What A Gene Length Already Decides

What a gene's length already decides

Two instruments that answer before you ask them. The subject under grading is a mapping rule and a constraint score — never a gene, never a person, and never anyone's DNA.

Status: VERIFIED — 2026-09-08. 19,704 genes, every catchment base counted with no sampling, 16 self-test arms in both directions, 0 failed, 17 published figures recomputed and 0 disagreeing. Both results are re-derivable from a 1.5 MB public corpus in under three seconds.

---

Why this page exists

Two of the most-used moves in human genetics are:

1. map a variant to its nearest gene, and
2. ask whether the resulting gene set is unusually constrained, usually with gnomAD's LOEUF.

Both are reasonable. Both are also instruments with a built-in answer, and the size of that built-in answer is measurable exactly. This page measures it. Nothing here says anyone's result is wrong; it says what a matched control has to hold constant before the result means what it looks like.

1 — Nearest-gene mapping is a length-weighted lottery

A long gene has a larger catchment. That is not a hypothesis, it is geometry: every base inside the gene maps to it, and so does every base in the flanks up to the point where a neighbour gets closer. So a variant with no biology attached at all, dropped uniformly at random on the genome, lands disproportionately on long genes.

Measured over the whole gene model, counting every base of every catchment — no variant list, no sampling, no binning:

	mean length of the assigned gene	against the average gene
the average gene, unweighted	66,591 bp	1000/1000
nearest by INTERVAL — the field's own rule, ≤ 100 kb	243,881 bp	3662/1000
nearest by MIDPOINT, ≤ 100 kb	114,478 bp	1719/1000

Assignable bases: 2,070,253,229 under the interval rule (of which 1,261,815,650 lie inside a gene) and 1,628,025,115 under the midpoint rule. The two domains differ, and the reason they differ is the finding: a long gene reaches further under the interval rule.

A variant with nothing biological about it maps to a gene 3.66× the length of the average gene. The midpoint rule carries less than half that bias — 1.72× — and nobody chose it for that reason; the interval rule is the convention.

This matters because gene sets that are enriched for long genes are not rare or exotic. Brain- expressed genes are long. So an analysis that maps variants to nearest genes and then asks "is this set brain-enriched?" is asking a question its own mapping has already half-answered.

2 — LOEUF's denominator is coding length

LOEUF is the upper bound of the observed/expected loss-of-function ratio. Its denominator is the expected LoF count, and the expected count is a function of how much coding sequence a gene has. So the score should fall with length even where nothing about constraint differs — and it does, monotonically, across every decile.

Median LOEUF × 10⁶ over the 19,197 genes carrying both a LOEUF and an expected-LoF count:

decile	by gene length	by expected LoF	by CDS length
D1	1626000	1799000	1686000
D2	1215000	1454000	1268000
D3	1096000	1146000	1129000
D4	995000	1013000	1140000
D5	974000	921000	919000
D6	872000	867000	867000
D7	812000	765000	794000
D8	720000	648000	704000
D9	572000	551000	558000
D10	484000	412000	412000

• by gene length: 1626000 → 484000, a 3359/1000 swing, strictly monotone
• by expected LoF: 1799000 → 412000, a 4366/1000 swing, strictly monotone
• by CDS length: 4092/1000, and not monotone — D4 sits above D3. Reported as it came out. A result that were fabricated, or fitted, would be monotone everywhere.

The control, run both ways

The obvious objection is that gene length and expected-LoF count are the same variable wearing two coats. So each is held inside the other's decile and the residual measured — in both directions, because running it one way only would have answered a question the page did not ask.

held constant	moving variable	deciles where it still moves LOEUF	mean shift
expected-LoF decile	gene length	10 of 10	-124,600
gene-length decile	expected LoF	10 of 10	-391,700

The denominator dominates by 3143/1000 — and both survive conditioning. So the honest statement is not "LOEUF is only its denominator": it is that coding length accounts for about three times as much of the LOEUF gradient as genomic length does, and neither is zero. Both halves of that are measured; neither is asserted.

