Title: Competition dynamics of phytoplankton species in eutrophic water columns

Abstract: The paradox of the plankton highlights the apparent contradiction between Gause's law of competitive exclusion and the observed diversity of phytoplankton. We are interested in the dynamics of phytoplankton populations in competition for light in a eutrophic water column. In the first part of the talk, we analyze a reaction-diffusion model introduced by J. Huismann and collaborators. By classifying the dynamics of two-species competition, our results suggest that competitive exclusion is prevalent. In the second part of the talk, we extend the model by treating light as a continuum of resources rather than a single resource. This is done by considering the visible light spectrum. We explore under what circumstance coexistence is possible from mathematical and biological perspectives. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and the overall turbidity of the water.