<p> Chapter 1 of this thesis describes the historical development and application of size-structured models and their role in modeling the population dynamics of biological systems. Chapter 2 presents a general model for the interaction of a size-structured population with its environment. The vital rates of the individuals are assumed to depend on a number of variables including the total population and the environment. A nonstandard finite difference approximation is developed for the general model and the convergence of the scheme to the unique weak solution of the nonlinear system of partial differential equations coupled with ordinary differential equations is established. Potential applications are presented in various fields ranging from shared resource dynamics to invasive species. Chapter 3 presents a first order finite difference scheme for phytoplankton dynamics subject to a vector of environmental variables in a well-mixed reactor. The biophysical problem yields a nonlinear partial differential equation coupled with a general system of nonlinear ordinary differential equations which represent the time-varying environmental conditions in the water column. Convergence results are established for the coupled system using the finite difference method. Numerical trials are presented to illustrate the performance of the model against a real dataset. Taking into account the combined effects of aggregate growth and coagulation, the model is used to investigate the role of the active fraction of the cell aggregate on algal bloom dynamics and nutrient consumption rates. The model is well-suited to complement microcosm studies and can accommodate the effects of a wide range of environmental conditions. Chapter 4 summarizes the main results, research and practical challenges associated with the application of general size-structured models, and suggestions for future work.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10002473 |
| Date | 28 January 2016 |
| Creators | Miller, Robert L. |
| Publisher | University of Louisiana at Lafayette |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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