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Since the mean vectors and covariance matrices of the distribution are equal to the sum of mean vectors and covariance matrices of additive components, the model would be able to exploit contextual factors more efficiently.
Let Σ G and Σ E denote the matrices of additive genetic and residual covariances among the q traits.
A Deli and A La Mé were matrices of additive relationships among Deli and La Mé individuals computed from pedigrees.
Covariance matrices of additive effects were V (u ) A σ A 2 in model MA and V (u ) = G σ A 2 in model MG, where A is the numerator relationship matrix and G is the genomic relationship matrix.
In RRGS_PAR, the progeny tests were analyzed with the same bivariate model as for RRS, except that matrices of additive relationships A Deli and A La Mé were replaced by molecular relationship matrices G Deli and G La Mé computed from parental genotypes, using observed allele frequencies [ 2, 3] and normalized to have average diagonal coefficients equal to one [ 25].
Note that (I t - Λ )-1 G0 (I t - Λ )-1 and (I t - Λ )-1 Ψ0 (I t - Λ )-1 are the covariance matrices of additive genetic effects (G 0 * ) and of residuals (R 0 * ) obtained from a standard multiple trait mixed model that accounts for covariance between genetic effects and residuals from different traits, but not for causal relationships between phenotypes [ 13, 25].
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This may be because the kinship matrix of additive effect has already captured much information about the kinship matrix of dominant effect.
is the matrix of additive genetic variances and covariances between environments, and is the variance/covariance matrix between genotypes.
The matrix of additive genetic relationships A was calculated using information on five generations of pedigree that included 2806 animals.
Indeed, G = X X ′ k can be regarded as an estimate of the realized matrix of additive relationships (Habier et al. 2007; VanRaden 2007).
G -matrices G-matrices We estimated the matrix of additive genetic variances and covariances (the G-matrix) for each Longshanks line separately using linear mixed effects models, also known as "animal models" [ 68].
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