Competition between two species for two complementary or substitutable resources.

The classical models of interspecific competition are phenomenological, that is, they purport to describe the trajectories followed by the abundances of both competitors, without specifying either mechanisms or the dynamics of what the competition is for, i.e. resources. Yet the conditions for the different outcomes of competition inferred from these models are most often interpreted in terms of resources. Here it is contended that the dynamics of resource supply and exploitation must be explicitly taken into account if these conditions are to be obtained in any accurate form. First, the distinction between perfectly substitutable, imperfectly substitutable and perfectly complementary resources is examined. This leads to an array of models intended to mirror interspecific exploitative competition for two resources for each category considered. Then, the conditions for the coexistence of the two competitors in each case are derived and presented with direct reference to the modes of resource use.