selection.index (version 2.0.0)

resim: Restricted Linear Phenotypic Eigen Selection Index (RESIM)

Description

Extends ESIM by imposing null restrictions: genetic gains for \(r\) selected traits are forced to zero while the index heritability for the remaining traits is maximised.

Usage

resim(
  pmat,
  gmat,
  restricted_traits = NULL,
  U_mat = NULL,
  selection_intensity = 2.063
)

Value

Object of class "resim", a list with:

summary

Data frame with b coefficients and key metrics.

b

Named numeric vector of RESIM coefficients.

Delta_G

Named vector of expected genetic gains per trait.

sigma_I

Index standard deviation.

hI2

Index heritability (leading eigenvalue of KP^(-1)C).

rHI

Index accuracy.

lambda2

Leading eigenvalue of the restricted eigenproblem.

K

Projection matrix used.

U_mat

Restriction matrix used.

restricted_traits

Integer vector of restricted trait indices.

implied_w

Implied economic weights.

selection_intensity

Selection intensity used.

Arguments

pmat

Phenotypic variance-covariance matrix (n_traits x n_traits).

gmat

Genotypic variance-covariance matrix (n_traits x n_traits).

restricted_traits

Integer vector of trait indices to restrict to zero genetic gain. Example: c(1, 3) restricts traits 1 and 3. Alternatively supply a custom restriction matrix via U_mat.

U_mat

Optional. Restriction matrix (n_traits x r) where each column defines one null restriction (\(\mathbf{U}^{\prime}\mathbf{C}\mathbf{b} = 0\)). Ignored if restricted_traits is provided.

selection_intensity

Selection intensity constant (default: 2.063).

Details

Projection matrix (Section 7.2): $$\mathbf{K} = \mathbf{I}_t - \mathbf{P}^{-1}\mathbf{C}\mathbf{U} (\mathbf{U}^{\prime}\mathbf{C}\mathbf{P}^{-1}\mathbf{C}\mathbf{U})^{-1} \mathbf{U}^{\prime}\mathbf{C}$$

Restricted eigenproblem: $$(\mathbf{K}\mathbf{P}^{-1}\mathbf{C} - \lambda_R^2 \mathbf{I}_t)\mathbf{b}_R = 0$$

Selection response and genetic gain: $$R_R = k_I \sqrt{\mathbf{b}_R^{\prime}\mathbf{P}\mathbf{b}_R}$$ $$\mathbf{E}_R = k_I \frac{\mathbf{C}\mathbf{b}_R}{\sqrt{\mathbf{b}_R^{\prime}\mathbf{P}\mathbf{b}_R}}$$

Implied economic weights: $$\mathbf{w}_R = \mathbf{C}^{-1}[\mathbf{P} + \mathbf{Q}_R^{\prime}\mathbf{C}]\mathbf{b}_R$$ where \(\mathbf{Q}_R = \mathbf{I} - \mathbf{K}\).

References

Ceron-Rojas, J. J., & Crossa, J. (2018). Linear Selection Indices in Modern Plant Breeding. Springer International Publishing. Section 7.2.

Examples

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

# Restrict traits 1 and 3 to zero genetic gain
result <- resim(pmat, gmat, restricted_traits = c(1, 3))
print(result)
summary(result)
}