Paleobiology's shareholder quorum subsampling targets the same coverage-standardized quantity as ecology's coverage-based rarefaction, but is a distinct estimator — not a rename

statistics-of-the-unseensample-coveragerarefactionpaleobiologyfossil-recordmultiple-discoverycross-domain-bridgepriority-and-lineage

The unseen-mass estimator (claim-unseen-species-problem-has-dual-origin-ecology-and-cryptanalysis) is the currency of sample coverage: the fraction of a population's probability mass that a sample has already captured, equal to one minus the estimated unseen mass. Anne Chao and Lou Jost built modern coverage-based rarefaction on it, proposing to compare communities by "standardizing samples by completeness rather than size" — because two samples of equal count can differ wildly in how much of their source diversity they represent.

Paleobiologists reached the same device independently. John Alroy's shareholder quorum subsampling (SQS) draws subsamples until a target sample coverage (a "quorum") is met, rather than to a fixed number of specimens, in order to compare fossil assemblages fairly and quantify how complete the fossil record actually is. Corrected 2026-08-28: SQS and coverage-based rarefaction are not the same estimator under two field-specific names, as this note originally read. A direct read of both primaries shows SQS is Alroy's own Monte Carlo resampling algorithm, distinct from the algorithm and the closed-form equation Chao and Jost later derived for the same target quantity (claim-chao-jost-2012-calls-alroys-sqs-a-different-algorithmic-technique-from-their-closed-form-estimator). What survives of the convergence reading: both sides are independently targeting the same underlying quantity — richness standardized to a fixed level of sample coverage — which is itself a case of convergent reinvention driven by the shared object, like the dual origin of the unseen-species problem itself and the vault's other lineage-free convergences (claim-merton-multiple-discovery-is-sciences-dominant-pattern, observation-privatized-law-enforcement-reinvented-without-shared-lineage). Whether that convergence is "the same name" or "a rename" is itself disputed between the two camps — see claim-alroy-and-chao-jost-dispute-priority-for-coverage-standardized-richness-naming.

This is the estimator that directly quantifies the gaps Mayr predicted from peripatric speciation, and it is a close cousin of the selection-and-censoring problem in the Osteological Paradox — both say a sample of the recovered is a biased window on the whole, and both try to correct for the unrecovered.

Correction history.

• 2026-08-28 — The [unverified-mechanism — needs primary] flag above was resolved by 10-inbox/raw/2026-08-28-is-alroys-shareholder-quorum-subsampling-really-the-same.md, a capture built specifically to answer question-verify-quorum-subsampling-equals-coverage-rarefaction-primary (now status: answered). It read both Chao & Jost (2012) and Alroy's own SQS.html page directly and found the load-bearing synthesis above — "the two are the same estimator" — does not hold: Chao & Jost's own paper repeatedly distinguishes Alroy's algorithm from their own algorithm and their closed-form equation, and Alroy's own account draws a further, independent distinction on what each method holds fixed during sampling. The title and body above are corrected accordingly; the surviving claim is that both methods target the same underlying quantity, not that they are the same estimator. Three new claim-notes carry the full finding: claim-chao-jost-2012-calls-alroys-sqs-a-different-algorithmic-technique-from-their-closed-form-estimator, claim-alroy-and-chao-jost-dispute-priority-for-coverage-standardized-richness-naming, claim-alroy-distinguishes-sqs-from-rarefaction-by-fixed-coverage-not-fixed-sample-size. (Correction by claude-sonnet-5.)