Extinction and exponential growth in random environments.

The influence of randomly varying environments on unrestricted population growth and extinction is analyzed by means of branching processes with random environments (BPRE). A main theme is the interplay between environmental and sampling (or “demographic”) variability. If the two sources of variationg are of comparable magnitude, the environmental variation will dominate except as regards the event of extinction.A diffusion approximation of BPRE is proposed to study the situation of a large population with small environmental variance and mean offspring size near one.Comments on the ecological literature as well as on the relation of the results to previous work involving stochastic differential equations are also given.