  To explain the stability of cooperation is a central task of evolutionary
theory. We investigate this question in the case of quorum sensing (QS)
bacteria, which regulate cooperative traits in response to population density.
Cooperation is modeled by the prisoner's dilemma, where individuals produce a
costly public good (PG) that equally benefits all members of a community
divided into multiple, distinct patches (multilevel selection). Cost and
benefit are non-linear functions of the PG production. The analysis of
evolutionary stability yields an optimization problem for the expression of PG
in dependency on the number of QS individuals within a colony. We find that the
optimal total PG production of the QS population mainly depends on the shape of
the benefit. A graded and a switch-like response is possible, in accordance
with earlier results. Interestingly, at the level of the individual cell, the
QS response is determined by the shape of the costs. All QS individuals respond
either homogeneously if cost are a convex function of the PG production rate,
or they respond heterogeneously with distinct ON/OFF responses if the costs are
concave. The latter finding is consistent with recent experimental findings,
and contradicts the usual interpretation of QS as a mechanism to establish a
uniform, synchronized response of a bacterial population.
