An increasing number of sudden transformations triggered by small forces has been identified in a variety of ecological systems. Such changes are usually termed regime shifts between alternative states and their unexpected nature makes them challenging to handle from a management perspective. In the face of our limited mechanistic insight on the dynamics of such transitions, developing generic early warning signals for ecosystem regime shifts becomes a formidable task. So far, most of the research has focused on developing potential early warnings in simple models which ignore spatial interactions. In this work we spatially extended three well studied models that belong to the class of systems which undergo regime shifts through a fold bifurcation. All models were run on a two dimensional lattice with different spatial distributions of an environmental factor (e.g., soil fertility, water level). Where each patch in the lattice is individually governed by the same dynamics which eventually lead to alternative stable states, the response of the global spatial system is modified due to connectivity between patches. Our aim was to investigate whether we could identify a leading indicator of the imminent shift in the global spatial system.
Results/Conclusions
We followed the evolution of both spatial correlation between patches and temporal correlation within patches, obtained from stationary distributions, as we gradually increased a control parameter which causes the system to switch to its alternative attractor. We evaluated whether spatial correlation between neighboring patches can be used as a leading indicator of a system approaching a transition. Our analyses showed that spatial correlation between neighboring patches increases before the transition of the global spatial system into its alternative stable state. We demonstrated that spatial correlation between neighbors performs better as an indicator to an impending regime shift in heterogeneous conditions when compared to temporal correlation indicators. Despite differences between the three models, spatial correlation between neighbors appears to be a parsimonious and reliable early warning signal for transitions in spatial systems.
