D.mat: Dominance relationship matrix

Description

C++ implementation of the dominance matrix. Calculates the realized dominance relationship matrix. Can help to increase the prediction accuracy when 2 conditions are met; 1) The trait has intermediate to high heritability, 2) The population contains a big number of individuals that are half or full sibs (HS & FS).

Usage

D.mat(X,nishio=TRUE,min.MAF=0,return.imputed=FALSE)

Value

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

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

$D: the D matrix
$imputed: the imputed marker matrix

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 ans Satoh. (2014), otherwise Su et al. (2012). See references.
min.MAF: Minimum minor allele frequency. The D matrix is not sensitive to rare alleles, so by default only monomorphic markers are removed.
return.imputed: When TRUE, the imputed marker matrix is returned.

Details

The additive marker coefficients will be used to compute dominance coefficients as: Xd = 1-abs(X) for diploids.

For nishio method: the marker matrix is centered by subtracting column means $M = X d - m s$ where ms is the column means. Then $A = M M^{'} / c$ , where $c = 2 \sum_{k} p_{k} (1 - p_{k})$ .

For su method: the marker matrix is normalized by subtracting row means $M = X d - 2 p q$ where 2pq is the product of allele frequencies times 2. Then $A = M M^{'} / c$ , where $c = 2 \sum_{k} 2 p q_{k} (1 - 2 p q_{k})$ .

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

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

Run this code

####=========================================####
#### EXAMPLE 1
####=========================================####
####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)
}

D <- D.mat(X)

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