Heritability Calculator: Broad-Sense vs. Narrow-Sense

This calculator clarifies a common point of confusion: the difference between broad-sense heritability (H²), which considers all genetic factors, and narrow-sense heritability (h²), which relies specifically on **additive genetic variance**. The initial premise that “broad-sense heritability uses only additive genetic variance” is incorrect, and this tool is designed to demonstrate why.

Calculate Heritability

What is Heritability? A Clarification

Heritability is a fundamental concept in genetics that measures the proportion of variation in a trait within a population that is due to genetic variation. However, there’s a critical distinction that addresses the statement: **broad-sense heritability uses only additive genetic variance in its calculation**. This statement is factually incorrect. It is **narrow-sense heritability (h²)** that exclusively uses additive genetic variance. Broad-sense heritability (H²) encompasses all sources of genetic variance.

Understanding this difference is crucial for fields like plant and animal breeding, evolutionary biology, and human genetics. Broad-sense heritability provides an estimate of the overall genetic influence on a trait, while narrow-sense heritability offers a more practical measure of how a trait will respond to selective pressures, as it is the additive component that is reliably passed from parent to offspring.

Heritability Formulas and Explanation

The calculation of heritability relies on partitioning the total observed variation of a trait, known as Phenotypic Variance (Vp), into its genetic and environmental components.

The foundational equation is:

Vp = Vg + Ve

Where Vg (Genetic Variance) is further broken down:

Vg = Va + Vd + Vi

• Narrow-Sense Heritability (h²) measures the proportion of phenotypic variance that is due to additive genetic variance alone. It is the most important measure for predicting the response of a population to natural or artificial selection.
  
  Formula: h² = Va / Vp
• Broad-Sense Heritability (H²) measures the proportion of phenotypic variance due to all genetic factors combined. This provides a more holistic but less predictive view of the genetic contribution to a trait.
  
  Formula: H² = Vg / Vp = (Va + Vd + Vi) / Vp

Description of Variance Components

Variable	Meaning	Unit	Typical Range
Vp	Total Phenotypic Variance	Unitless / Trait Unit²	Greater than 0
Vg	Total Genetic Variance	Unitless / Trait Unit²	0 to Vp
Ve	Environmental Variance	Unitless / Trait Unit²	0 to Vp
Va	Additive Genetic Variance	Unitless / Trait Unit²	0 to Vg
Vd	Dominance Genetic Variance	Unitless / Trait Unit²	0 to Vg
Vi	Epistatic Genetic Variance	Unitless / Trait Unit²	0 to Vg

Practical Examples

Example 1: Crop Yield

A plant breeder is studying the heritability of grain yield in a specific corn population.

• Inputs: Va = 30, Vd = 15, Vi = 5, Ve = 50
• Intermediate Calculations:
  • Vg = 30 + 15 + 5 = 50
  • Vp = 50 + 50 = 100
• Results:
  • h² (Narrow-Sense) = 30 / 100 = 0.30. This suggests that 30% of the variation in yield is due to additive effects, indicating a moderate potential for improvement through selective breeding.
  • H² (Broad-Sense) = 50 / 100 = 0.50. This shows that half of the total variation in yield is due to genetic factors of all types.

Example 2: Animal Body Weight

A researcher investigates the genetic basis for body weight variation in a controlled lab mouse population.

• Inputs: Va = 15, Vd = 5, Vi = 2, Ve = 78
• Intermediate Calculations:
  • Vg = 15 + 5 + 2 = 22
  • Vp = 22 + 78 = 100
• Results:
  • h² (Narrow-Sense) = 15 / 100 = 0.15. A low narrow-sense heritability implies that selecting for heavier mice will result in slow progress.
  • H² (Broad-Sense) = 22 / 100 = 0.22. While genetics play a role, the high environmental variance (Ve=78) indicates that factors like diet and housing have a much larger impact on body weight variation in this group.

How to Use This Heritability Calculator

1. Enter Variance Components: Input the estimated values for the four types of variance (Additive, Dominance, Epistatic, and Environmental) into their respective fields. These values are typically derived from complex statistical analysis of population data (e.g., parent-offspring regression or twin studies).
2. Observe Real-Time Results: The calculator automatically updates the results as you type. No need to press a calculate button.
3. Interpret the Outputs:
   • h² (Narrow-Sense): This is your key metric for predicting how a trait will change under selection. Higher values (closer to 1.0) mean selection will be more effective.
   • H² (Broad-Sense): This gives you a general idea of the total genetic influence on the trait’s variation. The gap between H² and h² reveals the impact of non-additive genetic effects (dominance and epistasis).
   • Variance Chart: The visual chart helps you quickly see the proportion of each component. It highlights why phenotypic variance is often mostly driven by environmental factors, and why additive variance can be a small fraction of the total genetic variance.
4. Reset or Copy: Use the “Reset” button to return to the default values. Use the “Copy Results” button to save your findings to your clipboard for notes or reports.

