Black Queen Hypothesis, partial privatization, and quorum sensing evolution

Microorganisms produce costly cooperative goods whose benefit is partially shared with nonproducers, called ‘mixed’ goods. The Black Queen Hypothesis predicts that partially privatization of benefits from the mixed goods has two major evolutionary implications. First, to favor strains producing several mixed goods over nonproducing strains. Second, to favor the maintenance of cooperative traits through different strains instead of having all cooperative traits present in a single strain (metabolic specialization). Despite the importance of quorum sensing regulation of mixed goods, it is not clear how partial privatization of benefits affects quorum sensing evolution. Here, we studied the influence of partial privatization of benefits on the evolution of quorum sensing. We developed a mathematical population genetics model of an unstructured microbial population considering four strains that differ in their ability to produce an autoinducer (quorum sensing signaling molecule) and a mixed good. Our model assumes that the production of the autoinducers and the mixed goods is constitutive and/or depends on quorum sensing. Our results suggest that partially privatized benefits cannot foster quorum sensing. This result occurs because: (1) a strain that produces both autoinducer and good (fully producing strain) cannot persist in the population; (2) the strain only producing the autoinducer and the strain producing mixed goods in response to the autoinducers cannot coexist, i.e., metabolic specialization cannot be fostered.