A 2D Differential Equations Model for Mutualism

We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model (Dean 1983), but corrects problems with singularities in that model. In addition, we investigate our model in more depth. The behavior of the system is investigated by varying the intrinsic growth rate for each of the species and analyzing the resulting bifurcations in system behavior. We are especially interested in transitions between facultative and obligate mutualism. The model reduces to the familiar LotkaVolterra model locally, but is more realistic globally in the case where mutualist interaction is strong. In particular, our model supports population thresholds necessary for survival in certain cases, but does this without allowing unbounded population growth. Experimental implications are discussed for a lichen population.