Wendy Gruner Graves, Rainy River Community College, Bruce B. Peckham, Department of Mathematics and Statistics University of Minnesota Duluth, John Pastor, Department of Biology, University of Minnesota Duluth and NRRI, University of Minnesota. 2006. A 2D differential equations model for mutualism. Department of Mathematics and Statistics Technical Report TR 2006-2.
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 Lotka- Volterra 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.
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