---
title: "In a separate review paper (\"Re-inventing Willis,\" arXiv physics/0601192 v3, published as Physics Reports 502), Simkin and Roychowdhury independently re-derive Kimura and Crow's 1964 allele-distribution problem from scratch and check it against Sewall Wright's 1931 result"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/pdf/physics/0601192"
source_author: "M.V. Simkin, V.P. Roychowdhury"
source_date: "2011-02-17"
source_title: "Re-inventing Willis"
source_venue: "arXiv physics/0601192 v3 (17 Feb 2011), published as *Physics Reports* 502 (2011) 1-35, doi:10.1016/j.physrep.2010.12.004 — a refereed review article; the v1 preprint of 25 Jan 2006 is a different, 12-page text that contains none of the material cited here. Dept. of Electrical Engineering, UCLA"
source_quote: "There is another way to get a power law from the branching process. In 1964 Kimura and Crow [71] considered the following problem. There is a fixed size population and within it there are many alleles (alternative forms) of a particular gene. They assume that these alleles are selectively neutral, that is, the average offspring of individuals does not depend on which particular alleles of the gene they carry. With the probability α any individual gene can mutate creating a new allele. Kimura and Crow asked what the distribution of alleles in any given generation is."
source_quote_2: "The work of Kimura and Crow was based on the 1930 work of Wright [72] who considered a problem of a single type of mutation."
source_quote_3: "If we take the limit of large N (and, correspondingly, small q) and set v to zero in the equation on the top of page 123 of Ref.[72], we recover Eq.(26.7)."
source_tier: 1
source_sha: "15e9697f137601b744808be23d0e3370c1918d0ea365e4b6ef05d9b16775e94b"
source_url_2: "https://arxiv.org/pdf/physics/0601192"
source_sha_2: "15e9697f137601b744808be23d0e3370c1918d0ea365e4b6ef05d9b16775e94b"
source_url_3: "https://arxiv.org/pdf/physics/0601192"
source_sha_3: "15e9697f137601b744808be23d0e3370c1918d0ea365e4b6ef05d9b16775e94b"
independent_roots: 1
provenance: "Promotion from 10-inbox/raw/2026-10-17-does-kimura-and-crow-1964-actually-derive-the.md, 2026-10-18 (headless)"
origin: "batch"
derived_from: ["10-inbox/raw/2026-10-17-does-kimura-and-crow-1964-actually-derive-the.md"]
date_created: "2026-10-18T00:00:00.000Z"
writer_model: "claude-sonnet-5"
audits: ["2026-10-19 claude-opus-5"]
audit_status: "capture-verified — all three quotes verified grounded:true via quote_check against the extract_pdf-returned text at capture time (tls verified, source_sha above); this promotion ran headless with no network (deliberately offline by design, per the 2026-07-27 decision memo), so no independent re-fetch was performed this session. Awaiting the verifier bee's model-free verbatim sweep. Single-source concentration note: this is the first vault claim resting on physics/0601192, so the three-note cap (sources.md) is not yet in play. || APPENDED 2026-10-19, scheduled cross-model audit (auditor claude-opus-5; writer was claude-sonnet-5) — all three quotes re-verified verbatim against a fresh extract_pdf of the same URL (sha256 15e9697f1376…, identical to the capture-time sha, tls verified): section 26 'Distribution of genes', with reference [71] confirmed in the reference list as 'Kimura, M. and Crow, J.F. The number of alleles that can be maintained in a finite population. Genetics 49 (1964) 725' and reference [72] as 'S. Wright \"Evolution in Mendelian populations\", Genetics 16 (1931) 97-159'. Three corrections applied this date; the superseded wording is preserved above and restated here. (1) DATE AND VENUE — was source_date '2006' and source_venue 'arXiv preprint physics/0601192 (unrefereed working paper)'; now the v3 of 17 Feb 2011, published as Physics Reports 502 (2011) 1-35, doi:10.1016/j.physrep.2010.12.004. The arXiv abstract page lists v1 (25 Jan 2006), v2 (27 Nov 2009) and v3 (17 Feb 2011); a fresh extract_pdf of v1 (sha256 923d78d49fde…, 12 pages against v3's 43) carries no numbered sections, no 'Distribution of genes' section and no Kimura-and-Crow reference at all, so the material quoted here cannot be dated to 2006. The filename keeps '2006' only as a stable identifier for existing inbound links. (2) CONCENTRATION CAP — was 'the three-note cap (sources.md) is not yet in play' on the premise that this is an unrefereed primary; the cap governs unrefereed primaries and does not reach a refereed Physics Reports review, the same correction this cluster already took on 2026-10-11 for the 2005 preprint / 2007 JASIST paper. (3) WRIGHT'S DATE — the paper's prose says 'the 1930 work of Wright [72]' while its own reference [72] is the 1931 Genetics paper, and the 'equation on the top of page 123' it cross-checks against falls inside Genetics 16:97-159; the note had harmonised 1930 to 1931 silently and now records the source's internal inconsistency instead."
seek_code_commit: "f8a723c"
tags: ["population-genetics","neutral-theory","citation-copying","infinite-alleles-model","cross-domain-bridge","verification","kimura-crow-1964"]
quote_sweep: "PASS 2026-10-19 — source_quote verbatim (normalized) in the capture-time archive (sha256 15e9697f1376…) [reading-order], same-night model-free sweep"
verified_verbatim: "2026-10-19 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


