Heritability - Definition

Definition

Any particular phenotype can be modelled as the sum of genetic and environmental effects:

Phenotype (P) = Genotype (G) + Environment (E).

Likewise the variance in the trait – Var (P) – is the sum of genetic effects as follows:

Var(P) = Var(G) + Var(E) + 2 Cov(G,E).

In a planned experiment Cov(G,E) can be controlled and held at 0. In this case, heritability is defined as:

.

H2 is the broad-sense heritability. This reflects all the genetic contributions to a population's phenotypic variance including additive, dominant, and epistatic (multi-genic interactions), as well as maternal and paternal effects, where individuals are directly affected by their parents' phenotype (such as with milk production in mammals).

These additional terms can be decomposed in some genetic models. An important example is capturing only a portion of the variance due to additive (allelic) genetic effects. This additive genetic portion is known as Narrow-sense heritability and is defined as

An upper case H2 is used to denote broad sense, and lower case h2 for narrow sense.

Additive variance is important for selection. If a selective pressure such as improving livestock is exerted, the response of the trait is directly related to narrow-sense heritability. The mean of the trait will increase in the next generation as a function of how much the mean of the selected parents differs from the mean of the population from which the selected parents were chosen. The observed response to selection leads to an estimate of the narrow-sense heritability (called realized heritability). This is the principle underlying artificial selection or breeding.