Hypothesis Test 12 — Extinction Risk Scales With Size
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
report.md
# Hypothesis Test 12 — Extinction Risk Scales With Size
**Test ID:** 12-extinction-size
**Theory:** 21/Paleontology · Extinction Risk Scales With Size (Incoprea Theory, Volume V, 2026)
**Date of test:** 2026-10-30
## Source (verbatim)
From `[local provenance path] Theories Vol V - 2026-10-30/theories/extinction-risk-scales-with-size.html`:
**Claim** (section 01, "The evidence"):
> "A three-quarter power scaling of extinction risk in Late Pleistocene mammals has been reported, together with a new theory of the size selectivity of extinction, which makes the exponent the object of explanation."
> "Body size downgrading of mammals over the late Quaternary has been documented as a systematic pattern, which is the aggregate signature a power-law selectivity would produce."
**Prediction** (section 03, "The theory"):
> "If risk scales as a power of body size, then the selectivity of an event is summarised by the exponent, and different mechanisms produce different exponents. Hunting, for instance, should select more steeply than climate, because it targets large individuals directly. … The prediction is that the exponent should be measurable and should differ between events with different suspected drivers, and that the same driver should produce a consistent exponent across regions."
Section 05 formalizes: **P1** risk should scale as a power of body size rather than stepwise; **P2** the exponent should differ between hunting-driven and climate-driven events; **P3** the same driver should give a consistent exponent across regions.
**Refutation** (section 06, "What would refute it"):
> "Selectivity that is stepwise rather than power-law, with no exponent differences between drivers, would leave the categorical account adequate."
## Why probable
- Polishchuk (2010, *Evolutionary Ecology Research* 12(1): 1–22, [KNAW record](https://pure.knaw.nl/portal/en/publications/the-three-quarter-power-scaling-of-extinction-risk-in-late-pleist/)) fit logistic models of Late Pleistocene extinction on log body mass and derived a predicted logistic slope of 0.75 (via population density allometry, Damuth) or 0.25 (via population growth rate, Fenchel) per log10 mass, with continent-specific subsets — the direct empirical ancestor of this claim.
- Smith et al. (2018, *Science* 360: 310–313) documented body-size downgrading of mammals over the late Quaternary — a systematic signature consistent with continuous size-selective loss.
- Mass is measured for nearly all mammal species, and extinction status is categorical, so a quantitative selectivity function is testable with standard regression.
## Method
**Dataset: PHYLACINE 1.2.1** (Faurby et al. 2018, *Ecology* 99: 2626, doi:10.1002/ecy.2443; update Faurby et al. 2020, doi:10.5281/zenodo.3690867). The figshare DOI 10.6084/m9.figshare.7043307 given in the brief returned 404; the data were obtained from the official GitHub mirror `https://github.com/MegaPast2Future/PHYLACINE_1.2` (master branch = v1.2.1, per the repo README). Downloaded archive: 10.6 MB (well under the 300 MB cap).
Files used:
- `Data/Traits/Trait_data.csv` — 5,831 species (all extant + late-Quaternary extinct mammals), adult body mass (Mass.g, no missing values), IUCN.Status.1.2 (LC 3,157; NT 350; VU 525; EN 464; CR 205; DD 777; EP 270; EX 82; EW 1), habitat and island-endemicity fields.
- `Data/Ranges/Present_natural/*.tif` — present-natural range rasters (5,831 GeoTIFFs, Behrmann cylindrical equal-area, 96.5 km cells, +proj=cea +lon_0=0 +lat_ts=30 +datum=WGS84), decoded with `tifffile`/`imagecodecs` (values 0/1).
**Region assignment.** Each occupied raster cell was inverse-projected to lat/lon and assigned to a zoogeographic region by explicit lat/lon masks (North America incl. Greenland; South America; Africa incl. Madagascar; Eurasia = Palearctic+Indomalaya incl. Sunda, Japan, Arabia; Sahul = Australia+New Guinea+Tasmania). A species' region = plurality of its present-natural cells; PHYLACINE `Island.Endemicity` routes "Occurs only on isolated islands" species to *Islands* and "Exclusively marine" species to *Marine*. Spot checks were correct (e.g., Mammuthus primigenius→Eurasia, Smilodon fatalis→NorthAmerica, Megatherium americanum→SouthAmerica, Diprotodon optatum→Sahul).
