Surviving the winds through pattern formation: mathematical modelling of heather stripes in Scotland

Abstract

Remarkable patterns of heather (Calluna vulgaris) and soil can be observed in some areas of Scotland. Bands of vegetation regularly alternate with bands of bare ground, with the whole pattern slowly moving in a direction perpendicular to the stripes. While previous studies have proposed that strong winds may play a role in shaping these patterns, the underlying mechanisms—particularly the initiation of the patterning—remain poorly understood. In this study, we develop a simple mathematical model based on two partial differential equations to capture local interactions between wind, soil and vegetation. Using dynamical systems theory and numerical simulations, we identify the conditions necessary for pattern formation and provide insight into how these patterns emerge and disappear. Furthermore, we derive a parametrisation, informed by existing literature, that produces results with realistic order of magnitude for pattern amplitude, wave length and travelling wave speed. Our model demonstrates that basic interactions between wind, soil and vegetation are sufficient to generate solutions consisting of moving bands of vegetation, closely resembling the observed real-world patterns. Our analysis reveals the role of Calluna vulgaris as an ecosystem engineer, facilitating its survival in harsh, wind-exposed environments by forming spatial patterns that extend its habitat range. Notably, our findings indicate that pattern onset does not require pre-existing soil patterning. Synthesis: Our results suggest that simple interactions between wind, soil and vegetation can drive the formation of periodic biogeomorphological patterns in wind-blasted ecosystems. This modelling approach has potential applications for understanding other ecosystems subject to strong winds and may contribute to conservation efforts for these sensitive habitats.