Mathematical Modeling and Disease Related Applications: A New Method of Estimating Bacterial Mutation Rates, Dynamics of Killer Yeast in a Chemostat, and Other Problems

Among the main mechanisms of evolution we find adaptation, genetic drift, gene flow, mutation, natural selection and speciation. The following thesis explores bacterial mutation rate, mutants, mutators, and how competition acts as a driving force of adaptation. In chapter 1, the system used in reference for mutation is the devolopment of Pseudomonas aeruginosa antibacterial resistance in the Cystic Fibrosis patients. Current methods for determining mutation rate are quite involved mathematically or complicated experimentally. A new method for estimating mutation rate is discussed and compared with two other widely used methods. In chapter 2, a microarray data set of different strains are compared. We find that the data set has strains that have sections of deleted genes. The two categories are analyzed across two different tests and genetic deletions are compared. The strains are also known to be mutators or non-mutators and the data will be used for strain classification. In chapter 3, a competition model of killer and non-killer yeast is used to predict the outcome of competition in a continuous culture under nutrient limitation (e.g. a chemostat). This research explores possible detrimental effect on fitness when yeast harbor the killer virus under chemostat conditions and when a non-killer yeast strain can out compete a killer-strain of yeast