An axiomatic theory for interaction between species in ecology: Gause's exclusion conjecture

I introduce an axiomatic representation, called ecoset, to consider interactions between species in ecological systems. For interspecific competition, the exclusion conjecture (Gause) is put in a symbolic way and used as a basic operational tool to consider more complex cases like two species with two superposed resources (niche differentiation) and apparent competitors. Competition between tortoises and invaders in Galapagos islands is considered as a specific example. Our theory gives us an operative language to consider elementary process in ecology and open a route to more complex systems.