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Communication Dans Un Congrès Année : 2015

MacArthur’s consumer-resource model

Le modèle ressource-consommateur de Mac Arthur

Résumé

The model of Mac Arthur assumes that resources Rj have logistic growth in the absence of consumers and consumers have simple linear functional responses. To reduce the dimensionality of the system, MacArthur made the additional assumption that resources have much faster dynamics than consumers. The quasi steady state approximation consists in setting Rj’=0. This equation can be solved for the equilibrium value of Rj as a function of Ni, which can be substituted into the equations of the consumers Ni, provided it is positive. The system then reduces to a classical Lotka–Volterra competition model for consumers.The reduction of the consumers-resource model to a Lotka-Volterra competition model is valid only when the resources have positive densities. We propose in this talk to revisit the theory and clarify this assumption that all resources must have positive densities. Canards are central to understand the dynamics of the slow-fast resource-consumer model.
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Dates et versions

hal-02602271 , version 1 (16-05-2020)

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Tewfik Sari. MacArthur’s consumer-resource model. AMS-EMS-SPM International Meeting, Jun 2015, Porto, Portugal. ⟨hal-02602271⟩
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