Vegetation patterns are abundant in arid and semiarid ecosystems, but how they form remains unclear. One of the most extended theories lies in the existence of scale-dependent feedbacks (SDF) in plant-to-plant and plant-water interactions. Short distances are dominated by facilitative interactions, whereas competitive interactions dominate at larger scales. These feedbacks shape spatially inhomogeneous distributions of water that ultimately drive the emergence of patterns of vegetation. Even though the presence of facilitative and competitive interactions is clear, they are often hard to disentangle in the field, and therefore their relevance in vegetation pattern formation is still disputable. Here, we review the biological processes that have been proposed to explain pattern formation in arid ecosystems and how they have been implemented in mathematical models. We conclude by discussing the existence of similar structures in different biological and physical systems.
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