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.
Highlights
Ecological stability refers to a range of concepts that describe how interacting systems of species and their environments vary over time (Donohue et al, 2013; Grimm & Wissel, 1997; Holling, 1973; Ives & Carpenter, 2007; Lewontin, 1969; May, 1973; Pimm, 1984; Pimm et al, 2019)
Throughout, we focus on three common stability metrics—resilience, resistance, and invariance—and explore how these change across levels of temporal, spatial, and ecological organisation (Donohue et al, 2016; Grimm & Wissel, 1997)
Our results demonstrate that resilience, resistance, and invariance can be related to simple statistical properties of dynamical systems, which allow general and robust scaling of these stability metrics across time, space, and level of ecological organisation
Summary
Ecological stability refers to a range of concepts that describe how interacting systems of species and their environments vary over time (Donohue et al, 2013; Grimm & Wissel, 1997; Holling, 1973; Ives & Carpenter, 2007; Lewontin, 1969; May, 1973; Pimm, 1984; Pimm et al, 2019). Measurements taken across different scales are not directly comparable, which limits opportunities for cross-system comparison and synthesis (Clark et al, 2019; Csillag et al, 2000; Levin, 1992; Wang et al, 2019) This scale dependence is a major challenge for conservation and management, because the scales that are most relevant for decision making often differ from those at which ecological systems are measured (Carpenter et al, 2001; Chesson, 2000; Isbell et al, 2018; Leibold & Chase, 2018; Levin, 1992). We seek to identify relationships that can: (1) be fitted using empirical data observed at one set of scales; (2) be extrapolated to accurately describe conditions across other scales; and (3) that are valid regardless of the underlying processes governing dynamics
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