Partitioning the flows and standing stocks of energy-matter in an ecosystem or food-web model according to the number of intercompartmental transfers a unit of substance experiences before it arrives at a compartment reveals two complementary views on ecosystem organization: the trophic structure of the ecosystem as a whole and the trophic niche of each compartment within the ecosystem. The trophic structure of an ecosystem comprises two complementary aspects: the distribution of flow and biomass over trophic levels and the distribution at each trophic level of the biomass from the different compartments, or of flow between compartments at two adjacent levels. This partitioning, termed food network unfolding, also explicitly quantifies two aspects of the trophic niche of the organisms in each ecosystem compartment; the trophic position of each compartment is represented by its distribution over all trophic levels, and the trophic function of each on any trophic level is represented by the diversity of resources on the previous trophic level that it uses and the diversity of consumers on the next trophic level that use it as a resource. These measures will allow ecosystem comparisons in time and space and comparisons of trophic divergence or convergence of organisms in the context of the whole ecosystem.