Effects of cooperation on competitive systems

A persistence-extinction theory of coupled cooperative-competitive systems is developed for three dimension Lotka-Volterra systems. Model conclusions indicate, as intuitively expected, that protocooperation can be beneficial for all species in the community. An outcome that is, perhaps, unexpected is that a protocooperative species can drive a stable competitive community to extinction. The models are successively modified to include a hierarchy of obligatory interactions. Obligatory cooperation generally leads to an increased degree of extinction from the perspective that it is generally attained under weaker conditions and generally involves more species.