Heritability: Definition, Formula (h² and H²) and Examples in Animals and Plants

By Dr. Zubair Khalid, DVM, MS, PhD · 2026-10-30

Heritability is the proportion of total phenotypic variation in a population that can be attributed to genetic differences among individuals. In its narrow sense (h²), it is the portion of that variation due to additive genetic effects, the component that parents pass on and that selection can act on.

The concept connects a measurable phenotype to the underlying genetic architecture of a population. A breeder uses it to predict how fast a herd or a field will respond to selection. A conservation biologist uses it to judge whether an endangered species can adapt to a shifting environment. A geneticist uses it to decide how much of a trait is worth mapping. Without heritability, quantitative genetics would have no bridge between the phenotype an observer scores and the breeding value a selection program needs.

What Is Heritability?

Heritability is a ratio of variances, not a property of an individual and not a property of a gene. A single animal does not have a heritability. A trait in a defined population, measured in a defined environment, does. Change the population, change the environment, and the number changes with them.

Three ideas anchor the definition.

First, heritability describes variation, not absolute value. A trait can be strongly genetically controlled and still show a heritability of zero if every individual in the population carries the same alleles. Conversely, a trait shaped heavily by the environment can still have a moderate heritability if environmental variation within that particular study is small.

Second, heritability is a dimensionless proportion that runs from 0 to 1 in the theoretical sense. An estimate near 0 means phenotypic differences are mostly environmental in the sampled population. An estimate near 1 means phenotypic differences are almost entirely genetic in that sample. Real estimates from livestock, crops, and wild populations usually fall in the middle, and many sit between 0.1 and 0.5.

Third, heritability is estimated, never measured directly. Every number in the literature is a statistical inference from family resemblance, pedigree, markers, or replicated genotypes, and each estimation method carries assumptions that shape the answer [1].

Term	Symbol	Numerator	Denominator	What it captures	Typical use
Broad-sense heritability	H²	Total genetic variance (additive + dominance + epistatic)	Phenotypic variance	All genetic contributions to variation	Clonal crops, full-sib family selection, traits with large dominance effects
Narrow-sense heritability	h²	Additive genetic variance only	Phenotypic variance	Heritable component that responds to selection	Predicting selection response, breeding value estimation
Repeatability	r	Genetic variance + permanent environmental variance	Phenotypic variance	Consistency of repeated records on one individual	Culling decisions, number of records needed
Genetic correlation	r_A	Covariance of breeding values	Product of the two additive standard deviations	Shared genetic control of two traits	Multi-trait selection, correlated response

The Heritability Formula

Partitioning Phenotypic Variance

Quantitative genetics begins with a decomposition of the phenotype. For any trait measured on a set of individuals, the total phenotypic variance (V_P) splits into a genetic component (V_G) and an environmental component (V_E):

V_P = V_G + V_E

When genotype and environment interact, a genotype-by-environment interaction term (V_GE) is added, so the fuller expression is V_P = V_G + V_E + V_GE.

The genetic variance itself is not one thing. It decomposes into three parts:

V_G = V_A + V_D + V_I

V_A is additive genetic variance. It reflects the average effect of substituting one allele for another across all genetic backgrounds, and it is the part that breeds true in the sense that offspring resemble parents in predictable ways.

V_D is dominance variance. It arises from interactions between alleles at the same locus, so a favorable combination in a parent may not be transmitted intact to an offspring.

V_I is interaction or epistatic variance. It arises from interactions between alleles at different loci.

The environmental variance is equally composite. It includes temporary effects such as feed quality in a given season, permanent effects such as a healed injury, maternal effects such as litter size or egg provisioning, and measurement error from the instrument or the observer [2].

Narrow-Sense Heritability (h²)

Narrow-sense heritability is the ratio of additive genetic variance to total phenotypic variance:

h² = V_A / V_P

This is the parameter that matters for selection. Additive effects are the ones transmitted in a predictable way, so the response of a population to selection depends on V_A and not on V_D or V_I. Estimators that yield h² include parent-offspring regression, half-sib family analysis, and marker-based genomic relationships.

