Genetic correlation
Encyclopedia
Genetic correlation is the proportion of variance
that two traits share due to gene
tic causes. Outside the theoretical boundary case of traits with zero heritability
, the genetic correlation of traits is independent of their heritability: i.e., two traits can have a very high genetic correlation even when the heritability of each is low and vice versa.
The genetic correlation, then, tells us how much of the genetic influence on two traits is common to both: if it is above zero, this suggests that the two traits are influenced by common genes
. This can be an important constraint on conceptualizations of the two traits: traits which seem different phenotypically but which share a common genetic basis require an explanation for how these genes can influence both traits.
.
Given a genetic covariance matrix, the genetic correlation is computed by standardizing this, i.e., by converting the covariance matrix to a correlation matrix. For example, if two traits, say height and weight have the following additive genetic variance-covariance matrix:
Then the genetic correlation is .55, as seen is the standardized matrix below:
In practice, structural equation modeling
applications such as OpenMx
are used to calculate both the genetic covariance matrix and its standardized form. In R
, cov2cor will standardize the matrix.
Typically, published reports will provide genetic variance components that have been standardized as a proportion of total variance (for instance in an ACE twin study
model standardised as a proportion of V-total = A+C+E). In this case, the metric for computing the genetic covariance (the variance within the genetic covariance matrix) is lost (because of the standardizing process), so you cannot readily estimate the genetic correlation of two traits from such published models. Multivariate models (such as the Cholesky decomposition
) will, however, allow the viewer to see shared genetic effects (as opposed to the genetic correlation) by following path rules. it is important therefore to provide the unstandardised path coefficients in publications.
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
that two traits share due to gene
Gene
A gene is a molecular unit of heredity of a living organism. It is a name given to some stretches of DNA and RNA that code for a type of protein or for an RNA chain that has a function in the organism. Living beings depend on genes, as they specify all proteins and functional RNA chains...
tic causes. Outside the theoretical boundary case of traits with zero heritability
Heritability
The Heritability of a population is the proportion of observable differences between individuals that is due to genetic differences. Factors including genetics, environment and random chance can all contribute to the variation between individuals in their observable characteristics...
, the genetic correlation of traits is independent of their heritability: i.e., two traits can have a very high genetic correlation even when the heritability of each is low and vice versa.
The genetic correlation, then, tells us how much of the genetic influence on two traits is common to both: if it is above zero, this suggests that the two traits are influenced by common genes
Gênes
Gênes is the name of a département of the First French Empire in present Italy, named after the city of Genoa. It was formed in 1805, when Napoleon Bonaparte occupied the Republic of Genoa. Its capital was Genoa, and it was divided in the arrondissements of Genoa, Bobbio, Novi Ligure, Tortona and...
. This can be an important constraint on conceptualizations of the two traits: traits which seem different phenotypically but which share a common genetic basis require an explanation for how these genes can influence both traits.
Computing the genetic correlation
Estimates of a genetic correlation obviously require a genetically informative sample, such as a twin studyTwin study
Twin studies help disentangle the relative importance of environmental and genetic influences on individual traits and behaviors. Twin research is considered a key tool in behavioral genetics and related fields...
.
Given a genetic covariance matrix, the genetic correlation is computed by standardizing this, i.e., by converting the covariance matrix to a correlation matrix. For example, if two traits, say height and weight have the following additive genetic variance-covariance matrix:
| Height | Weight | |
| Height | 36 | 36 |
| Weight | 36 | 117 |
Then the genetic correlation is .55, as seen is the standardized matrix below:
| Height | Weight | |
| Height | 1 | |
| Weight | .55 | 1 |
In practice, structural equation modeling
Structural equation modeling
Structural equation modeling is a statistical technique for testing and estimating causal relations using a combination of statistical data and qualitative causal assumptions...
applications such as OpenMx
OpenMx
OpenMx is an open source program for extended structural equation modeling. It runs as a package under R. Cross platform, it runs under Linux, Mac OS and Windows....
are used to calculate both the genetic covariance matrix and its standardized form. In R
R (programming language)
R is a programming language and software environment for statistical computing and graphics. The R language is widely used among statisticians for developing statistical software, and R is widely used for statistical software development and data analysis....
, cov2cor will standardize the matrix.
Typically, published reports will provide genetic variance components that have been standardized as a proportion of total variance (for instance in an ACE twin study
Twin study
Twin studies help disentangle the relative importance of environmental and genetic influences on individual traits and behaviors. Twin research is considered a key tool in behavioral genetics and related fields...
model standardised as a proportion of V-total = A+C+E). In this case, the metric for computing the genetic covariance (the variance within the genetic covariance matrix) is lost (because of the standardizing process), so you cannot readily estimate the genetic correlation of two traits from such published models. Multivariate models (such as the Cholesky decomposition
Cholesky decomposition
In linear algebra, the Cholesky decomposition or Cholesky triangle is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. It was discovered by André-Louis Cholesky for real matrices...
) will, however, allow the viewer to see shared genetic effects (as opposed to the genetic correlation) by following path rules. it is important therefore to provide the unstandardised path coefficients in publications.