Theoretical Ecology

, Volume 2, Issue 1, pp 3–12 | Cite as

Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems

Brief Communication


Ecosystems can undergo large-scale changes in their states, known as catastrophic regime shifts, leading to substantial losses to services they provide to humans. These shifts occur rapidly and are difficult to predict. Several early warning signals of such transitions have recently been developed using simple models. These studies typically ignore spatial interactions, and the signal provided by these indicators may be ambiguous. We employ a simple model of collapse of vegetation in one and two spatial dimensions and show, using analytic and numerical studies, that increases in spatial variance and changes in spatial skewness occur as one approaches the threshold of vegetation collapse. We identify a novel feature, an increasing spatial variance in conjunction with a peaking of spatial skewness, as an unambiguous indicator of an impending regime shift. Once a signal has been detected, we show that a quick management action reducing the grazing activity is needed to prevent the collapse of vegetated state. Our results show that the difficulties in obtaining the accurate estimates of indicators arising due to lack of long temporal data can be alleviated when high-resolution spatially extended data are available. These results are shown to hold true independent of various details of model or different spatial dispersal kernels such as Gaussian or heavily fat tailed. This study suggests that spatial data and monitoring multiple indicators of regime shifts can play a key role in making reliable predictions on ecosystem stability and resilience.


Catastrophic regime shifts Stability Resilience Early warning signals Indicators Spatial variance Spatial skewness 



This work is supported by National Science Foundation grant DEB-0410336. VG was also supported by Presidential Fellowship at The Ohio State University and a travel fellowship from Institute for Complex Adaptive Matter through National Science Foundation grant DMR-0456669.

Supplementary material

12080_2008_33_MOESM1_ESM.pdf (160 kb)
Online Appendices (160 KB)


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Ecology and Evolutionary BiologyPrinceton UniversityPrincetonUSA
  2. 2.Department of PhysicsThe Ohio State UniversityColumbusUSA

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