The ground · what a number does not say

The Heritability Mirror

You have read that a trait is 80% heritable and heard it as 80% genes, 20% upbringing. That is not what the number means — and the gap between the two is the most consequential misreading in all of popular science. Heritability is not how genetic a trait is. It is how much of the variation — in one population, in one environment — happens to line up with genes. Change the environment and the same genes give you a different number. Here is that, as a thing you can turn with your hand.

Drag the slider below. The little population never has its genes touched — every person keeps the exact genotype they were born with. The only thing you change is how unequal their environment is. Watch the heritability.

INSTRUMENT 1The same genes, any heritability you like

How unequal is the environment?

everyone's world identicalwildly unequal worlds

dot colour = the genes you were born with (never changes) dot position = the trait you end up with

Heritability H²

0.71

measured from these 280 people

Genetic variance

1.00

unchanged — always

Environmental variance

0.41

you are turning this

Move the slider all the way left and the heritability climbs toward 1.0 — not because the trait became "more genetic," but because you removed every other source of difference. Move it right and it falls toward 0. Same genes the whole time.

That is the whole trick, and it is not a trick — it is the definition. H² = V_G / (V_G + V_E): genetic variance over total variance. The numerator (the genes) never moved. The denominator did. So a high heritability can mean a trait is strongly genetic or simply that we have made everyone's environment alike — the number cannot tell you which. Heritability is a mirror of how equal the world is, held up to a population. It is not a property of the trait.

The reading to drop "Height is 80% heritable" does not mean your own height is 80% genes and 20% food. Heritability is about the spread between people, not the make-up of one person. Asking how much of your height is genetic is like asking how much of a drumbeat's area is the skin and how much is the stick — the question is shaped wrong.

INSTRUMENT 2Lewontin's two pots

Here is where the misreading does real damage. Take one handful of genetically varied seed. Split it in two. Sow one half in rich soil, the other in poor soil — but make each pot's soil perfectly uniform. Now drag the gap between the soils.

How much poorer is Pot B's soil?

same soilmuch poorer in Pot B

Heritability within each pot

100%

every difference inside a pot is genetic

The gap between the pots

8.2 cm

0% of it genetic

Inside each pot the soil is identical, so every difference between plants is genetic: heritability within a pot is 100%. Yet the two pots hold the same seed — so the gap between them is 0% genetic. It is entirely the soil.

Read that again, because a whole century of bad argument lives in the gap between its two halves: a trait can be 100% heritable inside each group and the difference between the groups be 100% environmental. The within-group number — however high, however real — carries no information about why two groups differ. Whenever you see "trait X is highly heritable, and group A scores below group B, therefore the gap is in their genes," you are watching someone walk straight off the end of this plank. The two pots are the counterexample, and they are not exotic: they are what heritability always is.

What the pots do and do not prove They do not prove any particular between-group gap is environmental. They prove the heritability within groups can never settle the question either way — you need to measure the environments themselves. High heritability is silent on between-group causes. That silence is the point.

INSTRUMENT 3Where the number comes from — and where it leaks

So where do figures like "80% heritable" come from? Most often from twins. Identical (monozygotic, MZ) twins share ~all their genes; fraternal (dizygotic, DZ) twins share ~half. If genes drive a trait, MZ twins should be more alike than DZ twins — and the size of that excess, doubled, estimates heritability. That is Falconer's formula: h² = 2 × (r_MZ − r_DZ). Set the two correlations:

Identical-twin correlation r_MZ

0.00.851.0

Fraternal-twin correlation r_DZ

0.00.451.0

A · genes

0.80

C · shared env

0.05

E · unshared

0.15

Identical twins are also treated more alike (break the equal-environments assumption)

The catch is the assumption hiding under the word "share." Falconer's formula credits the whole MZ-over-DZ excess to genes — but identical twins are also dressed alike, mistaken for each other, and kept closer than fraternal twins. Any extra shared environment they get gets counted as genetic. Tick the box above and watch the "genes" estimate jump without a single gene changing. This is the equal-environments assumption, and it is the seam every twin study is argued over. It is also part of why, when researchers went looking for the actual genes behind highly "heritable" traits, they kept coming up short — the missing heritability problem (open it below).

THE OTHER HALF"Heritable" never meant "fixed"

One last knot, because it does as much harm as the first. A high heritability says nothing about whether a trait can be changed. The two ideas feel like one and are not related at all.

Height is one of the most heritable traits we have (~0.8 in well-fed populations) — and average height rose by the better part of a foot across the twentieth century in many countries, purely on better nutrition. Strongly heritable, and moving fast.
PKU (phenylketonuria) is a single-gene, fully genetic disorder that once caused severe intellectual disability. Its effects are now almost entirely prevented by one environmental change: a low-phenylalanine diet. As "genetic" as a condition can be — and almost completely controllable.

Heritability measures the spread of variation in a population as it currently is. It is a snapshot, not a sentence. Change the environment — for everyone, or for one child — and the snapshot changes with it.

The check

Every number on this page is recomputed from first principles in research/the-heritability-mirror/verify.mjs — 19/19 passing. The instruments above run the very same formulas live in your browser, on the dots you can see.

