selection.index (version 2.0.0)

mrlpsi: Multistage Restricted Linear Phenotypic Selection Index (MRLPSI)

Description

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

Usage

mrlpsi(
  P1,
  P,
  G1,
  C,
  wmat,
  wcol = 1,
  C1,
  C2,
  stage1_indices = NULL,
  selection_proportion = 0.1,
  use_young_method = FALSE,
  k1_manual = 2.063,
  k2_manual = 2.063,
  tau = NULL
)

Value

List with components similar to mlpsi, plus:

• b_R1 - Restricted stage 1 coefficients

• b_R2 - Restricted stage 2 coefficients

• K1 - Restriction matrix for stage 1

• K2 - Restriction matrix for stage 2

Arguments

P1

Phenotypic variance-covariance matrix for stage 1 traits (n1 x n1)

P

Phenotypic variance-covariance matrix for all traits at stage 2 (n x n)

G1

Genotypic variance-covariance matrix for stage 1 traits (n1 x n1)

C

Genotypic variance-covariance matrix for all traits (n x n)

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)

stage1_indices

Integer vector specifying which traits correspond to stage 1 (default: 1:nrow(P1))

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 coefficients are computed as: $$\mathbf{b}_{R_1} = \mathbf{K}_1 \mathbf{b}_1$$ $$\mathbf{b}_{R_2} = \mathbf{K}_2 \mathbf{b}_2$$

where \(\mathbf{K}_1 = \mathbf{I}_1 - \mathbf{Q}_1\) and \(\mathbf{K}_2 = \mathbf{I}_2 - \mathbf{Q}_2\)

and \(\mathbf{Q}_i = \mathbf{P}_i^{-1}\mathbf{G}_i\mathbf{C}_i(\mathbf{C}_i'\mathbf{G}_i\mathbf{P}_i^{-1}\mathbf{G}_i\mathbf{C}_i)^{-1}\mathbf{C}_i'\mathbf{G}_i\)

References

Kempthorne, O., & Nordskog, A. W. (1959). Restricted selection indices. Biometrics, 15(1), 10-19.

Examples

if (FALSE) {
# Two-stage restricted selection
# Restrict trait 1 at stage 1, traits 1 and 3 at stage 2

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

P1 <- pmat[1:3, 1:3]
G1 <- gmat[1:3, 1:3]
P <- pmat
C <- gmat

# 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 <- mrlpsi(
  P1 = P1, P = P, G1 = G1, C = C, wmat = weights,
  C1 = C1, C2 = C2
)
}