  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 predicting
quantitative trends and the phase diagram.
