Broad-Sense Heritability (H²) Calculator
Estimate the proportion of trait variation due to genetics.
The portion of total phenotypic variation in a trait that is due to genetic differences among individuals. This is a statistical value and has no units.
The portion of total phenotypic variation that is due to environmental differences and experiences among individuals. This is also a unitless statistical value.
Broad-Sense Heritability (H²)
Total Phenotypic Variance (Vp): 10.0
Formula: H² = Vg / (Vg + Ve)
Chart: Contribution of Genetic (Vg) vs. Environmental (Ve) Variance to Total Phenotypic Variance (Vp)
What is Broad-Sense Heritability?
Broad-sense heritability (represented as H² or H2) is a fundamental concept in genetics that quantifies the degree to which phenotypic variation within a population can be attributed to genetic variation among individuals. In simpler terms, it answers the question: “How much of the differences we see in a trait (like height, weight, or disease susceptibility) are due to differences in genes?” Since broad-sense heritability uses all genetic variance in its calculation, it provides the most comprehensive measure of genetic influence.
This calculator is for anyone studying quantitative genetics, including students, breeders, and researchers. It helps to understand that H² is a population-specific measure, not a fixed value for a trait, and can change depending on the population and the environment being studied.
The Formula for Broad-Sense Heritability
The calculation is based on partitioning the total observable variation in a trait into its genetic and environmental components. The formula is elegantly simple:
H² = Vg / Vp
Where:
- Vp (Phenotypic Variance) is the total observed variation in a trait.
- Vg (Genetic Variance) is the portion of that variation caused by genetic differences.
The total phenotypic variance (Vp) is the sum of the genetic variance (Vg) and the environmental variance (Ve). Therefore, the full formula used in this calculator is:
H² = Vg / (Vg + Ve)
Broad-sense heritability uses all genetic variance in its calculation, which includes additive, dominance, and epistatic (gene-gene interaction) effects. This makes it a complete measure of the genetic contribution to a trait’s variation.
Variables Table
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Vg | Genetic Variance | Unitless (statistical variance) | 0 to positive infinity |
| Ve | Environmental Variance | Unitless (statistical variance) | 0 to positive infinity |
| Vp | Phenotypic Variance (Vg + Ve) | Unitless (statistical variance) | 0 to positive infinity |
| H² | Broad-Sense Heritability | Unitless (proportion) | 0.0 to 1.0 |
Practical Examples
Example 1: Crop Yield
A plant breeder is studying a new variety of corn. They measure the yield across many individual plants grown in a controlled environment and find the following variance components:
- Genetic Variance (Vg): 8.5
- Environmental Variance (Ve): 3.5
Using the calculator:
Vp = 8.5 + 3.5 = 12.0
H² = 8.5 / 12.0 = 0.71
A broad-sense heritability of 0.71 suggests that 71% of the observed variation in corn yield in this population is due to genetic differences, making it a good candidate for selective breeding.
Example 2: Animal Body Weight
A researcher studies the body weight of a specific fish species in a large lake. They find:
- Genetic Variance (Vg): 2.2
- Environmental Variance (Ve): 7.8
Using the calculator:
Vp = 2.2 + 7.8 = 10.0
H² = 2.2 / 10.0 = 0.22
A value of 0.22 indicates that only 22% of the variation in body weight is due to genetics, while 78% is due to environmental factors like food availability, water temperature, and competition. This information is crucial for understanding the population’s ecology. For more on this, see how to estimate heritability.
How to Use This Broad-Sense Heritability Calculator
Follow these simple steps to calculate H²:
- Enter Genetic Variance (Vg): Input the calculated variance component that is due to genetic factors into the first field.
- Enter Environmental Variance (Ve): Input the variance component attributed to environmental factors into the second field.
- Review the Results: The calculator will instantly update. The primary result is the Broad-Sense Heritability (H²), a value between 0 and 1. You will also see the intermediate calculation for Total Phenotypic Variance (Vp).
- Interpret the Chart: The bar chart visually represents how much of the total variance is genetic versus environmental, providing an intuitive understanding of the H² value.
Key Factors That Affect Broad-Sense Heritability
- Population Diversity: A more genetically diverse population will naturally have a higher Vg, potentially increasing the H² estimate.
- Environmental Uniformity: If an experiment is conducted in a highly controlled, uniform environment, Ve will be low, causing H² to be artificially high. Conversely, a highly variable environment increases Ve and decreases H².
- Measurement Accuracy: Errors in measuring a trait can inflate the environmental variance (Ve), leading to an underestimation of heritability.
- Gene-Environment Interaction: The model assumes Vg and Ve are independent. However, sometimes certain genotypes perform better in specific environments, an effect that can complicate heritability estimates.
- Developmental Stage: The heritability of a trait can change over an organism’s lifetime. For instance, the genetic influence on height is different in infants versus adults.
- Inclusion of All Genetic Factors: A key strength is that broad-sense heritability uses all genetic variance in its calculation, including dominance and epistasis, which are often excluded in simpler models like narrow-sense heritability. Understanding this is key to grasping the role of genetics.
Frequently Asked Questions (FAQ)
- What does a heritability of 1 mean?
- An H² of 1.0 means that 100% of the observed variation in the trait within that population is due to genetic differences among individuals (Ve = 0). This is rare in complex traits.
- What does a heritability of 0 mean?
- An H² of 0.0 means that all observed variation is due to environmental factors, and there is no genetic variation for the trait in the population (Vg = 0).
- Is heritability the same as inheritance?
- No. Heritability is a population-level statistic, not an individual one. It describes what proportion of variation *in a group* is due to genes. Inheritance refers to the genetic traits passed from parent to child.
- Why is it called “broad-sense”?
- Because it includes *all* sources of genetic variance (additive, dominance, and epistasis). This is in contrast to “narrow-sense” heritability (h²), which only considers additive genetic variance and is more useful for predicting response to selection in sexual populations.
- Can a trait be genetic but have low heritability?
- Yes. For example, having two eyes is a genetic trait in humans. But because there is virtually no variation in the number of eyes in the human population, the genetic variance (Vg) is zero, and thus the heritability of “number of eyes” is zero.
- Does high heritability mean a trait cannot be changed?
- No. Heritability describes the source of *variation*, not the fixedness of a trait. A highly heritable trait like height can still be heavily influenced by environmental factors like nutrition. More details on this can be found by researching the genetic epidemiology.
- Why are the input values unitless?
- Variance is a statistical measure. While the original trait (e.g., height in cm) has units, the variance (cm²) would have squared units. When you take the ratio of Vg to Vp, these units cancel out, resulting in a pure, unitless proportion for H².
- How does this relate to plant breeding?
- Breeders use heritability to predict how effectively they can improve a trait through selection. A high H² suggests that selecting individuals with desirable traits will lead to significant genetic gain in the next generation. This is a core part of plant breeding theory.