UC San Diego

In this dissertation, we present a comprehensive study on two sets of phenomenological models examining bacterial population dynamics, focusing on chemotaxis-driven expansion and microbial interactions in non-steady-state environments. Our first model provides a quantitative understanding of how chemotaxis and cell growth lead to the rapid expansion of bacterial populations. We establish analytical relations that describe the dependence of expansion speed and density profile on molecular, cellular, and environmental parameters. We demonstrate that expansion speeds can significantly increase when the environmental availability of chemicals is high relative to the cellular limits of chemical sensing. Our results offer a mathematical framework for investigating the roles of taxis in diverse ecological contexts across broad parameter regimes.The second set of models explores microbial interactions in non-steady-state environments, as ecological dynamics often feature large self-generated environmental changes driving microbes through distinct physiological states. We introduce a phenomenological model to investigate the dynamic coexistence of microbes in cyclic environments. By considering growth according to a global ecological coordinate, specifically total community biomass, our model bypasses specific interactions leading to different physiological states. Our analysis provides rigorous, quantitative criteria for the dynamic coexistence of many species in terms of differential species' dominance ("growth niche") along the ecological coordinates. Our research shifts the focus of ecosystem dynamics from bottom-up studies based on inter-species interaction to top-down studies based on accessible macroscopic observables such as growth rates and total biomass. This approach allows for a quantitative examination of community-wide characteristics. In summary, this dissertation presents a detailed analytical investigation of bacterial population dynamics, shedding light on the underlying processes of chemotaxis-driven expansion and microbial interactions in changing environments. The mathematical frameworks and insights provided have broad applicability to diverse ecological contexts and open up new avenues for understanding complex spatiotemporal dynamic processes in microbial ecosystems.