Questions: Heritability: Broad-Sense and Narrow-Sense

Question 1

Narrow-sense heritability (h²) for wheat grain yield in a farming region is 0.6, and the mean yield of selected high-yielding parents is 10 kg/plot above the population mean. What is the predicted response to selection (R)?

• A. 10 kg/plot — response equals the selection differential
• B. 6 kg/plot — response equals h² × S
• C. 0.6 kg/plot — response equals h² divided by S
• D. 16.7 kg/plot — response equals S divided by h²

Answer: (B)

The breeder's equation is R = h²S. With h² = 0.6 and S = 10, R = 0.6 × 10 = 6 kg/plot. Option A mistakes the selection differential for the response — that would only hold if h² = 1 (all phenotypic variation is additive genetic). The key insight is that only the additive fraction of phenotypic variation passes reliably from parent to offspring, so the response is always less than or equal to the selection differential.

Question 2

Average human height has increased by roughly 10 cm over the past century due to improved nutrition. Narrow-sense heritability (h²) of height is approximately 0.8. These facts together imply which of the following?

• A. A contradiction — high heritability means height is genetically fixed and cannot respond to environmental change
• B. That heritability has declined over the century as the environment became more important
• C. No contradiction — heritability measures sources of variation within a population, not whether a trait can be altered by the environment
• D. That the height increase must have a genetic cause, since heritability is so high

Answer: (C)

High heritability means that most of the variation in height *among individuals in that population at that time* is explained by genetic differences — it says nothing about whether the trait can change in response to environmental interventions. Improved nutrition raised average height by shifting the entire distribution, not by changing the heritability. Option A is the classic misinterpretation. Option D reverses the logic: the secular trend in height is driven by environmental (nutritional) change, not genetic change, which is why it happened too fast for natural selection to explain.

Question 3

A heritability estimate of zero for a trait in a given population means that genes play no role in producing that trait.

• T. True
• F. False

Answer: False

Heritability measures the proportion of phenotypic *variance* attributable to genetic *differences* among individuals in a population. A heritability of zero means that genetic differences don't explain the observed variation — perhaps because everyone in the population shares the same relevant genotypes, or because environmental variation swamps genetic variation. Genes may still be absolutely necessary for the trait (you can't have the trait without the relevant genes), but if genetic variation is absent or irrelevant, heritability is zero. The concept measures differences, not presence/absence of genetic involvement.

Question 4

Broad-sense heritability (H²) is always at least as large as narrow-sense heritability (h²) for the same trait in the same population.

• T. True
• F. False

Answer: True

H² = V_G / V_P where V_G includes all genetic variance (additive + dominance + epistatic). h² = V_A / V_P where V_A is only the additive component. Since V_A is a subset of V_G, we always have V_A ≤ V_G and therefore h² ≤ H². They are equal only when all genetic variance is additive (no dominance or epistatic effects). In practice, traits with significant dominance or epistasis show H² substantially larger than h².

Question 5

Why is narrow-sense heritability (h²) more relevant than broad-sense heritability (H²) for predicting how a trait will respond to natural selection or selective breeding?

Model answer: Because only additive genetic effects are reliably transmitted from parent to offspring. Dominance effects depend on which alleles pair together in each individual, and epistatic effects depend on combinations across loci — both are disrupted by segregation and recombination during reproduction. Additive effects, by contrast, contribute independently and predictably to offspring phenotypes. The breeder's equation R = h²S uses h² (not H²) precisely because only the additive fraction of genetic variance produces a heritable correlation between parent and offspring phenotypes.

H² can be high due to dominance and epistasis, creating the false impression that selection will produce rapid change. But if most of the genetic variance is non-additive, selected parents won't reliably pass their phenotypic advantage to their offspring, and selection response will be weak. This is why h² is the key parameter for animal and plant breeders and for evolutionary biologists modeling quantitative trait evolution.