Confidence Intervals for Extinction Risk: Validating Population Viability Analysis with Limited Data
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arXiv
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| Format: | Preprint |
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2025
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| author | Hakoyama, Hiroshi |
| author_facet | Hakoyama, Hiroshi |
| contents | Quantitative assessment of extinction risk requires confidence intervals (CIs) that remain informative with limited data. Their usefulness has long been debated because short observation spans can make uncertainty so large that population viability analysis appears impractical. I derive new CIs for extinction probability under the drift-Wiener process, a canonical model of extinction dynamics, by introducing transformed parameters $w$ and $z$ whose maximum-likelihood estimators follow noncentral $t$ distributions. The resulting $w$-$z$ method yields CIs with coverage close to the nominal level and shows that precision depends not only on data length but also on effect size: extinction probabilities that are sufficiently low or high can often be estimated reliably even from limited time series. I also propose an observation-error-and-autocovariance-robust (OEAR) estimator for settings with additive observation error and short-run dependence. Applied to two 64-year national harvest indices for Japanese eel (Anguilla japonica), the method gives Criterion E extinction probabilities far below the IUCN threatened-category thresholds, with narrow CIs, despite the species being listed as Endangered under Criterion A. These results show that extinction-risk CIs can be both statistically rigorous and practically informative for conservation assessment under limited data. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_09965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Confidence Intervals for Extinction Risk: Validating Population Viability Analysis with Limited Data Hakoyama, Hiroshi Methodology Statistics Theory 60J60, 60J65, 62M10, 62P12, 92D25 Quantitative assessment of extinction risk requires confidence intervals (CIs) that remain informative with limited data. Their usefulness has long been debated because short observation spans can make uncertainty so large that population viability analysis appears impractical. I derive new CIs for extinction probability under the drift-Wiener process, a canonical model of extinction dynamics, by introducing transformed parameters $w$ and $z$ whose maximum-likelihood estimators follow noncentral $t$ distributions. The resulting $w$-$z$ method yields CIs with coverage close to the nominal level and shows that precision depends not only on data length but also on effect size: extinction probabilities that are sufficiently low or high can often be estimated reliably even from limited time series. I also propose an observation-error-and-autocovariance-robust (OEAR) estimator for settings with additive observation error and short-run dependence. Applied to two 64-year national harvest indices for Japanese eel (Anguilla japonica), the method gives Criterion E extinction probabilities far below the IUCN threatened-category thresholds, with narrow CIs, despite the species being listed as Endangered under Criterion A. These results show that extinction-risk CIs can be both statistically rigorous and practically informative for conservation assessment under limited data. |
| title | Confidence Intervals for Extinction Risk: Validating Population Viability Analysis with Limited Data |
| topic | Methodology Statistics Theory 60J60, 60J65, 62M10, 62P12, 92D25 |
| url | https://arxiv.org/abs/2509.09965 |