3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item A statistical investigation into the properties and dynamics of biological populations experiencing environmental variability(2007-02-15T11:30:22Z) Varughese, Melvin MathewMuch research has been devoted towards the understanding of population behaviour. Such understanding has often been furthered through the development of theoretical population models. This research report explores a variety of population models and their implications. The implications of the various models are explored using both analytical results and simulations. Specific aspects of population behaviour studied include gross fluctuation characteristics and extinction probabilities for a population. This research report starts with an overview of Deterministic Models. This is followed by a study of Birth and Death Processes, Branching Processes and Models that incorporate environmental variability. Finally, we study the maximum likelihood approach to population parameter estimation. The more notable theoretical results derived include: the development of models that incorporate the population’s history; models that incorporate discontinuous environmental changes and the development of a means of parameter estimation for a Stochastic Differential Equation.Item Hydraulic and hydrological modelling of the Nyl River floodplain for environmental impact assessment(2006-03-13) Kleynhans, Martin ThomasThere have been various threats from upstream catchment developments to the water supply of the ecologically important Nylsvlei floodplain in South Africa. Hydrological modelling of the catchments and unsteady hydraulic modelling of the floodplain (including measured losses to evapotranspiration and infiltration) with biotic links to Oryza longistaminata revealed that existing developments within the catchments have decreased areas suitable for growth of this plant in the Nylsvley Reserve by 9% on average from 1973/74 to 2000/01 compared to the catchment in a virgin state. Construction of the proposed Olifantspruit Dam with environmental flow releases would have reduced these suitable areas by a further 9% on average. Catchment developments were found to have the greatest impact on floodplain inundation in average to dry years and would also reduce the frequency of occurrence of suitable conditions for growth of Oryza longistaminata.