General statistical scaling laws for stability in ecological systems

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.

Automated summary

Ecological stability refers to how interacting species in a system change over time and respond to disturbances. It is challenging to compare stability measurements across different sites and systems due to sampling scales and environmental context. Stochastic dynamical systems theory can be used to derive statistical scaling relationships for resilience, resistance, and invariance, aiding in predicting average stability across various scales and revealing unknown heterogeneity information.