Professor Hakoyama Publishes arXiv Preprint on Confidence Intervals for Extinction Risk
Hakoyama, H. (2025). Confidence Intervals for Extinction Risk: Validating Population Viability Analysis with Limited Data. arXiv preprint.
DOI: 10.48550/arXiv.2509.09965
PDF: https://arxiv.org/pdf/2509.09965
Quantitative assessment of extinction risk requires not only point estimates but also confidence intervals (CIs) that remain informative even when data are limited. However, their reliability has long been debated, since short observation spans tend to inflate uncertainty and reduce usefulness.
In this study, a new method is developed for constructing confidence intervals of the extinction probability $G$ under the Wiener process with drift, a canonical model of population viability analysis (PVA). The proposed approach uses correlated noncentral-t distributions for the transformed statistics $\hat{w}$ and $\hat{z}$, derived from the estimators of drift and variance, and exploits the geometric properties of $G(\hat{w},\hat{z})$ in parameter space.
Monte Carlo experiments show that the proposed intervals maintain nominal coverage while achieving narrower widths than conventional methods such as the delta method, moment-based approaches, and bootstrap.
A key result is that even with short time series, extinction probabilities that are very small or very large can be estimated reliably, resolving the long-standing concern that PVA fails under data scarcity.
Applying the method to three 64-year catch series for the Japanese eel (Anguilla japonica) as abundance indices, the estimated extinction risk was found to be well below the IUCN Criterion E thresholds for Critically Endangered (CR) and Endangered (EN), with sufficiently narrow and statistically precise confidence intervals. Although the Japanese eel is currently listed as Endangered (EN) under Criterion A (population decline), this analysis demonstrates that decline-based assessments substantially overestimate extinction risk in large populations.
These findings show that even under limited data conditions, extinction-risk confidence intervals can be constructed both rigorously and practically, providing empirical support for the reliability of PVA in IUCN Red List evaluations.