From individual behavior of phytoplankton to evolution equation

Phytoplankton, a mass of small plants (mostly algae) living in the water, comes out to be the main source of nutrient in oceans. That is why understanding of its bahaviour becomes so important and has been widely investigated. An individual based model, that describes spatial movement and processes of fragmentation and coagulation of phytoplankton structures, will be presented. The individuals in this model are phytoplankton aggregates (a number of cells joined by some organic glue) that move in the space, may split into smaller ones and have the possibility of joining together. After the formulation of the model in the setting of measure-valued stochastic process, we investigate its behaviour in the limit where the number of individuals grows to infinity. As a result of something like central limit theorem for our processes, we obtain the evolution equation on the density of the mass--spatial distribution of phytoplankton population.