Spatiotemporal dynamics of biocrust and vegetation on sand dunes

TL;DR

This paper develops a mathematical model using coupled nonlinear differential equations to analyze the complex spatiotemporal dynamics of biocrust and vegetation cover on sand dunes, highlighting the effects of wind and oscillatory regimes.

Contribution

It introduces a novel coupled differential equation model incorporating diffusion and advection to study biocrust-vegetation interactions on dunes, emphasizing wind effects and oscillatory behaviors.

Findings

Front propagation mainly driven by wind advection.

Low wind drift potential leads to spatial oscillatory domains.

High drift potential causes irregular, sensitive spatial patterns.

Abstract

We propose a model to study the spatiotemporal dynamics of biocrust and vegetation cover on sand dunes. The model consists of two coupled partial nonlinear differential equations and includes diffusion and advection terms for modeling the dispersal of vegetation and biocrust and the effect of wind on them. In the absence of spatial variability, the model exhibits self-sustained relaxation oscillations and regimes of bistability--the first state is dominated by biocrust and the second by vegetation. We concentrate on the one-dimensional dynamics of the model and show that the front that connects these two states propagates mainly due to the wind advection. In the oscillatory regime, the front propagation is complex. For low wind DP (drift potential) values, a series of spatially oscillatory domains develops as the front advances downwind. These domains form due to the oscillations of the spatially homogeneous states away from the front. However, for higher DP values, the dynamics is much more complex, becoming very sensitive to the initial conditions and exhibiting an irregular spatial pattern as small domains are created and annihilated during the front advance. Such irregular dynamics can be associated with the temporal variations of dune cover. In addition, similar behavior can be generated by other models that exhibit temporal oscillations and bistability.