Evaluating the component features of 'scaling' planktonic size spectra, commonly observed in marine ecosystems, is crucial for understanding the ecological and evolutionary processes from which they emerge. Here, we develop a theoretical framework that describes such spectra in terms of the size distributions of individual species, and test it against actual datasets of microbial size spectra from the Atlantic Ocean. We describe characteristics of size probability distributions of component species that are sufficient to support the observational evidence and infer that, when a power law describes the community size spectrum (thus suggesting critical self-organization of microbial ecosystem structure and function), a related power law links the total number of individuals of a given species to its mean size.