Broad-Sense Heritability (H²)

Broad-sense heritability is the ratio of total genetic variance to total phenotypic variance:

H² = V_G / V_P = (V_A + V_D + V_I) / V_P

It is always at least as large as h², and the gap between them measures the share of non-additive genetic variation. That gap is informative. In a meta-analysis of reef-building corals, narrow-sense estimates were consistently lower than broad-sense estimates across traits, which points to substantial non-additive genetic variation in those species [3]. The same pattern shows up in animal breeding. In beef and dairy bulls evaluated for semen production traits, broad-sense heritability ranged from 0.17 to 0.43 while narrow-sense heritability ranged from 0.04 to 0.11, meaning non-additive effects more than doubled the genetic share of variation for every trait and breed studied [4].

Broad-sense heritability is the right parameter when the breeding unit is a clone, a full-sib family, or a hybrid, because those units transmit whole genotypes rather than single alleles. In an apomictic tropical forage grass, full-sib family mean broad-sense heritability was high for agronomic traits (0.89 to 0.95) and moderate for nutritional quality traits (0.56 to 0.66), which supports selection at the family level rather than on individual plants [5].

The Formulas With Numbers

A hypothetical example makes the arithmetic concrete. Suppose a population of 500 beef heifers has a phenotypic variance in weaning weight of 400 kg². Suppose further that additive genetic variance is 100 kg², dominance variance is 20 kg², epistatic variance is 10 kg², and the remainder is environmental.

Total genetic variance is 100 + 20 + 10 = 130 kg². Broad-sense heritability is 130 / 400 = 0.325. Narrow-sense heritability is 100 / 400 = 0.25. The 0.075 difference is the non-additive share. A selection program in that population can only count on the 0.25 component for permanent genetic change, even though a quarter of the total genetic variation relevant to a specific cross may involve dominance.

The same logic works in the other direction. If a study reports h² = 0.4 and V_P = 25 units, then V_A = 0.4 × 25 = 10 units. An estimate of H² = 0.6 for the same trait would put V_G at 15 units, leaving 5 units of non-additive variance.

How Heritability Is Estimated

Resemblance Between Relatives

The classical approach compares phenotypes of relatives whose genetic relatedness is known. Parent-offspring regression has a slope equal to h² when parents and offspring are measured in the same environment and mating is random. Half-sib family analysis partitions variance among sire families into one quarter of the additive variance, which allows V_A to be recovered. Full-sib analysis confounds additive variance with dominance and common environment, so it estimates something closer to H².

These designs are powerful but fragile. They assume no assortative mating, no inbreeding, no shared environmental confound between relatives, and no selection that distorts the pedigree.

Mixed Models and Pedigree Data

Modern animal and plant breeding relies on linear mixed models that fit additive genetic relationships as a random effect. In the animal model, the relationship matrix is built from the pedigree and the additive genetic variance component is estimated by restricted maximum likelihood. The resulting variance component divided by the phenotypic variance gives h². When dominance and epistatic relationship matrices are added, the same framework delivers H² and the non-additive components.

Korean Hanwoo data from 16,971 genotyped animals illustrate the approach. Across five genetic models, additive genetic variance and narrow-sense heritability estimates stayed similar for carcass weight, eye muscle area, back fat thickness, and marbling score, except when additive-by-additive interaction was included. Dominance variance expressed as a proportion of phenotypic variance ranged from 1.7% to 3.4% for carcass weight and marbling score and was close to zero for eye muscle area [6]. That pattern says dominance matters more for some traits than others, and the choice of model should follow the biology rather than a default.

In Pura Raza Española horses, dominance variance components were estimated for reproductive and morphological traits using a pedigree of 11,331 individuals and records from 3,967 mares. The analysis asked whether dominance deviations were large enough to justify alternative models or mate allocation strategies [7]. Where dominance is measurable, mating design can exploit it. Where it is negligible, additive models remain sufficient.

