Heritability: Broad Sense and Narrow Sense in Quantitative Genetics

Heritability in Quantitative Genetics

Introduction to Heritability

Heritability is a key concept in quantitative genetics, describing the proportion of observed variation in a trait that can be attributed to genetic factors. It is essential for understanding how traits are inherited and how populations respond to selection, especially in breeding and evolutionary biology.

Partitioning Phenotypic Variance

Components of Phenotypic Variance

Total phenotypic variance (VT) in a population can be partitioned into genetic and environmental components. This partitioning helps to distinguish the sources of variation in quantitative traits.

• Genetic variance (VG): Variation due to genetic differences among individuals.

• Environmental variance (VE): Variation due to differences in environmental conditions experienced by individuals (e.g., light, temperature, nutrition).

The total variance can be expressed as:

$V_T = V_E + V_G$

Genetic variance can be further subdivided into:

• Additive genetic variance (VA): The sum of the average effects of individual alleles. This is the main component transmitted from parents to offspring.

• Dominance variance (VD): Variation due to interactions between alleles at the same locus (dominance effects).

• Epistatic variance (VI): Variation due to interactions between alleles at different loci (epistasis).

Thus, the full partition is:

$V_T = V_E + (V_A + V_D + V_I)$

or

$V_T = V_E + V_G$ where $V_G = V_A + V_D + V_I$

Examples of Genetic Variance Components

• Additive variance: Each additional allele adds a consistent, predictable effect to the phenotype (e.g., plant height increases by a fixed amount per allele).

• Dominance variance: The effect of an allele depends on the other allele present (e.g., heterozygote has the same phenotype as one homozygote, masking the other allele’s effect).

• Epistatic variance: Alleles at one gene can mask or alter the expression of alleles at another gene (e.g., recessive homozygous a masks the effect of B and b alleles).

Broad-Sense and Narrow-Sense Heritability

Definitions and Interpretation

Heritability quantifies the proportion of phenotypic variance attributable to genetic factors. There are two main types:

• Broad-sense heritability (H2): Measures the proportion of total phenotypic variance due to all genetic variance (additive, dominance, and epistatic).

• Narrow-sense heritability (h2): Measures the proportion of total phenotypic variance due only to additive genetic variance.

Formulas:

$H^2 = \frac{V_G}{V_T}$

$h^2 = \frac{V_A}{V_T}$

Interpretation:

• High h2 means a trait is strongly influenced by additive genetic factors and will respond well to selection.

• Low h2 means environmental factors or non-additive genetic effects are more important.

Examples of Narrow-Sense Heritability in Agriculture

Narrow-sense heritability is especially important in plant and animal breeding, as it predicts the response to selection.

Organism	Trait	Heritability (h2)
Cattle	Body weight	0.65
Cattle	Milk production	0.40
Corn	Plant height	0.70
Corn	Ear length	0.55
Corn	Ear diameter	0.14
Horse	Racing speed	0.60
Horse	Trotting speed	0.40
Pig	Back-fat thickness	0.70
Pig	Weight gain	0.40
Pig	Litter size	0.05
Poultry	Body weight (8 weeks)	0.50
Poultry	Egg production	0.20

Calculating Heritability

Estimating Broad-Sense Heritability

Broad-sense heritability is calculated as:

$H^2 = \frac{V_G}{V_T}$

Where:

• VG = Genetic variance

• VT = Total phenotypic variance

Estimating Narrow-Sense Heritability

Narrow-sense heritability is calculated as:

$h^2 = \frac{V_A}{V_T}$

Where:

• VA = Additive genetic variance

• VT = Total phenotypic variance

Predicting Offspring Phenotypes Using Narrow-Sense Heritability

Parent–Offspring Regression Equation

Narrow-sense heritability can be used to predict the mean phenotype of offspring based on parental values. The equation is:

$T_O = \mu + h^2 \left[ \frac{T_M + T_F}{2} - \mu \right]$

• TO: Predicted mean trait value of offspring

• μ: Population mean trait value

• TM: Trait value of male parent

• TF: Trait value of female parent

• h2: Narrow-sense heritability

Worked Example

• Population mean (μ): 100

• Male parent (TM): 110

• Female parent (TF): 120

• Narrow-sense heritability (h2): 0.4

Step 1: Calculate midparent value: (110 + 120)/2 = 115

Step 2: Deviation from mean: 115 - 100 = 15

Step 3: Multiply by h2: 0.4 × 15 = 6

Step 4: Add to mean: 100 + 6 = 106 (predicted offspring mean)

Heritability and Response to Selection

The Breeder’s Equation

The breeder’s equation relates heritability to the response to selection in a population:

$h^2 = \frac{R}{S}$

• R: Response to selection (difference between offspring mean and original population mean)

• S: Selection differential (difference between selected parents’ mean and original population mean)

Worked Example

• Mean of selected parents (Ts): 40

• Population mean (μ): 30

• Offspring mean (TO): 33

Selection differential: S = 40 - 30 = 10

Response to selection: R = 33 - 30 = 3

Heritability: $h^2 = \frac{3}{10} = 0.3$

Interpreting Heritability Values

Understanding the Extremes

• If h2 = 1: All variation is genetic; offspring mean equals selected parents’ mean.

• If h2 = 0: All variation is environmental; selection has no effect on offspring mean.

• Intermediate values: Both genetics and environment contribute; response to selection is proportional to h2.

Heritability and Population Genetics

Genetic Basis of Response to Selection

When a population responds to selection (R > 0), the frequency of beneficial alleles increases in the population. This connects quantitative genetics to population genetics, as selection alters allele frequencies over generations.

Summary Table: Key Equations in Heritability

Equation	Description
$H^2 = \frac{V_G}{V_T}$	Broad-sense heritability
$h^2 = \frac{V_A}{V_T}$	Narrow-sense heritability
$T_O = \mu + h^2 \left[ \frac{T_M + T_F}{2} - \mu \right]$	Predicting offspring mean
$h^2 = \frac{R}{S}$	Breeder’s equation (response to selection)