BiologyQuantitative GeneticsUniversity

AQAAPOntarioNSWCBSEGCE O-LevelMoECAPS

Narrow-sense Heritability

Measures the proportion of phenotypic variance attributable to additive genetic variance.

Understand the formulaSee the free derivationOpen the full walkthrough

h^{2} = \frac{V _{A}}{V _{P}}

Open Full Walkthrough Try Calculator

This public page keeps the free explanation visible and leaves premium worked solving, advanced walkthroughs, and saved study tools inside the app.

Core idea

Overview

Narrow-sense heritability ($h^2 = \frac{V_A}{V_P}$) is a key concept in quantitative genetics, quantifying the extent to which offspring resemble their parents due to additive genetic effects. It represents the proportion of the total phenotypic variance ($V_P$) in a trait that is due to additive genetic variance ($V_A$). This measure is crucial for predicting the response of a population to selection and for understanding the genetic basis of complex traits.

When to use: Apply this equation when studying quantitative traits (e.g., height, weight, yield) in populations to estimate the potential for evolutionary change or the effectiveness of selective breeding programs. It is used when you have estimates of additive genetic variance and total phenotypic variance for a specific trait.

Why it matters: Narrow-sense heritability is fundamental for understanding how traits evolve and how they can be manipulated through breeding. It informs agricultural practices, conservation efforts, and medical research by indicating the degree to which genetic factors contribute to observable differences among individuals, particularly those that can be passed on to the next generation.

Symbols

Variables

V_A = Additive Genetic Variance, V_P = Phenotypic Variance, h^2 = Narrow-sense Heritability

V_{A}

Additive Genetic Variance

u ni t s^{2}

V_{P}

Phenotypic Variance

u ni t s^{2}

h^{2}

Narrow-sense Heritability

d im e n s i o n l ess

Walkthrough

Derivation

Formula: Narrow-sense Heritability

Narrow-sense heritability quantifies the proportion of phenotypic variance due to additive genetic effects, crucial for predicting response to selection.

Genetic and environmental effects are independent (no GxE interaction).
No epistasis or dominance variance is considered for narrow-sense heritability.
The population is randomly mating.

Define Phenotypic Variance:

The total phenotypic variance ( $V_{P}$ ) observed in a population for a quantitative trait can be partitioned into genetic variance ( $V_{G}$ ) and environmental variance ( $V_{E}$ ). This is the simplest model, assuming no gene-environment interaction.

V_{P} = V_{G} + V_{E}

Partition Genetic Variance:

Genetic variance ( $V_{G}$ ) can be further partitioned into additive genetic variance ( $V_{A}$ ), dominance variance ( $V_{D}$ ), and epistatic (interaction) variance ( $V_{I}$ ). Additive genetic variance ( $V_{A}$ ) is the component that contributes directly to the resemblance between relatives and is most relevant for predicting response to selection.

V_{G} = V_{A} + V_{D} + V_{I}

Define Narrow-sense Heritability:

Narrow-sense heritability ( $h^{2}$ ) is defined as the ratio of the additive genetic variance ( $V_{A}$ ) to the total phenotypic variance ( $V_{P}$ ). It specifically measures the proportion of phenotypic variation that is due to additive genetic effects, which are directly transmissible from parents to offspring.

h^{2} = \frac{V _{A}}{V _{P}}

Note: This definition highlights the importance of $V_{A}$ for predicting how a population will respond to natural or artificial selection, as only additive genetic effects are reliably passed on.

Result

h^{2} = \frac{V _{A}}{V _{P}}

Source: Falconer, D. S., & Mackay, T. F. C. (1996). Introduction to Quantitative Genetics (4th ed.). Longman.

Free formulas

Rearrangements

Solve for $V_{A}$

Narrow-sense Heritability: Make $V_{A}$ the subject

V_{A} = h^{2} V_{P}

To make $V_{A}$ (additive genetic variance) the subject, multiply both sides of the narrow-sense heritability formula by $V_{P}$ .

Difficulty: 1/5

Solve for $V_{P}$

Narrow-sense Heritability: Make $V_{P}$ the subject

V_{P} = \frac{V _{A}}{h ^{2}}

To make $V_{P}$ (phenotypic variance) the subject, first multiply both sides by $V_{P}$ , then divide by $h^{2}$ .

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin with a slope equal to 1/V_P. A small x-value indicates that additive genetic variance contributes little to the total phenotypic variance, while a large x-value suggests that genetic differences are the primary driver of trait variation. The most important feature is the linear relationship, meaning that doubling the additive genetic variance results in a direct doubling of the narrow-sense heritability.

Graph type: linear

Why it behaves this way

Intuition

Envision the total variation of a trait in a population as a whole pie, where narrow-sense heritability represents the specific slice of that pie that can be reliably attributed to the additive effects of genes passed

h^{2}

The proportion of the total phenotypic variance in a trait that is due to additive genetic variance.

