Toyo Vignal, Okinawan Institute of Science and Technology in Japan, discusses her article: Surviving the winds through pattern formation: Mathematical modelling of heather stripes in Scotland.
In some remote areas of the Scottish highlands, one can encounter intriguing vegetation patterns consisting of regularly arranged plants and bare soil. The first time I encountered such patterns was in Summer 2021, while exploring Papa Stour, a small, secluded island in Shetland.
Clearly, the vegetation cover exhibited an unusual structure. It was mostly heather, which I recognised from its little bell-shaped flowers. Given the secluded location, this pattern was most likely a form of self-organisation, i.e. the plants spontaneously arranged themselves that way. This was of particular interest to me, as a maths PhD student supervised by experts on modelling vegetation pattern formation, and someone personally quite fond of this topic.
The existing models I knew about consisted of equations capturing how dryland vegetation could self-organise into strikingly regular patterns in response to water scarcity. The equations and their analysis built upon Alan Turing’s (yes, THE Alan Turing) seminal work on pattern formation. In 1952, Turing showed how simple interactions can give rise to complex natural patterns. In dry ecosystems, plants help each other by increasing soil water infiltration, and also compete for scarce water, leading to patterns of spots, gaps, stripes, or labyrinths, resembling prints on animal coats.
Although the heather pattern in Papa Stour was visually similar to those in drylands, Shetland is far from arid. Surely, water scarcity could not drive these patterns. I dove into the scientific literature searching for any mention of “heather stripes” in Scotland, looking for an alternative explanation. I did not find much, but what I found was good. There was a 1984 Journal of Ecology paper written by Neil Bayfield. On the second page, there was a picture of patterns even more remarkable than the ones I had seen in Shetland. These were observed in the Cairngorms, a Scottish national park. Even more interesting, the heather stripes slowly migrated, about a centimetre a year! Bayfield hypothesised that the patterns were caused by strong winds and moved in the direction of the prevailing winds. This seemed likely enough, because both the Cairngorms and Shetland compete for the record of the strongest wind gust ever measured in the UK, with measuring instruments often blown away or destroyed. Yet, many questions remained. Through what mechanisms could wind drive pattern formation and movement? How did the patterns begin: did they require a pre-patterning of the ground? And finally, what would cause these patterns to disappear?
This was the perfect set up for a mathematical model. By writing equations describing the interplay between vegetation, wind, and soil, and following the analysis introduced by Alan Turing, I could test whether some proposed mechanisms were sufficient to trigger pattern formation. Furthermore, numerical simulations would allow me to test the effects of different wind speeds or other environmental factors. The results were very clear: yes, a few simple interactions between wind, vegetation, and soil-wind-driven soil erosion, along with heather’s ability to stabilise soil and the shelter provided by small ridges, were enough to generate these patterns. This suggests that heather acts as an “ecosystem engineer”, shaping its environment by trapping soil and creating shelters where it can persist under extreme winds. The equations also demonstrated that patterns could occur on initially flat ground, because no soil pre-patterning was required. There was a minimal wind speed above which patterns would start forming, and a maximal wind speed above which only bare ground subsisted. As intuitively expected, our model showed that the pattern migration speed increased with wind speed, and that stronger winds would lead to a decrease in pattern amplitude, frequency and bandwidth.
What began as a curious observation on a windswept island unfolded into a deeper understanding of how plants, soil, and wind can create living patterns. These formations are not only aesthetically pleasing, they are also opportunities to study properties of stressed ecosystems.
