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.

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The mysterious 'fairy circles' are vegetation-free discs that cover vast areas along the pro-Namib Desert. Despite 30 yr of research their origin remains unknown. Here we adopt a novel approach that focuses on analysis of the spatial patterns of fairy circles obtained from representative 25-ha aerial images of north-west Namibia. We use spatial point pattern analysis to quantify different features of their spatial structures and then critically inspect existing hypotheses with respect to their ability to generate the observed circle patterns. Our working hypothesis is that fairy circles are a self-organized vegetation pattern. Finally, we test if an existing partial-differential-equation model, that was designed to describe vegetation pattern formation, is able to reproduce the characteristic features of the observed fairy circle patterns. The model is based on key-processes in arid areas such as plant competition for water and local resource-biomass feedbacks.The fairy circles showed at all three study areas the same regular spatial distribution patterns, characterized by Voronoi cells with mostly six corners, negative correlations in their size up to a distance of 13 m, and remarkable homogeneity over large spatial scales. These results cast doubts on abiotic gas-leakage along geological lines or social insects as causal agents of their origin. However, our mathematical model was able to generate spatial patterns that agreed quantitatively in all of these features with the observed patterns. This supports the hypothesis that fairy circles are selforganized vegetation patterns that emerge from positive biomass-water feedbacks involving water transport by extended root systems and soil-water diffusion. Future research should search for mechanisms that explain how the different hypotheses can generate the patterns observed here and test the ability of self-organization to match the birth-and death dynamics of fairy circles and their regional patterns in the density and size with respect to environmental gradients.