When are exotic fishes that look like the locals more likely to establish — and when are the strangers? Darwin's oldest invasion riddle had two contradicting answers for 160 years. The species a lake could hold but doesn't tells you which answer applies.
In 1859 Darwin noticed something that has annoyed ecologists ever since: he could argue, equally well, that an exotic species closely related to the natives should be more likely to invade — and that it should be less likely. Both arguments are still standing.
A newcomer related to the residents is pre-adapted to the same climate, water chemistry and habitat that let its cousins live there. It arrives already suited to the place. Closely related exotics should succeed.
A newcomer related to the residents wants the same niche and shares their predators, parasites and diseases. It walks straight into competition and enemies. Closely related exotics should fail.
Darwin himself floated both. That is the “naturalization conundrum.” Decades of fish studies then came back contradicting each other — some found close relatives establishing more, some less. Neither camp could make the other's data go away.
● counted from the released CSV The dataset behind this paper is a register of who was put where, and whether it took. Every figure in this box is tallied directly from Fish introductions.csv in the replication package — not from the abstract.
The published analysis works on the subset of lakes where dark diversity can be estimated — the paper reports a 340-year record across 516 Swedish lakes. The raw register here is the fuller ledger those 516 were drawn from.
Sweden's lakes are sorted into three bioregions. The register is overwhelmingly one of them — which matters later, because the framework is a story about lakes as discrete basins.
673 classified lakes: 601 boreal, 64 alpine, 8 continental (lake.bioregion.classified.csv).
Count the fish actually swimming in a lake and you have its observed diversity. But some species are absent even though the lake would suit them perfectly — kept out only by history, distance, or bad luck. That absent-but-suitable set is the lake's dark diversity.
How do you infer it without a fish census of a parallel universe? By co-occurrence. If species X reliably turns up wherever the conditions that suit species Y occur, then a Y-suitable lake missing X marks X as part of that lake's dark diversity. The paper estimates this with the hypergeometric method in the DarkDiv R package — the same tool used across plant and animal community ecology.
Once you have the observed set and the dark set for a lake, two numbers drop out — and these two numbers are the whole trick.
Everything that could live here: the species present plus the dark-diversity species. A big pool is a rich, permissive lake; a small pool is a spare, selective one.
How much of the possible pool actually showed up. Defined as log((Tpool − Tdark) / Tdark) — high completeness means the lake is nearly “full,” low completeness means most of its suitable species are missing.
In the paper's own notation: Tpool = observed + dark completeness = log((Tpool−Tdark)/Tdark). Both are computed per lake, then fed into the model as the context that decides which of Darwin's answers applies.
That is the move. Darwin's two camps weren't measuring different fish — they were, without knowing it, measuring different lakes. Pool size and completeness are the axis nobody had folded in.
Below: establishment probability (up the side) against how phylogenetically distant the newcomer is from the residents (across the bottom, close → distant). The two sliders set the lake's dark-diversity context. As you move them, the slope of the curve flips sign — and with it, which of Darwin's answers is winning.
● real finding the direction of the flip — small pool + high completeness favors close relatives; large pool + low completeness favors distant exotics — is the paper's reported result. ◐ my curve the exact heights are an illustrative teaching model, a logistic emulation P = logistic(b · MPD) whose slope b swings negative → positive as the pool grows and completeness drops. It is not the fitted GLMM.
The paper fits a binomial generalized linear mixed model (GLMM). The response is the establishment outcome (0 = failed, 1 = succeeded). The key predictor is SES-MPD — the standardized mean phylogenetic distance between the introduced species and the native community. Low SES-MPD means a close relative; high means a distant one.
| Piece | In the model |
|---|---|
| Response | Introduction_outcome, 0/1, binomial with a logit link |
| Key predictor | MPD (phylogenetic distance of the newcomer from the natives) |
| Moderators | species-pool size (Tpool) and community completeness |
| The trick | the interactions MPD×pool and MPD×completeness — they let the MPD slope change sign by context |
| Random effects | lake identity and introduced-species identity |
Written out: outcome ~ MPD + pool + completeness + MPD:pool + MPD:completeness + (1|species) + (1|lake). The paper's Fig. 3 draws the prediction curves at the 10 / 30 / 50 / 70 / 90% quantiles of pool size and completeness — five copies of the curve above, fanning from downhill to uphill. That fan is the whole result.
The framework is a real advance. It also does far less than the headline makes it sound like. Both are true, and the second half is the part people skip.
What improved is forecasting: given a lake's dark-diversity context, you can better guess whether a close or a distant exotic is the bigger risk. That is a screening and prioritization lens, most useful before an invasion happens. It removes nothing, kills nothing, and reverses nothing already established. A better weather forecast is not a change in the weather.
Every “absent-but-suitable” species is a statistical guess from co-occurrence patterns, not a fish someone counted. That is the paper's own caveat. If the co-occurrence assumptions bend — and in a warming, human-stocked system they can — the pool and completeness numbers bend with them. The dials are estimated, so the flip is estimated.
The whole framework leans on the lake being a discrete basin with a clean species-pool boundary. That is why Swedish lakes work so well: each is its own bounded world. An open, connected river blurs exactly the two things the model needs — where one “pool” ends and how “complete” a stretch is. So it does not transfer cleanly to a system like the Mississippi.
For the invasive / Asian carp already loose in North America's connected waterways, the value here is not fixing an established invasion — the framework can't. Its use would be forecasting the next most-invasible connected waters, so barriers and monitoring go where they'll matter most. A screening tool for the frontier, not a cure for what's already through.
● from the paper “…smaller species pools and higher community completeness favor the establishment of exotic fishes closely related to native fishes in the Swedish lakes, whereas larger species pools and lower community completeness favor distant exotics.” That is the whole result, quoted — and it is a forecasting result, filed under Living Systems and cross-listed to the Methodology & Doctrine wing (the Caliper Room's reconcile-by-reframing-the-reference-pool move, kin to The Better Ruler).