Catastrophic shifts in ecosystems: spatial early warnings and management procedures (Inspired in the physics of phase transitions)

Ecosystems are complex systems which can respond to gradual changes of their conditions by a sudden shift to a contrasting regime or alternative stable state (ASS). Predicting such critical points before they are reached is extremely difficult and providing early warnings is fundamental to design management protocols for ecosystems. Here we study different spatial versions of popular ecological models which are known to exhibit ASS. The spatial heterogeneity is introduced by a local parameter varying from cell to cell in a regular lattice. Transport of biomass among cells occurs by simple diffusion. We investigate whether different quantities from statistical mechanics -like the variance, the two-point correlation function and the patchiness- may serve as early warnings of catastrophic phase transitions between the ASS. In particular, we find that the patch-size distribution follows a power law when the system is close to the catastrophic transition. We also provide links between spatial and temporal indicators and analyze how the interplay between diffusion and spatial heterogeneity may affect the earliness of each of the observables. Finally, we comment on similarities and differences between these catastrophic shifts and paradigmatic thermodynamic phase transitions like the liquid-vapor change of state for a fluid like water.

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