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

Source: R/constrained_genomic_indices.R
cppg_lgsi.Rd

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

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

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

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
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)
} # }