Key Factors That Affect Heritability

• Population Genetic Structure: Heritability is specific to the population being measured. A population with little genetic diversity will have low heritability for a trait, even if that trait is heavily controlled by genes.
• Environmental Variation: In a highly controlled, uniform environment, Ve is low, which can artificially inflate heritability estimates. Conversely, a highly variable environment increases Ve and lowers heritability.
• Measurement Accuracy: Errors in measuring the phenotype contribute to Ve, reducing the calculated heritability. Precise measurements are crucial for accurate estimates.
• Gene-Environment Interaction (GxE): The formula assumes genetic and environmental effects are independent. However, sometimes the effect of a gene depends on the environment, a complexity that standard models don’t capture and can alter heritability.
• Age and Developmental Stage: The heritability of a trait can change over an organism’s lifetime. For example, the heritability of height in humans is different in childhood versus adulthood. You can learn more about this by reading a phenotype expression guide.
• Method of Estimation: Different statistical methods (e.g., parent-offspring comparison, twin studies, genomic analysis) can yield different heritability estimates due to their underlying assumptions. Using a statistical variance calculator can help explore these assumptions.

Frequently Asked Questions (FAQ)

1. Why is the statement “broad-sense heritability uses only additive genetic variance” incorrect?

This is incorrect because it confuses broad-sense with narrow-sense heritability. Broad-sense (H²) is a measure of all genetic influences (Va + Vd + Vi), while narrow-sense (h²) specifically isolates the additive component (Va), which is reliably passed to offspring. For more detail, see our article on the components of genetic drift.

2. Why is narrow-sense heritability (h²) more useful for breeders?

Breeders want to predict how a population will respond to selection. Only the additive effects of genes are predictably passed from parents to offspring. Dominance and epistatic effects are shuffled and broken up during sexual reproduction, making them unreliable for predicting the traits of the next generation. Therefore, h² is the breeder’s most valuable metric.

3. Can heritability be 100% (or 1.0)?

Theoretically, yes. A heritability of 1.0 would mean all variation in a trait within a population is due to genetic differences, with zero environmental influence. This is extremely rare in real-world biology. Even for highly genetic traits, there is usually some environmental component or measurement error.

4. Can heritability be 0%?

Yes. If there is no genetic variation for a trait in a population (e.g., in a clonal population or an inbred line), then Vg = 0, and heritability is 0. This doesn’t mean genes don’t control the trait, only that there are no genetic differences among individuals to account for the phenotypic variation.

5. Do the variance values have units?

The units of variance are the square of the original trait’s units (e.g., cm² for height in cm). However, for simplicity and general applicability, they are often treated as unitless ratios in calculators like this, as heritability itself is a dimensionless ratio (a proportion).

6. What is a “good” heritability value?

It depends on the context. For selective breeding, an h² above 0.3 is often considered useful for making progress. For complex human traits, h² values are often lower. There’s no universal “good” value; its utility is relative to the research or breeding goal.

7. Does high heritability mean a trait cannot be changed by the environment?

No, this is a common misconception. Heritability describes the source of variation in a population, not the degree to which a trait is fixed. A highly heritable trait like height can still be profoundly affected by environmental factors like nutrition.

8. Where do the initial variance numbers come from?

They are estimated from population data using statistical techniques. For example, by measuring traits in parents and offspring across many families, one can perform a regression analysis to estimate the additive genetic variance (Va). Full-sibling and half-sibling studies can help parse out dominance (Vd) and epistatic (Vi) variances.

Related Tools and Internal Resources

Explore these related topics to deepen your understanding of quantitative genetics and population dynamics:

• Phenotype Expression Guide: Learn how genotypes translate into observable traits.
• Statistical Variance Calculator: A tool for basic statistical variance calculations.
• Genetic Drift Simulation: Understand how random chance affects allele frequencies in a population.
• Population Growth Calculator: Model how populations change over time based on different factors.
• Allele Frequency Calculator: Calculate allele and genotype frequencies in a population.
• Hardy-Weinberg Equilibrium Calculator: Test if a population is evolving.