Small population effects in stochastic population dynamics

The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results. Supported in part by DOE Office of Basic Science, Chemical Division. Reported at SMB03, the August 2003 meeting of the Society for Mathematical Biology.