clgsi: Combined Linear Genomic Selection Index (CLGSI)

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

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
)

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)

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

References

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

Examples

## Not run: 
# 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)

## End(Not run)

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