Geodesic
Resource Competition: A Bifurcation Theory Approach
B. W. Kooi1 ; P. S. Dutta2, 3 ; U. Feudel2
1 Department of Theoretical Biology, VU University de Boelelaan 1085, 1081 HV Amsterdam, The Netherlands
2 Theoretical Physics/Complex Systems, ICBM Carl von Ossietzky Universität, PF 2503, 26111 Oldenburg, Germany
3 Department of Mathematics, Indian Institute of Technology Ropar Rupnagar-140001, Punjab, India
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 6, pp. 165-185.

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We develop a framework for analysing the outcome of resource competition based on bifurcation theory. We elaborate our methodology by readdressing the problem of competition of two species for two resources in a chemostat environment. In the case of perfect-essential resources it has been extensively discussed using Tilman’s representation of resource quarter plane plots. Our mathematically rigorous analysis yields bifurcation diagrams with a striking similarity to Tilman’s method including the interpretation of the consumption vector and the resource supply vector. However, our approach is not restricted to a particular class of models but also works with other trophic interaction formulations. This is illustrated by the analysis of a model considering interactively-essential or complementary resources instead of prefect-essential resources. Additionally, our approach can also be used for other ecosystem compositions: multiple resources–multiple species communities with equilibrium or oscillatory dynamics. Hence, it gives not only a new interpretation of Tilman’s graphical approach, but it constitutes an extension of competition analyses to communities with many species as well as non-equilibrium dynamics.
DOI : 10.1051/mmnp/20138611

B. W. Kooi 1 ; P. S. Dutta 2, 3 ; U. Feudel 2

1 Department of Theoretical Biology, VU University de Boelelaan 1085, 1081 HV Amsterdam, The Netherlands
2 Theoretical Physics/Complex Systems, ICBM Carl von Ossietzky Universität, PF 2503, 26111 Oldenburg, Germany
3 Department of Mathematics, Indian Institute of Technology Ropar Rupnagar-140001, Punjab, India 
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B. W. Kooi; P. S. Dutta; U. Feudel. Resource Competition: A Bifurcation Theory Approach. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 6, pp. 165-185. doi : 10.1051/mmnp/20138611. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20138611/

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