crlgsi: Combined Restricted Linear Genomic Selection Index (CRLGSI)

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

Combined Restricted Linear Genomic Selection Index (CRLGSI)

Description

Implements the CRLGSI which combines phenotypic and genomic information with restrictions on genetic gains. This extends CLGSI to include constraints.

Usage

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

Arguments

T_C	Combined variance-covariance matrix (2t x 2t) where t = n_traits. Structure: [P, P_yg; P_yg', P_g] where P = phenotypic var, P_g = GEBV var, P_yg = covariance between phenotypes and GEBVs. Can be computed automatically if phen_mat and gebv_mat are provided.
Psi_C	Combined genetic covariance matrix (2t x t). Structure: [G; C_gebv_g] where G = genetic var, C_gebv_g = Cov(GEBV, g). Can be computed automatically if gmat and reliability are provided.
phen_mat	Optional. Matrix of phenotypes (n_genotypes x n_traits)
gebv_mat	Optional. Matrix of GEBVs (n_genotypes x n_traits)
pmat	Optional. Phenotypic variance-covariance matrix
gmat	Optional. Genotypic variance-covariance matrix
wmat	Economic weights matrix (n_traits x k), or vector
wcol	Weight column to use if wmat has multiple columns (default: 1)
restricted_traits	Vector of trait indices to restrict (default: NULL)
U	Constraint matrix (2t x n_constraints for combined traits). Alternative to restricted_traits. Ignored if restricted_traits is provided.
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 6.3):

The CRLGSI combines phenotypic and genomic data with restrictions.

Coefficient vector: beta_CR = K_C * beta_C

Where K_C incorporates the restriction matrix.

Selection response: R_CR = (k_I / L_I) * sqrt(beta_CR' * T_C * beta_CR)

Expected gains: E_CR = (k_I / L_I) * (Psi_C * beta_CR) / sqrt(beta_CR' * T_C * beta_CR)

Value

List with:

• summary - Data frame with coefficients and metrics

• b - Vector of CRLGSI coefficients (\beta_{CR})

• b_y - Coefficients for phenotypes

• b_g - Coefficients for GEBVs

• E - Expected genetic gains per trait

• R - Overall selection response

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 # Genotypic component
pmat <- cov(phen_mat)

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

# Restrict traits 2 and 4
result <- crlgsi(
  phen_mat = phen_mat, gebv_mat = gebv_mat,
  pmat = pmat, gmat = gmat, wmat = w,
  restricted_traits = c(2, 4), reliability = 0.7
)
print(result$summary)

## End(Not run)

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