Modelling dryland vegetation patterns : nonlocal dispersal, temporal variability in precipitation and species coexistence
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Spatiotemporal patterns of vegetation are a characteristic feature of dryland ecosystems occurring on all continents except Antarctica. The development of an understanding of their ecosystem dynamics is an issue of considerable socio-economic importance as both the livestock and agricultural sectors in dryland economies heavily depend on ecosystem functioning. Mathematical modelling is a powerful tool to disentangle the complex ecosystem dynamics. In this thesis, I present theoretical models to explore the impact of nonlocal seed dispersal and temporal precipitation variability on dryland vegetation patterns and propose several mechanisms that enable species coexistence within vegetation patterns. To do so, I present extensions of the Klausmeier reaction-advection-diffusion model, a well-established model describing the ecohydrological dynamics of vegetation patterns. Model analyses focus on pattern onset at high precipitation values (i.e. on the transition from uniformly vegetated to spatially patterned states) to assess the impact of nonlocal seed dispersal and precipitation seasonality and intermittency, and on comprehensive bifurcation analyses, including results on pattern existence and stability to investigate coexistence of species in the mathematical framework. Results include the inhibition of pattern onset due to long-range seed dispersal and put emphasis on the functional response of plants to low soil moisture levels to understand effects of rainfall intermittency. Moreover, results suggest that coexistence is facilitated by resource heterogeneities induced by the plant’s spatial self-organisation and highlight the importance of considering out-of-equilibrium solutions.