phenomic_genomic_varcov: Phenomic-Genomic Variance-Covariance Matrix (Phi)

In selection.index: Analysis of Selection Index in Plant Breeding

Phenomic-Genomic Variance-Covariance Matrix (\Phi)

Description

Computes the combined phenomic-genomic variance-covariance matrix (\Phi or P_L), which is the block matrix representing the joint distribution of phenotypes and GEBVs.

Structure: \Phi = [[P, P_y\gamma], [P_y\gamma', \Gamma]]

where: - P = Var(y) = phenotypic variance-covariance - \Gamma = Var(\gamma) = genomic variance-covariance - P_y\gamma = Cov(y, \gamma) = covariance between phenotypes and GEBVs

Usage

phenomic_genomic_varcov(
  phen_mat = NULL,
  gebv_mat = NULL,
  P = NULL,
  Gamma = NULL,
  P_yg = NULL,
  method = "pearson",
  use = "complete.obs"
)

Arguments

phen_mat	Matrix of phenotypes (n_genotypes x n_traits). Optional if P and P_yg are provided.
gebv_mat	Matrix of GEBVs (n_genotypes x n_traits). Optional if Gamma and P_yg are provided.
P	Phenotypic variance-covariance matrix (n_traits x n_traits). Optional if phen_mat is provided.
Gamma	Genomic variance-covariance matrix (n_traits x n_traits). Optional if gebv_mat is provided.
P_yg	Covariance between phenotypes and GEBVs (n_traits x n_traits). Optional if phen_mat and gebv_mat are provided.
method	Character string specifying correlation method: "pearson" (default), "kendall", or "spearman"
use	Character string specifying how to handle missing values: "complete.obs" (default), "pairwise.complete.obs", etc.

Details

The phenomic-genomic covariance matrix is used in: - GESIM (Genomic Eigen Selection Index Method) - Combined phenotypic + genomic selection indices

The matrix is constructed as:

\Phi = \begin{bmatrix} P & P_{y\gamma} \\ P_{y\gamma}' & \Gamma \end{bmatrix}

where the off-diagonal blocks are transposes, ensuring symmetry.

You can provide either: 1. Raw data: phen_mat + gebv_mat (matrices computed internally) 2. Pre-computed matrices: P + Gamma + P_yg

Value

Symmetric block matrix \Phi (2*n_traits x 2*n_traits)

References

Cerón-Rojas, J. J., & Crossa, J. (2018). Linear Selection Indices in Modern Plant Breeding. Springer International Publishing. Chapter 8.

Examples

## Not run: 
# Simulate data
set.seed(123)
n_genotypes <- 100
n_traits <- 7
phen_mat <- matrix(rnorm(n_genotypes * n_traits, mean = 15, sd = 3),
  nrow = n_genotypes, ncol = n_traits
)
gebv_mat <- matrix(rnorm(n_genotypes * n_traits, mean = 10, sd = 2),
  nrow = n_genotypes, ncol = n_traits
)

# Compute phenomic-genomic covariance
Phi <- phenomic_genomic_varcov(phen_mat, gebv_mat)
print(dim(Phi)) # Should be 14 x 14 (2 * 7 traits)

## End(Not run)

selection.index documentation built on March 9, 2026, 1:06 a.m.