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