Varughese, Melvin Mathew2007-02-152007-02-152007-02-15http://hdl.handle.net/10539/2003Student Number : 9908888R - MSc research report - School of Statistics and Actuarial Science - Faculty of ScienceMuch 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.10270 bytes15055 bytes10124 bytes36294 bytes57786 bytes42567 bytes143007 bytes275796 bytes371919 bytes46377 bytes293575 bytes171791 bytes40890 bytes23172 bytes148935 bytes11061 bytesapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfenstatisticspopulationenvironmentmodelssimulationsecologyThesis