School of Mathematical Ecology and Complexity, University of Warwick, Coventry CV4 7AL, UNITED KINGDOM.
The main aim of the thesis is to explore the interaction between pattern and process in vegetation ecology using a variety of mathematical and statistical methods. Of particular interest is what information about the dynamics of the underlying system can be gained through a single spatial snapshot, such as an aerial photograph or satellite image. The hypotheses are related to seagrass ecology, whose growth is primarily clonal and broadly exists as a monoculture and thus makes it an ideal candidate to study these interactions. The thesis broadly concerns two forms of spatial pattern and the underlying dynamics that give rise to them. The first concerns regular pattern formation, where the pattern has a characteristic length scale. Examples are abundant in natural systems, such as mussel beds, semi-arid ecosystems as well as seagrass. The developments concerned with regular pattern formation include methods of detection in a large spatial dataset, a novel stochastic model of vegetation that produces regular pattern with plausible mechanisms, the development of a new methodology to fit regular spatial pattern data to the model and the impact as well as evolutionary mechanisms of regular patterning in the presence of disease.
The second form of spatial pattern exhibited in a wide variety of sessile species is scale-free or fractal patterning. Certain scaling heuristics, such as the boundary dimension of a vegetation cluster or the power-law exponent of the patch-size distribution have been used to infer properties of the dynamics. We explore these heuristics using a variety of plausible models of vegetation growth and find the circumstances under which there is a clear relationship between the spatial heuristics and the dynamics. These are then supplemented by viewing vegetation growth as an aggregation process. A novel model of vegetation aggregation with death is produced to find the origin of the ubiquitous power-law patch-size distribution found in nature. Finally the impact of scaling on the spread of disease is explored.