mppg_lpsi: Multistage Predetermined Proportional Gain Linear Phenotypic...

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

Multistage Predetermined Proportional Gain Linear Phenotypic Selection Index (MPPG-LPSI)

Description

Implements the two-stage Predetermined Proportional Gain LPSI where breeders specify desired proportional gains between traits at each stage.

Usage

mppg_lpsi(
  P1,
  P,
  G1,
  C,
  wmat,
  wcol = 1,
  d1,
  d2,
  stage1_indices = NULL,
  selection_proportion = 0.1,
  use_young_method = FALSE,
  k1_manual = 2.063,
  k2_manual = 2.063,
  tau = NULL
)

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)
d1	Vector of desired proportional gains for stage 1 (length n1)
d2	Vector of desired proportional gains for stage 2 (length n)
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 (Chapter 9.3.1, Eq 9.17):

The PPG coefficients are computed using the projection matrix method:

\mathbf{b}_{M_1} = \mathbf{b}_{R_1} + \theta_1 \mathbf{U}_1(\mathbf{U}_1'\mathbf{G}_1\mathbf{P}_1^{-1}\mathbf{G}_1\mathbf{U}_1)^{-1}\mathbf{d}_1

\mathbf{b}_{M_2} = \mathbf{b}_{R_2} + \theta_2 \mathbf{U}_2(\mathbf{U}_2'\mathbf{C}\mathbf{P}^{-1}\mathbf{C}\mathbf{U}_2)^{-1}\mathbf{d}_2

where:

• \mathbf{b}_{R_i} = \mathbf{K}_{M_i}\mathbf{b}_i are restricted coefficients

• \mathbf{K}_{M_i} = \mathbf{I} - \mathbf{Q}_{M_i} is the projection matrix

• \theta_i is the proportionality constant computed from \mathbf{d}_i

• \mathbf{U}_i = \mathbf{I} (all traits constrained)

\mathbf{b}_{M_1} = \mathbf{K}_{M_1} \mathbf{b}_1

\mathbf{b}_{M_2} = \mathbf{K}_{M_2} \mathbf{b}_2

where \mathbf{K}_{M_i} is computed to achieve proportional gains specified by \mathbf{d}_i

Value

List with components similar to mlpsi, plus:

• b_M1 - PPG stage 1 coefficients

• b_M2 - PPG stage 2 coefficients

• b_R1 - Restricted stage 1 coefficients

• b_R2 - Restricted stage 2 coefficients

• K_M1 - PPG projection matrix for stage 1

• K_M2 - PPG projection matrix for stage 2

• theta1 - Proportionality constant for stage 1

• theta2 - Proportionality constant for stage 2

• gain_ratios_1 - Achieved gain ratios at stage 1

• gain_ratios_2 - Achieved gain ratios at stage 2

References

Tallis, G. M. (1962). A selection index for optimum genotype. Biometrics, 18(1), 120-122.

Examples

## Not run: 
# Two-stage proportional gain selection
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

# Desired proportional gains
d1 <- c(2, 1, 1) # Trait 1 gains twice as much at stage 1
d2 <- c(3, 2, 1, 1, 1, 0.5, 0.5) # Different proportions at stage 2

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

result <- mppg_lpsi(
  P1 = P1, P = P, G1 = G1, C = C, wmat = weights,
  d1 = d1, d2 = d2
)

## End(Not run)

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