  When a collection of phenotypically diverse organisms compete with each other
for limited resources, with competition being strongest amongst the most
similar, the population can evolve into tightly localised clusters. This
process can be thought of as a simple model of the emergence of species. Past
studies have neglected the effects of demographic noise and studied the
population on a macroscopic scale, where species formation is found to depend
upon the shape of the curve describing the decline of competition strength with
phenotypic distance. In the following, we will show how including the effects
of demographic noise leads to a radically different conclusion. Two situations
are identified: a weak-noise regime in which the population exhibits patterns
of fluctuation around the macroscopic description, and a strong-noise regime
where species appear spontaneously even in the case that all organisms have
equal fitness.
