Antibiotic resistance and the evolution of group-beneficial traits. II: A metapopulation model

Inspired by the evolution of antibiotic resistance in bacteria, we have developed a model that examines the evolution of “producers” (who secrete a substance that breaks down antibiotics) and non-producers. In a previous study, we found that frequency-dependent selection could favor an intermediate frequency of producers in a single, large population. Here we develop a metapopulation model that examines the evolution of producers and non-producers. Our results indicate that in a metapopulation with many groups, each of size N, the equilibrial frequency of producers decreases with group size. Even when N is high (e.g. 150 individuals/group), however, a significant frequency of producers is still predicted. We also found that the equilibrial frequency of producers increases as the minimum numbers of producers necessary to provide protection to non-producers increases. Lastly, increasing the benefit/cost ratio (b/c) for producers increases their equilibrial frequency.