Competition by allelopathy proceeds in traveling waves: colicin-immune strain aids colicin-sensitive strain

Producing toxic chemicals to suppress both the growth and survivorship of local competitors is called allelopathy; some strains of the bacteria Escherichia coli produce a toxin (named colicin) which may kill colicin-sensitive neighbors while they themselves are immune. In a previous paper, the competitive outcome between colicin-producing and colicin-sensitive strains was shown to differ between a spatially structured and a completely mixed population. In this paper, we analyze the role of a third, "colicin-immune," strain, which does not produce colicin but is immune to it. Without spatial structure, the colicin-immune strain suppresses the colicin-producing strain and enables the colicin-sensitive strain to win. In a spatially structured population, modeled as a reaction-diffusion system, we examine the speed of boundaries between areas dominated by different strains in traveling waves and the events after the collision of two such boundaries. The colicin-immune strain passes through the area dominated by the colicin-sensitive strain and drives the colicin-producing strain to extinction. Subsequently the colicin-sensitive strain occupies the whole population.