Phytoplankton are microscopic plant-like organisms that drift in the water column of lakes and oceans. They grow abundantly around the world and are responsible for the consumption of at least 60% carbon dioxide on earth. They are the foundation of the marine food chain. Nutrients and light are the essential resources for the growth of the phytoplankton. In this talk we shall restrict our attentions to eutrophic ecosystems where nutrient supplies are ample, and species compete only for light.
First we consider the competition of species in a well-mixing water column. The model takes a form of system of ordinary differential equations. In this case we consider the effect with or without photo-inhibition to the growth of phytoplankton species. We classify the asymptotic behavior of the solutions. Then we consider the competition of species in a poorly mixing water column. The model takes a form of nonlocal reaction-advectiondiffusion system. We first prove the global convergence of the solution for the case of single population growth. Then we apply the global bifurcation theory to obtain the coexistence of two species.