Tragedy of the commons in the chemostat

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...

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Bibliographic Details
Published in:PloS one 2017-12, Vol.12 (12), p.e0186119-e0186119
Main Authors: Schuster, Martin, Foxall, Eric, Finch, David, Smith, Hal, De Leenheer, Patrick
Format: Article
Language:English
Subjects:
Behavior
Behavioral evolution
Biological evolution
Biology and Life Sciences
Competitive advantage
Conflicts of interest
Cooperation
Dynamic tests
Ecology and Environmental Sciences
Enzymes
Evolution
Game Theory
Growth rate
Low level
Models, Chemical
Nutrient availability
Nutrient uptake
Nutrients
Physical Sciences
Population
Prisoner Dilemma
Pseudomonas aeruginosa
Social Sciences
Species
Tragedy of the commons
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0186119