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Ben-Gurion University of the Negev (2010)

Dynamics of vegetation patterns in water-limited systems

Kletter, Assaf Y.

Titre : Dynamics of vegetation patterns in water-limited systems

Auteur : Kletter, Assaf Y.

Université de soutenance : Ben-Gurion University of the Negev

Grade  : Doctor of Philosophy PhD 2010

In this dissertation we study the dynamics of vegetation patterns in water-limited systems. Two major forms of vegetation patterns have been observed in drylands : nearly periodic patterns with characteristic length scales, and amorphous, scale-free patterns with wide patch-size distributions. The former has been studied extensively using spatially explicit mathematical models. The research described in this dissertation will be based on oneoftheaforesaidmodels. We discuss the model and two of its main previous results : the formation of regular vegetation patterns due to Turing-like instability, and the accumulation of soil-water under a vegetation patch, a phenomenon termed “ecosystem engineering”. Both of these phenomena are linked to three water-biomass feedbacks : increased infiltration at the vegetated patch, reduced evaporation at the patch due to shading, and root-augmentation as the plant grows. The key feature of the model, and the reason we chose it over other available models, is that it captures all three feedbacks. The implications of a stochastic rainfall regime is the first to be studied with the model. We find that most results found for constant precipitation carry over to the case of intermittent rainfall, with a few important novelties. For intermittent precipitation, the functionalformsofthewateruptakeandconsequentlyofthevegetationgrowthrateplay an important role. Nonlinear, concave-up forms of water uptake as a function of soil moisture lead to a beneficial effect of rainfall intermittency, with a stronger effect when vegetation feedbacks are absent. The emergence of scale-free vegetation patterns is the next subject. It has been attributed to global competition over a limiting resource, but the physical and ecological origin of this phenomenon is poorly understood. Using the model, a general mechanism for global competition is unraveled : fast spatial distribution of the water resource relative to processes that exploit or absorb it. Two possible realizations of this mechanism are studied, identifying physical and ecological conditions for scale-free patterns. A discussion is made on the implications of this study for interpreting signals of imminent desertification. We further show that the asymptotic dynamics of scale-free vegetation patterns involve patch coarsening similar to Ostwald ripening in two-phase mixtures. Numerical simulationsofthemodelforwater-limitedvegetationdemonstrateit,and furthers tudyis madebydrawingananalogytoasimplermodel,an activator-inhibitor systemthatshares many properties with the vegetation system. This simple system shed slight on the mechanism behind the patch coarsening. While ecological implications of patch coarsening may not be highly significant due to the long time scales involved, the results, however, raise an interesting pattern formation question associated with the incompatibility of processes that stabilize vegetation spots and the condition of global competition. We conclude this work by discussing the results in light of the model limitations, and discuss possible directions for future research.

Mots Clés : Phytogeography. — Vegetation dynamics — Arid regions — Mathematical models. — Vegetation dynamics — Arid regions — Mathematical models.

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