Human footprint on ecosystems is growing, and ecosystems cope with these changes in different ways. Arid ecosystems are likely to shift abruptly to desert in a sudden and often irreversible manner because of climatic changes or human activities. Such ecosystem shifts can even happen when external changes are gradual, and the conditions under which they occur are still not well understood. For about a third of the world's population who live in arid regions, these shifts are of great importance because they result in a substantial reduction in the biological and economic productivity of these drylands. Models have shown that positive feedbacks between vegetation and its abiotic environment are important mechanisms explaining ecosystem shifts. In harsh habitats, such as arid ecosystems, organisms can indeed alter the physical conditions, making a stressful habitat more hospitable, e.g. by creating shelter or increasing resource availability. For plants, such effects occur locally, below or close to their canopy. Consequently, vegetation tends to grow in clumps which are scattered in an otherwise barren landscape, forming spatial vegetation patterns. This thesis addresses these spatial vegetation patterns: the ecological mechanisms underlying their formation and their potential role as indicators of impending desertification. How do vegetation patterns respond to increasing stress (e.g., increasing aridity), and in particular, do ecosystems have a unique appearance just before a shift? Can specific vegetation patterns help predict when and how ecosystem shifts might occur? We developed mathematical models of arid ecosystems' dynamics including vegetation's ability to improve the local environment, and we used these models to learn how to interpret spatial vegetation patterns. We studied how different positive feedback mechanisms and dispersal strategies affect the type of vegetation patterns that emerges. We analyzed how these patterns respond to changes in the climate and human pressures, such as grazing, at ecological and evolutionary timescales. We found that looking at spatial vegetation patterns gives insight into the ecological mechanism responsible for their formation, the history of the ecosystem, and the ecosystem's "health" (i.e., likelihood to switch to a desert). In particular, we discovered spatial patterns that only occur when an arid ecosystem is about to become a desert, and that the characteristics of these patterns depend on the underlying ecological mechanisms. Further empirical tests are now needed to confirm that spatial vegetation patterns can indeed be used as indicators of imminent desertification. Our findings are appealing because they could represent a significant step toward the development of a widely applicable desertification monitoring system. Since it is fairly straight forward to analyze satellite images, such a monitoring system could help land managers in the near future to map vulnerable regions, and adapt the management of these regions before a potentially disastrous shift occurs
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