Genomic Relationships and the Base Population Problem

Marker-based heritability replaces the pedigree relationship matrix with a genomic relationship matrix built from genome-wide single nucleotide polymorphisms. This has two advantages: it captures realized relationships that a recorded pedigree misses, and it works in populations with shallow or missing pedigree records. It has one disadvantage that is easy to overlook.

A recent analysis of the definition-estimation gap argues that heritability estimated from family and pedigree data describes a hypothetical base population in which all individuals are assumed to be independent and non-inbred, not the current population being selected [1]. The difference is not trivial. The author introduces a pedigree sparsity coefficient (PSC) that corrects genetic variance and heritability from the base population to the current population. For very dense pedigree data, the correction lets breeders read the genetic basis of a trait in the population they actually manage and predict genetic gain from selection within that population [1]. The same correction extends to genomic heritability, where the pedigree relationship matrix is replaced by a genomic one [1].

The practical lesson is that a heritability estimate carries an implicit reference population. If that reference population is not the one in front of you, the number needs adjustment before it drives a decision.

Measurement Error

Environmental variance includes measurement error, and measurement error biases heritability downward when it inflates the denominator without contributing to the genetic signal. It also biases selection gradients and predicted response to selection. Transient, nonpersistent biological fluctuations act like measurement error even when the instrument is perfect.

Repeated measurements are the standard remedy, but the timing of repeats matters. Short-term repeats capture transient variability, while long-term repeats help isolate permanent environmental effects. Including both variance components in a quantitative genetic model yields unbiased estimates of heritability, selection gradients, and predicted response [2]. A study that reports a heritability estimate without stating its measurement protocol is missing a piece of the evidence needed to judge it.

The Breeder's Equation

The breeder's equation converts heritability into a prediction of genetic change. In its simplest form:

R = h² × S

R is the response to selection, the change in population mean between generations. S is the selection differential, the difference between the mean of the selected parents and the mean of the whole population. h² is narrow-sense heritability.

The equation makes the role of each component explicit. Doubling the selection differential doubles the response. Doubling h² doubles the response. A trait with h² = 0.05 barely moves no matter how hard the breeder selects, while a trait with h² = 0.5 moves five to ten times faster under the same selection pressure.

A standardized form is often used in plant and animal breeding:

R = i × σ_P × h²

Here i is the selection intensity, which depends on the proportion of individuals retained (roughly 2.67 when the top 1% are selected and about 1.40 when the top 25% are selected), and σ_P is the phenotypic standard deviation. This form makes the tradeoff visible. Intense selection on a small population raises i but erodes effective population size and additive variance, which lowers the response over the long run.

The multivariate breeder's equation extends the logic to correlated traits:

Δz̄ = G β

where Δz̄ is the vector of predicted mean changes, G is the additive genetic covariance matrix among traits, and β is the vector of selection gradients. Using G rather than a single h² captures the fact that selecting on one trait drags correlated traits along. An analysis of Pacific salmon used this multivariate form to project how artificial selection against small males could affect female length at maturity and fecundity, because the genetic architecture of growth rate is shared across sexes [8]. The projection showed that selection on male size can produce unexpected changes in female traits when genetic correlations are nonzero.

The breeder's equation has limits. Phenotypic measurement error, omitted traits under selection, inaccurate variance estimates, and nonlinear genotype-phenotype relationships all bias the prediction, and the bias is often systematic rather than random [9]. A method built on a Kalman filter treats the breeder's equation as a baseline and adds a bias term estimated from the record of past changes, then updates its parameters each generation. In artificial selection experiments on the Drosophila wing and in simulations with a complex genotype-to-phenotype map, this approach outperformed the standard breeder's equation, particularly when traits under selection were omitted from the model [9]. The prediction problem is not solved, but it is being sharpened.

