Tragedy of the commons in the chemostat

Martin Schuster, Eric Foxall, David Finch, Hal Smith, Patrick De Leenheer

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present a proof of principle for the phenomenon of the tragedy of the commons that is at the center of many theories on the evolution of cooperation. Whereas the tragedy is commonly set in a game theoretical context, and attributed to an underlying Prisoner’s Dilemma, we take an alternative approach based on basic mechanistic principles of species growth that does not rely on the specification of payoffs which may be difficult to determine in practice. We establish the tragedy in the context of a general chemostat model with two species, the cooperator and the cheater. Both species have the same growth rate function and yield constant, but the cooperator allocates a portion of the nutrient uptake towards the production of a public good -the “Commons” in the Tragedy- which is needed to digest the externally supplied nutrient. The cheater on the other hand does not produce this enzyme, and allocates all nutrient uptake towards its own growth. We prove that when the cheater is present initially, both the cooperator and the cheater will eventually go extinct, hereby confirming the occurrence of the tragedy. We also show that without the cheater, the cooperator can survive indefinitely, provided that at least a low level of public good or processed nutrient is available initially. Our results provide a predictive framework for the analysis of cooperator-cheater dynamics in a powerful model system of experimental evolution.

Original languageEnglish (US)
Article numbere0186119
JournalPLoS One
Volume12
Issue number12
DOIs
StatePublished - Dec 1 2017

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Chemostats
nutrient uptake
Nutrients
nutrients
Growth
dynamic models
Food
Social Justice
Theoretical Models
enzymes
Enzymes
Specifications

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)

Cite this

Schuster, M., Foxall, E., Finch, D., Smith, H., & De Leenheer, P. (2017). Tragedy of the commons in the chemostat. PLoS One, 12(12), [e0186119]. https://doi.org/10.1371/journal.pone.0186119

Tragedy of the commons in the chemostat. / Schuster, Martin; Foxall, Eric; Finch, David; Smith, Hal; De Leenheer, Patrick.

In: PLoS One, Vol. 12, No. 12, e0186119, 01.12.2017.

Research output: Contribution to journalArticle

Schuster, M, Foxall, E, Finch, D, Smith, H & De Leenheer, P 2017, 'Tragedy of the commons in the chemostat', PLoS One, vol. 12, no. 12, e0186119. https://doi.org/10.1371/journal.pone.0186119
Schuster M, Foxall E, Finch D, Smith H, De Leenheer P. Tragedy of the commons in the chemostat. PLoS One. 2017 Dec 1;12(12). e0186119. https://doi.org/10.1371/journal.pone.0186119
Schuster, Martin ; Foxall, Eric ; Finch, David ; Smith, Hal ; De Leenheer, Patrick. / Tragedy of the commons in the chemostat. In: PLoS One. 2017 ; Vol. 12, No. 12.
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