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In many desert ecosystems vegetation is both patchy and dynamic: vegetated areas are interspersed with patches of bare ground, and both the positioning and the species composition of the vegetated areas exhibit change through time. These characteristics lead to the emergence of multi-scale patterns in vegetation that arise from complex relationships between plants, soils and transport processes. Previous attempts to probe the causes of spatial complexity and predict responses of desert ecosystems tend to be limited in their focus: models of dynamics have been developed with no consideration of the inherent patchiness in the vegetation, or else models have been developed to generate patterns with no consideration of the dynamics. Here we develop a general modelling framework for the analysis of ecosystem change in deserts that is rooted in the concept of connectivity and is derived from a detailed process-based understanding. We explicitly consider spatial interactions among multiple vegetation types and multiple resources, and our model is formulated to predict responses to a variety of endogenous and exogenous disturbances. The model is implemented in the deserts of the American Southwest both to test hypotheses of the causes of the invasion of woody shrubs, and to test its ability to reproduce observed spatial differences in response to drought in the twentieth century. The model's performance leads us to argue that vertical and lateral connectivity are key emergent properties of the ecosystem, which both control its behaviour and provide indicators of its state. If this argument is shown to be compatible with field observations, the model presented here will provide a more certain approach towards preventing further degradation of semi-arid grasslands.