Genomic selection has changed the practical use of the equation. Genomic prediction estimates breeding values from dense markers, which shortens the generation interval and raises prediction accuracy. A simulation framework for multi-environment plant breeding showed how the classical response to selection can be recast to answer a breeder's real questions, for example how many entries must be selected to achieve a defined probability of capturing the truly best line and what probability of obtaining the top entries follows from selecting a given number of candidates [10].

Heritability Examples in Animals

Heritability of Traits in Livestock

Livestock breeding is where heritability has the most direct economic consequences, and the estimates span a wide range.

Behavior is a useful case because it is easy to assume that behavior is mostly environmental. In 1,032 Japanese Black cattle fitted with wearable sensors, heritability estimates for seven behavioral classes (feeding, lying, moving, standing, ruminating, ruminating while lying, and ruminating while standing) were generally low, ranging from 0.02 to 0.37, and accounted for 22.7% to 67.5% of the corresponding repeatability [11]. The gap between heritability and repeatability is the permanent environmental component. Genetic correlations between behavioral traits and carcass traits were also low in magnitude, ranging from -0.28 to 0.29, though several were statistically significant and interpretable. Animals that fed and moved less and ruminated more tended to have favorable carcass profiles [11].

Fatty acid composition behaves very differently. In 2,494 Japanese Black cattle genotyped and phenotyped for monounsaturated fatty acid content and oleic acid (C18:1), narrow-sense heritability estimates were 0.52 to 0.53 for monounsaturated fatty acids and 0.57 for oleic acid. Dominance genetic variance accounted for 0.04 to 0.07 and 0.04 to 0.05 of phenotypic variance respectively, and runs-of-homozygosity variance contributed about 0.02 [12]. This is a trait where additive effects dominate, which is why marker-assisted and genomic selection for marbling-related fatty acid profiles has moved quickly.

Semen production traits sit at the other end. In Japanese Black and Holstein bulls, additive variance explained only 0.04 to 0.11 of phenotypic variance, while adding dominance and epistatic effects raised broad-sense heritability to 0.17 to 0.43 for semen volume, sperm concentration, sperm motility, post-thaw motility, and sperm number [4]. The authors concluded that non-additive effects play an important role and should be considered in genetic improvement programs for these traits.

Growth traits respond strongly to sustained selection. In Ross 308 broiler breeders tracked across four successive generations, fourth-generation birds were heavier than first-generation birds at 60 weeks of age, with males at 5,036.5 g versus 4,744.3 g and females at 4,152.2 g versus 3,858.3 g [13]. That progressive phenotypic improvement across generations is the signature of additive genetic variance being converted into genetic gain by selection.

Wild Populations

Heritability in the wild is harder to estimate because pedigrees are incomplete and environments vary, but it is measurable and consequential.

In a pedigreed wild population of the brown anole lizard (Anolis sagrei), body size was heritable and genetically correlated with adult reproductive success in both sexes. Selection through adult reproductive success consistently favored larger body size and was stronger in males. Across five annual cohorts, both mean phenotypic values and breeding values for body size increased, and the increases exceeded what genetic drift would produce [14]. This is a direct demonstration that additive genetic variance in a wild population can produce rapid evolutionary change when selection is consistent.

Sex-specific heritability complicates the picture. In four populations representing three species of Pacific salmon, heritability of length at maturity was estimated separately for each sex, and selection gradients were estimated alongside them. The multivariate breeder's equation was then used to project how artificial selection against small males could affect female length and fecundity. The results showed that selection on male body size does not automatically produce larger females, because the fastest-growing males mature earliest and at the smallest size [8]. Sex-specific heritability means a single h² for the species can mislead.

Corals show what a comparative synthesis can reveal. A meta-analysis of 95 heritability estimates across 19 reef-building coral species found low heritability (h² < 0.25) for gene expression metrics, intermediate heritability (h² = 0.25 to 0.50) for photochemistry, growth, and bleaching, and high heritability (h² > 0.50) for survival and immune responses [3]. Some of these values exceed what is typical in other taxa, particularly for survival and growth. No detectable effect of temperature on heritability emerged, but narrow-sense estimates were generally lower than broad-sense estimates, indicating significant non-additive genetic variation across traits [3]. Trait heritability also varied with coral life stage, with bleaching and growth in juveniles behaving differently from the same traits in adults.

