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

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

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

Description

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).

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}}

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.

References

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

Examples

## Not run: 
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)

## End(Not run)

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