The false classification of extinction risk in noisy environments

Abundance trends are the basis for many classifications of threat and recovery status, but they can be a challenge to interpret because of observation error, stochastic variation in abundance (process noise) and temporal autocorrelation in that process noise. To measure the frequency of incorrectly detecting a decline (false-positive or false alarm) and failing to detect a true decline (false-negative), we simulated stable and declining abundance time series across several magnitudes of observation error and autocorrelated process noise. We then empirically estimated the magnitude of observation error and autocorrelated process noise across a broad range of taxa and mapped these estimates onto the simulated parameter space. Based on the taxa we examined, at low classification thresholds (30% decline in abundance) and short observation windows (10 years), false alarms would be expected to occur, on average, about 40% of the time assuming density-independent dynamics, whereas false-negatives would be expected to occur about 60% of the time. However, false alarms and failures to detect true declines were reduced at higher classification thresholds (50% or 80% declines), longer observation windows (20, 40, 60 years), and assuming density-dependent dynamics. The lowest false-positive and false-negative rates are likely to occur for large-bodied, long-lived animal species.