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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 appro...

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Detalles Bibliográficos
Autores principales: Schuster, Martin, Foxall, Eric, Finch, David, Smith, Hal, De Leenheer, Patrick
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5737893/
https://www.ncbi.nlm.nih.gov/pubmed/29261671
http://dx.doi.org/10.1371/journal.pone.0186119
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author Schuster, Martin
Foxall, Eric
Finch, David
Smith, Hal
De Leenheer, Patrick
author_facet Schuster, Martin
Foxall, Eric
Finch, David
Smith, Hal
De Leenheer, Patrick
author_sort Schuster, Martin
collection PubMed
description 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.
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spelling pubmed-57378932017-12-29 Tragedy of the commons in the chemostat Schuster, Martin Foxall, Eric Finch, David Smith, Hal De Leenheer, Patrick PLoS One Research Article 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. Public Library of Science 2017-12-20 /pmc/articles/PMC5737893/ /pubmed/29261671 http://dx.doi.org/10.1371/journal.pone.0186119 Text en © 2017 Schuster et al http://creativecommons.org/licenses/by/4.0/ This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Schuster, Martin
Foxall, Eric
Finch, David
Smith, Hal
De Leenheer, Patrick
Tragedy of the commons in the chemostat
title Tragedy of the commons in the chemostat
title_full Tragedy of the commons in the chemostat
title_fullStr Tragedy of the commons in the chemostat
title_full_unstemmed Tragedy of the commons in the chemostat
title_short Tragedy of the commons in the chemostat
title_sort tragedy of the commons in the chemostat
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5737893/
https://www.ncbi.nlm.nih.gov/pubmed/29261671
http://dx.doi.org/10.1371/journal.pone.0186119
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