If a trait has high heritability, does that mean the environment does not matter?

No. Heritability measures the share of variation among individuals in a given population due to genetic differences; a trait can be highly heritable yet still be strongly shaped by the environment, and changing the environment can shift the whole population.

How can many genes produce a smooth bell-shaped distribution of a trait?

When numerous genes each add a small increment and combine with random environmental effects, the many possible combinations sum into an approximately normal distribution, which is why polygenic traits vary continuously rather than in discrete classes.

Quantitative and Heritable Variation

Many important traits, from height to yield, vary continuously because they are shaped by many genes of small effect together with the environment; quantitative genetics describes this variation statistically and asks how much of it is heritable.

Definition

Heritability is the proportion of the phenotypic variance of a trait in a particular population that is due to genetic differences among individuals, the central quantity describing how strongly a continuous trait is inherited.

Scope

This topic covers the polygenic model of continuous traits, the partitioning of phenotypic variance into additive, dominance, and environmental components, the distinction between broad-sense and narrow-sense heritability, the breeder's equation and response to selection, and the use of resemblance between relatives to estimate genetic parameters. It deals with the statistical structure of quantitative variation; the localization of the contributing loci is treated in the adjacent topic.

Core questions

How can a trait that varies continuously be explained by discrete Mendelian genes?
How is phenotypic variance partitioned into genetic and environmental components?
What is the difference between broad-sense and narrow-sense heritability?
How does the breeder's equation predict the response of a trait to selection?

Key concepts

Polygenic inheritance and the infinitesimal model
Phenotypic, genetic, and environmental variance
Broad-sense versus narrow-sense heritability
The breeder's equation and selection response
Resemblance between relatives

Mechanisms

Continuous variation arises when many loci, each with a small additive effect, contribute to a trait whose distribution is further smoothed by environmental variation; the additive genetic variance determines how predictably offspring resemble selected parents, which is why narrow-sense heritability governs the response to selection.

Clinical relevance

Quantitative genetics is the engine of plant and animal breeding through selection on heritable variation, and heritability estimates frame the interpretation of complex human traits and diseases, though such estimates are population- and environment-specific and do not imply that a trait is unchangeable.

History

Fisher's 1918 paper reconciled the continuous variation studied by the biometricians with Mendelian inheritance by showing that many small-effect genes produce a normal distribution, founding quantitative genetics; Wright, Falconer, and later Lynch and Walsh developed the variance-component and selection-response framework.

Key figures

Ronald Fisher
Sewall Wright
Douglas Falconer
Michael Lynch

Seminal works

fisher1918
falconerMackay1996

Frequently asked questions

If a trait has high heritability, does that mean the environment does not matter?: No. Heritability measures the share of variation among individuals in a given population due to genetic differences; a trait can be highly heritable yet still be strongly shaped by the environment, and changing the environment can shift the whole population.
How can many genes produce a smooth bell-shaped distribution of a trait?: When numerous genes each add a small increment and combine with random environmental effects, the many possible combinations sum into an approximately normal distribution, which is why polygenic traits vary continuously rather than in discrete classes.