Quantitative genetics is the study of the inheritance of traits that show a continuous distribution of phenotypes in a segregating population. Traits that are controlled by many genes also exhibit quantitative inheritance as each gene segregates in a Mendelian fashion. Even when there are only a few genes involved, the trait variation will show a continuous distribution due to the results of measurement error and environmental effects.

Quantitative or biometrical genetics is considered to have been founded in the early 20^th century, notably by R.A. Fisherâ™s article which showed that the inheritance of continuously varying traits is consistent with Mendelian principles.

Simply put, the phenotypic value (P) of an individual is the combined result of its genotype (G) and the effects of the environment (E):

P = G + E

Genotype refers to the total genetic variation. This includes not only the effects of nuclear genes, but also the effects of mitochondrial genes and the interactions between genes. Genotypic variation can be partitioned into additive and dominance variation:

Additive variation represents the cumulative effect of individual loci, therefore the overall mean is equal to the summed contribution of these loci.

Dominance variation represents interaction between alleles. If a trait is controlled by a dominant allele, then both homozygous and heterozygous individuals will display the same phenotypic value.

Quantitatively varying traits are also affected by the environment (E). This can be further subdivided into pure environmental effect and interaction between genes and the environment. In other words, how different genotypes respond in different environments. Finally, interaction (I) between different genes can modify the observed phenotypes. This is called epistasis, or non-allelic interaction, distinguishing it from dominance. So, the equation above can be better written as:

P = A + D + E + I

However, since geneticists are interested in studying and identifying variation and its source in a given population, this equation is better described below. The total phenotypic variation (V) of a population is the sum of the variation in additive (A), dominance(D), gene-interaction (I), environmental (E)and gene-environment interaction (GE) effects:

V_P = V_A + V_D + V_I + V_E + V_GE

Being able to estimate how the total variance is partitioned between genetic and environmental effects is important to quantitative geneticists trying to improve a given trait. If the proportion of variation is mostly due to genetic effects (heritable), then selecting for individuals that possess the desired genetic value is a worthwhile investment. If however, the genetic variance is low (and therefore the environmental variation has more impact on phenotype), then a more strategic approach would be to optimize environmental conditions.

Heritability estimates how much of the phenotypic variation can be explained by genetic, or genetic-environmental effects. Broad-sense heritability (H²) refers to the inclusion of all potential sources of genetic variation (additive, dominance, epistatic, maternal and paternal effects):

H² = V_G/V_P

To only know the ratio of additive genetic variation to the total phenotypic variation observed, V_A can be used in the equation instead of V_G, and this becomes the narrow-sense heritability (h²):

h² = V_A/V_P

Calculating narrow-sense heritability is important for predicting how a trait will respond to selection (response to selection refers to the gain in the mean of the population compared to the mean of the selected parents). However, important to note, is that the estimate of heritability is not an absolute measurement of how genes and environment determine a phenotype, but specific to the population and environment under analysis.

Heritability can be calculated by separating out and estimating the components of variance as shown above using analysis of variance (ANOVA), or by using regression. In a graph plotting progeny performance and average parental trait values, the slope of the regression line approximates the heritability of the trait. The concept of using regression to explain biological relationships in this was first introduced by Francis Galton, who noticed that if the mean diameter of progeny peas was plotted against the mean diameter of parental peas, a straight line could be drawn between them. He referred to this property as the coefficient of regression. One other consideration is that genes can affect many different traits. Any change in such a gene will affect all of these traits. The covariance in phenotype of two traits (A₁ and A₂) can be used to calculate their genetic correlation using the following equation:

“The correlation between relatives on the supposition of Mendelian inheritance” Trans. Roy. Soc. Edinb., 52: 399-433. (1918) http://en.wikipedia.org/wiki/The_Correlation_Between_Relatives_on_the_Supposition_of_Mendelian_Inheritance