Although plants are not common in areas with sand dunes, they play an important role in stabilizing the movement of sand and fixing the position of dunes. Indeed, there is often a relentless competition between plants and sand, which has been harnessed for thousands of years by people living in such regions to control the movement of dunes.

Orencio Durán and Hans Herrmann of the University of Stuttgart in Germany developed their equations using scientific observations of sand-dune behaviour in desert regions. For example, scientists have observed that crescent-shaped "barchan" dunes change into parabolic-shaped dunes when colonized by plants. This transformation is thought to be the first step in halting the movement of a sand dune.

The Stuttgart physicists have used the equations to define a "fixation index", θ, which is the ratio between the rate at which a sand dune erodes and how quickly a plant can grow and inhibit erosion. The equations reveal that plants can transform a barchan dune into a parabolic dune when θ has a value less than 0.5 and plant-growth trumps erosion. Conversely, if θ is greater than 0.5, wind-induced sand erosion stops plants from growing and a barchan dune can continue to move.

"Our results will help allow scientists to make long-term predictions (over thousands of years) about how coastal dunes evolve," Herrmann told PhysicsWeb. “They might even have an impact on environmental issues, like how to increase biodiversity." The research may also aid in protecting semi-arid regions that are threatened by desertification processes.

Durán and Herrmann now plan to repeat their calculations with different types of plants and for varying amounts of rainfall. They also hope to actually test their predictions in the desert.