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Combined Restricted Linear Genomic Selection Index (CRLGSI)

Source: R/constrained_genomic_indices.R
crlgsi.Rd

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

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

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

Examples

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