Catastrophic Phase Transitions and Early Warnings in a Spatial Ecological Model

TL;DR

This paper investigates early warning signals for catastrophic regime shifts in a spatial ecological model, analyzing spatial indicators like patchiness and correlation functions, and explores how diffusion and heterogeneity influence the detectability of these signals.

Contribution

It introduces spatial indicators such as patch-size distribution and correlation functions as early warnings for ecological regime shifts, linking spatial and temporal signals and examining effects of diffusion.

Findings

Patch-size distribution follows a power law near transitions.

Spatial indicators can serve as early warnings.

Lower diffusion enhances the effectiveness of early signals.

Abstract

Gradual changes in exploitation, nutrient loading, etc. produce shifts between alternative stable states (ASS) in ecosystems which, quite often, are not smooth but abrupt or catastrophic. Early warnings of such catastrophic regime shifts are fundamental for designing management protocols for ecosystems. Here we study the spatial version of a popular ecological model, involving a logistically growing single species subject to exploitation, which is known to exhibit ASS. Spatial heterogeneity is introduced by a carrying capacity parameter varying from cell to cell in a regular lattice. Transport of biomass among cells is included in the form of 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. We find that possible remedial procedures, which can be followed after these early signals, are more effective as the diffusion becomes lower. Finally, we comment on similarities and differences between these catastrophic shifts and paradigmatic thermodynamic phase transitions like the liquid-vapour change of state for a fluid like water.