Geometric Brownian motion is a commonly used model in theoretical
population biology. Here that model is augmented to allow for movement
between a finite number of spatially heterogeneous "patches" within the
environment. It is seen that peripatetic organisms may inhabit such an
environment even when each individual patch is unfavorable enough to
guarantee extinction in the absence of migration.
The content of the talk is taken largely from "Stochastic Population
Growth in Spatially Heterogeneous Environments," by Evans, Ralph,
Schreiber, and Sen (arXiv.org).