E.mat: Epistatic relationship matrix

In sommer: Solving Mixed Model Equations in R

Epistatic relationship matrix

Description

Calculates the realized epistatic relationship matrix of second order (additive x additive, additive x dominance, or dominance x dominance) using hadamard products with the C++ Armadillo library.

Usage

E.mat(X,nishio=TRUE,type="A#A",min.MAF=0.02)

Arguments

X	Matrix (n \times m) of unphased genotypes for n lines and m biallelic markers, coded as {-1,0,1}. Fractional (imputed) and missing values (NA) are allowed.
nishio	If TRUE, Nishio and Satoh (2014) (orthogonal parameterization of Vitezica et al. 2013), otherwise Su et al. (2012) (see Details in the D.mat help page).
type	An argument specifying the type of epistatic relationship matrix desired. The default is the second order epistasis (additive x additive) type="A#A". Other options are additive x dominant (type="A#D"), or dominant by dominant (type="D#D").
min.MAF	Minimum minor allele frequency, a finite value between zero and 0.5. Markers at or below this threshold and all constant markers are removed. The default is 0.02.

Details

The result is the element-wise (Hadamard) product E=A\circ A, E=A\circ D, or E=D\circ D. Mean imputation, allele-frequency estimation and marker filtering are shared between the component matrices. Their definitions and input requirements are the same as in A.mat and D.mat. As in A.mat, the correction from inadvertent median imputation to mean imputation can change results for missing genotypes.

Value

The epistatic relationship matrix is returned.

References

Covarrubias-Pazaran G (2016) Genome assisted prediction of quantitative traits using the R package sommer. PLoS ONE 11(6): doi:10.1371/journal.pone.0156744

Endelman, J.B., and J.-L. Jannink. 2012. Shrinkage estimation of the realized relationship matrix. G3:Genes, Genomes, Genetics. 2:1405-1413. doi: 10.1534/g3.112.004259

Nishio M and Satoh M. 2014. Including Dominance Effects in the Genomic BLUP Method for Genomic Evaluation. Plos One 9(1), doi:10.1371/journal.pone.0085792

Su G, Christensen OF, Ostersen T, Henryon M, Lund MS. 2012. Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers. PLoS ONE 7(9): e45293. doi:10.1371/journal.pone.0045293

Examples

####=========================================####
####random population of 200 lines with 1000 markers
####=========================================####
X <- matrix(rep(0,200*1000),200,1000)
for (i in 1:200) {
  X[i,] <- sample(c(-1,0,0,1), size=1000, replace=TRUE)
}

E <- E.mat(X, type="A#A") 
# if heterozygote markers are present can be used "A#D" or "D#D"

sommer documentation built on Oct. 25, 2026, 5:06 p.m.