TY - JOUR
T1 - A bifurcation analysis of a differential equations model for mutualism
AU - Graves, Wendy Gruner
AU - Peckham, Bruce
AU - Pastor, John
PY - 2006/11
Y1 - 2006/11
N2 - 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.
AB - 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.
KW - Bifurcation analysis
KW - Differential equations
KW - Lotka-Volterra
KW - Mathematical model
KW - Mutualism
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U2 - 10.1007/s11538-006-9070-3
DO - 10.1007/s11538-006-9070-3
M3 - Article
C2 - 16937233
AN - SCOPUS:33750732974
SN - 0092-8240
VL - 68
SP - 1851
EP - 1872
JO - Bulletin of mathematical biology
JF - Bulletin of mathematical biology
IS - 8
ER -