In this talk, we are interested in the analytical study of a nonlinear Stochastic Partial Differential Equation arising as a model of phytoplankton aggregation. This SPDE consists in an integro-differential advection-diffusion equation with a branching noise. It has been derived as an Eulerian version of an individual-based model which provides an explanation of the aggregation behavior in phytoplankton in terms of attraction mechanisms among cells caused by chemical signals, a branching process (random births and deaths), in addition to individual random dispersal of cells described by Brownian motions. Existence  of weak solutions and uniqueness are established through weak convergence and tightness arguments 

Phytoplankton Aggregation, Nonlinear Stochastic Partial Differential Equation, Weak Solution, Tightness , Semigroups