**Filters.** *Homo sapiens* excluded. Main models use terrestrial species only (Terrestrial=1). Extinct = EP + EX + EW (all late-Quaternary: Late Pleistocene–Holocene, since ~130 ka). Threatened = VU/EN/CR vs LC/NT (DD excluded from the threat model, retained as extant in the extinction model).
**Models.** Binomial logistic regression by maximum likelihood (`scipy.optimize.minimize`, BFGS); standard errors from the observed-information Hessian; Wald z and p. Power-law vs stepwise compared by AIC (continuous log10 mass vs 4 quartile mass bins). Region contrast by a joint model with region × log10-mass interaction, plus a pooled hunting (Americas+Sahul) vs climate (Eurasia) interaction model.
## Results
### A1. Present-natural mammals: logit(threatened) ~ log10 mass (N = 3,700 terrestrial species; 1,001 threatened)
| model | slope ± SE (per log10 g) | z | p | OR per 10× mass | AIC |
|---|---|---|---|---|---|
| continuous log10 mass | **+0.501 ± 0.033** | 15.1 | <0.0001 | 1.65 | **4084.0** |
| stepwise (4 mass bins) | — | — | — | — | 4105.9 |
Continuous (power-law) fits better than stepwise by ΔAIC = +21.9 (smaller AIC wins).
Per-region threatened slopes (terrestrial): NorthAmerica +0.192 ± 0.105 (z=1.84, p=0.066); SouthAmerica +0.698 ± 0.102 (N=696); Sahul +0.608 ± 0.139 (N=325); Eurasia +0.746 ± 0.060 (N=1,129); Africa +0.181 ± 0.080 (N=539). Slopes span 0.18–0.75 — size selectivity is universal in direction but not constant across regions.
### A2. Late-Quaternary extinction: logit(extinct) ~ log10 mass (N = 3,928 terrestrial species in the five continental regions; 222 extinct)
| model | slope ± SE (per log10 g) | z | p | OR per 10× mass | AIC |
|---|---|---|---|---|---|
| continuous log10 mass (pooled) | **+1.520 ± 0.078** | 19.5 | <0.0001 | 4.57 | **999.7** |
| stepwise (4 mass bins) | — | — | — | — | 1297.2 |
Continuous model wins by ΔAIC = +297.5 — strongly against the stepwise alternative (P1's refutation condition fails). Size selectivity is large: among terrestrial species, 156/320 (>44 kg) vs 66/3,609 (≤44 kg) went extinct (48.8% vs 1.8%).
**Per-region extinction slopes from the joint region × mass model:**
| Region | driver label | slope ± SE | N (extinct) |
|---|---|---|---|
| Americas (NA+SA) | hunting | +2.225 ± 0.176 | 1,557 (102) |
| Sahul (Australia+NG) | hunting | +1.223 ± 0.157 | 413 (62) |
| Eurasia | climate | +2.013 ± 0.229 | 1,345 (47) |
| Africa | — | +1.580 ± 0.346 | 613 (11) |
**Slope differences vs Eurasia (the claimed contrast):** Americas − Eurasia = +0.212 ± 0.288 (z=0.74, **p=0.46**); Sahul − Eurasia = **−0.789 ± 0.277 (z=−2.85, p=0.0044)**; Africa − Eurasia = −0.432 ± 0.415 (p=0.30). Hunting regions are *not* steeper than the climate region; Sahul is significantly *shallower*.
**Hunting vs climate pooled:** logit(extinct) = −11.69 + 2.013·log10M + 3.371·hunt − 0.267·log10M×hunt. Baseline extinction is much higher in hunting regions (hunt intercept +3.371 ± 1.250, p=0.007; 164/1,970 vs 47/1,345 extinct) but the mass slope interaction is **−0.267 ± 0.252 (p=0.29)** — no steeper size selectivity in hunting regions.
