In an effort to better understand how vegetation "bands" together in areas where water is sparse, a new study uses a mathematical model to determine the levels of precipitation within certain pattern formations form.
The greater the plant density in a given area, the greater the amount of rainwater is able to seep into the ground due to dense roots and other forms of organic material within the soil. And while several mathematical models attempt to explain this process of banded vegetation, the most established is the Klausmeier.
Based on a water redistribution hypothesis that assumes rain falling on bare ground only infiltrates the ground minimally and that the majority runs downhill in the direction of the next vegetation band, the Klausmeier model assumes that it is here, at this next band, that the majority of rainwater seeps into the soil, promoting plant growth. The implication then is that moisture levels are higher on the uphill edge of the band, causing the bands to move uphill with each generation.
Using this model, author Jonathan A. Sherratt determines the critical rainfall level needed for pattern formation based on a wide range of variables, including rainfall, evaporation, plant uptake, downhill flow and plant loss.
Furthermore, Sherratt investigates the uphill migration speeds of the bands.
"My research focuses on the way in which patterns change as annual rainfall varies. In particular, I predict an abrupt shift in pattern formation as rainfall is decreased, which dramatically affects ecosystems," he said in a statement. "The mathematical analysis enables me to derive a formula for the minimum level of annual rainfall for which banded vegetation is viable; below this, there is a transition to complete desert."
Knowing this, Sherratt says, can aid in decisions regarding resource allocation or environmental policies.
"Since many semi-arid regions with banded vegetation are used for grazing and/or timber, this prediction has significant implications for land management," Sherratt said. "Another issue for which mathematical modeling can be of value is the resilience of patterned vegetation to environmental change. This type of conclusion raises the possibility of using mathematical models as an early warning system that catastrophic changes in the ecosystem are imminent, enabling appropriate action (such as reduced grazing)."