cppg_lgsi: Combined Predetermined Proportional Gains Linear Genomic...

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

Combined Predetermined Proportional Gains Linear Genomic Selection Index (CPPG-LGSI)

Description

Implements the CPPG-LGSI which combines phenotypic and genomic information while achieving predetermined proportional gains between traits. This is the most general constrained genomic index.

Usage

cppg_lgsi(
  T_C = NULL,
  Psi_C = NULL,
  d,
  phen_mat = NULL,
  gebv_mat = NULL,
  pmat = NULL,
  gmat = NULL,
  wmat = NULL,
  wcol = 1,
  U = NULL,
  reliability = NULL,
  k_I = 2.063,
  L_I = 1,
  GAY = NULL
)

Arguments

T_C	Combined variance-covariance matrix (2t x 2t)
Psi_C	Combined genetic covariance matrix (2t x t)
d	Vector of desired proportional gains (length n_traits or n_constraints)
phen_mat	Optional. Matrix of phenotypes for automatic T_C computation
gebv_mat	Optional. Matrix of GEBVs for automatic T_C computation
pmat	Optional. Phenotypic variance-covariance matrix
gmat	Optional. Genotypic variance-covariance matrix
wmat	Optional. Economic weights for GA/PRE calculation
wcol	Weight column to use if wmat has multiple columns (default: 1)
U	Optional. Constraint matrix (n_traits x n_constraints)
reliability	Optional. Reliability of GEBVs (r^2)
k_I	Selection intensity (default: 2.063)
L_I	Standardization constant (default: 1)
GAY	Optional. Genetic advance of comparative trait for PRE calculation

Details

Mathematical Formulation (Chapter 6, Section 6.4):

Coefficient vector: beta_CP = beta_CR + theta_CP * delta_CP

Where beta_CR is from CRLGSI and:

theta_CP = (beta_C' * Phi_C * (Phi_C' * T_C^{-1} * Phi_C)^{-1} * d_C) / (d_C' * (Phi_C' * T_C^{-1} * Phi_C)^{-1} * d_C)

Selection response: R_CP = (k_I / L_I) * sqrt(beta_CP' * T_C * beta_CP)

Value

List with:

• summary - Data frame with coefficients and metrics

• b - Vector of CPPG-LGSI coefficients (\beta_{CP})

• b_y - Coefficients for phenotypes

• b_g - Coefficients for GEBVs

• E - Expected genetic gains per trait

• theta_CP - Proportionality constant

• gain_ratios - Ratios of achieved to desired gains

Examples

## Not run: 
# Simulate data
set.seed(123)
n_genotypes <- 100
n_traits <- 5

phen_mat <- matrix(rnorm(n_genotypes * n_traits, 15, 3), n_genotypes, n_traits)
gebv_mat <- matrix(rnorm(n_genotypes * n_traits, 10, 2), n_genotypes, n_traits)

gmat <- cov(phen_mat) * 0.6
pmat <- cov(phen_mat)

# Desired proportional gains
d <- c(2, 1, 1, 0.5, 0)

w <- c(10, 8, 6, 4, 2)

result <- cppg_lgsi(
  phen_mat = phen_mat, gebv_mat = gebv_mat,
  pmat = pmat, gmat = gmat, d = d, wmat = w,
  reliability = 0.7
)
print(result$summary)
print(result$gain_ratios)

## End(Not run)

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