Two major forms of vegetation patterns have been observed in drylands: nearly periodic patterns with characteristic length scales, and amorphous, scale-free patterns with wide patch-size distributions. The emergence of scale-free patterns has been attributed to global competition over a limiting resource, but the physical and ecological origin of this phenomenon is not understood. Using a spatially explicit mathematical model for vegetation dynamics in water-limited systems, we unravel a general mechanism for global competition: fast spatial distribution of the water resource relative to processes that exploit or absorb it. We study two possible realizations of this mechanism and identify physical and ecological conditions for scale-free patterns. We conclude by discussing the implications of this study for interpreting signals of imminent desertification.

We study a mathematical model for the dynamics of patterned dryland vegetation in the presence of rainfall intermittency, adopting a spatially explicit approach. We find that most results found for constant precipitation carry over to the case of intermittent rainfall, with a few important novelties. For intermittent precipitation, the functional forms of the water uptake and consequently of the vegetation growth rate play an important role. Nonlinear, concave-up forms of water uptake as a function of soil moisture lead to a beneficial effect of rainfall intermittency, with a stronger effect when vegetation feedbacks are absent. The results obtained with the explicit-space model employed here are in keeping with those provided by simpler, implicit-space approaches, and provide a more complete view of vegetation dynamics in arid ecosystems.

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