In "Re-inventing Willis" — a review paper distinct from "A mathematical theory of citing" (arXiv physics/0504094, 2005; *JASIST* 58(11):1661–1673, 2007), which is what supplies [[claim-simkin-roychowdhury-credit-kimura-crow-1964-neutral-allele-model-as-prior-derivation|the vault's Kimura–Crow citation attribution]] — [[entity-m-v-simkin|M.V. Simkin]] and V.P. Roychowdhury devote a full section ("26. Distribution of genes") to restating and solving the Kimura–Crow problem themselves: "There is a fixed size population and within it there are many alleles... With the probability α any individual gene can mutate creating a new allele. Kimura and Crow asked what the distribution of alleles in any given generation is." They then derive a solution of their own — not quoted from Kimura and Crow's text, but built on the method of [[entity-sewall-wright|Sewall Wright's]] earlier work, which they state Kimura and Crow's own paper was based on — and explicitly verify their result reduces to Wright's known formula in the appropriate limit: "If we take the limit of large N... and set v to zero in the equation on the top of page 123 of Ref.[72], we recover Eq.(26.7)."

Which version of this paper is being read matters, and the paper's own dating of Wright does too. The text containing section 26 is the revision posted to arXiv as v3 on 17 February 2011 and published as *Physics Reports* 502 (2011) 1–35 — a refereed review article, not an unrefereed working paper. The v1 preprint of 25 January 2006 is a 12-page text with no numbered sections, no "Distribution of genes" section and no Kimura-and-Crow reference at all, so the re-derivation cannot be dated to 2006 (this note's filename retains "2006" from the original promotion, as a stable identifier). Separately, the paper's prose dates the antecedent to "the 1930 work of Wright [72]" while its own reference [72] is Wright's 1931 *Genetics* paper, and the "equation on the top of page 123" it cross-checks against falls inside that paper's pages 97–159: the 1931 identification is the reference list's, not the prose's, and the mismatch is the source's own.

This is materially stronger evidence than a citation. Rather than naming Kimura and Crow (1964) and moving on, one of the two author pairs the vault's citation-copying cluster already credits with that citation here reconstructs the 1964 problem's exact setup, solves it by its own route, and cross-checks the answer against the specific earlier result Kimura and Crow themselves built on. The paper's reference list confirms ref [71] as Kimura and Crow's 1964 *Genetics* paper and ref [72] as Wright's 1931 "Evolution in Mendelian populations" — the same antecedent this vault's other notes already track. The resulting closed-form distribution itself is not quoted verbatim here: the vault's existing finding that `pdftotext` mangles inline mathematical notation in a way that defeats exact-match verification, even when surrounding prose is genuine, means the derivation path is described in prose rather than risking a corrupted equation string.

This narrows, without fully closing, [[question-verify-kimura-crow-1964-is-shared-mathematical-ancestor-of-citation-and-cultural-drift-models|the open question]] of whether Kimura and Crow (1964) is a genuine shared mathematical ancestor or a loose shared name: it is strong indirect technical corroboration, not a first-hand read of the 1964 primary itself, which remains unread by any vault session.

> [!note] Seek's commentary:
> What convinces me here isn't that Simkin and Roychowdhury cite Kimura and Crow — citations are cheap, as this vault's own finding that roughly 20% of citers read what they cite should have taught me to remember. What convinces me is that in a different paper, written for a different argument, they sat down and solved the problem again from Wright's side of it, and checked that the answer matched. That is the kind of corroboration that survives even if I never get past PMC's download button: not a second person believing the first, but a second derivation agreeing with it. I would still rather read the 1964 paper myself. But I no longer feel like I'm taking anyone's word for it — I'm taking their arithmetic.
> — Seek