Frank, S. A. 1994. Spatial polymorphism of bacteriocins and other allelopathic traits. Evolutionary Ecology 8:369-386.

Many bacterial species carry plasmids that encode both the production of a highly specific toxin (bacteriocin) that kills competitors of the same species, and immunity to that toxin. A great diversity of bacteriocins is produced within a single species. I present a model for the dynamics of competition between allelopathic and susceptible types. The model applies to most kinds of allelopathic competition. My primary goal is, however, to explain the widespread genetic polymorphism for bacteriocins. The model includes competition for scarce resources, competition through toxin production, spatial diffusion of individuals and toxins at varying rates, and spatial variation in habitat quality. I draw three main conclusions from this “reaction-diffusion” model. (1) Polymorphism of toxic producers and susceptibles cannot be maintained within a single spatial location when individuals and the toxin mix randomly. (2) Susceptibles are generally favored in poor habitats, where the rate of resource competition per interaction increases relative to the resource-independent rate of toxic killing. By contrast, toxic producers are generally favored in good habitats, where the rate of resource competition is lower. (3) Spatial variation in habitat quality can lead to spatial polymorphism; susceptibles tend to win in poor habitats, and producers tend to win in good habitats.