Confidence intervals for extinction risk: Validating population viability analysis with limited data

Abstract The assessment of extinction risk remains a key component of IUCN and CITES evaluations. However, it has been argued that, under realistic data limitations, confidence intervals (CIs) for extinction probability often span the entire 0–1 range, rendering such assessments meaningless. I revisit the issue by analytically deriving accurate CIs under the drift–Wiener process, a canonical model of extinction dynamics. In this model, extinction probability depends on the time horizon, growth rate, environmental variance and initial population size relative to the threshold. As functions of the original parameters, I define two transformed parameters, and , whose maximum‐likelihood estimators follow noncentral distributions. When the initial population is far above the threshold relative to expected drift and environmental variability (), asymptotically reduces to a function of alone, enabling exact CIs. In contrast, for , the estimates of and are strongly negatively correlated, so I construct a CI for by evaluating at opposite corners of the confidence rectangle for . This yields CIs with accurate nominal coverage. Using this approach, I examine how the observation span of available time series affects the width of the CI for extinction probability. A key finding is that the CI width depends on both the data and the parameters, particularly on effect size—the distance between the true and the maximally uncertain midpoint (). Even with limited time‐series data, extinction probabilities that are sufficiently low or high can be reliably estimated, addressing a long‐standing concern that population viability analysis (PVA) becomes unreliable under data scarcity. I also propose an observation‐error‐and‐autocovariance‐robust (OEAR) estimator for under additive observation error and short‐run dependence. Applying this method to two 64‐year national harvest indices for Japanese eel ( Anguilla japonica ), I find that Criterion E extinction probabilities are far below the thresholds for the IUCN threatened categories, with narrow CIs. Although the species is currently listed as Endangered under Criterion A (population decline), this discrepancy is consistent with theory showing that decline‐based assessments can substantially overestimate extinction risk in large populations.