Indicates how much of the observable differences among individuals for a trait can be directly inherited and acted upon by selection.

V_{A}

The component of genetic variance that arises from the average effects of individual alleles, independent of dominance or epistasis.

The portion of genetic variation that 'breeds true' and is most relevant for predicting how a population will respond to selection.

V_{P}

The total observable variation among individuals in a population for a specific trait.

Represents all the differences observed in a trait, encompassing genetic, environmental, and interaction effects.

Free study cues

Insight

Canonical usage

Narrow-sense heritability is a dimensionless quantity, representing a proportion, and thus requires that the additive genetic variance and total phenotypic variance are expressed in consistent units, which then cancel

Common confusion

A common mistake is to assign units to $h^{2}$ or to use different units for $V_{A}$ and $V_{P}$ , which would prevent their cancellation and result in an incorrect dimensionless value.

Dimension note

Narrow-sense heritability is a ratio of two variances, both measured in the squared units of the phenotypic trait (e.g., $c m^{2}$ for height, $k g^{2}$ for weight).

Unit systems

$h^{2}$ dimensionless · Represents a proportion, ranging from 0 to 1.

$V_{A}$ unit of trait squared · Must be in the same squared units as V_P for unit cancellation.

$V_{P}$ unit of trait squared · Must be in the same squared units as V_A for unit cancellation.

Ballpark figures

Quantity:

One free problem

Practice Problem

In a population of dairy cows, the additive genetic variance ( $V_{A}$ ) for milk production is estimated to be 150 units $^{2}$ , and the total phenotypic variance ( $V_{P}$ ) is 400 units $^{2}$ . Calculate the narrow-sense heritability for milk production.

Additive Genetic Variance150 units^2

Phenotypic Variance400 units^2

Solve for: $h_{p} o w_{2}$

Hint: Ensure both variances are in consistent units.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Predicting the response of a crop yield to selective breeding over generations.

Study smarter

Tips

$h^{2}$ ranges from 0 to 1. A value of 0 means no additive genetic contribution, 1 means all phenotypic variance is additive genetic.
$V_{A}$ is the variance due to additive effects of alleles, which are directly passed from parent to offspring.
$V_{P}$ is the total phenotypic variance, including genetic, environmental, and interaction effects.
Heritability is specific to a population and environment; it is not a fixed value for a trait.

Avoid these traps

Common Mistakes

Confusing narrow-sense heritability with broad-sense heritability ( $H^{2} = V_{G} / V_{P}$ ).
Interpreting heritability as the proportion of a trait determined by genes in an individual.
Assuming heritability is constant across different environments or populations.

Common questions

Frequently Asked Questions

Narrow-sense heritability quantifies the proportion of phenotypic variance due to additive genetic effects, crucial for predicting response to selection.

Apply this equation when studying quantitative traits (e.g., height, weight, yield) in populations to estimate the potential for evolutionary change or the effectiveness of selective breeding programs. It is used when you have estimates of additive genetic variance and total phenotypic variance for a specific trait.

Narrow-sense heritability is fundamental for understanding how traits evolve and how they can be manipulated through breeding. It informs agricultural practices, conservation efforts, and medical research by indicating the degree to which genetic factors contribute to observable differences among individuals, particularly those that can be passed on to the next generation.

Confusing narrow-sense heritability with broad-sense heritability ($H^2 = V_G / V_P$). Interpreting heritability as the proportion of a trait determined by genes in an individual. Assuming heritability is constant across different environments or populations.

Predicting the response of a crop yield to selective breeding over generations.

$h^2$ ranges from 0 to 1. A value of 0 means no additive genetic contribution, 1 means all phenotypic variance is additive genetic. $V_A$ is the variance due to additive effects of alleles, which are directly passed from parent to offspring. $V_P$ is the total phenotypic variance, including genetic, environmental, and interaction effects. Heritability is specific to a population and environment; it is not a fixed value for a trait.

References

Sources

Introduction to Quantitative Genetics by D.S. Falconer and T.F.C. Mackay
Wikipedia: Heritability
Falconer, D.S., and Mackay, T.F.C. Introduction to Quantitative Genetics. 4th ed. Pearson Education Limited, 1996.
Griffiths, A.J.F., Wessler, S.R., Carroll, S.B., and Doebley, J. Introduction to Genetic Analysis. 11th ed. W. H. Freeman, 2015.
Wikipedia article 'Heritability'
Falconer, D. S., & Mackay, T. F. C. (1996). Introduction to Quantitative Genetics (4th ed.). Longman.

Narrow-sense Heritability

Overview

Variables

Derivation

Define Phenotypic Variance:

Partition Genetic Variance:

Define Narrow-sense Heritability:

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Broad-sense Heritability

Phenotypic Variance

Response to Selection

Frequently Asked Questions

Sources