selection.index (version 2.0.0)

clgsi: Combined Linear Genomic Selection Index (CLGSI)

Description

Implements the Combined Linear Genomic Selection Index where selection combines both phenotypic observations and Genomic Estimated Breeding Values (GEBVs). This is used for selecting candidates with both phenotype and genotype data (e.g., in a training population).

Usage

clgsi(
  phen_mat = NULL,
  gebv_mat = NULL,
  pmat,
  gmat,
  wmat,
  wcol = 1,
  P_y = NULL,
  P_g = NULL,
  P_yg = NULL,
  reliability = NULL,
  selection_intensity = 2.063,
  GAY = NULL
)

Value

List with components:

• b_y - Coefficients for phenotypes

• b_g - Coefficients for GEBVs

• b_combined - Full coefficient vector [b_y; b_g]

• P_combined - Combined variance matrix

• Delta_H - Expected genetic advance per trait

• GA - Overall genetic advance

• PRE - Percent relative efficiency

• hI2 - Index heritability

• rHI - Index accuracy

• summary - Data frame with all metrics

Arguments

phen_mat

Matrix of phenotypes (n_genotypes x n_traits). Can be NULL if P_y and P_yg are provided.

gebv_mat

Matrix of GEBVs (n_genotypes x n_traits). Can be NULL if P_g and P_yg are provided.

pmat

Phenotypic variance-covariance matrix (n_traits x n_traits)

gmat

Genotypic variance-covariance matrix (n_traits x n_traits)

wmat

Economic weights matrix (n_traits x k), or vector

wcol

Weight column to use if wmat has multiple columns (default: 1)

P_y

Optional. Phenotypic variance-covariance matrix computed from data (n_traits x n_traits). If NULL (default), uses pmat or computes from phen_mat using cov().

P_g

Optional. GEBV variance-covariance matrix (n_traits x n_traits). If NULL (default), computed from gebv_mat using cov().

P_yg

Optional. Covariance matrix between phenotypes and GEBVs (n_traits x n_traits). If NULL (default), computed from phen_mat and gebv_mat using cov().

reliability

Optional. Reliability of GEBVs (r^2, the squared correlation). See lgsi() for details.

selection_intensity

Selection intensity i (default: 2.063 for 10% selection)

GAY

Optional. Genetic advance of comparative trait for PRE calculation

Details

Mathematical Formulation:

The CLGSI combines phenotypic and genomic information: $$I = \mathbf{b}_y' \mathbf{y} + \mathbf{b}_g' \hat{\mathbf{g}}$$

Coefficients are obtained by solving the partitioned system: $$\begin{bmatrix} \mathbf{b}_y \\ \mathbf{b}_g \end{bmatrix} = \begin{bmatrix} \mathbf{P} & \mathbf{P}_{y\hat{g}} \\ \mathbf{P}_{y\hat{g}}' & \mathbf{P}_{\hat{g}} \end{bmatrix}^{-1} \begin{bmatrix} \mathbf{G} \\ \mathbf{C}_{\hat{g}g} \end{bmatrix} \mathbf{w}$$

Where: - \(\mathbf{P}\) = Var(phenotypes) - \(\mathbf{P}_{\hat{g}}\) = Var(GEBVs) - \(\mathbf{P}_{y\hat{g}}\) = Cov(phenotypes, GEBVs) - \(\mathbf{G}\) = Genotypic variance-covariance - \(\mathbf{C}_{\hat{g}g}\) = Cov(GEBV, true BV)

References

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

Examples

if (FALSE) {
# Generate example data
gmat <- gen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
pmat <- phen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])

# Simulate phenotypes and GEBVs
set.seed(123)
n_genotypes <- 100
n_traits <- ncol(gmat)

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
)
colnames(phen_mat) <- colnames(gmat)
colnames(gebv_mat) <- colnames(gmat)

# Economic weights
weights <- c(10, 5, 3, 3, 5, 8, 4)

# Calculate CLGSI
result <- clgsi(phen_mat, gebv_mat, pmat, gmat, weights, reliability = 0.7)
print(result$summary)
}