**P3 check (consistency within a driver):** Americas vs Sahul slopes differ by 1.001 ± 0.235 (z=4.25, **p ≈ 2×10⁻⁵**) — the two hunting regions do not share an exponent.
**Sensitivity — restricted to mass ≥ 5 kg** (N=732, 188 extinct): Eurasia +2.048 ± 0.281; Americas +2.478 ± 0.334 (vs Eurasia: +0.430 ± 0.437, p=0.32); Sahul +5.983 ± 1.237 (mass×Sahul p=0.0019); Africa +1.161 ± 0.445. Truncating to megafauna makes Sahul steepest (Australia's ≥5 kg fauna is nearly all extinct) but leaves Americas ≈ Eurasia, and the hunting-region slopes still disagree with each other (2.48 vs 5.98).
**Sensitivity — include island species:** pooled extinction slope +1.151 ± 0.051 (N=4,535, 339 extinct) — still strongly positive. Extinct species excluded from the main continent analysis: 127 island endemics (85 EP + 42 EX, median mass 1.24 kg) and 1 marine (Hydrodamalis gigas).
## Verdict
**PARTIAL**
The size effect is real, strong, and continuous: threatened status rises with log10 mass (slope +0.50 ± 0.03) and late-Quaternary extinction even more so (+1.52 ± 0.08; 49% of >44 kg terrestrial species extinct vs 1.8% below), and the continuous power-law form beats a stepwise alternative decisively (ΔAIC 297.5). The categorical account is *not* adequate — P1 survives. But the claimed regional exponent pattern fails: the hunting-dominated regions are not steeper than climate-dominated Eurasia (Americas +0.21 ± 0.29 vs Eurasia, p=0.46; Sahul significantly *shallower*, −0.79 ± 0.28, p=0.004; pooled hunting×mass interaction −0.27 ± 0.25, p=0.29), and the two hunting regions disagree with each other (2.22 vs 1.22, p≈2×10⁻⁵), so the exponent does not act as the claimed driver diagnostic (P2 and P3 not supported; the refutation condition for the regional-diagnostic part is met).
## Limitations
- Region assignment is range-derived (present-natural rasters) with plurality voting; wide-ranging species are assigned to a single region, and 127 island-endemic extinct species (many small-bodied) were excluded from the continental contrast.
- Marine mammals excluded from main models (Steller's sea cow, the one extinct marine species, drops out).
- Masses of extinct species are literature estimates; PHYLACINE present-natural ranges for extinct species are reconstructions ("where they would live today"), not prehistoric ranges.
- A logistic slope per log10 gram is not literally a power-law exponent of P(mass); it is the pre-specified test and matches the functional form of the source literature (Polishchuk 2010).
- The Sahul result is truncation-sensitive: including Australia's many small-bodied extinctions flattens its slope; restricting to ≥5 kg makes it the steepest region. Americas ≈ Eurasia holds under both.
- No phylogenetic correction (extinct species cluster taxonomically).
- IUCN threat statuses reflect present-day anthropogenic pressure, not the Late Pleistocene event; the two analyses test different processes, as the hypothesis itself does.
- Stepwise comparison used 4 quartile bins; results could shift with different binning.
## Files
- `report.md` — this report
- `code/extinction_test.py` — full reproducible analysis (data loading, raster decoding, region assignment, logistic fits, figure)
- `code/results_console.txt` — console output of the analysis
- `data/Trait_data.csv` — PHYLACINE 1.2.1 trait table (raw, 2.7 MB)
- `data/phylacine_1.2.tar.gz` — downloaded GitHub archive (10.6 MB); extracted under `data/phylacine/`
- `data/phylacine/Data/Ranges/Present_natural/*.tif` — 5,831 range rasters (raw)
- `data/species_region.csv` — cached species→region mapping
- `data/extinction_analysis_table.csv`, `data/threat_analysis_table.csv` — analysis samples
- `figures/size_selectivity.png` — panel A: threatened vs mass with logistic fit; panel B: extinction curves by region; panel C: slope ± SE by region
Working report — not peer reviewed. Educational information, not medical advice. AI-assisted test: DeepSeek.