selection.index (version 2.0.0)

lgsi: Linear Genomic Selection Index (LGSI)

Description

Implements the Linear Genomic Selection Index where selection is based solely on Genomic Estimated Breeding Values (GEBVs). This is used for selecting candidates that have been genotyped but not phenotyped (e.g., in a testing population).

Usage

lgsi(
  gebv_mat,
  gmat,
  wmat,
  wcol = 1,
  reliability = NULL,
  selection_intensity = 2.063,
  GAY = NULL
)

Value

List with components:

• b - Index coefficients

• P_gebv - GEBV variance-covariance matrix

• reliability - Reliability values used

• Delta_H - Expected genetic advance per trait

• GA - Overall genetic advance in the index

• PRE - Percent relative efficiency (if GAY provided)

• hI2 - Index heritability

• rHI - Index accuracy

• sigma_I - Standard deviation of the index

• summary - Data frame with all metrics

Arguments

gebv_mat

Matrix of GEBVs (n_genotypes 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)

reliability

Optional. Reliability of GEBVs (correlation between GEBV and true BV). Can be: - Single value (applied to all traits) - Vector of length n_traits (one per trait) - NULL (default): estimated from GEBV variance (assumes reliability = GEBV_var / G_var)

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 LGSI maximizes the correlation between the index I = b' * gebv and

Index coefficients: \(\mathbf{b} = \mathbf{P}_{\hat{g}}^{-1} \mathbf{C}_{\hat{g}g} \mathbf{w}\)

Where: - \(\mathbf{P}_{\hat{g}}\) = Var(gebv) - variance-covariance of GEBVs - \(\mathbf{C}_{\hat{g}g}\) = Cov(gebv, g) - covariance between GEBVs and true breeding values

If reliability (r) is known: \(\mathbf{C}_{\hat{g}g} = \text{diag}(r) \mathbf{P}_{\hat{g}}\)

Expected response: \(\Delta \mathbf{H} = \frac{i}{\sigma_I} \mathbf{C}_{\hat{g}g} \mathbf{b}\)

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])

# Simulate GEBVs (in practice, these come from genomic prediction)
set.seed(123)
n_genotypes <- 100
n_traits <- ncol(gmat)
gebv_mat <- matrix(rnorm(n_genotypes * n_traits, mean = 10, sd = 2),
  nrow = n_genotypes, ncol = n_traits
)
colnames(gebv_mat) <- colnames(gmat)

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

# Calculate LGSI
result <- lgsi(gebv_mat, gmat, weights, reliability = 0.7)
print(result$summary)
}