Heritability Examples in Plants

Plant breeding provides some of the cleanest heritability estimates because replication, controlled environments, and designed mating schemes are all feasible.

In guineagrass (Megathyrsus maximus), a tropical forage species constrained by apomixis and polyploidy, 175 F1 families from 27 sexual female parents and nine apomictic male parents were evaluated across three Colombian environments for agronomic traits and one location for nutritional quality. General combining ability accounted for 58.6% to 80.1% of the main genetic variance depending on the trait. Full-sib family mean broad-sense heritability was 0.89 to 0.95 for agronomic traits and 0.56 to 0.66 for nutritional quality traits, supporting selection at the family level [5]. In an apomictic species, the family is the unit that reproduces, so H² rather than h² is the parameter that governs gain.

In Ethiopian barley, 260 genotypes evaluated across four sites produced narrow-sense heritability estimates of roughly 0.69 to 0.72 for extract content and grain size, with coefficients of variation spanning 5.37% to 32.63% [15]. A companion analysis of the same germplasm reported narrow-sense heritability estimates from 0.52 to 0.97 across nine agronomic and nutritional traits [16]. The wide range within one crop is normal. Traits close to flowering time are often highly heritable, while traits shaped by grain filling under variable rainfall are not.

In sorghum, heritability was used as a design tool rather than just a description. Wavelength ratios from hyperspectral data were screened for co-heritability with leaf nitrogen content and specific leaf area, and the selected synthetic traits raised multi-trait genomic prediction ability by up to 17% over single-trait models [17]. The reasoning is that a secondary trait with high heritability and high genetic correlation to the target can carry information about the target even when the target itself is expensive or noisy to measure.

Environmental Context and Limits of a Single Estimate

Heritability is not a constant, and two lines of evidence show why.

Selection and genetic variation can covary across environments. A simple analytical model showed that when the same ecological factor influences both the strength of selection and the expression of genetic variation in a trait, a correlation between the two arises. That correlation has a modest effect on the mean evolutionary response but a large effect on its variance, increasing among-population or among-generation variation in response when the correlation is positive and diminishing it when negative [18]. Temperature and competition were identified as factors unlikely to generate the correlation because they affected one parameter more than the other, while environmental novelty was identified as a factor that merits investigation [18].

Fluctuating selection is a second layer. A modeling framework integrating population and quantitative genetics simulated populations under various selection regimes and applied spectral analysis to allele frequency trajectories. The simulations clarified the conditions that sustain oscillations in allele frequencies over time and showed how genetic factors such as heritability and number of causative loci interact with ecological factors such as season length, the difference in phenotypic optima between seasons, and population size dynamics [19]. In a population experiencing periodic selection, a single-generation heritability estimate is a snapshot of a moving target.

The genotype-phenotype map adds a third complication. Quantitative genetics approximates the map with linear models, while developmental biology finds it to be highly nonlinear and complex. When predictions from the multivariate breeder's equation were compared with observed change under a model of organ development, disagreements were frequent because the map was nonlinear [20]. This does not invalidate the breeder's equation. It defines the conditions under which the linear approximation holds and points to where improvements such as bias correction are needed [9].

Common Mistakes and Limitations

The most frequent error is treating heritability as a fixed property of a trait. A trait does not carry an h² value the way a gene carries a sequence. The number belongs to a population in an environment, and it moves when either moves.

The second error is reading h² as "the percent of an individual's trait that is genetic." An individual's phenotype is not a pie chart of genes and environment. Heritability describes variance across a population, and it says nothing about the developmental origin of one animal's or one plant's phenotype.

The third error is assuming high heritability means environment does not matter. A trait can have h² = 0.8 in an environment where everyone receives adequate nutrition, and the same trait can fall to 0.2 when nutrition varies widely. The genetic variance did not shrink. The environmental variance grew.

