Spatial variance and spatial skewness: leading indicators of regime shifts in spatial ecological systems |
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Authors: | Vishwesha Guttal C Jayaprakash |
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Institution: | (1) Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA;(2) Department of Physics, The Ohio State University, 191 W Woodruff Ave, Columbus, Ohio 43210-1117, USA |
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Abstract: | 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.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. |
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Keywords: | Catastrophic regime shifts Stability Resilience Early warning signals Indicators Spatial variance Spatial skewness |
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