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Thesis Format



Doctor of Philosophy


Applied Mathematics


Wahl, Lindi M.


We use mathematical models to study prophages, viral genetic sequences carried by bacterial genomes. In this work, we first examine the role that plasmid prophage play in the survival of de novo beneficial mutations for the associated temperate bacteriophage. Through the use of a life-history model, we determine that mutations first occurring in a plasmid prophage are far more likely to survive drift than those first occurring in a free phage. We then analyse the equilibria and stability of a system of ordinary differential equations that describe temperate phage-host dynamics. We elucidate conditions on dimensionless parameters to determine a parameter regime that guarantees coexistence of all populations. We then develop a resource-explicit model to investigate further the lysis-lysogeny decision in variable environments. A novel feature of our model is the inclusion of a distinct stationary phase for the hosts and lysogens. Through the application of evolutionary invasion techniques, we determine that as variability increases, bacteriophage populations tend to evolve to a fully lysogenic state, so long as the hosts and lysogens are able to enter stationary phase. This lead us to question the evolutionary fates of prophage in fast- and slow-growing bacterial species. Using a partial differential equation model developed previously, we fit distributions of prophage lengths for both growth classes and observe several significant differences in strategies of the phage that infect both growth classes. Specifically, we demonstrate that phages infecting fast-growing hosts have a much higher rate of lysogeny. Our work sheds light on the long-standing question, "why be temperate?", offering novel explanations regarding the evolution of temperate bacteriophage.

Summary for Lay Audience

Bacteriophages (or ``phages'' for short) are viral particles that predate on bacteria. Phages are pivotal players in the evolution of bacteria, and as such provide interesting avenues for experimental and theoretical work. These microscopic predators are able to infect through two main methods. The first has been studied extensively, wherein the phage infects and immediately kills the host. Phages that utilise this first strategy are often used in ``phage therapy" treatments, where they eliminate antibiotic resistant bacteria from an infected human. The second involves the phage becoming integrated into the bacterial genome, and laying dormant for some time. The second strategy has puzzled researchers, as it does not seem to directly benefit the phage. The question as to why the phage evolved such a strategy is the focus of our work. Although some biologists have offered insight into this evolutionary question, we further their work by developing mathematical models of phage-bacteria dynamics. We identify that mutations beneficial to the phage are more likely to propagate forward if they occur when the phage is integrated. We also find that this integration may be an important strategy for the survival of the phage, if the host is living in a highly variable environment. We, therefore, hope our work has generated new answers to this biological puzzle.

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License