ISAAC KLAPPER, JACK DOCKERY, AND HAL SMITH

Biological systematics studies suggest that species are discretized in niche space. That is, rather than seeing a continuum of organism types with respect to continuous environmental variations, instead observers find discrete species or clumps of species, with one clump separated from another in niche space by a gap. Here, using a simple one dimensional reaction-diffusion model with a smoothly varying environmental condition, we investigate conditions for a discrete speciation instability of a continuously varying species structure in the context of asexually reproducing microbes. We find that significant perturbation of heterogeneity is required for instability, but that conditions for such perturbations might reasonably occur, for example through influence of boundary conditions.