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Theory of cooperation in a micro-organismal snowdrift game

Zhenyu Wang and Nigel Goldenfeld
Phys. Rev. E 84, 020902(R) – Published 26 August 2011

Abstract

We present a mean-field model for the phase diagram of a community of micro-organisms, interacting through their metabolism so that they are, in effect, engaging in a cooperative social game. We show that as a function of the concentration of the nutrients glucose and histidine, the community undergoes a phase transition separating a state in which one strain is dominant to a state which is characterized by coexisting populations. Our results are in good agreement with recent experimental results, correctly reproducing quantitative trends and predicting the phase diagram.

  • Figure
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  • Received 1 November 2010

DOI:https://doi.org/10.1103/PhysRevE.84.020902

©2011 American Physical Society

Authors & Affiliations

Zhenyu Wang and Nigel Goldenfeld

  • Department of Physics, Center for the Physics of Living Cells and Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Loomis Laboratory of Physics, 1110 West Green Street, Urbana, Illinois 61801, USA

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Issue

Vol. 84, Iss. 2 — August 2011

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