Early Warnings for Catastrophic Shifts in Ecosystems: Comparison between Spatial and Temporal Indicators

The task of providing leading indicators of catastrophic regime shifts in ecosystems is fundamental in order to design management protocols for those systems. Here we address the problem of lake eutrophication (that is, nutrient enrichment leading to algal blooms) using a simple spatial lake model. We discuss and compare different spatial and temporal early warning signals announcing the catastrophic transition of an oligotrophic lake to eutrophic conditions. In particular, we consider the spatial variance and its associated patchiness of eutrophic water regions. We found that spatial variance increases as the lake approaches the point of transition to a eutrophic state. We also analyze the spatial and temporal early warnings in terms of the amount of information required by each and their respective forewarning times. From the consideration of different remedial procedures that can be followed after these early signals we conclude that some of these indicators are not early enough to avert the undesired impending shift.