E.mat: Epistatic relationship matrix

Description

Calculates the realized epistatic relationship matrix of second order (additive x additive, additive x dominance, or dominance x dominance).

Usage

E.mat(X,min.MAF=NULL,max.missing=NULL,impute.method="mean",tol=0.02,
      n.core=1,shrink=FALSE,return.imputed=FALSE, type="A#A", ploidy=2)

Arguments

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.

min.MAF

Minimum minor allele frequency. The A matrix is not sensitive to rare alleles, so by default only monomorphic markers are removed.

max.missing

Maximum proportion of missing data; default removes completely missing markers.

impute.method

There are two options. The default is "mean", which imputes with the mean for each marker. The "EM" option imputes with an EM algorithm (see details).

tol

Specifies the convergence criterion for the EM algorithm (see details).

n.core

Specifies the number of cores to use for parallel execution of the EM algorithm (use only at UNIX command line).

shrink

Set shrink=TRUE to use the shrinkage estimation procedure (see Details).

return.imputed

When TRUE, the imputed marker matrix is returned.

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").

ploidy

The ploidy of the organism. The default is 2 which means diploid but higher ploidy levels are supported.

Value

If return.imputed = FALSE, the $n \times n$ epistatic relationship matrix is returned.

If return.imputed = TRUE, the function returns a list containing

$E: the E matrix
$imputed: the imputed marker matrix

Details

it is computed as the Hadamard product of the epistatic relationship matrix (A); E=A#A.

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

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

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

Poland, J., J. Endelman et al. 2012. Genomic selection in wheat breeding using genotyping-by-sequencing. Plant Genome 5:103-113. doi: 10.3835/plantgenome2012.06.0006

Examples

Run this code

# NOT RUN {
####=========================================####
####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"
# }

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