Geometry of exclusion principles in discrete systems

AbstractUsing an n-species system of difference equations with very general density dependent growth functions, we prove that weak dominance and invariance gives the exclusion of all the (n − 1)-dominated species in the system. This result is applied to very specific competition models. An example of coexistence in a competition model with no invariance is studied. A notion of strong dominance is developed in a general setting and shown to imply exclusion of the (n − 1)-dominated species. An example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given