selection.index (version 2.0.0)

ppg_lpsi: Predetermined Proportional Gains (PPG-LPSI)

Description

Implements the PPG-LPSI where breeders specify desired proportional gains between traits rather than restricting specific traits to zero. Based on Tallis (1962).

Usage

ppg_lpsi(pmat, gmat, k, wmat = NULL, wcol = 1, GAY)

Value

List with:

• summary - Data frame with coefficients and metrics

• b - Vector of PPG-LPSI coefficients

• Delta_G - Expected genetic gains per trait

• phi - Proportionality constant

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)

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) {
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)
}