Genetics
Heritability
Broad-sense H² vs narrow-sense h², twin studies, and the breeder's equation R = h² × S
Heritability is the fraction of a trait's variation within a population that is explained by genetic differences among its members — not the fraction of the trait "caused by genes" in any single person. Formally, broad-sense heritability H² = VG / VP divides all genetic variance by total phenotypic variance, while narrow-sense heritability h² = VA / VP counts only the additive component that parents transmit predictably. It is a population-specific, environment-dependent number: equalizing environments raises it, cloning genotypes lowers it toward zero. Estimated from twin, adoption, and pedigree designs and now from SNP data, heritability drives Jay Lush's breeder's equation R = h² × S, yet — crucially — it says nothing about whether a trait can be changed. Human height is roughly 80% heritable, and yet mean height still rose about 20 cm across a century.
- Broad-senseH² = VG / VP
- Narrow-senseh² = VA / VP
- SelectionR = h² × S
- Twin estimateH² ≈ 2(rMZ − rDZ)
- Height h²~0.8 (twin studies)
- FormalizedFisher 1918 · Lush 1937
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Why heritability matters
- It is the engine of all selective breeding. Every improvement in milk yield, crop grain size, and racehorse speed runs on narrow-sense heritability through the breeder's equation R = h² × S. Dairy cattle milk yield (h² ≈ 0.25–0.30) has more than doubled since the 1960s because breeders selected on estimated breeding values; genomic selection now shortens the generation interval further.
- It anchors quantitative and psychiatric genetics. Twin registries in Sweden, Denmark, and the UK have estimated heritabilities for thousands of traits — schizophrenia around 0.80, height around 0.80, BMI around 0.75, major depression around 0.35–0.40 — telling researchers where to expect genetic signal before spending on genotyping.
- It sets the ceiling for genomic prediction. A polygenic score can never explain more of a trait's variance than that trait's heritability. Knowing height is ~80% heritable told the field that a good height predictor was mathematically possible; knowing many outcomes are far less heritable tempers the promise of DNA-based forecasting.
- It exposed the missing-heritability puzzle. The mismatch between twin-study heritability and early GWAS yield — height 80% heritable but only ~5% explained in 2010 — forced the field to confront extreme polygenicity, driving sample sizes from thousands to millions and inventing whole-genome variance methods like GCTA/GREML.
- It is routinely weaponized and misread. Because "heritable" sounds like "fixed" or "genetic destiny," heritability estimates have been misused to argue that group differences are innate. Lewontin's 1970 seedbox argument showed why a high within-group heritability is silent about the cause of between-group differences — a distinction that remains the crux of every responsible discussion of the statistic.
- It reveals gene–environment structure. Because heritability changes with the environment, comparing h² across contexts is informative in itself. The Turkheimer 2003 finding that IQ heritability was near zero in the poorest families and high in affluent ones (a gene × socioeconomic-status interaction) is a heritability result that is fundamentally about environment.
Common misconceptions
- "80% heritable means 80% of my height comes from my genes." Heritability is a property of populations, not individuals. It says 80% of the variation between people tracks genetic differences; it does not partition any one person's height into a genetic slice and an environmental slice. That individual decomposition is not even well-defined.
- "High heritability means the trait can't be changed." Heritability measures variance, not malleability. Phenylketonuria is caused by a highly heritable genotype, yet its devastating phenotype is almost entirely prevented by a low-phenylalanine diet. Vision is highly heritable; eyeglasses fix it. Environment can move a mean without touching heritability.
- "Heritability is a fixed constant of the trait." There is no single heritability of height or IQ — only the heritability in a specified population and environment. Equalize the environment and it rises; make the genotypes uniform and it falls. Exporting an estimate from one population to another is invalid.
- "A high within-group heritability implies group differences are genetic." This is the Lewontin fallacy. Two random samples of the same genetically variable seed lot, grown in rich versus poor soil, differ entirely for environmental reasons, even though within each lot heritability is 100%. Within-group and between-group variance are separate quantities.
- "Heritability tells you how strongly a trait is inherited." No — a trait with no genetic variance in the population has zero heritability even if it is genetically specified. Number of fingers is genetically encoded but has near-zero heritability because almost all observed variation is due to accidents, not alleles.
