Electronic Thesis and Dissertation Repository


Master of Science


Applied Mathematics


Dr. Lindi M. Wahl


Mobile genetic elements (MGEs) are ubiquitous among prokaryotes, and have important implications to many areas, such as the evolution of certain genes, bioengineering and the spread of antibiotic resistance. In order to understand the complex dynamics of MGEs, mathematical models are often used. One model that has been used to describe the dynamics of mobile promoters (a class of MGEs) is the birth-death-diversification model. This model is unique in that it allows MGEs to diversify to create new families. In this thesis, I analyze the dynamics of this model; in particular, I examine equilibrium distributions, extinction probabilities and mean time until extinction for MGE lineages. I find that diversification indirectly increases MGE propagation through increased horizontal gene transfer rates; therefore, diversification increases population growth rates and decreases extinction probability. Overall, this work indicates that diversification of elements should be considered in order to fully understand the dynamics of MGEs in prokaryotes.