Modelling dryland vegetation patterns : nonlocal dispersal, temporal variability in precipitation and species coexistence
Abstract
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.