- "Narrow-sense and broad-sense heritability are interchangeable." Only additive variance (VA) is transmitted intact through meiosis, so only h² predicts response to selection and resemblance between relatives. H² (which also counts dominance and epistasis) is always ≥ h² and can badly overpredict a breeding program that relies on it.
How heritability works
Quantitative genetics begins by partitioning the total observed variation in a trait — its phenotypic variance VP — into components. The foundational split, formalized by Ronald Fisher in his 1918 paper "The Correlation between Relatives on the Supposition of Mendelian Inheritance," is VP = VG + VE + VG×E, where VG is genetic variance, VE is environmental variance, and VG×E captures gene–environment interaction. Fisher's insight was that continuous, "blending"-looking traits are fully compatible with discrete Mendelian genes once many loci of small effect are summed — reconciling the biometricians and the Mendelians in a single equation.
The genetic variance itself decomposes further: VG = VA + VD + VI. Additive variance (VA) comes from the average, dose-like effect of substituting one allele for another, summed across loci. Dominance variance (VD) arises from interactions between the two alleles at a single locus (departures from additivity within a locus). Epistatic or interaction variance (VI) arises from interactions between alleles at different loci. This ordering matters because meiosis shuffles alleles into new combinations every generation: the additive effects average out predictably across gametes, but dominance and epistatic combinations are broken apart and re-formed anew, so they do not transmit reliably from parent to offspring.
That transmission asymmetry is why there are two heritabilities. Broad-sense heritability, H² = VG / VP, asks what fraction of all trait variation is genetic in any sense. Narrow-sense heritability, h² = VA / VP, asks what fraction is due to the additive genetic effects that are faithfully passed on. Because VA ≤ VG, we always have h² ≤ H² ≤ 1. Narrow-sense h² is the operational quantity: it equals the slope when you regress offspring trait values on the average of their two parents (the midparent), and it equals twice the slope of an offspring-on-single-parent regression.
The payoff is Jay Lush's breeder's equation, R = h² × S. Suppose you select breeders whose mean exceeds the population mean by a selection differential S. The offspring generation's mean shifts by the response R, and R is exactly h² × S because only the additive fraction of the parents' superiority is heritable. If h² = 0.5 and you breed from animals 20 cm above average, the next generation gains 10 cm. Iterated over generations — as in the Illinois maize experiment — this drives populations far beyond their starting range, and it fails precisely when h² is low because there is no additive variance for selection to act on.
Estimating h² and H² means estimating variance components from the resemblance of relatives, since relatives share known fractions of their genes: monozygotic twins ~1.0, full siblings and dizygotic twins ~0.5, half siblings ~0.25. Classical designs (twin ACE models, offspring–midparent regression, half-sib analysis) and modern genomic methods (GREML/GCTA, which estimate variance from genome-wide SNP relatedness, and LD-score regression from GWAS summary statistics) all exploit the same logic: the more genes two individuals share, the more they should resemble each other for a heritable trait, and the strength of that scaling is the heritability.
Broad-sense H² vs narrow-sense h²
| Property | Broad-sense H² | Narrow-sense h² |
|---|---|---|
| Formula | VG / VP | VA / VP |
| Variance counted | Additive + dominance + epistatic | Additive only |
| Transmitted through meiosis | No (D and I reshuffled) | Yes (additive averages out) |
| Predicts resemblance of relatives | Only for clones / identical twins | Yes, across all relatives |
| Predicts response to selection | No — overestimates | Yes — R = h² × S |
| Estimated from | MZ-twin correlation; clonal lines | Offspring–midparent slope; half-sib design |
| Range | 0 to 1, always ≥ h² | 0 to 1, always ≤ H² |
| Key user | Human twin genetics, general theory | Animal & plant breeding |
How the estimate is measured: twin, family, and genomic designs
| Design | Comparison used | Estimates | Key assumption / limitation |
|---|---|---|---|
| Classical twin (ACE) | MZ vs DZ twin correlations | H² ≈ 2(rMZ − rDZ); A/C/E variance | Equal-environments assumption; assumes no assortative mating or G×E confounds |
| Adoption study | Adoptee vs biological vs adoptive parents | Genetic vs shared-rearing variance | Selective placement; restricted range of adoptive homes |
| Offspring–midparent regression | Offspring on mean of two parents | Slope = h² directly | Assumes negligible shared environment between parents and offspring |
| Half-sib (paternal) design | Variance among sire families | h² from sire component × 4 | Standard in animal breeding; needs large families |
| GREML / GCTA (SNP) | Genome-wide SNP relatedness vs phenotype | SNP heritability h²SNP | Captures common variants only; misses rare/structural variation |
| LD-score regression | GWAS summary statistics vs LD | h²SNP and genetic correlations | Needs matched LD reference; common-variant only |
Famous experiments and history
- Fisher's 1918 synthesis. In "The Correlation between Relatives on the Supposition of Mendelian Inheritance" (Transactions of the Royal Society of Edinburgh), Ronald Fisher introduced the term "variance," partitioned it into additive, dominance, and environmental components, and proved that continuous traits obey Mendelism with many small-effect loci — the birth of quantitative genetics. Sewall Wright's path analysis, developed in the same period, provided a complementary route to the same variance decomposition.
