Heritability in broad sense and narrow sense

Heritability in broad sense (H²) is calculated using the following formula :

H² = S_g²/S_p²

Therefore, H² simply gives a measure of the proportion of phenotypic variance which is due to genotype. However, this does not tell us what proportion of an individual's phenotype is due to genotype. Moreover, H² depends on the population in which it is measured and also depends on the set of environments in which the population was grown. For instance in a genotypically homogeneous population (e.g. homozygous parents or F₁ hybrids between them), S_g² = 0 and therefore H² = 0. It does not mean that genes do not control the phenotype, but no part of the variation can be ascribed to genetic variation. Similarly lack of heterogeneity in environment may lead to a high estimate of H², but it does not mean that the trait is insensitive to all environments.

Since H² can not tell us how will a particular trait behave in a particular environment, its utility is limited. In view of this, animal and plant breeders often prefer to estimate heritability in narrow sense (h²), which is based on the knowledge about gene action. For this purpose genetic variance (S_g²) is partitioned into additive genetic variance (S_a²) and dominance genetic variance (S_d²). If A and a are two alleles at a locus controlling a quantitative trait, the S_a² is associated with the average effect of substitution of A for a in a homozygote (aa →AA) and S_d²is associated with partial dominance of A over a in heterozygotes. Once S_a²is calculated from given data, S_d²can be calculated as follows (The details of methods for computations of S_a² and S_d²are beyond the scope of this section and the reader is advised to consult a book on Biometrical Genetics for further details) :

S_d²= S_g²- S_a².

The heritability in narrow sense (h²) is used as a measure of relative proportion of S_a² as follows :

h² = S_a²/ S_p² (as against H² = S_g²/ S_p²)

The usefulness of this partitioning of genetic variance lies in the prediction about the effect of selective breeding. Greater is the value of h², better are the chances that the selected individuals will maintain their superiority over the population as a whole. This kind of assurance and confidence is not available when we use H² (heritability in broad sense). Further, if h² is high, the selection will bring about an improvement, but if h² is low it means that S_d² should be high and heterozygotes will be superior to homozygotes and heterosis breeding should be preferred as done in maize.