The competitive exclusion principle versus biodiversity through competitive segregation and further adaptation to spatial heterogeneities.

In this work we introduce a general class of spatially heterogeneous competing species models where the species are assumed to disperse in a random way through the inhabiting region in the presence of some refuge patches where they are free from the aggressions of the antagonist species. Our model shows that the competitive exclusion principle fails to be true under these circumstances, as the species can segregate within their respective refuge areas when the intensity of the aggressions from competitors severely increase. Going beyond, segregation mechanisms, as a result from competition, combined with subsequent species differentiation, as a consequence from territorial heterogeneities--after a certain number of generations--might ultimately explain the extraordinary biodiversity of the Earth's biosphere, which seems to be confirmed by fossil registers in zoo-paleontology. Actually, the existence of Lazaro' species strongly support the validity of the predictions made from our prototype model.