Early warnings of regime shifts in spatial dynamics using the discrete Fourier transform

In ecosystems with spatial dispersion of nutrients, organic matter, or organisms, dispersal may dampen variability that could provide an early warning of regime shifts. The discrete Fourier transform (DFT) of spatial pattern rescales system dynamics into spatial frequencies where early warnings may be sharpened. We analyzed four spatial ecological models with the DFT. Different models represented single species in discrete and continuous time, and two different prey-harvester systems. In all four systems, the DFT of transient data exhibited substantial increases prior to the critical transitions. The DFT adds to the arsenal of early warning indicators for spatially structured ecosystems. In addition it provides information about the spatial frequencies where destabilization first begins.