Abstract:
<p>Drylands, comprising arid and semi-arid areas and the dry subtropics, over some 40% of the world's land area and support approximately 2 billion people, including at least 1 billion who depend on dryland agriculture and grazing. 10-20% of drylands are estimated to have already undergone degradation or desertification, and lack of monitoring and assessment remains a key impediment to preventing further desertification. Change in vegetation cover, specifically in the spatial organization of vegetation may occur prior to irreversible land degradation, and can be used to assess desertification risk. Coherent spatial structures arise in the distribution of dryland vegetation where plant growth is localized in regular spatial patterns. Such "patterned vegetation" occurs across a variety of vegetation and soil types, extends over at least 18 million ha, occurs in 5 continents and is economically and environmentally valuable in its own right.</p>
<p>Vegetation patterning in drylands arises due to positive feedbacks between hydrological forcing and plant growth so that the patterns change in response to trends in mean annual rainfall. Mathematical models indicate that vegetation patterns collapse to a desertified state after undergoing a characteristic set of transformations so that the condition of a pattern at any point in time can be explicitly linked to ecosystem health. This dissertation focuses on the mathematical description of vegetation patterns with a view to improving such predictions. It evaluates the validity of current mathematical descriptions of patterning for the specific case of small-scale vegetation patterns and proposes alternative hypotheses for their formation. It assesses the significance of seed dispersal in determining pattern form and dynamics for two cases: vegetation growing on flat ground with isotropic patterning, and vegetation growing on slopes and having anisotropic (i.e. directional) patterning. Thirdly, the feedbacks between local biomass density and infiltration capacity, one of the positive feedbacks believed to contribute to patterning, are quantified across a wide range of soil and climatic conditions, and new mathematical descriptions of the biomass-infiltration relationship are proposed. Finally the influence of land surface microtopography on the partitioning of rainfall into infiltration and runoff is assessed.</p>
