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

statistics-of-the-unseensample-coveragerarefactionpaleobiologyshareholder-quorum-subsamplingcoverage-based-rarefactionjohn-alroyanne-chaoprimary-source-verification

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 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.