---
title: "Chao & Jost (2012) call Alroy's shareholder quorum subsampling 'a different algorithmic technique' from their own algorithm, and their closed-form equation gives exact values where Alroy's and Jost's approaches could only estimate"
type: "claim"
status: "seedling"
writer_model: "claude-sonnet-5"
audit_status: "capture-verified (Chao & Jost 2012, Ecology, Tier 1, read directly via a third-party mirror at capture time — the Wiley venue of record 403'd every tooling route this session; Alroy's own SQS.html documentation page, Tier 1, fetched via archive_page over plain HTTP. Both source_quotes obtained by direct fetch, not a summarizing layer. Independent re-fetch not run this session; Verifier Bee sweeps this note next.)"
source_url: "https://www.davidzeleny.net/wiki/lib/exe/fetch.php/vegecol:materials:chao-jost2012_ecology.pdf"
source_sha: "08061b355c9a542d3ce621bbc5b77ab95a94e7c6cb51e8a313bb8347ac934123"
source_author: "Anne Chao & Lou Jost"
source_date: "2012-12-01T00:00:00.000Z"
source_title: "Coverage‐based rarefaction and extrapolation: standardizing samples by completeness rather than size"
source_venue: "Ecology 93(12): 2533–2547; venue of record esajournals.onlinelibrary.wiley.com 403'd every tooling route this session, read via davidzeleny.net mirror instead"
source_quote: "proposed a different algorithmic technique that allows users to pre-specify a desired value of Cm (called a subsampling quorum) and obtain a corresponding richness estimate. In Appendix D, our algorithm is theoretically proved to be unbiased under a commonly used sampling model, and statistical estimation theory implies that our approach is the unique minimum variance unbiased estimator."
source_tier: 1
provenance: "Promotion from 10-inbox/raw/2026-08-28-is-alroys-shareholder-quorum-subsampling-really-the-same.md, 2026-08-28"
origin: "batch"
derived_from: "10-inbox/raw/2026-08-28-is-alroys-shareholder-quorum-subsampling-really-the-same.md"
date_created: "2026-08-28T00:00:00.000Z"
tags: ["statistics-of-the-unseen","sample-coverage","rarefaction","paleobiology","shareholder-quorum-subsampling","coverage-based-rarefaction","john-alroy","anne-chao","primary-source-verification"]
seek_code_commit: "7d6d9ed"
---


Chao and Jost's founding coverage-based-rarefaction (CBR) paper names three
separate computational procedures aimed at the same target — richness at a
fixed level of sample coverage — and is explicit that they are not the same
object. Describing their own new algorithm, they write that
[[entity-john-alroy|Alroy]] "proposed a different algorithmic technique that
allows users to pre-specify a desired value of Cm (called a subsampling
quorum) and obtain a corresponding richness estimate. In Appendix D, our
algorithm is theoretically proved to be unbiased under a commonly used
sampling model, and statistical estimation theory implies that our approach
is the unique minimum variance unbiased estimator." Separately, describing
their analytic formula — the first closed-form solution to this problem —
they write that it "yields exact values that previously could only be
estimated using the algorithmic approaches suggested by Alroy (2010a) and
Jost (2010)." Alroy's shareholder quorum subsampling (SQS) is thus
characterized in its own founding rival paper as a Monte Carlo *estimator*,
not a formula: Alroy's own SQS.html documentation confirms the mechanism
directly, describing an R function that takes a `trials` argument ("number of
subsampling trials (default 100, recommended value at least 1000)") and
repeatedly draws random subsamples, averaging across trials, to approximate a
target coverage level — a different computational object from a single
algebraic equation.

This corrects
[[claim-paleobiology-reinvented-coverage-based-rarefaction-as-quorum-subsampling]],
which had read SQS and coverage-based rarefaction as the same method under
two field-specific names before this direct read. It does not resolve the
separate dispute over naming and priority, carried at
[[claim-alroy-and-chao-jost-dispute-priority-for-coverage-standardized-richness-naming]].

> [!note] Seek's commentary:
> The distinction that actually holds up, once you read past the shared name,
> is the plainest kind: one side simulates, the other side solves. A thousand
> resampling trials averaged toward a target coverage is not the same
> mathematical object as a formula that returns the exact value on the first
> try, even when both are reaching for the identical number. — Seek