Step 1: Two ways to average

Made-up group with two species:

• Species A: 1,000 sightings, moved up 10 m
• Species B: 10 sightings, moved up 200 m

Pooled: A has 100 times more sightings, so it wins the vote. Equal weight: each species gets one vote: (10 + 200) / 2 = 105.

Step 2: The key idea

The average height of all sightings can go up for two different reasons:

1. Real movement: butterflies actually live higher now.
2. Who gets recorded: people start recording more of a species that always lived high up.

Analogy: a class's average height goes up when the basketball team joins. Nobody grew.

Pooling mixes reason 1 and reason 2 together. Comparing each species with itself removes reason 2.

Step 3: Recording grew a lot, and unevenly

Generalist sightings grew 4.4 times (1,201 to 5,235). Specialist sightings grew 2.6 times (1,414 to 3,698).

The growth wasn't even across species, so the mix of species in each period changed. Sightings are records of where people saw butterflies, not counts of how many butterflies there are.

Step 4: Generalists, one mountain species inflates the pool

Cyaniris semiargus lives around 1,300 m, far above the group's ~750 m. It went from 8 to 241 sightings (0.7% to 4.6% of the group).

It only moved +18 m itself, but being recorded more adds roughly +22 m to the pooled average. That's most of the generalists' "win".

Step 5: Generalists, the busiest species moved down

• Maniola jurtina: 673 later sightings, moved -119 m
• Argynnis paphia: 412 later sightings, -43 m
• Ochlodes sylvanus: 662 later sightings, -9 m

If you track each species against itself (busy species still count more), generalists moved only about +12 m.

So the +37 m pooled number is mostly reason 2 (who got recorded), not real movement.

Step 6: Specialists, the big movers are rarely seen

The species on the top left moved 250-385 m uphill but have very few sightings (e.g. Polyommatus dorylas: +374 m from 5 sightings).

Pooling nearly ignores them. Equal weight gives each one a full vote, which is why equal weight shows such a big specialist shift.

Flip side: a species with only 5 sightings gives a noisy estimate. That's the weakness of equal weight.

Step 7: Specialists, the pool fills up with lowland species

Lowland specialists like Brenthis ino (~625 m) and Maculinea nausithous (~550 m) got a bigger share of later sightings. High species like Lysandra coridon got a smaller share.

That drags the specialists' pooled average down by roughly 40 m, even though the specialists themselves moved up about +74 m.

Step 8: The scoreboard

Only the pooled method says generalists moved more. Every method that compares each species with itself says specialists moved more.

What this means for the proposal

• Solid: 74 of 102 species were recorded higher in 1990-2019 than in 1950-1979.
• Not solid: "mobile generalists moved more". It only shows up when changes in who got recorded leak into the average.
• Pooling isn't "wrong". It answers "where are the sightings now?" Equal weight answers "how far did the typical species move?" Your research question is the second one.
• Bigger issue: sightings depend on where people looked. More hikers at high altitude would push every number up.

Safe line: "Pooled sightings mix real range shifts with changes in which species get recorded. When we follow each species over time, specialists shifted further uphill."

All numbers are descriptive, with no significance tests. The ~22 m and ~40 m effects are rough estimates. Equal weight only uses species with at least 5 sightings in both periods (16 generalists, 32 specialists).