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Related to narrow sense heritability: additive genetic variance


In a population, the ratio of the total genetic variance to the total phenotypic variance.



the degree to which the phenotypic variation of any trait in a population of animals or plants (or group of them) is determined by the genotypic differences among individuals.

The term “heritability” was introduced in 1939 by the American geneticist J. Lush. The total variation in a population is the total result of genotypic variation and the variation caused by environmental factors. Since the degree of variation can be measured by variance (that is, the square of the mean of the square deviation of the variants from the mean of the variational series), the population-genetic parameter h2, or the coefficient of heritability, is used to characterize heritability. The formula in the broad sense is:

where σp2 is the total phenotypic variance, σg2 is the genotypic variance determined by the genotypic differences among individuals, and σE2 is the variance caused by fluctuations in the environment. h12, the coefficient of heritability in the narrow sense, is also distinguished: h12 = σA2/σp2; in this case account is taken not of the entire genotypic variation but only of one of its components σA2, the variance determined by the differences in the additive genes (the effect of these genes on a trait is summed arithmetically). The σA2 index is important for selection because selection is achieved mainly through additive genes or polygenes.

The values of h2 and h12 are expressed in fractions of less than 1, less often in percent. The special methods available for determining h2 are based chiefly on establishing the phenotypic resemblance among individuals related to different degrees for which correlation, regression, and other factors are used. The coefficient of heritability applies only to populations and not to individuals. The values of h2 depend on the nature of the trait studied. For example, the traits associated with reproduction have fairly low h2 (for example, h2 of fertility in sheep, pigs, and mice is 0.1–0.2), whereas constitutional traits are fairly high h2 (h2 of head length in cattle is 0.6–0.7, and h2 of skin folds in sheep 0.5–0.8).

The differences between h2 of economically useful traits in specific herds of breeding animals and plant populations are of practical importance. However, these differences may vary considerably, depending on the conditions under which the animals are maintained and fed or on the agrotechnical conditions under which plants are grown, as well as the breeding methods used. The value of h2 cannot be absolutely precise, but the important thing is whether the value is large, medium, or small because the value of h2 makes it possible to evaluate both the genetic structure of a population and the methods of selection needed to achieve the best results.


Nikoro, Z. S. , and P. F. Rokitskii. “Primenenie i sposoby opredeleniia koeffitsienta nasleduemosti.” Genetika, 1972, vol. 8, no. 2.
Rokitskii, P. F. Vvedenie ν statisticheskuiu genitiku. Minsk, 1974.
Falconer, D. S. Introduction to Quantitative Genetics. Edinburgh-London, 1960.