Consumer-resource theory predicts dynamic transitions between outcomes of interspecific interactions

Interactions between two populations are often defined by their interaction outcomes; that is, the positive, neutral, or negative effects of species on one another. Yet, signs of outcomes are not absolute, but vary with the biotic and abiotic contexts of interactions. Here, we develop a general theory for transitions between outcomes based on consumer-resource (C-R) interactions in which one or both species exploit the other as a resource. Simple models of C-R interactions revealed multiple equilibria, including one for species coexistence and others for extinction of one or both species, indicating that species densities alone could determine the fate of interactions. All possible outcomes (+ +), (+ -), (- -), (+ 0), (- 0), (0 0) of species coexistence emerged merely through changes in parameter values of C-R interactions, indicating that variation in C-R interactions resulting from biotic and abiotic conditions could determine shifts in outcomes. These results suggest that C-R interactions can provide a broad mechanism for understanding context- and density-dependent transitions between interaction outcomes.