Revealing Physical Mechanisms of Pattern Formation and Switching in Ecosystems via Nonequilibrium Landscape and Flux

TL;DR

This paper introduces a landscape-flux field theory to understand the physical mechanisms behind pattern formation and switching in nonequilibrium ecosystems, providing insights and early warning signals for critical transitions.

Contribution

The study develops a novel landscape-flux field theory using spatial mode expansion to explain pattern dynamics and switching in ecosystems, linking thermodynamics with spatial pattern transitions.

Findings

Flux drives pattern switching in ecosystems

Peaks in flux and entropy production indicate transition boundaries

The approach offers early warning signals for critical pattern transitions

Abstract

Spatial patterns are widely observed in numerous nonequilibrium natural systems, often undergoing complex transitions and bifurcations, thereby exhibiting significant importance in many physical and biological systems such as embryonic development, ecosystem desertification, and turbulence. However, how spatial pattern formation emerges and how the spatial pattern switches are not fully understood. Here, we developed a landscape-flux field theory via the spatial mode expansion method to uncover the underlying physical mechanism of the pattern formation and switching. We identified the landscape and flux field as the driving force for spatial dynamics and applied this theory to the critical transitions between spatial vegetation patterns in semi-arid ecosystems, revealing that the nonequilibrium flux drives the switchings of spatial patterns. We uncovered how the pattern switching emerges through the optimal pathways and how fast this occurs via the speed of pattern switching. Furthermore, both the averaged flux and the entropy production rate exhibit peaks near pattern switching boundaries, revealing dynamical and thermodynamical origins for pattern transitions, and further offering early warning signals for anticipating spatial pattern switching. Our work thus reveals physical mechanisms on spatial pattern-switching in semi-arid ecosystems and, more generally, introduces a useful approach for quantifying spatial pattern switching in nonequilibrium systems, which further offers practical applications such as early warning signals for critical transitions of spatial patterns.