Coupled oscillations in food webs: balancing competition and mutualism in simple ecological models

As in other oscillating systems, oscillations of consumer resource pairs in ecological systems may be coupled such that complex behavior results. The form of that coupling may determine the nature and extent of this behavior. Two biologically significant forms of coupling are here investigated: first, where consumers consume each other's resources (CR coupling, representing competition between the two consumers), and second, where the resources are in competition with one another (RR coupling, potentially representing indirect mutualism between the two consumers). Interestingly, CR coupling leads to in-phase synchrony of the oscillations, whereas RR coupling leads to antiphase synchrony. With either form of coupling, if the coupling remains weak, synchronous behavior is generated in the two systems. At strong levels of coupling, when the two forms act simultaneously, a balance between competition and mutualism is generated, which is manifest differently at different levels of resource coupling.