Understanding Heritability: Broad vs. Narrow Sense
Before delving into the specifics of the narrow sense heritability formula, it is essential to distinguish between the different types of heritability:
Broad Sense Heritability (H2)
- Represents the proportion of total phenotypic variance that is attributable to all genetic variance, including additive, dominance, and epistatic interactions.
- Expressed as:
\[
H^2 = \frac{\sigma^2_G}{\sigma^2_P}
\]
where:
- \(\sigma^2_G\) = total genetic variance
- \(\sigma^2_P\) = total phenotypic variance
Narrow Sense Heritability (h2)
- Focuses solely on the additive genetic variance, which is the component of genetic variance that can be transmitted from parents to offspring.
- It is more relevant for predicting the response to selection because additive effects are inherited in a predictable manner.
- The formula for narrow sense heritability is central to breeding programs aiming to improve specific traits.
Defining Narrow Sense Heritability
Narrow sense heritability (h2) is defined as the ratio of the additive genetic variance (\(\sigma^2_A\)) to the total phenotypic variance (\(\sigma^2_P\)):
\[
h^2 = \frac{\sigma^2_A}{\sigma^2_P}
\]
This ratio indicates the proportion of observed variation in a trait that is due to additive genetic effects, which are the effects that can be summed up across loci and reliably passed from parents to offspring.
The Narrow Sense Heritability Formula
The core formula for narrow sense heritability can be expressed as:
\[
h^2 = \frac{\text{Additive Genetic Variance} (\sigma^2_A)}{\text{Phenotypic Variance} (\sigma^2_P)}
\]
where:
- \(\sigma^2_A\) (additive genetic variance) reflects the variance attributable to the additive effects of genes.
- \(\sigma^2_P\) (phenotypic variance) includes all sources of variation in the phenotype, such as genetic, environmental, and their interactions.
In practice, the heritability is estimated using various methods, including:
1. Parent-Offspring Regression Method
2. Sibling Analysis
3. Variance Components Analysis (ANOVA) or Maximum Likelihood Estimation
4. Selection Response Method
Each method involves specific calculations and assumptions, which we will explore further.
Methods of Estimating Narrow Sense Heritability
Estimating h2 accurately is vital for making predictions about the response to selection. Here are the most common methods:
1. Parent-Offspring Regression
- Concept: The phenotypic values of offspring are regressed against the phenotypic values of their parents.
- Formula:
\[
h^2 = \text{Regression coefficient of offspring on parent}
\]
- Procedure:
- Plot offspring phenotype against parent phenotype.
- Calculate the slope of the regression line.
- The slope provides an estimate of h2 in the case of a single parent; if using mid-parent values, it provides a more accurate estimate.
- Advantages:
- Simple to implement.
- Useful when individual parent-offspring data are available.
- Limitations:
- Assumes no environmental covariance between parent and offspring.
- Requires large sample sizes for accuracy.
2. Sibling Analysis
- Concept: Comparing phenotypic similarities among siblings, especially monozygotic (identical) and dizygotic (fraternal) twins in humans.
- Application: In plant and animal breeding, half-sibs or full-sibs are used.
- Calculation:
- Based on the variance among siblings, heritability can be estimated as:
\[
h^2 = \frac{4 \times \text{Covariance among siblings}}{\text{Phenotypic variance}}
\]
- Advantages:
- Useful in natural populations and breeding populations.
- Limitations:
- Environmental effects shared among siblings can bias estimates.
3. Variance Components Analysis (ANOVA)
- Concept: Partitioning phenotypic variance into genetic and environmental components through experimental designs.
- Procedure:
- Use analysis of variance to estimate variance components.
- Calculate additive genetic variance (\(\sigma^2_A\)) from the variance among related individuals.
- Heritability is then:
\[
h^2 = \frac{\sigma^2_A}{\sigma^2_P}
\]
- Advantages:
- More precise, especially with well-designed experiments.
