Genetic covariances
Pairwise genetic covariances for variables with the same experimental design and equal variance
getGenCov(y1, y2, X = NULL, Z = NULL, K = NULL,
U = NULL, d = NULL, scale = TRUE, mc.cores = 1, ...)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 |
Z |
(numeric matrix) Design matrix for random effects. When |
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 |
|
mc.cores |
(integer) Number of cores used. The analysis is run in parallel when |
... |
Other arguments passed to the function 'fitBLUP' |
Assumes that both y1 and y2 follow the basic linear mixed model that relates phenotypes with genetic values of the form
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,σ2u1K) and u2 ~ N(0,σ2u2K), and environmental terms are assumed e1 ~ N(0,σ2e1I) and e2 ~ N(0,σ2e2I).
The genetic covariance σ2u1,u2 is estimated from the formula for the variance for the sum of two variables as
where σ2u3 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 σ2e1,e2 is estimated as
where σ2e3 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.
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.
Marco Lopez-Cruz (maraloc@gmail.com) and Gustavo de los Campos
require(SFSI) data(wheatHTP) X = scale(X[1:200,])/sqrt(ncol(X)) # Subset and scale markers G = tcrossprod(X) # Genomic relationship matrix y = as.vector(scale(Y[1:200,"YLD"])) # Subset response variable WL = scale(WL[1:200,20:40]) # Subset reflectance data fm = getGenCov(y,WL,K=G) covU = fm$covU # Genetic covariance covP_corrected = fm$covU+fm$covE # Phenotypic covariance covP_uncorrected = cov(y,WL) # Genetic covariance plot(covP_corrected,covP_uncorrected) plot(covU,covP_uncorrected) plot(covU,covP_corrected)
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