Planktonic communities are extremely diverse and include a vast number of rare species. The dynamics of these rare species is best described by individual-based models. However, individual-based approaches to planktonic diversity face substantial difficulties, due to the large number of individuals required to make realistic predictions. In this paper, we study the diversity of planktonic communities by means of a spatial coalescence model that incorporates transport by oceanic currents. As a main advantage, our approach requires simulating a number of individuals equal to the size of the sample one is interested in, rather than the size of the entire community. By theoretical analysis and simulations, we explore the conditions upon which our coalescence model is equivalent to individual-based dynamics. As an application, we use our model to predict the impact of chaotic advection by oceanic currents on biodiversity. We conclude that the coalescent approach permits one to simulate marine microbial communities much more efficiently than with individual-based models.