Resource competition theory has been used by ecologists to predict outcomes of competition between phytoplankton, and their distribution in the environment (Tilman, 1977). Here we use this theoretical framework to gain insights into the solutions of a global three dimensional physical-biogeochemical-ecosystem numerical model. This model is initialized with many phytoplankton types, whose growth traits are drawn randomly from observed ranges. The resulting spatially varying ecosystem structure is therefore self organizing rather than imposed. In particular, the model successfully characterizes the observed distribution of the picocyanobacteria Prochlorococcus, which dominate the phytoplankton communities of much of the tropical and subtropical oceans. We use the theoretical framework, modified to include the effects of light, temperature and grazing on phytoplankton abundances, to investigate the physical and ecological factors that underpin the modeled biogeography. We find that Prochlorococcus dominate regions where the physical environment is very stable, and at least one of their required nutrients are drawn down to low levels that are consistent with the theoretical predictions. In these stable regions the chemical environment is regulated by the characteristics of the ecosystem structure.