Toxin-mediated competition in weakly motile bacteria

•Competition between toxin-producing and toxin-susceptible bacteria is modelled by extending classical two-species Lotka–Volterra competition in one spatial dimension to explicitly include toxin production by one species.•Solutions are constructed comprising two single-species colonies, forming travelling waves in which one colony expands at the expense of the other.•For a sufficiently strong toxin, the susceptible species cannot grow near the producing colony. Thus an inhibition zone is formed, an area void of bacteria that separates the two colonies.•Once an inhibition zone is formed, the two species no longer compete locally for resources, allowing the producer to increase its colony size effectively unimpeded by the susceptible.