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Test 03 — Extinction risk scales with generation time

README.md

# Test 03 — Extinction risk scales with generation time

**Result.** The published claim is backwards on its own central comparison, and the either–or it proposes does not survive. Across 7,319 tetrapod species with observed body mass, observed maximum longevity and an observed IUCN assessment, the risk of being listed Vulnerable, Endangered or Critically Endangered **rises** with longevity, not falls: each standard deviation of log longevity multiplies the odds of being threatened by 1.55 (95% CI on the log-odds 0.35–0.52). Body mass does nearly the same work (OR 1.48 per SD, 95% CI 0.31–0.47), and on its own it sorts threatened from non-threatened species slightly **better** than longevity does (AUC 0.674 versus 0.656; difference −0.018, genus-cluster bootstrap 95% CI −0.042 to +0.005). The claim's illustration — a small short-lived species at higher risk than a large long-lived one — is exactly inverted in these data: 9.9% of small short-lived species are threatened, against 29.4% of large long-lived ones.

The honest summary is not "mass wins". It is that the dichotomy is false. Both traits carry independent signal, mass is at least as informative as the longevity proxy, and the direction of the longevity effect is the opposite of the one posted.

## What was tested

The hypothesis is quoted verbatim in `hypothesis.md`, together with the support and refutation criteria written before any number was computed. In brief, the entry claims that extinction risk "scales inversely with generation time rather than with body size", predicts that risk correlates with generation time better than with mass (P1), that "small long-lived species should be high risk" (P2), and that recovery rate should scale with generation time (P3). The refutation is that risk tracking mass at controlled generation time would restore the mass proxy.

The entry contradicts itself about the sign: the claim and its illustration imply that longer generation time means lower risk, while P2 implies that long life at small size means higher risk. We therefore tested both directions rather than choosing the convenient one.

## Method

- **Data.** TetrapodTraits 3.0.1 (Zenodo 10.5281/zenodo.22536349), one row per species, 33,281 species in the file. The primary sample keeps species with a non-imputed IUCN category in LC/NT/VU/EN/CR, non-imputed body mass and observed maximum longevity: **7,319 species** (628 amphibians, 2,472 birds, 2,437 mammals, 1,782 reptiles). Extinct and extinct-in-the-wild species are excluded because they are outcomes rather than risks.
- **Proxy.** The database gives maximum longevity, not generation time. Generation time is typically a fraction of maximum longevity, so the proxy rescales the variable without reordering species; this is stated as a limitation, not a footnote.
- **Model.** Logistic regression of threatened status on standardised log10 longevity, standardised log10 body mass and class fixed effects, with analytical standard errors and a 500-repetition genus-cluster bootstrap. Genus clustering is a crude stand-in for phylogeny; it is not a phylogenetic comparative model.
- **Discrimination.** Rank-based AUC for each trait alone, and for the fitted joint model, with the same bootstrap.
- **Quadrants.** Sample medians of mass (93 g) and longevity (10.1 years) split the sample into four cells.

## Result

**Direction.** Longer-lived species are more threatened, in the pooled model and inside every class. The joint model gives a longevity coefficient of +0.435 (SE 0.044) and a mass coefficient of +0.391 (SE 0.041); both are far from zero. In raw units, a tenfold increase in maximum longevity multiplies the odds of being threatened by 2.82; a tenfold increase in mass multiplies them by 1.39. The decile curve (figure 1) rises apart from one dip in the fourth decile, and rises from 10.7% in the shortest-lived tenth to 43.7% in the longest-lived tenth, with a single dip in the fourth decile.

**Which trait sorts better.** Longevity alone reaches AUC 0.656 (bootstrap 95% CI 0.629–0.680); mass alone reaches 0.674 (0.647–0.702). The joint model reaches 0.718. The difference between the two single-trait AUCs is −0.018 with a CI that includes zero, so the honest statement is that they are hard to separate and mass is, if anything, ahead — not that longevity is better, as P1 requires.

**The quadrant test.** If P2 were right, the small-long-lived cell would be the high-risk one. It is the second-lowest:

| | short-lived | long-lived |
|---|---:|---:|
| small | 9.9% (n = 2,563) | 15.9% (n = 1,095) |
| large | 18.7% (n = 1,078) | 29.4% (n = 2,583) |

The interaction between small size and long life is negative and imprecise (OR 0.86, p = 0.28), which is the opposite sign to P2 and not distinguishable from no interaction.

**Within classes.** The longevity coefficient is positive in all four classes and significant in all four: amphibians +0.39 (p = 0.003), birds +0.48, mammals +0.39, reptiles +0.45. Mass is positive and significant in birds, mammals and reptiles, and slightly negative and non-significant in amphibians (−0.10, p = 0.53). The result is not an artefact of pooling birds with amphibians.

**P3 is untestable here.** Recovery rate after perturbation is not in the database. We did not substitute a different quantity and call it P3.

## Sensitivity

- Admitting species whose IUCN status is imputed (n = 7,428) leaves the coefficients at 0.438 (longevity) and 0.387 (mass).
- Trimming the top and bottom 1% of body mass (n = 7,184) leaves longevity at 0.432 but raises mass to 0.471 — mass becomes the larger coefficient. This is the one specification in which the claim's first criterion is met, and it is met by the *refutation's* variable.
- Longevity in quintiles gives a monotone odds ratio against the shortest-lived quintile: 1.24, 1.53, 1.57, 2.75. The log-linear form is not hiding a threshold; the top quintile is simply much more exposed.

