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Resource Competition: A Bifurcation TheoryApproach

Published online by Cambridge University Press:  28 November 2013

B. W. Kooi ,
P. S. Dutta  and
U. Feudel
B. W. Kooi*
Affiliation:
Department of Theoretical Biology, VU University de Boelelaan 1085, 1081 HV Amsterdam, The Netherlands
P. S. Dutta
Affiliation:
Theoretical Physics/Complex Systems, ICBM Carl von Ossietzky Universität, PF 2503, 26111 Oldenburg, Germany Department of Mathematics, Indian Institute of Technology Ropar Rupnagar-140001, Punjab, India
U. Feudel
Affiliation:
Theoretical Physics/Complex Systems, ICBM Carl von Ossietzky Universität, PF 2503, 26111 Oldenburg, Germany
*
⋆Corresponding author. E-mail: bob.kooi@vu.nl
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Abstract

We develop a framework for analysing the outcome of resource competition based onbifurcation theory. We elaborate our methodology by readdressing the problem ofcompetition of two species for two resources in a chemostat environment. In the case ofperfect-essential resources it has been extensively discussed using Tilman’srepresentation of resource quarter plane plots. Our mathematically rigorous analysisyields bifurcation diagrams with a striking similarity to Tilman’s method including theinterpretation of the consumption vector and the resource supply vector. However, ourapproach is not restricted to a particular class of models but also works with othertrophic interaction formulations. This is illustrated by the analysis of a modelconsidering interactively-essential or complementary resources instead ofprefect-essential resources. Additionally, our approach can also be used for otherecosystem compositions: multiple resources–multiple species communities with equilibriumor oscillatory dynamics. Hence, it gives not only a new interpretation of Tilman’sgraphical approach, but it constitutes an extension of competition analyses to communitieswith many species as well as non-equilibrium dynamics.

Keywords

bifurcation analysiscompetitive exclusioncomplementary resourcesresource competitionresource quarter plane plot
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 6: Ecology , 2013 , pp. 165 - 185
Copyright
© EDP Sciences, 2013

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