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Algorithms to generate walks (chains of unit-length, freely-jointed segments) and polygons (closed walks) in spherical confinements have been developed in the last few years. These algorithms generate polygons inside spherical confinement based on their mathematically derived probability distributions. The generated polygons do not occupy any volume { although that would be useful for some applications. This thesis investigates how to generate walks and polygons which occupy some volume in spherical confinement. More specifically, in this thesis, existing methods described in the literature have been studied and implemented to generate walks and polygons in confinement. Additionally, these methods were adapted to design, develop, and implement an algorithm which generates walks and polygons in confinement with thick segments, that is, segments which occupy volume. Data is collected by generating walks and polygons of different lengths with and without thickness inside the spherical confinements of various radii to compare walks and polygons with thickness with those generated without thickness. The analysis of the collected data shows that a. the newly developed algorithm indeed generates polygons which are thicker than those generated with the volumeless algorithm; and b. the newly developed algorithm generates polygons which are different from the polygons generated by the volumeless algorithm. The analysis also includes an assessment of the computational cost of generating thick polygons.

Alfalfa is an important forage crop in North America which can also escape cultivation and establish in unmanaged habitats. Genetically modified (GM) alfalfa has been approved for environmental release in Canada and the United States and the occurrence of alfalfa in unmanaged natural and semi-natural habitats may compromise the successful co-existence of GM and non-GM alfalfa. To-date, little information has been available on the nature and dynamics of roadside alfalfa populations and their ability to become feral. Such knowledge is necessary to design efficient trait confinement protocols and to enhance the co-existence of GM and non-GM alfalfa within agricultural regions. The overall aim of this work was to characterize roadside alfalfa populations and to establish their role in novel trait movement. A roadside survey revealed the widespread occurrence of feral alfalfa populations in southern Manitoba. We described the seedbanks of roadside alfalfa populations, seedling recruitment and adult reproductive success, indicating that alfalfa is capable of establishing self-perpetuating feral populations in unmanaged habitats. We also noted the successful establishment of alfalfa in a grass sward representing roadside vegetation. Roadside mowing can reduce (and perhaps prevent) seed production in roadside alfalfa; however, mowing failed to drive the populations to extinction in the short-term. Herbicide (2,4-D) applications controlled alfalfa plants but seeds in the seedbank may still contribute to new seedling recruitment. The roadside alfalfa populations we worked with exhibited high levels of genetic diversity, indicating an absence of past population bottlenecks or genetic drift. In addition, phenotypic characterization provided evidence that roadside alfalfa populations were experiencing selection pressure for adaptive traits including winter survivability, rhizome production and prostrate growth habit; all traits that favor persistence in unmanaged habitats. We also noted the occurrence of high (>60%) levels of outcrossing in feral alfalfa populations, establishing their role as sources and sinks for novel traits. Our findings indicate that alfalfa populations occurring in unmanaged habitats need to be considered in trait confinement protocols in order to reduce the adventitious presence (AP) of novel traits and to enhance the successful co-existence of GM and non-GM alfalfa.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on February 25, 2008) Vita. Includes bibliographical references.

Thesis (M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ. 42-43)

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (M.S.)--University of Michigan, 1978.

Thesis (M.S.)--University of Michigan, 1985.

Thesis--University of Michigan, 1971.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1982. / Typescript. Vita. Description based on print version record. Includes bibliographical references (leaves 235-242).