## What this test cannot see

Species are not independent observations. Shared ancestry means the effective sample is far smaller than 7,319, and a phylogenetic logistic regression could shrink or reverse a coefficient that is driven by clade composition. Genus-cluster bootstrap intervals address the clustering only crudely. The longevity proxy is not generation time, and the database's observed-longevity subset is biased toward species someone has kept or studied in captivity — amphibians and reptiles in particular. IUCN categories are themselves partly assessed from range and population trends that correlate with body size and life history, so some of the association is definitional: a large, slow-breeding species is easier to list. Finally, the analysis is cross-sectional: it says nothing about which trait causes decline, only which trait marks listed species.

## Disclosure

Designed and executed with AI assistance (DeepSeek, via its coding agent). Not peer reviewed. This is a comparative analysis of published conservation assessments, not ecological advice.

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*Figures: `figures/threat_by_longevity_decile.png`, `figures/discrimination.png`, `figures/quadrants.png`. Numbers: `results.json`. Data: `data.csv`. Fetch and hash record: `SOURCE.md`.*

hypothesis.md

# Hypothesis, quoted verbatim, and pre-specified criteria

**Source.** *Original Theories*, Volume VIII, entry 25 (slug `extinction-scales-with-generation-time`), published in the Incoprea research notebook at `incoprea.com/research`. Quoted from the corpus export `frontier-theories-8/build/data_v8_2.py`.

## The claim, verbatim

> Extinction risk scales inversely with generation time rather than with body size, so a small short-lived species can be at higher risk than a large long-lived one in the same habitat.

**Mechanism, verbatim.** (not stated in the source entry; the entry gives predictions instead)

**Predictions, verbatim.**

- P1: Risk should correlate with generation time better than with mass.
- P2: Small long-lived species should be high risk.
- P3: Recovery rate should scale with generation time.

**Refutation, verbatim.**

> Risk tracking mass at controlled generation time would restore the proxy.

## A defect in the claim, noted before the test

The claim says risk scales *inversely* with generation time, and its illustration says a small **short-lived** species can be at higher risk than a large **long-lived** one. Both imply that longer generation time means **lower** risk (a negative slope). P2 says the opposite: **small long-lived** species should be at **high** risk (a positive slope). The entry is internally inconsistent about the sign.

We therefore pre-specify two directional tests rather than one:

- **D1 (claim sentence):** threatened probability falls as generation time rises, controlling for body mass.
- **D2 (prediction P2):** threatened probability rises with generation time at small body mass (positive interaction between small mass and long life).

Both are reported. If they disagree, the direction of the claim is unresolved by these data and we say so.

## Operationalisation

- **Generation time.** The database gives maximum longevity, not generation time. We use `MaxLongevity` (years) as the proxy, and state in the README that generation time is typically a fraction of maximum longevity, so the proxy scales the variable but does not change its rank order. Longevity is observed, not imputed, in the primary sample.
- **Body size.** `BodyMass_g`, observed.
- **Extinction risk.** IUCN category from `ThreatStatus`: threatened = VU + EN + CR versus LC + NT. EX and EW are excluded (they are outcomes, not risks), as are the legacy LR codes. Species whose status is imputed (`ImputedThreatStatus = 1`) are excluded from the primary sample and re-admitted in a sensitivity analysis.
- **Unit and scope.** Species are the unit, all tetrapods with observed longevity and mass. Species are not independent (shared ancestry), so p-values are read as descriptive and every interval is a genus-cluster bootstrap.

## Pre-specified support and refutation

The test is **supported** if all three hold:

1. In the joint model with class fixed effects, standardised log-longevity has a larger absolute coefficient than standardised log-mass, and its 95% cluster-bootstrap interval excludes zero.
2. Longevity alone discriminates threatened from non-threatened species better than mass alone (difference in AUC > 0 with a 95% cluster-bootstrap interval excluding zero).
3. The sign matches D1 or D2 consistently, and the quadrant test in P2 points the same way.

The **refutation** holds if, at controlled longevity, mass carries the larger and more precise coefficient, or if the AUC ranking reverses. A null result — neither variable discriminating — is reported as a failure to decide, not as support for either account.

**P3 is not testable with this database.** It requires recovery trajectories after perturbation, which TetrapodTraits does not contain. We say so rather than substituting a different quantity.

## Sensitivity analyses (named before running)

1. Include imputed threat statuses.
2. Birds only, then mammals only (the two classes with the densest longevity data).
3. Drop the top and bottom 1% of body mass.
4. Ordinal outcome (LC < NT < VU < EN < CR) via proportional-odds, as an alternative to the binary split.
5. Longevity in five bins, to check that the log-linear form is not hiding a threshold.

## What would change the answer

A phylogenetic comparative analysis (PGLS or phylogenetic logistic regression) with a dated tree could reverse a coefficient that is driven by clade composition. We do not have the tree in this package, and we flag the omission as the largest limitation rather than pretending the species-level p-values carry phylogenetic weight.

Included code and results

• tests/03-tetrapod-generation/data.csv
• tests/03-tetrapod-generation/results.json
• tests/03-tetrapod-generation/run.py