H² = V_G/(V_G+V_E) is proven monotone-decreasing in V_E with the genetics held fixed — and a seeded population of P = G + E reproduces it (sim ≈ closed form to ±0.02).
The two pots: within-pot heritability computes to exactly 1.000000; the between-pot mean gap equals the soil offset to machine precision; the genetic gap is exactly 0.
Falconer's A = 2(r_MZ − r_DZ), C = 2r_DZ − r_MZ, E = 1 − r_MZ recover four known A/C/E models exactly; the equal-environments violation inflates A by exactly 2(c_MZ − c_DZ).
The "missing heritability" gap is the cited literature's subtraction, recomputed: 0.80 − 0.45 = 0.35 (twin vs common-SNP estimate for height).

What is cited, not derived: the specific empirical heritabilities (height ≈ 0.8; the ~0.49 average across all human traits in Polderman 2015) and the SNP/GWAS figures. Those are measurements from the literature — math can show what they imply, not conjure the values. Sources below.

The apparatus — definitions, assumptions, and what is genuinely contested

Definitions. Broad-sense heritability H² = V_G/V_P (all genetic variance over total phenotypic variance); narrow-sense h² = V_A/V_P (only the additive genetic variance — the part that responds to selection and is estimated by Falconer's formula). The page uses "heritability" loosely for the proportion-of-variance idea both share; the twin estimate is narrow-sense. Standard reference: Falconer & Mackay, Introduction to Quantitative Genetics (4th ed., 1996).

The population-dependence is not a flaw — it is the meaning. Because H² has V_E in its denominator, it is defined only relative to a particular population in a particular range of environments. R. C. Lewontin laid this out in "The analysis of variance and the analysis of causes" (Am. J. Hum. Genet. 26:400–411, 1974): a variance partition answers "how much do causes vary here," never "how much does each cause matter."

The two pots are Lewontin's own thought-experiment from "Race and intelligence" (Bulletin of the Atomic Scientists 26(3):2–8, 1970), aimed at the claim that a heritable trait's between-group gap must be genetic. In his original he uses open-pollinated (genetically variable) corn seed grown in two controlled nutrient regimes — Knop's solution complete in one, nitrate-halved and zinc-removed in the other — not literal garden soil; "richer vs poorer soil" here is a plain-language paraphrase of those two regimes. The logic the instrument preserves is exact: the seed in both pots is the same genetically-variable population and each pot's environment is uniform, so within-pot heritability is exactly 1 and the between-pot mean gap is exactly the environmental difference. (Beware a common retelling that uses two inbred lines and within-line heritability of zero — the logically-inverted version; Lewontin's own is the high-within-heritability one shown here.)

Twin assumptions. r_MZ = A + C and r_DZ = ½A + C hold under random mating, no gene–environment correlation or interaction, and the equal-environments assumption (EEA) — that MZ and DZ pairs share their trait-relevant environments to the same degree. The EEA is the most-debated premise in the field; critics argue MZ twins' more similar treatment inflates h² (the instrument shows the exact bias), while defenders find real violations whose effect on estimates is generally modest — Felson (2014) tested and relaxed the EEA across many outcomes and found it materially changed only one (neuroticism). We take no side beyond showing the mechanism.

Missing heritability. Twin studies put height's heritability near 0.8; the first wave of genome-wide association hits explained only a few percent, and SNP-based variance estimation (the GREML method of Yang et al., Nat. Genet. 42:565–569, 2010, implemented in the GCTA software) recovered ~0.45 — the gap named by Maher, "Personal genomes: The case of the missing heritability" (Nature 456:18–21, 2008). For height specifically the gap has since largely closed, as imputed and rarer variants were added (Wood et al. 2014; Yang et al. 2015); the broader puzzle — and how much of it reflects twin-estimate inflation versus undiscovered variants — remains partly open.

What we did not do. No real genomic or twin data is used — the dots are seeded simulations chosen to make the logic visible, exactly as the verifier specifies. The empirical heritability figures are cited, not measured here. Numbers carry the honest caveat that real estimates come with confidence intervals this page does not draw.

Sources

Lewontin, R. C. (1970). "Race and intelligence." Bulletin of the Atomic Scientists 26(3):2–8. (The two-pots analogy.)
Lewontin, R. C. (1974). "The analysis of variance and the analysis of causes." American Journal of Human Genetics 26:400–411.
Falconer, D. S. & Mackay, T. F. C. (1996). Introduction to Quantitative Genetics (4th ed.). Longman. (Definitions; the twin formula.)
Polderman, T. J. C. et al. (2015). "Meta-analysis of the heritability of human traits based on fifty years of twin studies." Nature Genetics 47:702–709. (Average heritability across 17,804 traits ≈ 0.49.)
Silventoinen, K. et al. (2003). "Heritability of adult body height: a comparative study of twin cohorts in eight countries." Twin Research 6(5):399–408. (Height heritability ~0.8, men up to ~0.9.)
Yang, J. et al. (2010). "Common SNPs explain a large proportion of the heritability for human height." Nature Genetics 42:565–569. (The GREML method, later released as GCTA.)
Maher, B. (2008). "Personal genomes: The case of the missing heritability." Nature 456:18–21.
Felson, J. (2014). "What can we learn from twin studies? A comprehensive evaluation of the equal environments assumption." Social Science Research 43:184–199.
Phenylketonuria: Blau, N., van Spronsen, F. J. & Levy, H. L. (2010), "Phenylketonuria," The Lancet 376:1417–1427. Secular height trend: NCD Risk Factor Collaboration (2016), "A century of trends in adult human height," eLife 5:e13410.