Quantitative Traits, Variance Components and Heritability
Many quantitative traits reflect several genes and environmental effects. Under stated assumptions, phenotypic variance can be divided into components. Broad-sense heritability uses total genetic variance; narrow-sense heritability uses additive genetic variance. Both describe a specified population and environment, not an individual's inherited percentage.
What a learner can do afterwards
- Splits stated variance components under a simplified model and calculates broad-sense or narrow-sense heritability.
- Predicts how heritability changes when environmental variance changes, with the relevant genetic variance and model assumptions held fixed.
- Rejects the interpretation that a heritability of 0.6 means sixty per cent of an individual's trait comes from genes.
1 · Read
Quantitative traits, such as height, are measured on a numerical scale. Many reflect several genes and environmental effects. They can vary continuously, but their distribution need not be an exact bell curve. The mean describes the centre of the measurements. Variance measures their spread around that mean. A difference between two means does not tell you their variances.
Use the simplified model V_P = V_G + V_E: phenotypic variance equals genetic plus environmental variance. Here we assume no genotype-environment covariance and omit genotype-by-environment interaction. Additive genetic variance V_A describes variation associated with average allele effects that add together. Other genetic components can include dominance and interactions between genes, like the epistasis studied earlier.
Broad-sense heritability H² = V_G/V_P divides total genetic variance by phenotypic variance. Narrow-sense h² = V_A/V_P uses additive genetic variance in the numerator. The superscript is part of the notation; do not square the ratio again. Here V_P = 100, V_G = 50 and V_A = 30, so H² = 0.5 and h² = 0.3. Use h² in the basic prediction of response to selection.
Heritability depends on the population and conditions. With V_P = V_G + V_E and V_G fixed, decreasing V_E raises H²; increasing V_E lowers it. The same reasoning applies to h² if V_A is also fixed. More uniform conditions may reduce V_E, but environmental changes can also alter genetic effects. Unchanged alleles alone do not fix every variance component.
H² = 0.6 assigns 60 percent of phenotypic variance to genetic differences in the specified population and conditions. It does not divide one person's height into genetic and environmental percentages. In an experiment with matching genetic distributions, different nutrient treatments can change group mean heights. That environmental effect on a mean does not give a heritability estimate.
H² uses genetic variance; h² uses additive genetic variance. Both describe variation in a specified population and environment, not percentages of one person's trait.
Lesson, questions and flashcards written for this dataset.
Readings and flashcards written for this dataset. Linked videos: Khan Academy, Heritability and Genes, traits, and the environment.
More to read
A mean and a variance answer different questions
Consider two sets of plant heights, measured in centimetres: 8, 10, 12 and 6, 10, 14. Both sets have a mean of 10. The second set is more spread out. A shared mean therefore does not imply a shared variance.
Quantitative traits are recorded numerically. Many involve several genes as well as environmental effects. Their values can form a continuous range without forming an exact bell curve. The number of genes alone does not fix the distribution's shape.
Now consider an experiment in which groups with matching genetic distributions receive different nutrient treatments. A difference in their mean heights can demonstrate an environmental effect. It does not supply genetic variance or phenotypic variance. Those quantities are needed to calculate heritability.
Keep the measurement question separate from the inheritance question: a mean locates the centre, variance describes spread, and heritability compares specified variance components.
Choose the numerator before dividing
Suppose phenotypic variance is 80. Of this, genetic variance is 40 and additive genetic variance is 24. Broad-sense heritability is H² = 40/80 = 0.5. Narrow-sense heritability is h² = 24/80 = 0.3. The denominator is the same, but the numerators answer different questions.
V_G includes total genetic variance. V_A is its additive component, associated with average allele effects that add together. Dominance and interactions between genes can contribute other genetic components. The basic prediction of response to selection uses h², not H².
Our two-component calculation model is V_P = V_G + V_E. It assumes no genotype-environment covariance and leaves out genotype-by-environment interaction. Studies where those effects matter need a fuller model.
The superscript ² belongs to the heritability notation. After calculating the variance ratio, do not square it again. Neither ratio divides an individual's measured trait into inherited and environmental percentages.
State what stays fixed
Use V_P = V_G + V_E and hold genetic variance at 18. If environmental variance is 12, H² = 18/30 = 0.6. If environmental variance increases to 42, H² = 18/60 = 0.3. The genetic numerator has not changed; the denominator has doubled.
This comparison depends on its stated conditions. More uniform growing conditions may reduce environmental variance, but a change in conditions can also change genetic effects. Having the same alleles does not guarantee the same genetic variance in every environment.
An environmental change can affect the mean, the variance, or both. A taller average does not by itself tell you that heritability increased or decreased.
Report a heritability estimate with its population and measurement conditions. It describes variation within that setting. It cannot, by itself, identify the causes of a mean difference between populations or assign a genetic percentage to one individual.
Explore more
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.