Variance decomposition {noia}

Decomposition of Genetic Variance

Description

Variance decomposition in a classical operation in quantitative genetics (e.g. Fisher 1918, Lynch and Walsh 1998). The genetic variance, i.e. the part of phenotypic variance that can be identify as due to genetic factors, can be decomposed into several orthogonal components (generally, the part due to additive factors Var(A), to dominance factors Var(D), and to genetic interactions Var(I)).

Usage

varianceDecomposition(obj)
## S3 method for class 'noia.vardec'
print(x, ...)

Arguments

obj

An object of class "noia.linear", the output of linearRegression or of class "noia.linear.gpmap", the output of linearGPmapanalysis.

x

An object of class "noia.vardec", the output of varianceDecomposition.

...

No effect for the moment.

Details

The details of the variance decomposition are provided for all levels of interaction: Var(A) and Var(D) for marginal effects, Var(AA), Var(AD) and Var(DD) for 2nd order interactions, etc.

Value

varianceDecomposition returns a list of vectors. Each element of the list corresponds to an order of interactions, and the vectors detail the variance decomposition within each level. print.noia.vardec prints the previous list in a nice way, and computed the percentage of genetic variance explained by each variance component.

Author(s)

Arnaud Le Rouzic

References

Alvarez-Castro JM, Carlborg O. (2007). A unified model for functional and statistical epistasis and its application in quantitative trait loci analysis. Genetics 176(2):1151-1167.

Fisher RA. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Thans. Roy. Soc. Edinburgh 52:339-433.

Le Rouzic A, Alvarez-Castro JM. (2008). Estimation of genetic effects and genotype-phenotype maps. Evolutionary Bioinformatics, 4.

Lynch M, Walsh B (1998) Genetics and Analysis of Quantitative Traits. Sunderland, MA; Sinauer Associates.

See Also

linearRegression

Examples

map <- c(0.25, -0.75, -0.75, -0.75, 2.25, 2.25, -0.75, 2.25, 2.25)
pop <- simulatePop(map, N=500, sigmaE=0.2, type="F2")

# Regression

linear <- linearRegression(phen=pop$phen, gen=cbind(pop$Loc1, pop$Loc2))

# Variance decomposition
varianceDecomposition(linear)