships can reveal information about unobserved heterogeneity across time, space, or species. We anticipate that these methods will be useful for cross-study synthesis of stability data, extrapolating measurements to unobserved scales, and identifying underlying causes and consequences of heterogeneity.