The assumption of spatial homogeneity does not apply in many grazing systems, especially in arid and semiarid environments. If average rainfall is too low to allow for a continuous vegetation cover, vegetation will typically show a patchy distribution with a matrix of bare soil interspersed with vegetated patches. On degraded soils, a negative feedback between grazing and plant growth causes two equilibria, one of bare soil and a vegetated state (Figure 3). Given that these two states may coexist spatially side by side, this process would explain the frequently observed spatial pattern of a two-phase mosaic, where vegetated patches are interspersed into a matrix of bare soil (see Ecosystem Patterns and Processes). This idea was tested in several modeling studies that explored spatially explicit or implicit modifications of the nonspa-tial models based on eqn . These models were successful in reproducing patterns similar to the observed ones. This result is a first step toward showing the validity of the underlying hypothesis. However, it is well known that models based on substantially different mechanisms or processes may reproduce the same pattern. Thus, more rigorous comparisons between nature and models will be needed to test the validity of the hypothesis modeled.
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