The fourth error is confusing narrow-sense and broad-sense values. When a paper reports H² = 0.6, that number cannot be plugged into the breeder's equation to predict selection response unless additive variance is known separately. In the bull semen data, the gap between H² (0.17 to 0.43) and h² (0.04 to 0.11) is large enough that using the wrong parameter would overpredict response by a factor of two to four [4].

The fifth error is transferring an estimate across populations without justification. An h² estimated in a temperate dairy population under intensive feeding does not describe a pasture-based herd in a different climate. The base-population issue compounds this. Estimates from pedigree and family data describe a hypothetical base population of independent, non-inbred individuals, and correcting to the current population requires a term such as the pedigree sparsity coefficient [1].

The sixth error is ignoring measurement error. Transient fluctuations and instrument noise bias heritability, selection gradients, and predicted response, and unbiased estimates require repeated measurements designed with the timing of repeats in mind [2].

The seventh error is overreading a single generation of selection response. Predicted and observed responses can disagree because the genotype-phenotype map is nonlinear, because unmeasured traits are under selection, or because variance estimates are imprecise [20]. A prediction that fails is diagnostic information, not proof that heritability is meaningless.

A final limitation is scale. Heritability estimates from small samples carry wide confidence intervals, and estimates from highly selected populations can be deflated because selection has already removed much of the additive variance. Individual breeding decisions and health screening still need a veterinarian or a qualified breeding advisor who can weigh the animal in front of them against its population context.

Quick Review

Heritability is the proportion of phenotypic variance in a population explained by genetic variance, not a property of an individual or a gene.
Narrow-sense heritability, h² = V_A / V_P, is the additive fraction and the parameter that predicts selection response.
Broad-sense heritability, H² = V_G / V_P, includes dominance and epistatic variance and is at least as large as h².
The breeder's equation R = h² × S converts heritability and selection differential into predicted genetic gain.
Estimates are population-specific and environment-specific, and pedigree-based estimates refer to a hypothetical base population that may need correction [1].
Measurement error and transient environmental effects bias heritability downward and require repeated measurements to control [2].
Reported values in real systems range widely, from 0.02 to 0.37 for cattle behavior traits [11] to 0.52 to 0.57 for Japanese Black cattle fatty acids [12] and 0.89 to 0.95 for full-sib family means in guineagrass [5].

Frequently Asked Questions

What is heritability in simple terms?

Heritability is a number between 0 and 1 that describes how much of the differences among individuals in a population come from genetic differences rather than environmental ones. A value near 0 means the environment explains most of the variation, and a value near 1 means genes explain most of it.

What is the heritability formula?

Narrow-sense heritability is h² = V_A / V_P, where V_A is additive genetic variance and V_P is total phenotypic variance. Broad-sense heritability is H² = V_G / V_P, where V_G includes additive, dominance, and epistatic variance. Phenotypic variance itself decomposes as V_P = V_G + V_E + V_GE.

What is the difference between narrow-sense and broad-sense heritability?

Narrow-sense heritability counts only additive genetic effects, the part that reliably passes from parent to offspring and drives selection response. Broad-sense heritability counts all genetic effects, including dominance and epistasis, so it is always equal to or larger than the narrow-sense value.

Can heritability be greater than 1 or less than 0?

In theory, no. Both are ratios of variance components, and the genetic component cannot exceed the total phenotypic variance. In practice, a published estimate can fall outside the range because of sampling error, small sample size, or model misspecification, and such values signal a problem with the analysis rather than a biological discovery.

Why do heritability estimates differ between populations?

Because heritability is a ratio, and both the numerator and the denominator change with the population and the environment. A population with little additive variance, or one measured across a wide range of environments, will show a lower heritability than a genetically diverse population measured under uniform conditions.

What is the breeder's equation used for?

The breeder's equation, R = h² × S, predicts how much a population mean will change in one generation of selection. It is used to plan selection programs, compare candidate traits, and forecast genetic gain in livestock, crops, and conservation breeding.