Census
- BirdLife rows read
- …
- Migration = 3
- …
- Numeric HWI among them
- …
- Missing migration, excluded
- …
- Inference = YES among score 3
- …
- Measured score-3 rows
- …
01
The certificate
An empty interval, fully counted
- The claim
- No score-3 BirdLife record has HWI in [3.3, 13.4]; … score-1 or score-2 records do.
- Domain swept
- All … BirdLife rows read; all … score-3 rows tested.
- Method
- Read every row, select Migration = 3, test 3.3 ≤ HWI ≤ 13.4.
- Positive control
- Arctic tern at HWI 69.1
- Planted witness
- Synthetic row at HWI 8.8, absent
- Result
- ∅ the empty set
- Bound
- AVONET Supplementary dataset 1, version 7, BirdLife 5.0 table, printed one-decimal species means.
The real table is empty in the stated band.
02
Operate the census
Change the records,
keep the rule
The filter never changes: a migration score and an HWI interval go in; matching rows come out. Switch taxonomy or remove inferred traits and every displayed count is scanned again.
…fully migratory records swept
…in HWI 3.3 to 13.4
…score 1 or 2 in the same band
…lowest fully migratory HWI
broader, rounder winghand-wing index →more pointed wing
Open the frontier records raw evidence
The first fully migratory value is 13.5. These are the rows at that frontier in the selected table. “Complete measures” counts individuals with a complete set of morphometric measurements.
| Species | HWI | Migration | Inference | Individuals | Complete measures |
|---|
03
The non-vacuous question
Would chance leave
this much runway?
Finding that the minimum is 13.5 does not make 13.4 interesting. So erase the migration labels, randomly put the same number of “fully migratory” labels back, and ask how often their minimum lands at least as high as the observed floor.
This null model is deliberately blunt. It holds the count fixed but ignores ancestry, habitat, body size, latitude, and all other structure. It tests random label assignment, not a causal theory of wing evolution.
observed floor
…
HWI
labels reassignedcomputing…
random assignments at least this extremerunning…
Monte Carlo p, add-one estimaterunning…
exact fixed-count permutation probabilitycomputing…
Computing the all-assignment result…
Ready. The initial 5,000 assignments use a fixed seed so the check is reproducible.
04
Find where emptiness ends
Move the boundary
The same row search now asks for HWI at or below a ceiling. At 13.4 it returns nothing for score 3. One tenth later, two records arrive. Switch to score 2 and a penguin reaches 3.3.
0
score-3 records at or below HWI 13.4
- The set is empty.
05
The check
What was counted,
what was chosen
Every count below is recomputed from the shipped rows on load. The workbook itself is not shipped; a deterministic extractor verifies its MD5 and rebuilds the compact data file.
Definitions in the workbook
Score 1: sedentary. Score 2: a minority migrates long distances, most migrate shorter distances, or movements are nomadic or altitudinal. Score 3: a majority undertakes long-distance migration.
HWI: 100 times Kipp’s distance divided by wing length. It is a wing-shape proxy, not a migration-distance measurement.
Free choices
The upper edge, 13.4, is the last printed tenth before the observed score-3 minimum. The lower edge, 3.3, keeps the partial-migration boundary in view. Both were chosen after seeing the records.
The permutation statistic, the group minimum, is fixed before shuffling. The model randomly reassigns labels while preserving their number. It does not condition on relatedness or ecology.
Uncertainty and exclusions
Twenty-three BirdLife rows have no migration score and are excluded, not treated as sedentary. Thirty-nine fully migratory HWI values use some inferred biometric traits. Species means can hide sex, age, specimen, population, and geographic variation.
Taxonomic crosswalks change row counts. Values are rounded to one decimal. The 13.5 frontier is a record boundary, not a physiological threshold.
Three published tables, same printed floor
| Taxonomy | Rows | Score 3 | In band | At 13.5 | Minimum |
|---|
Bounded verdictCONSISTENT with the AVONET v7 records. No universal physiological law is asserted.
06
Primary sources
Records and reasons
- 01
Tobias et al., AVONET Supplementary dataset 1, Figshare v7. The species records used here, distributed under CC BY 4.0. The downloaded workbook’s MD5 is shown in the research note.
- 02
Tobias et al. (2022), AVONET: morphological, ecological and geographical data for all birds. Describes the 11,009-species trait compilation and its three taxonomic formats.
- 03
Sheard et al. (2020), Ecological drivers of global gradients in avian dispersal inferred from wing morphology. Defines HWI as a wing-shape proxy and reports its strong association with migration.
- 04
Egevang et al. (2010), Tracking of Arctic terns Sterna paradisaea reveals longest animal migration. Independent biological grounding for the positive-control species.