gesim: Linear Genomic Eigen Selection Index Method (GESIM)

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

Linear Genomic Eigen Selection Index Method (GESIM)

Description

Implements the GESIM by maximising the squared accuracy through the generalised eigenproblem combining phenotypic data with GEBVs (Genomic Estimated Breeding Values). No economic weights are required.

Usage

gesim(pmat, gmat, Gamma, 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).
Gamma	Covariance between phenotypes and GEBVs (n_traits x n_traits). This represents Cov(y, gamma) where gamma are GEBVs.
selection_intensity	Selection intensity constant k_I (default: 2.063 for 10% selection).

Details

Eigenproblem (Section 8.2):

(\mathbf{\Phi}^{-1}\mathbf{A} - \lambda_G^2 \mathbf{I}_{2t})\boldsymbol{\beta}_G = 0

where:

\mathbf{\Phi} = \begin{bmatrix} \mathbf{P} & \mathbf{\Gamma} \\ \mathbf{\Gamma} & \mathbf{\Gamma} \end{bmatrix}

\mathbf{A} = \begin{bmatrix} \mathbf{C} & \mathbf{\Gamma} \\ \mathbf{\Gamma} & \mathbf{\Gamma} \end{bmatrix}

Implied economic weights:

\mathbf{w}_G = \mathbf{A}^{-1}\mathbf{\Phi}\boldsymbol{\beta}

Selection response:

R_G = k_I \sqrt{\boldsymbol{\beta}_G^{\prime}\mathbf{\Phi}\boldsymbol{\beta}_G}

Expected genetic gain per trait:

\mathbf{E}_G = k_I \frac{\mathbf{A}\boldsymbol{\beta}_G}{\sqrt{\boldsymbol{\beta}_G^{\prime}\mathbf{\Phi}\boldsymbol{\beta}_G}}

Value

Object of class "gesim", a list with:

summary

Data frame with coefficients and metrics.

b_y

Coefficients for phenotypic data.

b_gamma

Coefficients for GEBVs.

b_combined

Combined coefficient vector.

E_G

Expected genetic gains per trait.

sigma_I

Standard deviation of the index.

hI2

Index heritability (= leading eigenvalue).

rHI

Accuracy r_{HI}.

R_G

Selection response.

lambda2

Leading eigenvalue.

implied_w

Implied economic weights.

selection_intensity

Selection intensity used.

References

Ceron-Rojas, J. J., & Crossa, J. (2018). Linear Selection Indices in Modern Plant Breeding. Springer International Publishing. Section 8.2.

Examples

## Not run: 
gmat <- gen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
pmat <- phen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])

# Simulate GEBV covariance (in practice, compute from genomic predictions)
Gamma <- gmat * 0.8 # Assume 80% GEBV-phenotype covariance

result <- gesim(pmat, gmat, Gamma)
print(result)

## End(Not run)

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