Density-dependent private benefit leads to bacterial mutualism.

Microorganisms produce and secrete materials that are beneficial for themselves and their neighbors. We modeled the situation when cells can produce different costly secretions which increase the carrying capacity of the population. Strains that lose the function of producing one or more secretions avoid the cost of production and can exhaust the producers. However, secreting substances provides a private benefit for the producers in a density-dependent way. We developed a model to examine the outcome of the selection among different types of producer strains from the nonproducer strain to the partial producers, to the full producer strain. We were interested in circumstances under which selection maintains partners that produce complementary secreted materials thus forming an interdependent mutualistic interaction. We show that interdependent mutualism is selected under a broad range of conditions if private benefit decreases with density. Selection frequently causes the coexistence of more and less generalist cooperative strains, thus cooperation and exploitation co-occur. Interdependent mutualism is evolved under more specific circumstances if private benefit increases with density and these general observations are valid in a well-mixed and a structured deme model. We show that the applied population structure allows the invasion of rare cooperators and supports cooperation in general.