Title: Species coexistence and metapopulation persistence in
stochastic environments

Abstract: Populations, whether they be viral particles, bio-chemicals,
plants or animals, experience temporal and spatial fluctuations in
abiotic factors such as temperature, nutrient availability, and
precipitation. This environmental variation in conjunction with biotic
interactions can facilitate or disrupt persistence of the populations.
Understanding the precise nature of these interactive effects is a
central issue in population biology receiving increasing attention
from theoretical, empirical, and applied perspectives.

One approach to examining the interplay between these deterministic
and stochastic forces is the construction and analysis of stochastic
difference/differential equations. In this talk, I will discuss recent
results on stochastic persistence and boundedness for these models.
Stochastic boundedness asserts that asymptotically the population
process tends to remain in compact sets. In contrast, stochastic
persistence requires that the population process tends to be
``repelled'' by some ''extinction set''. Using the theory, I will
illustrate how environmental noise can facilitate coexistence of
competing species and how dispersal in stochastic environments can
rescue locally extinction prone populations. Empirical demonstrations
of the theory from Kansas prairies, acorn woodpecker populations, and
microcosm experiments will be discussed.