Using wavelength and slope to infer the historical origin of semiarid vegetation bands

Significance Self-organized vegetation patterns are a characteristic feature of semiarid regions. On gentle slopes banded patterns (stripes) are typical, and their wavelength is probably the most accessible statistic for patterned vegetation. Recent data show that on steeper slopes wavelengths are usually shorter, contradicting previous predictions of mathematical models. I resolve this “contradiction” by a detailed theoretical study of pattern generation. Moreover I show that the wavelength–slope relationship has a wholly unexpected predictive power, enabling one to infer whether the patterns arose from degradation of uniform vegetation or colonization of bare ground. When combined with climate records, this gives valuable insights into the historical origin of the patterns. Landscape-scale patterns of vegetation occur worldwide at interfaces between semiarid and arid climates. They are important as potential indicators of climate change and imminent regime shifts and are widely thought to arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. Recent field studies have found an inverse correlation between pattern wavelength and slope, in apparent contradiction with the predictions of mathematical models. Here I show that this “contradiction” is based on a flawed approach to calculating the wavelength in models. When pattern generation is considered in detail, the theory is fully consistent with empirical results. For realistic parameters, degradation of uniform vegetation generates patterns whose wavelength increases with slope, whereas colonization of bare ground gives the opposite trend. Therefore, the empirical finding of an inverse relationship can be used, in conjunction with climate records, to infer the historical origin of the patterns. Specifically, for the African Sahel my results suggest that banded vegetation originated by the colonization of bare ground during circa 1760–1790 or since circa 1850.