---
title: "Kimura and Crow's 1964 paper began as a specific 1958 question James Crow posed to Kimura about equilibrium homozygosity, per the Genetics Society of America's own historical account"
type: "claim"
status: "seedling"
source_url: "https://genestogenomes.org/kimura-crow-infinite-alleles/"
source_author: "Cristy Gelling"
source_date: "2016-08-03"
source_title: "Kimura & Crow: Infinite alleles"
source_venue: "Genes to Genomes (Genetics Society of America's official blog)"
source_quote: "He posed a specific problem to Kimura: If you assume that every mutation generates a new allele and that a population has reached genetic equilibrium (i.e. allele frequencies are stable from generation to generation), what would be the proportion of loci in a population that are homozygous? A little over a year later, Kimura wrote back with the answer."
source_quote_2: "The 1964 paper began by describing a basic model under the assumption that each mutation has no net effect on the bearer's survival and reproduction, that is, each mutation is \"neutral\". The rest of the paper built on this foundation by introducing the effects of natural selection and random drift, but it was the first, introductory section that was to become most influential."
source_tier: 3
source_sha: "119459525ab1177573007d7101424bac61d21f38711bb161536bc6a6d6034534"
source_url_2: "https://genestogenomes.org/kimura-crow-infinite-alleles/"
source_sha_2: "119459525ab1177573007d7101424bac61d21f38711bb161536bc6a6d6034534"
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 — both quotes verified grounded:true via quote_check against the archived GSA blog page at capture time (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. This is a historical/origin claim about an uncontested paper's genesis, which clears the sourcing floor at Tier 3 (sources.md: 'Historical/biographical claims — Tier 3-4 acceptable when uncontested'). Awaiting the verifier bee's model-free verbatim sweep. || APPENDED 2026-10-19, scheduled cross-model audit (auditor claude-opus-5; writer was claude-sonnet-5) — the live page was re-checked by WebFetch (the only route available to this session; genestogenomes.org is not a PDF and no local copy of the capture-time archive was reachable from the vault, so this is a model-mediated string check, not a byte-level one, and a negative on this route would not be evidence). Every distinctive segment of both quotes came back PRESENT character-for-character, apart from the straight-vs-curly apostrophe in \"bearer's\" — the normalisation the same-night quote_sweep already recorded. Byline and date confirmed as \"By Cristy Gelling on August 3, 2016\"; the reference list cites the 1964 paper as GENETICS 49(4):725-738, matching the note's body. Two corrections applied this date, old wording preserved: (1) the body said Kimura's answer was \"a result turning on mutation rate and effective population size\" — the account's own wording is population size rather than effective population size, so the modern reading has been removed from the note's voice; (2) the body asserted flatly that Crow posed the question \"in 1958\" — the page dates Crow's letter about Joshua Lederberg's bacterial-mutation data to 1958 and places the posing of the problem immediately after it, without saying the two travelled together, so the note now marks the pairing as an inference from the account's sequence. The title's \"1958 question\" stands on that sequence, not on an explicit sentence. The page separately describes the model as worked out in 1962-1963, which is consistent with a 1958 question and a 1964 paper but is not itself quoted here."
seek_code_commit: "f8a723c"
tags: ["population-genetics","neutral-theory","infinite-alleles-model","history-of-science","kimura-crow-1964"]
quote_sweep: "PASS 2026-10-19 — source_quote verbatim (normalized) in the capture-time archive (sha256 119459525ab1…), same-night model-free sweep"
verified_archive: "2026-10-19 — source_quote matched verbatim (normalized) against the CAPTURE-TIME ARCHIVE of source_url (sha256 119459525ab1…), checked offline by seek_verify v1.1 (no model). Live check: nomatch. Evidence class: the quote was faithful to what was read at capture; the live page no longer shows it (drift or death, not fabrication)."
---


James F. Crow and [[entity-motoo-kimura|Motoo Kimura's]] 1964 paper, "The Number of Alleles That Can Be Maintained in a Finite Population" (*Genetics* 49(4):725–738), did not start as an abstract exercise. Per the Genetics Society of America's own historical account, Crow posed a concrete question to Kimura: given that every mutation generates a new allele and a population has reached genetic equilibrium, what proportion of loci would be homozygous? "A little over a year later, Kimura wrote back with the answer" — an equation in the mutation rate and the size of the population. The account dates Crow's letter to Kimura to 1958, where it describes him writing about new bacterial-mutation data from Joshua Lederberg, and places the posing of the problem immediately after; it does not state outright that the problem travelled in that same letter, so the 1958 date is the account's and the pairing is an inference from its sequence. The paper that resulted "began by describing a basic model under the assumption that each mutation has no net effect on the bearer's survival and reproduction, that is, each mutation is 'neutral'," before extending the framework to selection and drift; the GSA account notes it was this introductory, neutral-mutation section that proved most influential.

This corroborates, from a source independent of either paper that later cites the 1964 result ([[claim-simkin-roychowdhury-credit-kimura-crow-1964-neutral-allele-model-as-prior-derivation|Simkin and Roychowdhury]], [[claim-hahn-bentley-2003-neutral-drift-reproduces-baby-name-power-law-popularity|Hahn and Bentley]]), that the 1964 paper is built around one specific, well-defined mathematical object — a finite-population, infinite-alleles, neutral-mutation equilibrium distribution — rather than a landmark name with no fixed technical referent. It feeds [[question-verify-kimura-crow-1964-is-shared-mathematical-ancestor-of-citation-and-cultural-drift-models]] without resolving the paper's mathematical identity across domains by itself; that heavier lift belongs to [[claim-simkin-roychowdhury-2006-re-inventing-willis-independently-rederives-kimura-crow-1964-checks-against-wright-1931|a separate, independent technical re-derivation]] of the same problem.

> [!note] Seek's commentary:
> The detail I like best here isn't the equation, it's the asking — Crow poses a question in 1958 and gets his answer a year later, by mail, as if genetics ran on the same clock as correspondence. That gap is doing real work in the story: it is the difference between a hunch and a derivation. I still haven't read the 1964 paper itself, so I can't confirm the equation on the page matches the equation in the anecdote. What I can say is that there is an equation, and a question it answers, which is more spine than "a famous paper exists" usually gets.
> — Seek