Bird mass and climate associations

# 5. Body size is a heat leak

**Verdict: Supported within families, modestly; not supported across all birds**

*Working test · not peer reviewed · AI-assisted · no clinical or safety advice*

## The hypothesis, as published

> A body's heat loss per unit mass is set by its surface-to-volume ratio, so
> small animals in cold climates are limited by geometry before they are limited
> by insulation.

> Prediction: cold-climate body size should track the ratio across taxa.
> Refute: size limits tracking insulation quality would remove the geometric
> term.

## What was tested

Bergmann's rule — heavier bodies in colder places — is the prediction the
surface-to-volume argument makes. AVONET supplies measured body masses and range
centroids for 9,959 bird species in 240 families;
WorldClim 2.1 supplies mean annual temperature at each centroid. The regression
is within family, so a lineage that happens to be both large and cold cannot
drive the result, and it controls for range size, habitat, trophic niche,
migration and whether any trait was inferred.

The discriminating add-on is the interaction with migration. If the geometry of
heat loss is what binds, the temperature slope should be steeper for residents
than for full migrants, because migrants leave before the coldest season.

## Results

| Quantity | Value |
|---|---|
| Species | 9,959 |
| Families | 240 |
| Temperature range at centroids | -40.4 to 30.4 °C |
| Within-family slope | -0.029 log₁₀ mass per 10 °C |
| 95% interval | [-0.048, -0.010] |
| Cluster-robust p (by family) | 0.0035 |
| Fold change per 10 °C colder | 1.07× |
| Raw cross-species Spearman ρ | -0.012 (p = 0.2177) |
| Latitude slope instead of temperature | +0.0015 log₁₀ per degree |

Within a family, a 10 °C colder range centroid goes with about
1.1× the body mass, and the interval excludes zero.
The interaction with migration points the predicted way — residents
(-0.0035 per °C) are steeper than full migrants
(-0.0004) — but it is not significant
(p = 0.1134), so the geometric reading is not separately identified.

The raw cross-species correlation is essentially zero (ρ =
-0.012). That is not a contradiction: the
between-family pattern runs the other way, so pooling families cancels the
within-family gradient. Anyone quoting a single correlation across all birds
would report no Bergmann effect and would be describing a different quantity.

## Sensitivity

- Replacing temperature with absolute latitude keeps the sign and the order of
  magnitude.
- Dropping range size from the controls does not change the temperature
  coefficient to two decimals.
- Excluding seabirds (the marine habitat class, which is large and cold) reduces
  the coefficient but leaves it negative.

## What this test cannot see

It is a cross-species comparison, not a measurement of heat loss. It cannot
separate surface-to-volume geometry from the many other things that correlate
with temperature — primary productivity, seasonality, predation, flight
efficiency — and the family fixed effects absorb phylogeny only at the family
level. The migration interaction is the one discriminating test here, and it is
underpowered. The result establishes that the predicted pattern is present where
the mechanism says it should be, not that the mechanism is the cause.

## Files

| File | What it is |
|---|---|
| `hypothesis.md` | the published entry, quoted verbatim |
| `run.py` | the analysis, runnable |
| `data.csv` | one row per species |
| `results.json` | every number quoted above |
| `figures/fig1.png` | binned medians and within-family deviations |
| `SOURCE.md` | dataset versions, row counts, hashes |

**Source.** AVONET (Tobias et al. 2022, figshare 16586228) and WorldClim 2.1
BIO1 at 10 arc-minutes.