Vegetation Patterns: Structures and Dynamics

Abstract

Vegetation patterns are a hallmark of ecosystem self-organization, emerging from the intrinsic dynamics of nonlinear feedback mechanisms and spatiotemporal interactions. This review systematically explores and examines the structural characteristics of these patterns, the phenomena of multistability, and their implications for ecosystem stability through the lens of mathematical modeling and dynamical systems theory. In particular, reaction-diffusion models serve as a key analytical tool, revealing how local positive feedback and non-local negative feedback drive selforganized spatial structures via Turing bifurcation. Bifurcation theory and potential landscape analysis further elucidate ecosystem multistability, quantifying critical transitions among uniform vegetation, patterned states, and bare soil under environmental conditions. Advances in spatial metrics, including traditional statistical measures (e.g. variance, autocorrelation) and emerging complexity-based indicators (e.g. hyperuniformity, spatial permutation entropy) provide robust methods for detecting ecological functional shifts and early-warning signs of regime shifts. Additionally, restoration strategies grounded in structural optimization, such as optimal control theory, offer a theoretical framework for vegetation pattern reconstruction and stability regulation, particularly in arid and semi-arid regions. Future research should integrate multiscale modeling and interdisciplinary approaches to deepen our understanding of vegetation structure-function relationships. Such efforts will yield both theoretical insights and practical solutions for mitigating global ecological degradation and climate change.