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

Hakoyama, H.

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 G 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, w and z, whose maximum-likelihood estimators follow noncentral t distributions. When the initial population is far above the threshold relative to expected drift and environmental variability (z >> 0), G asymptotically reduces to a function of w alone, enabling exact CIs. In contrast, when z is much less than 0, the estimates of w and z are strongly negatively correlated, so I construct a CI for G by evaluating G(w,z) at opposite corners of the confidence rectangle for (w,z). 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 G and the maximally uncertain midpoint (G ~ 0.5). 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 G(w,z) 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.

Key Words: confidence intervals, extinction probability, IUCN Red List criteria, limited data, observation-error-and-autocovariance-robust estimator, population viability analysis, sensitivity analysis, wiener process with drift