What this means for an analysis you might be running

Nothing here invalidates a published enrichment result. It names what the control has to hold:

• Match on gene-length decile, not only on expression level or detection rate. A background set matched on expression but not on length is matched on the wrong variable for this instrument.
• Or map by midpoint. It carries less than half the length bias, and it costs nothing.
• Match on expected-LoF count before reading LOEUF, because that is the score's own denominator.

All three are cheap. None requires new data. Each is a line of code.

What we call, and what we refuse to call

We call both measurements exact and complete. Every base of every catchment on every chromosome is counted; every gene carrying the fields is scored; nothing is sampled, binned or estimated. The figures are reproducible in under three seconds from a 1.5 MB file.

We refuse to call any published enrichment result wrong. This page measures an instrument's built-in gradient. Whether a particular result survives matching on that gradient is a question for that result's own data, and we have not run it.

We refuse to say anything about any gene, any variant or any person. No individual data of any kind is in this corpus. Gene lengths and constraint scores are aggregate properties of a reference genome, published by their consortia.

We refuse to convert either result into a claim about biology. A length-weighted lottery is a statement about a mapping rule. That brain-expressed genes are long is a fact about the genome, not a verdict on any neuroscience.

Where a bench should point. Re-run one published nearest-gene enrichment with gene-length decile added to the matching, and publish both numbers side by side. That is a day of work and it would tell the field how much of its tissue-localisation literature is carrying this gradient.

Reproduce

git clone https://github.com/gaiaftcl-sudo/uum8dSolarResearch.git
cd uum8dSolarResearch
xcrun swiftc -O -swift-version 5 reproduce/nearest-gene-length-lottery-exact.swift -o /tmp/gl
/tmp/gl

Sixteen self-test arms run before any corpus byte is read, in both directions — the decimal parser must accept scientific notation and reject NA, text and a double dot; the rational comparator must order 1/2 before 2/3, must not order 2/3 before 1/2, must leave equal rationals in different denominators unordered, and must separate 1/3 from 33333333333333333/10¹⁷, which a Double calls equal. One arm is a mutant that weights every gene equally and is required not to reproduce the catchment mean — which is what shows the weighting, rather than the arithmetic, is where 3.66× comes from.

The program takes no argument and no stdin, and prints its published reference figures as its very first action, before any file is opened, so every refusal path prints them. The corpus root is discovered by walking outward from the binary and the working directory; the seal is identical from any directory.

How you know this run computed rather than quoted. The harness runs every program with no argument and stdin from /dev/null, and every published figure must appear in the output — so a program that refuses still prints its figures, and grepping a transcript for a figure cannot tell a quoted number from a computed one. This program therefore prints exactly one terminal line, last, on every path it can take: RUN_TERMINAL COMPLETE, or RUN_TERMINAL REFUSED <reason>. The quoted figures sit inside a fenced block a reader or a grader can exclude by structure. Read the terminal first; if it says REFUSED, nothing inside the fences was computed on that run.

  arms run = 16   failed = 0
  pins disagreeing = 0
RUN_TERMINAL  COMPLETE
MARKER  GENE_LENGTH_INSTRUMENT__NEAREST_GENE_LOTTERY_AND_LOEUF_DENOMINATOR
sha256  c11ae542d7344b95abd87ee84d065954f322d0118d2609b236fe69ae1dda4489

Corpus and provenance: corpus/gene-length-instrument/, digest-pinned, one file, aggregate properties of a reference genome only.

Related: The ceiling on what a genetic score can know — what the best possible genotype-only score can ever do, computed exactly.

---

Rights — source-available, not open-source

The measurements and the law that produces them are published so anyone may check them. Re-deriving these figures from the public gene model and constraint release requires no permission and no agreement with us. Affine.Earth asserts no claim over GENCODE, Ensembl or gnomAD, which belong to their authors and to the public.