mrlgsi: Multistage Restricted Linear Genomic Selection Index (MRLGSI)

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

Multistage Restricted Linear Genomic Selection Index (MRLGSI)

Description

Implements the two-stage Restricted Linear Genomic Selection Index where certain traits are constrained to have zero genetic gain at each stage using GEBVs.

Usage

mrlgsi(
  Gamma1,
  Gamma,
  A1,
  A,
  C,
  G1,
  P1,
  wmat,
  wcol = 1,
  C1,
  C2,
  selection_proportion = 0.1,
  use_young_method = FALSE,
  k1_manual = 2.063,
  k2_manual = 2.063,
  tau = NULL
)

Arguments

Gamma1	GEBV variance-covariance matrix for stage 1 traits (n1 x n1)
Gamma	GEBV variance-covariance matrix for all traits at stage 2 (n x n)
A1	Covariance matrix between GEBVs and true breeding values for stage 1 (n1 x n1)
A	Covariance matrix between GEBVs and true breeding values for stage 2 (n x n1)
C	Genotypic variance-covariance matrix for all traits (n x n)
G1	Genotypic variance-covariance matrix for stage 1 traits (n1 x n1)
P1	Phenotypic variance-covariance matrix for stage 1 traits (n1 x n1)
wmat	Economic weights vector or matrix (n x k)
wcol	Weight column to use if wmat has multiple columns (default: 1)
C1	Constraint matrix for stage 1 (n1 x r1)
C2	Constraint matrix for stage 2 (n x r2)
selection_proportion	Proportion selected at each stage (default: 0.1)
use_young_method	Logical. Use Young's method for selection intensities (default: FALSE). Young's method tends to overestimate intensities; manual intensities are recommended.
k1_manual	Manual selection intensity for stage 1
k2_manual	Manual selection intensity for stage 2
tau	Standardized truncation point

Details

Mathematical Formulation:

The restricted genomic coefficients are:

\mathbf{\beta}_{R_1} = \mathbf{K}_{G_1}\mathbf{\beta}_1

\mathbf{\beta}_{R_2} = \mathbf{K}_{G_2}\mathbf{w}

where restriction matrices are computed similarly to RLGSI

Value

List with components similar to mlgsi, plus:

• beta_R1 - Restricted stage 1 coefficients

• beta_R2 - Restricted stage 2 coefficients

• K_G1 - Restriction matrix for stage 1

• K_G2 - Restriction matrix for stage 2

References

Ceron-Rojas, J. J., & Crossa, J. (2018). Linear Selection Indices in Modern Plant Breeding. Springer International Publishing. Chapter 9, Section 9.5.

Examples

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

reliability <- 0.7
Gamma1 <- reliability * gmat[1:3, 1:3]
Gamma <- reliability * gmat
A1 <- reliability * gmat[1:3, 1:3]
A <- gmat[, 1:3]

# Constraint matrices
C1 <- matrix(0, nrow = 3, ncol = 1)
C1[1, 1] <- 1 # Restrict trait 1 at stage 1

C2 <- matrix(0, nrow = 7, ncol = 2)
C2[1, 1] <- 1 # Restrict trait 1 at stage 2
C2[3, 2] <- 1 # Restrict trait 3 at stage 2

weights <- c(10, 8, 6, 4, 3, 2, 1)

result <- mrlgsi(
  Gamma1 = Gamma1, Gamma = Gamma, A1 = A1, A = A,
  C = gmat, G1 = gmat[1:3, 1:3], P1 = pmat[1:3, 1:3],
  wmat = weights, C1 = C1, C2 = C2
)

## End(Not run)

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