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A Bifurcation Analysis of a Differential Equations Model for Mutualism

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Abstract

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, A.M., Am. Nat. 121(3), 409–417 (1983)], but corrects problems due to singularities in that model. In addition, we investigate our model in more depth 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 for large populations 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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Authors and Affiliations

  1. Lake Superior College, Duluth, MN, USA

    Wendy Gruner Graves

  2. Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, MN, USA

    Bruce Peckham

  3. Department of Biology, University of Minnesota Duluth and NRRI, Duluth, MN, USA

    John Pastor

Authors
  1. Wendy Gruner Graves
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  2. Bruce Peckham
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  3. John Pastor
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Correspondence to Wendy Gruner Graves.

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Graves, W.G., Peckham, B. & Pastor, J. A Bifurcation Analysis of a Differential Equations Model for Mutualism. Bull. Math. Biol. 68, 1851–1872 (2006). https://doi.org/10.1007/s11538-006-9070-3

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  • DOI: https://doi.org/10.1007/s11538-006-9070-3

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