4. Response to Selection (Breeder’s Equation)
- Concept: Heritability can be inferred from the response to selection (\(R\)) and the selection differential (\(S\)) using the breeder’s equation:
\[
R = h^2 \times S
\]
- Application:
- Measure the mean phenotype before and after selection.
- Calculate the response and selection differential.
- Rearrange to estimate heritability:
\[
h^2 = \frac{R}{S}
\]
Significance and Applications of Narrow Sense Heritability
Understanding and estimating narrow sense heritability has broad implications:
1. Plant and Animal Breeding
- Determines the potential for improvement of traits through selection.
- High h2 indicates that selection will be effective.
- Guides breeders in choosing traits to focus on.
2. Evolutionary Biology
- Helps predict how populations will respond to natural selection.
- Understanding the genetic basis of traits under selection pressure.
3. Conservation Genetics
- Assists in understanding the genetic variability within populations.
- Guides management strategies to preserve genetic diversity.
4. Medical Genetics and Human Traits
- Helps quantify the inheritance of complex traits and diseases.
- Informs public health strategies.
Factors Affecting Heritability Estimates
Several factors can influence the accuracy and interpretation of heritability estimates:
- Environmental Variance: High environmental variance can reduce heritability estimates.
- Population Structure: Non-random mating and population stratification can bias estimates.
- Genotype-Environment Interaction: When different genotypes respond differently to environments, heritability estimates may vary across environments.
- Sampling Error: Small sample sizes can lead to unreliable estimates.
Limitations of Narrow Sense Heritability
While useful, the concept has limitations:
- Context-Dependence: Heritability estimates are specific to populations and environments; they do not apply universally.
- Non-Additive Effects Ignored: Dominance and epistatic interactions are not captured.
- Assumption of Random Mating: Violations can bias estimates.
- Static Nature: Heritability can change over time with shifts in genetic and environmental variance.
Conclusion
The narrow sense heritability formula—\[
h^2 = \frac{\sigma^2_A}{\sigma^2_P}
\]—is a cornerstone of quantitative genetics, providing a quantitative measure of the transmissibility of traits due to additive genetic factors. Its estimation through various methods allows geneticists and breeders to predict the response to selection, understand the genetic architecture of traits, and make informed decisions in genetic improvement programs. Despite its limitations, understanding and accurately estimating narrow sense heritability remains crucial in advancing breeding strategies, conserving genetic diversity, and unraveling the genetic basis of complex traits. As research progresses, integrating molecular genetic data with traditional heritability estimates continues to enhance our understanding of heredity and the potential for genetic improvement across species.
Frequently Asked Questions
What is the formula for narrow sense heritability?
The formula for narrow sense heritability (h²) is h² = VA / VP, where VA is the additive genetic variance and VP is the total phenotypic variance.
How is narrow sense heritability different from broad sense heritability?
Narrow sense heritability considers only additive genetic variance (VA), whereas broad sense heritability includes all genetic variance components, such as dominance and epistatic variances.
Why is narrow sense heritability important in plant and animal breeding?
Because it predicts the response to selection by estimating the proportion of phenotypic variation attributable to additive genetic factors, which are reliably transmitted to offspring.
How can narrow sense heritability be estimated in practice?
It can be estimated using parent-offspring regression, sibling analysis, or variance components analysis from controlled breeding experiments.
What assumptions are made when using the narrow sense heritability formula?
Assumptions include that the traits are influenced primarily by additive genetic factors, environmental effects are random and not correlated with genetics, and the population is in genetic equilibrium.
Can the narrow sense heritability formula be applied to all traits?
No, it is most applicable to traits primarily controlled by additive genes; traits with significant dominance or epistatic interactions may require different models.
What does a high narrow sense heritability value indicate?
It indicates that a large proportion of the phenotypic variation is due to additive genetic factors, suggesting that selection will be effective in improving the trait.
