Phages are viruses that infect bacteria and exploit the bacterial metabolism to replicate. The ecological impact of phages is far reaching, and includes such mechanisms as the control of bacterial abundance and the promotion of nutrient turnover in environments. A recent study of microbial and viral abundances across ecosystems was conducted and published in Knowles et al. (Nature 2016). In this work, it was observed that as the abundance of microbes in ecosystems increased, the virus to microbe ratio decreased. This trend was proposed to correspond to an emergence of lysogeny, in which phages integrate their genome into the bacteria. A Piggyback-the-Winner model was suggested to describe these observed dynamics, instead of the established Kill-the-Winner model. In this thesis we have used dynamical systems to describe the bacteria-phage system and to explore the dynamics of the two models. We propose a mathematical model that incorporates lysogeny into bacteria-phage communities as a result of excess energy resources. This model predicts bacteria and phage equilibrium concentrations that align with the environmental observations and recovers qualitative trends from the data. Based on these results we propose a speciation model that includes both the dynamics of the Piggyback-the-Winner and Kill-the-Winner models as a way to promote the evolution of new species. Our model provides an interpretation of the observed dynamics of bacteria-phage interactions across ecosystems and leads to specific predictions that can be tested to validate these theoretical results.
