Existence and construction of large stable food webs

Ecological diversity is ubiquitous despite the restrictions imposed by competitive exclusion and apparent competition. To explain the observed richness of species in a given habitat, food-web theory has explored nonlinear functional responses, self-interaction, or spatial structure and dispersal-model ingredients that have proven to promote stability and diversity. We return instead here to classical Lotka-Volterra equations, where species-species interaction is characterized by a simple product and spatial restrictions are ignored. We quantify how this idealization imposes constraints on coexistence and diversity for many species. To this end, we introduce the concept of free and controlled species and use this to demonstrate how stable food webs can be constructed by the sequential addition of species. The resulting food webs can reach dozens of species and generally yield nonrandom degree distributions in accordance with the constraints imposed through the assembly process. Our model thus serves as a formal starting point for the study of sustainable interaction patterns between species.