| Summary: | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2003. === Includes bibliographical references (leaves 141-154) and index. === This thesis applies principles of statistical physics and non-equilibrium dynamics to problems of scale, randomness, and growth in plant communities. It includes three projects related by their methodology and distinct in the nature of their applications. In the first project, we analyze the relationship between resource availability and species richness in community and regional level models of plant/tree communities. At local scales, vegetative communities tend to follow a unimodal relationship between resources and species richness. However, as per the results of species-energy theory, they tend to obey a monotonically increasing relationship at large scales. We use a multi-species neutral contact process coupled to a heterogeneous resource landscape to explain the scale-dependent transition. We find that the unimodal curve at the community scale may be understood as a tradeoff between colonization of and competition for limited resources. We then construct statistical aggregates of community level ecosystems and find two necessary conditions for a scale-dependent transition: (i) the spatial distribution of resources is highly correlated and (ii) the extent of species pools increases in regions with higher overall resources. The second project integrates the analysis of size-structured populations into the study of the contact process. We introduce the contact process with ontogeny to describe the growth and spread of organisms with size-structured juvenile and adult stages. We derive a mean field theory of the contact process with ontogeny, which we solve yielding an additional oscillatory phase. The mean field phase diagram is found in terms of A, the dimensionless reproductive rate, and 0, the dimensionless growth rate. === (cont.) However, the oscillatory phase is not borne out in explicitly spatial Monte Carlo simulations, in contrast to the regularity with which oscillations are observed for well-stirred models of size-structured populations. Instead we find a "corralled" phase where the growth of new seeds interfere with one another, limiting basal area and number of adults, and leading to a unimodal relationship between density p and reproductive rate A. We analyze the onset of the corralled phase by analyzing spatial correlations and find that this self-limiting phase is characterized by distinct peaks in the radial distribution function. We also determine the universality class of the transition between life and death and point out where generalizations of the model may be applied to plant/tree communities. The final project addresses the size distributions of systems where growth is limited by geometric constraints. We develop a model termed packing limited growth (PLG) which describes the interaction and growth of sessile organisms. We show that a class of models previously introduced in the context of growth and nucleation kinetics may be mapped onto PLG. We develop a scaling theory which connects the fractal dimension of packings to the approach to the fully packed state. The equilibrium size distribution of PLG models is shown to depend on dimensionality, anisotropy, and geometric shape. Numerical estimates of fractal dimensions are calculated in d = 2, 3, and 4. === by Joshua Stephen Weitz. === Ph.D.
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