5.8 Heritability

Because in animal breeding we only make use of the prediction of A, and not of G, we should simplify the model of P = G + E to P = A + E. Note that this last E is larger than before because as we cannot estimate them, E also contains the D and I components. It now becomes more obvious why we call σ²_E the error variance: it contains more than only the effect of the environment.

Footnote: animal breeders tend to be a bit sloppy in the way they use terms. If they talk about P = G + E, they mean P = A + E, unless they specifically tell otherwise. Also, if they mention σ²_G then they mean σ²_A, unless they specifically tell otherwise.

The additive genetic effect is the part of the genetic component that is passed on from both parents to their offspring. In other words: the additive genetic effect is heritable. To indicate how heritable a certain trait is, a parameter is defined that indicates what proportion of the variation you observe (the phenotypic variance) is determined by (additive) genetic differences between animals (the additive genetic variance). This parameter is called the heritability and is indicated with the symbol h².

It is possible to estimate the heritability for a trait in a population if phenotypes and genetic relationships (pedigree) is available. A h² of 0.3 indicates that 30% of the variation you observe in your phenotypes is due to additive genetic differences between the animals. If ALL phenotypic differences are due to genetic differences, then the h² will be 1.0. Larger than 1.0 by definition is not possible. Similarly, if the differences between animals are NOT determined by their genetics, then the h² = 0.0. Smaller than 0.0 by definition is not possible.