Persistence in the shadow of killers

Killing is perhaps the most definite form of communication possible. Microbes such as yeasts and gut bacteria have been shown to exhibit killer phenotypes. The killer strains are able to kill other microbes occupying the same ecological niche, and do so with impunity. It would therefore be expected that, wherever a killer phenotype has arisen, all members of the population would soon be killers or dead. Surprisingly, (1) one can find both killer and sensitive strains in coexistence, both in the wild and in in vitro experiments, and (2) the absolute fitness cost of the killer phenotype often seems to be very small. We present an explicit model of such coexistence in a fragmented or discrete environment. A killer strain may kill all sensitive cells in one patch (one piece of rotting fruit, one cave or one human gut, for example), allowing sensitives to exist only in the absence of killer strains on the same patch. In our model, populations spread easily between patches, but in a stochastic manner: one can imagine spores borne by the wind over a field of untended apple trees, or enteric disease transmission in a region in which travel is effectively unrestricted. What we show is that coexistence is not only possible, but that it is possible even if the absolute fitness advantage of the sensitive strain over the killer strain is arbitrarily small. We do this by performing a specifically targeted mathematical analysis on our model, rather than via simulations. Our model does not assume large population densities, and may thus be useful in the context of understanding the ecology of extreme environments.