Implements the PPG-LPSI where breeders specify desired proportional gains between traits rather than restricting specific traits to zero. Based on Tallis (1962).
Arguments
- pmat
Phenotypic variance-covariance matrix (n_traits x n_traits)
- gmat
Genotypic variance-covariance matrix (n_traits x n_traits)
- k
Vector of desired proportional gains (length n_traits). Example: k = c(2, 1, 1) means trait 1 should gain twice as much as traits 2 and 3.
- wmat
Optional weight matrix for GA/PRE calculation
- wcol
Weight column number (default: 1)
- GAY
Genetic advance of comparative trait (optional)
Value
List with:
summary- Data frame with coefficients and metricsb- Vector of PPG-LPSI coefficientsDelta_G- Expected genetic gains per traitphi- Proportionality constant
Details
Mathematical Formulation (Chapter 3, Section 3.2):
The PPG-LPSI achieves gains in specific proportions: Delta_G = phi*k
Coefficient formula (Tallis, 1962): $$b = P^{-1}G(G'P^{-1}G)^{-1}k$$
Where: - k = Vector of desired proportions - phi = Proportionality constant (determined by selection intensity and variances)
The constraint ensures Delta_G1:Delta_G2:Delta_G3 = k1:k2:k3
Examples
if (FALSE) { # \dontrun{
gmat <- gen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
pmat <- phen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
# Gains in ratio 2:1:1:1:1:1:1
k <- c(2, 1, 1, 1, 1, 1, 1)
result <- ppg_lpsi(pmat, gmat, k)
} # }