- Jay Lush and the word "heritability." Working on animal breeding at Iowa State in the 1930s and 1940s, Jay Lush formalized narrow-sense heritability and the breeder's equation in Animal Breeding Plans (1937). His students carried the framework into the dairy and poultry industries, turning R = h² × S into a working engineering tool.
- The Illinois Long-Term Selection Experiment (1896–present). Started by Cyril Hopkins at the University of Illinois, this is the longest-running genetics experiment on Earth. Selecting maize for kernel oil content moved the high-oil line from about 5% to over 20% oil across more than 100 generations — direct proof that additive variance sustains response to selection for a century without exhaustion.
- Lewontin's seedbox argument (1970). In "Race and Intelligence," Richard Lewontin used the thought experiment of splitting one genetically variable seed lot between rich and poor soil to show that a heritability of 100% within each group is completely consistent with a between-group difference that is 100% environmental — the definitive refutation of using within-group h² to explain group means.
- Missing heritability and GCTA (2010). After GWAS explained only ~5% of height variance despite 80% twin heritability, Jian Yang, Peter Visscher and colleagues (Nature Genetics, 2010) used genome-wide SNP relatedness (GCTA/GREML) to show that common SNPs collectively captured about 45% of height variance — the effects were real but individually too small to reach significance. By the 2022 GIANT/deCODE meta-analysis of over 5 million people, common variants captured the large majority of height's heritability.
- Turkheimer's gene × environment result (2003). Eric Turkheimer and colleagues found that in 7-year-old twins from impoverished families the heritability of IQ was near zero while shared-environment variance dominated, whereas in affluent families heritability approached the usual high estimates — a landmark demonstration that heritability itself is a function of the environment.
Frequently asked questions
What is the difference between broad-sense and narrow-sense heritability?
Both are ratios of genetic variance to total phenotypic variance, but they count different genetic components. Broad-sense heritability, H² = V_G / V_P, includes all genetic variance: additive (V_A), dominance (V_D, from allelic interactions within a locus), and epistatic (V_I, from interactions between loci). Narrow-sense heritability, h² = V_A / V_P, counts only the additive variance — the part that behaves in a simple 'dose' fashion and is transmitted predictably from parent to offspring. The distinction matters because only V_A survives the reshuffling of meiosis intact: dominance and epistatic combinations are broken up when gametes form and reassemble in new individuals. That is why narrow-sense h², not H², is the term that predicts response to selection and resemblance between relatives. For most quantitative traits, additive variance dominates, so h² and H² are often close but not identical — H² is always greater than or equal to h².
Does high heritability mean a trait is genetically fixed or cannot be changed by the environment?
No — this is the single most common misconception. Heritability describes how much of the variation between individuals in a population is due to genetic differences; it says nothing about whether the trait can be changed by the environment. Height in well-nourished populations is roughly 80% heritable, yet average adult height in the Netherlands rose about 20 cm over 150 years and Dutch men gained around 8 cm in the second half of the twentieth century alone — a purely environmental shift (nutrition, healthcare) with no change in the gene pool. A classic illustration: if you sow genetically variable seed in uniformly rich soil, height differences are almost entirely genetic (high heritability), but if you then move all the plants to poor soil they all grow short — the environment changed the mean dramatically even though heritability stayed high. Heritability is about variance, not malleability.
