We develop a framework for analysing the outcome of resource competition based onbifurcation theory. We elaborate our methodology by readdressing the problem ofcompetition of two species for two resources in a chemostat environment. In the case ofperfect-essential resources it has been extensively discussed using Tilman’srepresentation of resource quarter plane plots. Our mathematically rigorous analysisyields bifurcation diagrams with a striking similarity to Tilman’s method including theinterpretation of the consumption vector and the resource supply vector. However, ourapproach is not restricted to a particular class of models but also works with othertrophic interaction formulations. This is illustrated by the analysis of a modelconsidering interactively-essential or complementary resources instead ofprefect-essential resources. Additionally, our approach can also be used for otherecosystem compositions: multiple resources–multiple species communities with equilibriumor oscillatory dynamics. Hence, it gives not only a new interpretation of Tilman’sgraphical approach, but it constitutes an extension of competition analyses to communitieswith many species as well as non-equilibrium dynamics.
