The ratio of public and private benefit determines sensitivity to catastrophic population collapse in a microbial Volunteer’s dilemma

Guy Harvey Oceanographic Center Facility

Abstract Cooperation plays diverse roles in bacteria, plants, animals, and humans. Cheaters, who capture the public benefits without paying the associated costs, can often outcompete cooperators and make the entire population more sensitive to collapse under adverse conditions. One mechanism to cooperate is to produce a public good whose benefit is shared. The production of a public good appears evolutionarily unstable, because cooperation tends to decrease the fitness of the individual, while promoting those of others that did not produce the public good themselves (i.e., cheaters). As a result, cheaters seem to hold a fitness advantage, and thus should outcompete cooperators. However, cooperation can persist in the presence of cheaters. One mechanism that can account for the persistence of public goods, and thus cooperation, is that public goods can have private benefits that are retained by the cooperator. While theoretical and experimental studies have examined the use of public goods in cooperation, studies have yet to determine how the ratio of public and private benefit affects growth and survival of populations consisting of cooperators and cheaters. To address this question, we used a mathematical simulation alongside a microbial cooperator-cheater system to demonstrate that the balance between public and private benefit of a public good determines the sensitivity of the population to catastrophic population collapse in a well-mixed environment. Specifically, we find that populations consisting of both cooperators and cheaters are most sensitive to collapse at intermediate initial percentages of cheaters. This sensitivity increases as the ratio of public to private good decreases. Furthermore, if the public good provides a sufficiently large private benefit and a weak public benefit, we find that increasing the amount of a stressor can counterintuitively increase total population growth. Overall our results contribute to our understanding of the principles that guide the maintenance and stability of cooperation, and may have implications in infectious disease.