The ability of rare types to invade populations is important for the maintenance of diversity and spread of beneficial variants. Spatial structure promotes strategies of interference competition by limiting diffusion of interference toxins and resources, often allowing interference competitors to invade when rare. Consistent with previous results in other microbial systems, toxin production by Saccharomyces cerevisiae is advantageous in spatially structured, high-density environments, but not in unstructured environments. However, at low density and at low frequency, rare toxin producers cannot invade populations of common, sensitive, toxin nonproducers. This is because the likelihood of interaction between toxin producers and sensitives depends upon the density and frequency of both competitors.