We examine the degree to which fitting simple dynamic models to time series
of population counts can predict extinction probabilities. This is both an
active branch of ecological theory and an important practical topic for re
source managers. We introduce an approach that is complementary to recently
developed techniques for estimating extinction risks (e.g., diffusion appr
oximations) and, like them, requires only count data rather than the detail
ed ecological information available for traditional population viability an
alyses. Assuming process error, we use four different models of population
growth to generate snapshots of population dynamics via time series of the
lengths commonly available to ecologists. We then ask to what extent we can
identify which of several broad classes of population dynamics is evident
in the time series snapshot Along the way, we introduce the idea of "variat
ion thresholds," which are the maximum amount of process error that a popul
ation may withstand and still have a specified probability of surviving for
a given length of time. We then show how these thresholds may be useful to
both ecologists and resource managers, particularly when dealing with larg
e numbers of poorly understood species, a common problem faced by those des
igning biodiversity reserves.