This study addresses interspecific competition for a nutrient resource that is stored within individuals in habitats with both temporal and spatial variation. In such environments, population structure is induced by the mixture at any location of individuals with different amounts of stored nutrient, acquired elsewhere in the habitat. Focusing on phytoplankton competing for phosphorus in a partially mixed water column, an individual-based Lagrangian model is used to represent this population structure, and partial differential equations that approximate competitive dynamics are constructed by averaging over this population structure. Although the approximation model overestimates the benefit of resource storage to competitive fitness, both approaches predict that species with high storage capacity are favored by periodic resource pulses that are short lived but large in magnitude. Such storage specialists can competitively exclude or coexist with species that have advantages in maximal nutrient uptake and population growth rates. For very infrequent resource pulses, competitive dynamics become close to neutral. Thus, persistence of diverse species that are differentiated in nutrient storage and uptake capabilities is favored by resource pulses occurring with periods that are many times the average generation time of competitors.