A new model for vegetation patterns is introduced. The model reproduces a wide range of patterns observed in water-limited regions, including drifting bands, spots, and labyrinths. It predicts transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation, through intermediate states of spot, stripe, and hole patterns. It also predicts wide precipitation ranges where different stable states coexist. Using these predictions we propose a novel explanation of desertification phenomena and a new approach to classifying aridity.

Habitat and species richness in drylands are affected by the dynamics of a few key species, termed "ecosystem engineers." These species modulate the landscape and redistribute the water resources so as to allow the introduction of other species. A mathematical model is developed for a pair of ecosystem engineers commonly found in drylands: plants forming vegetation patterns and cyanobacteria forming soil crusts. The model highlights conditions for habitat creation and for high habitat richness, and suggests a novel mechanism for species loss events as a result of environmental changes.

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Vegetation gap patterns in arid grasslands, such as the "fairy circles" of Namibia, are one of nature's greatest mysteries and subject to a lively debate on their origin. They are characterized by small-scale hexagonal ordering of circular bare-soil gaps that persists uniformly in the landscape scale to form a homogeneous distribution. Pattern-formation theory predicts that such highly ordered gap patterns should be found also in other water-limited systems across the globe, even if the mechanisms of their formation are different. Here we report that so far unknown fairy circles with the same spatial structure exist 10,000 km away from Namibia in the remote outback of Australia. Combining fieldwork, remote sensing, spatial pattern analysis, and process-based mathematical modeling, we demonstrate that these patterns emerge by self-organization, with no correlation with termite activity; the driving mechanism is a positive biomasswater feedback associated with water runoff and biomass-dependent infiltration rates. The remarkable match between the patterns of Australian and Namibian fairy circles and model results indicate that both patterns emerge from a nonuniform stationary instability, supporting a central universality principle of pattern-formation theory. Applied to the context of dryland vegetation, this principle predicts that different systems that go through the same instability type will show similar vegetation patterns even if the feedback mechanisms and resulting soil-water distributions are different, as we indeed found by comparing the Australian and the Namibian fairy-circle ecosystems. These results suggest that biomass-water feedbacks and resultant vegetation gap patterns are likely more common in remote drylands than is currently known.drylands | spatial pattern | Triodia grass | Turing instability | vegetation gap P attern-formation theory (1) and the influence of Alan Turing's work on understanding biological morphogenesis (2) are increasingly recognized in environmental sciences (3). Vegetation patterns resulting from self-organization occur frequently in waterlimited ecosystems and, similar to Turing patterns, show pattern morphologies that change from gaps to stripes (labyrinths) to spots with decreasing plant-available moisture (4-6). The patterns may emerge on completely flat and homogeneous substrate and are induced by positive feedbacks between local vegetation growth and water transport toward the growth location.