Variation Thresholds for Extinction and Their Implications for Conservation Strategies.

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 resource managers. We introduce an approach that is complementary to recently developed techniques for estimating extinction risks (e.g., diffusion approximations) and, like them, requires only count data rather than the detailed ecological information available for traditional population viability analyses. 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 "variation thresholds," which are the maximum amount of process error that a population 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 large numbers of poorly understood species, a common problem faced by those designing biodiversity reserves.