Ecologists have long known that all ecosystems receive considerable quantities of materials from outside their boundaries (e.g., Elton 1927), and quantifying the magnitude of such fluxes has long been a central tenet of ecosystem ecology (e.g., Odum 1971). Thus, one might think that the consequences of such fluxes for food webs would be well understood. However, food webs have traditionally been viewed as if they were isolated from surrounding habitats, a habit that has been particularly persistent in the modeling of food webs. When fluxes from the outside have been considered, they have largely been restricted to constant inputs directly affecting the base of the food web (e.g., solar energy or nutrients), and usually only such issues as their effects on equilibrium conditions have been considered (e.g., the well-known relationships between nutrient inputs and average densities of various food web members).