The tragedy of the commons in the chemostat

The question of the evolution of and sustainability of cooperative behavior is a much studied topic in ecology. It has often been asserted that in a competitive mixed population of cooperators and dependent cheaters, both will be driven to extinction. In reference to Lloyd's 1833 story of herders, this is often called the tragedy of the commons. We give an explicit model, in the setting of the chemostat, where the expected outcome can be established as a theorem. This is joint work with Martin Schuster, Eric Foxall, Hal Smith, and Patrick De Leenheer.