Hypotheses about the origin of vegetation pattern formation in semi-arid\ud areas around the world almost all include a common feature of semi-arid areas: the presence\ud of a positive feedback between plant density and water infiltration. We investigate whether\ud this positive feedback and the spatial redistribution of runoff water are sufficient to explain\ud vegetation pattern formation. For this purpose, we analyze a spatially explicit model consisting\ud of partial differential equations using a method for demonstrating pattern formation\ud (Turing analysis). Our analysis reveals that pattern formation can occur in semi-arid areas\ud given only the positive feedback between plant density and local water infiltration coupled\ud with the spatial redistribution of runoff water. Thus, slope and underlying heterogeneity\ud are not essential conditions. Other factors in the model, such as herbivory, plant dispersal,\ud rainfall, and drought tolerance of plants, appear to determine under what conditions pattern\ud formation is likely but are not the primary factors that generate the patterns. The model is\ud in agreement with field observations and indicates the conditions for which vegetation\ud pattern formation can be expected in arid and semi-arid grazing systems
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