This thesis studies the two fundamental mechanisms of bacterial evolution β horizontal gene transfer and spontaneous mutation, in the bacterium Escherichia coli through novel experimental assays and mathematical simulations. First, I will develop a growth assay utilizing the quantitative polymerase chain reaction (qPCR) to provide real-time enumeration of genetic marker abundance within bacterial populations. Second, I will focus on horizontal gene transfer in E. coli occurring through a process called conjugation. By fitting the qPCR data to a resource limited, logistic growth model, I will obtain estimated values of several key parameters governing the dynamics of DNA transfer through conjugation under two different conditions: i) in the absence of selection; ii) in the presence of negative selection pressure β bacteriophage infection. Last, I will investigate spontaneous mutation through qPCR assay of competition between wild-type and mutator phenotype E. coli. Mutator phenotype has an elevated mutation rate due to defects in DNA proofreading and repairing system. By introducing antibiotic selective pressure, I will examine the fixation probability of mutators competing with wild-type in novel environment. I also will utilize simulations to study the impact of three parameters on the fixation probability