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Ben-Gurion University of the Negev (2016)

Regime shifts in spatially extended ecosystems

Zelnik, Yuval

Titre : Regime shifts in spatially extended ecosystems

Auteur : Zelnik, Yuval

Etablissement de soutenance : Ben-Gurion University of the Negev

Grade : Doctor of Philosophy (PhD) 2016

Dynamical systems, and ecosystems in particular, change their state and behavior due to external and internal influences. A major goal of ecology is to understand ecosystems, and thus to predict their dynamical behavior and response to perturbations. Despite the large spatial scales of many ecosystems, their analysis is often done using a mean-field approach that ignores their spatial structure. This dissertation aims to understand the transitions that ecosystems undergo, with emphasis on their response to both changes in parameters and to perturbations, considering the specific effects of their spatial nature. When discussing ecosystems of dryland vegetation, this naturally reflects on a major concern over the last decades relating to the desertification process that many habitats may be undergoing. Over the last two decades new light has been shed on the spontaneous formation of the spatial heterogeneity of biota, explained by the theory of pattern formation. The existence of vegetation patchiness often has a significant effect on the internal dynamics of the ecosystem. In particular, transitions between different ecosystem states, often named regime shifts, may be dramatically different due to this form of spatial structure. The possibility of abrupt (catastrophic) regime shift has been discussed extensively in the literature, and this study aims to investigate the validity of such results for explicitly spatial systems, and develop an understanding of transitions that are unique to spatially extended systems. The focus of this research is thus on unique aspects to such spatial systems, and their relevance to the prevailing dynamics. My research was divided into three main topics : Dynamics between patterned vegetation and bare-soil states, fairy circles and their interpretation as localized states, and system transitions as a response to external perturbations. In the first part, I chose four models that describe dryland vegetation exhibiting pattern formation, and used them to examine possible regime shifts. We found that the system typically has a wide range of possible wavelengths, so that it could respond to local disturbances by a change of its wavelength. We also found that in all models examined, patterned vegetation can invade a bare-soil state, while the opposite cannot occur. The second part concerns a case-study of an ecosystem that may undergo gradual regime shifts, the fairy circles. These are gaps of bare soil in a uniform matrix of perennial grass found mainly in Namibia. We suggested a pattern-forming model based only on interaction of water and vegetation to explain the gap formation and the spatial distribution of the circles. Using an analysis of satellite images and precipitation records, we showed significant correlations between the dynamics of the fairy circles and the precipitation. The third part focuses on identifying and quantifying system response to different external influences, where we found a strong asymmetry in the behavior of the system between different bistability ranges. We conclude that the spatial nature of ecosystems significantly affects their dynamics and response to external influences, and suggest future directions of research in this field.

Mots clés : regime shifts, pattern formation, localized states, homoclinic snaking, bistability, desertification, fairy circles, dryland vegetation

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