Multistage Restricted Linear Genomic Selection Index (MRLGSI)

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

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

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

References

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

Examples

if (FALSE) { # \dontrun{
# 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
)
} # }