Resource competition: a bifurcation theory approach.

B.W. Kooi, P.S. Dutta, U. Feudel

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

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. © 2013 EDP Sciences.
Original languageEnglish
Pages (from-to)165-185
JournalMathematical Modelling of Natural Phenomena
Volume8
DOIs
Publication statusPublished - 2013

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Bifurcation Theory
Resources
Chemostats
Ecosystems
Chemical analysis
Chemostat
Nonequilibrium Dynamics
Bifurcation Diagram
Ecosystem
Methodology
Formulation
Interaction
Model

Cite this

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title = "Resource competition: a bifurcation theory approach.",
abstract = "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. {\circledC} 2013 EDP Sciences.",
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Resource competition: a bifurcation theory approach. / Kooi, B.W.; Dutta, P.S.; Feudel, U.

In: Mathematical Modelling of Natural Phenomena, Vol. 8, 2013, p. 165-185.

Research output: Contribution to JournalArticleAcademicpeer-review

TY - JOUR

T1 - Resource competition: a bifurcation theory approach.

AU - Kooi, B.W.

AU - Dutta, P.S.

AU - Feudel, U.

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AB - 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. © 2013 EDP Sciences.

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