SFSI (version 1.2.0)

getGenCov: Genetic covariances

Description

Pairwise genetic covariances for variables with the same experimental design and equal variance

Usage

getGenCov(y1, y2, X = NULL, Z = NULL, K = NULL, 
          U = NULL, d = NULL, scale = TRUE, 
          mc.cores = 1, warn = FALSE, ...)

Value

Returns a list object that contains the elements:

• varU1: genetic variance for response variable 1.

• varU2: (vector) genetic variances for response variable 2.

• varE1: error variance for response variable 1.

• varE2: (vector) error variances for response variable 2.

• covU: (vector) genetic covariances between response variables 1 and 2.

• covE: (vector) environmental covariances between response variables 1 and 2.

Arguments

y1

(numeric vector) Response variable 1

y2

(numeric matrix) Response variable 2. The number of rows must be equal to length of vector y1

X

(numeric matrix) Design matrix for fixed effects. When X=NULL a vector of ones is constructed only for the intercept (default)

Z

(numeric matrix) Design matrix for random effects. When Z=NULL an identity matrix is considered (default) thus G = K; otherwise G = Z K Z' is used

K

(numeric matrix) Kinship relationships

U

(numeric matrix) Eigenvectors from spectral value decomposition of G = U D U'

d

(numeric vector) Eigenvalues from spectral value decomposition of G = U D U'

scale

TRUE or FALSE to scale y1 and y2 by their corresponding standard deviations so the resulting variables will have unit variance

mc.cores

(integer) Number of cores used. The analysis is run in parallel when mc.cores is greater than 1. Default is mc.cores=1

warn

TRUE or FALSE to whether show warnings

...

Other arguments passed to the function 'fitBLUP'

Author

Marco Lopez-Cruz () and Gustavo de los Campos

Details

Assumes that both y₁ and y₂ follow the basic linear mixed model that relates phenotypes with genetic values of the form

y₁ = X b₁ + Z u₁ + e₁

y₂ = X b₂ + Z u₂ + e₂

where b₁ and b₂ are the specific fixed effects, u₁ and u₂ are the specific genetic values of the genotypes, e₁ and e₂ are the vectors of specific environmental residuals, and X and Z are common design matrices conecting the fixed and genetic effects with replicates. Genetic values are assumed to follow a Normal distribution as u₁ ~ N(0,σ²_u1K) and u₂ ~ N(0,σ²_u2K), and environmental terms are assumed e₁ ~ N(0,σ²_e1I) and e₂ ~ N(0,σ²_e2I).

The genetic covariance σ²_u1,u2 is estimated from the formula for the variance for the sum of two variables as

σ²_u1,u2 = 1/2(σ²_u3 - σ²_u1 - σ²_u2)

where σ²_u3 is the genetic variance of the variable y₃ = y₁ + y₂ that also follows the same model as for y₁ and y₂.

Likewise, the environmental covariance σ²_e1,e2 is estimated as

σ²_e1,e2 = 1/2(σ²_e3 - σ²_e1 - σ²_e2)

where σ²_e3 is the error variance of the variable y₃.

Solutions are found using the function 'fitBLUP' (see help(fitBLUP)) to sequentialy fit mixed models for all the variables y₁, y₂ and y₃.

Examples

  require(SFSI)
  data(wheatHTP)
  
  index = which(Y$trial %in% 1:6)     # Use only a subset of data
  Y = Y[index,]
  X = scale(X_E1[index,30:50])        # Subset reflectance data
  M = scale(M[index,])/sqrt(ncol(M))  # Subset and scale markers
  G = tcrossprod(M)                   # Genomic relationship matrix
  y = as.vector(scale(Y[,"E1"]))      # Scale response variable
  
  fm = getGenCov(y,X,K=G)
  
  covU = fm$covU                     # Genetic covariance
  covP_corrected = fm$covU+fm$covE   # Phenotypic covariance
  covP_uncorrected = cov(y,X)        # Sample phenotypic covariance
  
  plot(covP_corrected,covP_uncorrected)
  plot(covU,covP_uncorrected)
  plot(covU,covP_corrected)