Phenomic-Genomic Variance-Covariance Matrix ($\Phi$) — phenomic_genomic

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.

Value

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

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

References

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

Examples

if (FALSE) { # \dontrun{
# 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)
} # }