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actually been observed among environmental and clinical isolates [13, 14] The ques-
tion then is, under what conditions cheating strains will increase to such an extent
that QS breaks down as a regulatory system of cooperative behaviorperhaps with the
consequence that the cooperative behavior itself cannot be maintained.
Brookfi eld [15] and Brown and Johnstone [16] have analyzed models of the evolu-
tion of bacterial QS. Although differing in modeling approach, both have studied the
evolution of QS in the context of explicit 2-level selection, where selection at the indi-
vidual level operates against cooperation, while selection at the group level favors QS.
These studies conclude that under fairly broad conditions either stable polymorphism
may arise in bacterial populations between strains that exhibit QS and strains that do
not [15] or the average resource investment into quorum signaling takes positive val-
ues, the actual investment depending on group size and within-group relatedness [16].
Since kin selection appears to be central for the evolution of altruistic cooperation, it
is required that cooperation preferentially takes place among related individuals. As
Hamilton [2] suggested, this could be brought about either by kin discrimination or
by limited dispersal. The fi rst mechanism may play some role in microbial communi-
ties, for example if a public good produced by a specifi c strain can only be utilized
by clonemates [10]. However, limited dispersal is probably much more important in
microbes because due to the clonal reproduction mode it would tend to keep close rela-
tives together. This implies that the spatial population structure plays a key role in the
evolution of bacterial cooperation.
In a previous work [17] we have analyzed the evolutionary stability of QS using a
CA approach, which is eminently suitable to investigate the role of spatial population
structure. There we asked whether QS could be stable as a regulatory mechanism of
bacteriocin (anti-competitor toxin) production, and concluded that it could be main-
tained only when the competing strains were unrelated, and not when the bacteriocin is
aimed at related strains which can share the signaling and responding genes involved
in QS.
Here, we analyze a much more general model of the evolution of QS regulated
cooperation, again using the CA approach. In fact, QS regulated cooperation can be
viewed as a superposition and interaction between two cooperative behaviors: the co-
operative QS communication system which coordinates another cooperative behavior
(e.g., production of a public good). Both forms of cooperation are potentially vulner-
able to being parasitized by cheating strains. We allow the reward and the cost of coop-
eration, the level of dispersal and the sensitivity of the QS system (the signal strength
required to induce production of a public good) to vary, and ask for which parameter
combinations cooperation and QS will evolve and be maintained, to what extent the
presence of a QS system affects the evolution and maintenance of cooperation, how
vulnerable the system is for social cheating and how equilibrium levels of QS and
cooperation depend on the parameter values.
MATERIALS AND METHODS
The model we use is a two-dimensional CA of toroidal lattice topology. Each of the
300 × 300 grid-points of the square lattice represent a site for a single bacterium; all
