G.matrix {snpReady}

Estimation of Genomic Relationship Matrix

Description

It generates four different types of Genomic Relationship Matrix (GRM)

Usage

G.matrix(M, method=c("VanRaden", "UAR", "UARadj", "GK"), format=c("wide", "long"), 
         plot = FALSE)

Arguments

M

matrix. Matrix of markers in which n individuals are in rows and p markers in columns. This matrix do not need to be centered.

method

Method to built the GRM. Four methods are currently supported. "VanRaden" indicates the method proposed by Vanraden (2008) for additive genomic relationship and its counterpart for dominance genomic relationship. "UAR" and "UARadj" are methods proposed by Yang et al. (2010) for additive genomic relationship. "GK" represents the Gaussian kernel for additive genomic. See Details

format

Type of object to be returned. wide returns a n \times n matrix. long returns the low diagonal from GRM as a table with 3 columns. See Details

plot

If TRUE, a graphical output is produced. See Details

Details

G.matrix provides four different types of relationship matrix. The VanRaden represents the relationship matrix estimated as proposed by Vanraden (2008):

G = \frac{XX'}{trace(XX')/n}

X is the centered marker matrix. For any marker locus i, x_i = m_i - 2p_{i} where m_i is the vector of SNP genotypes coded as allele couting (0, 1 and 2).

UAR is the genomic relationship matrices proposed by Yang et al. (2010) and named as Unified Additive Relationship (UAR). This matrix is then obtained by

G_{UAR} = A_{jk} = \frac{1}{N} \sum_i{A_{ijk}} = \left \{ \begin{array}{ll} \frac{1}{N} \sum_i{\frac{(x_{ij} - 2p_{i})(x_{ik} - 2p_i)}{2p_i(1-p_i)}}, j \neq k \\ 1 + \frac{1}{N} \sum_i{\frac{x_{ij}^{2}(1 + 2p_{i})x_{ij} + 2p_i^{2}}{2p_i(1-p_i)}}, j = k \end{array} \right.

where p_i is the allele frequency at SNP i and x_{ij} is the SNP genotype that takes a value of 0, 1 or 2 for the genotype of the j^{th} individual at SNP i. The same authors proposed an adjustment in the original UAR matrix (UARadj) to reduce the bias in estimation of variance in the relationship in causal loci. Thus:

G_{UARadj} = \left \{ \begin{array}{ll} \beta A_{jk}, j \neq k \\ 1 + \beta(A_{jk} - 1), j = k \end{array} \right.

where \beta = 1 - frac{c + 1/N}{var(A_{jk}}, c is a constant dependent on MAF of causal variants assumed as 0. GK represents the Gaussian kernel, obtained by

K (x_i, x_{i'}) = \frac{exp(-d_{ii'}^2)}{quantile(d^2, 0.5)}

where d_{ii'}^2 is the square of euclidian distance between two individuals The format argument is the desired output format. For "wide", the relationship output produced is in matrix format, with n \times n dimension. If "long" is the chosen format, the inverse of the relationship matrix is computed and converted to a table. In this case, the low triangular part of the relationship matrix is changed to a table with three columns representing the respective rows, columns, and values (Used mainly by ASReml)

If the relationship matrix is not positive definite, a near positive definite matrix is created and solved, followed by a warning message.

Value

It returns the GRM. If the method is VanRaden, additive and dominance matrices are produced. Otherwise, only the additive form. If plot is TRUE a heat map of the pairwise relationship is save as pdf into the working directory . Also, a 3D plot with the three first principal components is generated.

References

Pérez-Elizalde, S.,Cuevas, J.; Pérez-Rodríguez, P.; Crossa, J. (2015) Selection of The Bandwidth Parameter in a Bayesian Kernel Regression Model for Genomic-Enabled Prediction. J Agr Biol Envir S, 20-4:512-532

Yang, J., Benyamin, B., McEvoy, B.P., et al (2010) Common SNPs explain a large proportion of the heritability for human height. Nature Genetics 42:565-569

VanRaden, P.M. (2008) Efficient Methods to Compute Genomic Predictions. Journal of Dairy Science, 91:4414-4423

Examples

#(1) Additive and dominance relationship matrix 
data(maize.hyb)
x <- G.matrix(maize.hyb, method = "VanRaden", format = "wide")
A <- x$Ga
D <- x$Gd