Quantitative genetics

Quantitative genetics is the study of continuous traits (such as height or weight) and its underlying mechanisms. It is effectively an extension of simple Mendelian inheritance in that the combined effect of the many underlying genes results in a continuous distribution of phenotypic values.

History
The field was founded, in evolutionary terms, by the originators of the modern synthesis, R.A. Fisher, Sewall Wright and J. B. S. Haldane, and aimed to predict the response to selection given data on the phenotype and relationships of individuals.

Analysis of Quantitative trait loci, or QTL, is a more recent addition to the study of quantitative genetics. A QTL is a region in the genome that affects the trait or traits of interest. Quantitative trait loci approaches require accurate phenotypic, pedigree and genotypic data from a large number of individuals.

Traits
Quantitative genetics is not limited to continuous traits, but to all traits that are determined by many genes. This includes:
 * Continuous traits are quantitative traits with a continuous phenotypic range. They are usually polygenic, and may also have a significant environmental influence.
 * Meristic trait or other ordinal numbers are expressed in whole numbers, such as number of offspring, or number of bristles on a fruit fly. These traits can be either treated as approximately continuous traits or as threshold traits.
 * Some qualitative traits can be treated as if they have an underlying quantitative basis, expressed as a threshold trait (or multiple thresholds). Some human diseases (such as, schizophrenia) have been studied in this manner.

Basic principles
The phenotypic value (P) of an individual is the combined effect of the genotypic value (G) and the environmental deviation (E):
 * P = G + E

The genotypic value is the combined effect of all the genetic effects, including nuclear genes, mitochondrial genes and interactions between the genes. It is therefore often subdivided in an additive (A) and a dominance component (D). The additive effect described the cumulative effect of the individual genes, while the dominance effect is the result of interactions between those genes. The environmental deviation can be subdivided in a pure environmental component (E) and an interaction factor (I) describing the interaction between genes and the environment. This can be described as:
 * P = A + D + E + I

The contribution of those components cannot be determined in a single individual, but they can be estimated for whole populations by estimating the variances for those components, denoted as:
 * VP = VA + VD + VE + VI

The heritability of a trait is the proportion of the total (i.e. phenotypic) variation (VP) that is explained by the genetic variation. This is the total genetic variation (VG) in broad sense heritabilities (H2), while only the additive genetic variation (VA) is used for narrow sense heritabilities (h2), often simply called heritability. The latter gives an indication how a trait will respond to natural or artificial selection.

Resemblance between relatives
Central in estimating the variances for the various components is the principle of relatedness. A child has a father and a mother. Consequently, the child and father share 50% of their genes, as do the child and the mother. However, the mother and father normally do not share genes as a result of shared ancestors. Similarly, two full siblings share also on average 50% of the genes with each other, while half sibs share only 25% of the genes. This variation in relatedness can be used to estimate which proportion of the total phenotypic variance (VP) is explained by the above-mentioned components.

Correlated traits
Although some genes have only an effect on a single trait, many genes have an effect on various traits. Because of this, a change in a single gene will have an effect on all those traits. This is calculated using covariances, and the phenotypic covariance (CovP) between two traits can be partitioned in the same way as the variances described above. The genetic correlation is calculated by dividing the covariance between the two traits by the square root of the product of the variances for the two traits:
 * $$Genetic\ correlation = \frac{Cov_{A_{1, 2}}}\sqrt$$