Why is heritability population-specific and environment-dependent?
Because heritability is a ratio, V_G / V_P, both parts of which depend on the population and its environment. If you equalize environments — same diet, same schooling, same climate — you shrink the environmental variance V_E, so the same genetic variance now accounts for a larger fraction of a smaller total, and heritability rises. If instead you make the genotypes more uniform (as in an inbred line or a cloned crop) you shrink V_G, and heritability falls toward zero even for a strongly biological trait. A famous consequence: the heritability of educational attainment or IQ is measured to be higher in affluent, resource-equal populations than in deprived ones, because in deprivation the environmental variance swamps the genetic. A heritability estimate is therefore a snapshot of one population in one environment and cannot be exported to a different group — a point central to Richard Lewontin's 1970 critique of between-group heritability claims.
How do twin and family studies estimate heritability?
The classic twin design compares monozygotic (identical) twins, who share essentially 100% of their genes, with dizygotic (fraternal) twins, who share on average 50% of their segregating genes, like ordinary siblings. If a trait is genetically influenced, identical twins should resemble each other more than fraternal twins. Falconer's formula estimates broad-sense heritability as roughly twice the difference in correlations: H² ≈ 2 × (r_MZ − r_DZ). More rigorous models (ACE decomposition) partition variance into additive genetics (A), shared/common environment (C), and non-shared environment (E) using structural equation modeling. Adoption studies separate genes from rearing environment by comparing adoptees with both biological and adoptive parents, and pedigree or animal-breeding designs use the regression of offspring on midparent (the slope equals h² directly). All of these assume, sometimes shakily, that identical and fraternal twins share environments to the same degree — the equal-environments assumption.
What is the breeder's equation and response to selection?
The breeder's equation, R = h² × S, is the central prediction of quantitative genetics. R is the response to selection — how much the population mean shifts in the offspring generation. S is the selection differential — how far the selected parents' mean deviates from the whole population's mean. h² is narrow-sense heritability. If you breed only from the tallest 10% of a herd whose mean exceeds the population by S = 20 cm, and the trait's h² = 0.5, the next generation's mean rises by R = 0.5 × 20 = 10 cm. This is why narrow-sense heritability, not broad-sense, governs breeding: only additive variance is faithfully transmitted through gametes. The equation underlies the century-long Illinois Long-Term Selection Experiment in maize (started 1896), where selecting for oil content moved the high line's kernel oil from about 5% to over 20%, and it powers modern genomic selection in livestock and crops.
What is missing heritability?
Missing heritability is the gap between the heritability estimated from twin and family studies and the much smaller fraction that early genome-wide association studies (GWAS) could explain with individually significant variants. Human height, for example, is about 80% heritable by twin studies, yet the first large GWAS around 2010 identified common variants accounting for only about 5% of variance — the rest was 'missing.' Proposed explanations include: thousands of variants of tiny effect below genome-wide significance thresholds (polygenicity), rare variants not captured by common-SNP arrays, structural variation, gene–gene and gene–environment interactions, and possible overestimation by twin studies. Methods that sum the effects of all SNPs at once (GCTA/GREML, Yang et al. 2010) recovered much of the gap — showing about half of height's heritability sits in common SNPs — and by 2022 GWAS meta-analyses of over five million people captured the large majority of the common-variant heritability, largely resolving the puzzle for height while it persists for many complex diseases.
Is heritability the same as inheritance?
No. Inheritance is the biological transmission of alleles from parent to offspring — the Mendelian machinery of genes passing down generations. Heritability is a population-level statistic that quantifies how much of the observed variation in a trait tracks genetic differences among individuals in that specific population and environment. A trait can be perfectly inherited genetically yet have zero heritability: number of fingers is genetically specified, but almost all variation you see (missing fingers) comes from accidents, so its heritability is near zero because there is essentially no genetic variance driving the variation. Conversely, a trait can show high heritability while its between-population differences are entirely environmental. The word 'heritability' invites confusion precisely because it sounds like it measures how strongly a trait is inherited — but it measures the sources of variance, not the strength of genetic causation in any individual.