getGenCov: Genetic covariances

In MarcooLopez/SFSI_data: Sparse Family and Selection Index

Description

Obtaing 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, ...)

Arguments

y1	Response variable 1
y2	Response variable 2. Must be a matrix with the number of rows equal to length of vector y2
X	Design matrix for the fixed effects. When X=NULL a vector of ones is constructed only for the intercept (default)
Z	Design matrix for the random effects. When Z=NULL an identity matrix is considered (default) thus G = K; otherwise G = Z K Z' is used
K	Kinship relationships matrix
U	Matrix with eigenvectors from spectral value decomposition of G = U D U'
d	Vector with 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	Number of cores used. The analysis is run in parallel when mc.cores is greater than 1. Default is mc.cores=1
...	Other arguments passed to fitBLUP function

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 g₁ + e₁ y₂ = X b₂ + Z g₂ + e₂

where b₁ and b₂ are the specific fixed effects, g₁ and g₂ 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 g₁ ~ N(0,σ²_u1K) and g₂ ~ 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

Author(s)

Marco Lopez-Cruz ([e-mail]) and Gustavo de los Campos

Examples

  require(SFSI)
  require(ggplot2)
  data(wheatHTP)
  
  X = scale(X[1:200,])         # Subset and scale markers
  G = tcrossprod(X)/ncol(X)    # Genomic relationship matrix
  y = scale(Y[1:200,"YLD"])    # Subset response variable
  WL = scale(WL[1:200,20:40])  # Subset reflectance data
  
  fm <- getGenCov(y,WL,K=G)
  
  dat = data.frame(covU=fm$covU,covP_corrected=fm$covU+fm$covE,
        covP_uncorrected=cov(y,WL)[1,])
  
  covariance=rep(c("covU","covP_corrected","covP_uncorrected"),each=length(fm$covU))
  dat = data.frame(covariance,x=rep(1:length(fm$covU),3),
                  y=c(fm$covU,fm$covU+fm$covE,cov(y,WL)[1,]))
  ggplot(dat,aes(x,y,group=covariance,color=covariance))+geom_point()+geom_line()    

MarcooLopez/SFSI_data documentation built on April 15, 2021, 10:53 a.m.