Genome-Wide Linear Eigen Selection Index Method (GW-ESIM)

Implements the GW-ESIM by incorporating genome-wide marker effects directly into the eigen selection index framework. Uses N marker scores alongside phenotypic data.

Usage

gw_esim(pmat, gmat, G_M, M, selection_intensity = 2.063)

Arguments

pmat

Phenotypic variance-covariance matrix (n_traits x n_traits).

gmat

Genotypic variance-covariance matrix (n_traits x n_traits).

G_M

Covariance between phenotypes and marker scores (n_traits x N_markers).

M

Variance-covariance matrix of marker scores (N_markers x N_markers).

selection_intensity

Selection intensity constant \(k_I\) (default: 2.063 for 10% selection).

Value

Object of class "gw_esim", a list with:

summary

Data frame with key metrics.

b_y

Coefficients for phenotypic data.

b_m

Coefficients for marker scores.

b_combined

Combined coefficient vector.

E_W

Expected genetic gains per trait.

sigma_I

Standard deviation of the index.

hI2

Index heritability (= leading eigenvalue).

rHI

Accuracy.

R_W

Selection response.

lambda2

Leading eigenvalue.

selection_intensity

Selection intensity used.

Details

Eigenproblem (Section 8.3): $$(\mathbf{Q}^{-1}\mathbf{X} - \lambda_W^2 \mathbf{I}_{(t+N)})\boldsymbol{\beta}_W = 0$$

where: $$\mathbf{Q} = \begin{bmatrix} \mathbf{P} & \mathbf{G}_M \\ \mathbf{G}_M^{\prime} & \mathbf{M} \end{bmatrix}$$ $$\mathbf{X} = \begin{bmatrix} \mathbf{C} & \mathbf{G}_M \\ \mathbf{G}_M^{\prime} & \mathbf{M} \end{bmatrix}$$

Selection response: $$R_W = k_I \sqrt{\boldsymbol{\beta}_W^{\prime}\mathbf{Q}\boldsymbol{\beta}_W}$$

Expected genetic gain per trait: $$\mathbf{E}_W = k_I \frac{\mathbf{X}\boldsymbol{\beta}_W}{\sqrt{\boldsymbol{\beta}_W^{\prime}\mathbf{Q}\boldsymbol{\beta}_W}}$$

References

Ceron-Rojas, J. J., & Crossa, J. (2018). Linear Selection Indices in Modern Plant Breeding. Springer International Publishing. Section 8.3.

Examples

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

# Simulate marker data
N_markers <- 100
n_traits <- nrow(gmat)
G_M <- matrix(rnorm(n_traits * N_markers, sd = 0.5), n_traits, N_markers)
M <- diag(N_markers) + matrix(rnorm(N_markers^2, sd = 0.1), N_markers, N_markers)
M <- (M + t(M)) / 2 # Make symmetric

result <- gw_esim(pmat, gmat, G_M, M)
print(result)
} # }