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To explain the stability of cooperation is a central task of evolutionarytheory. 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 acostly public good (PG) that equally benefits all members of a communitydivided into multiple, distinct patches (multilevel selection). Cost andbenefit are non-linear functions of the PG production. The analysis ofevolutionary stability yields an optimization problem for the expression of PGin dependency on the number of QS individuals within a colony. We find that theoptimal total PG production of the QS population mainly depends on the shape ofthe benefit. A graded and a switch-like response is possible, in accordancewith earlier results. Interestingly, at the level of the individual cell, theQS response is determined by the shape of the costs. All QS individuals respondeither homogeneously if cost are a convex function of the PG production rate,or they respond heterogeneously with distinct ON/OFF responses if the costs areconcave. The latter finding is consistent with recent experimental findings,and contradicts the usual interpretation of QS as a mechanism to establish auniform, synchronized response of a bacterial population.

Homogeneous and Heterogeneous Response of Quorum-Sensing Bacteria in an Evolutionary Context