Math. Model. Nat. Phenom.
Volume 8, Number 6, 2013Ecology
|Page(s)||165 - 185|
|Published online||28 November 2013|
Resource Competition: A Bifurcation Theory Approach
1 Department of Theoretical Biology, VU
University de Boelelaan 1085, 1081 HV
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
Corresponding author. E-mail: email@example.com
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.
Mathematics Subject Classification: 34C23 / 92D40 / 92D25
Key words: bifurcation analysis / competitive exclusion / complementary resources / resource competition / resource quarter plane plot
© EDP Sciences, 2013
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