selection.index (version 2.0.0)

rlpsi: Restricted Linear Phenotypic Selection Index (RLPSI)

Description

Implements the Restricted LPSI where genetic gains are constrained to zero for specific traits while maximizing gains for others. Based on Kempthorne & Nordskog (1959).

Usage

rlpsi(pmat, gmat, wmat, wcol = 1, restricted_traits = NULL, C = NULL, GAY)

Value

List with:

• summary - Data frame with coefficients (b.*), GA, PRE, Delta_G, rHI, hI2

• b - Numeric vector of selection index coefficients

• Delta_G - Named vector of realized correlated responses per trait

• C - Constraint matrix used

Arguments

pmat

Phenotypic variance-covariance matrix (n_traits x n_traits)

gmat

Genotypic variance-covariance matrix (n_traits x n_traits)

wmat

Weight matrix (n_traits x k), or vector

wcol

Weight column number (default: 1)

restricted_traits

Vector of trait indices to restrict (default: NULL). If provided, a constraint matrix C is auto-generated to enforce zero gain on these traits. Example: c(1, 3) restricts traits 1 and 3 to zero gain.

C

Constraint matrix (n_traits x n_constraints). Each column is a restriction. Alternative to restricted_traits for custom constraints. Ignored if restricted_traits is provided.

GAY

Genetic advance of comparative trait (optional)

Details

Mathematical Formulation (Chapter 3, Section 3.1):

The RLPSI minimizes the mean squared difference between I = b'y and H = w'g subject to the restriction: C'Delta_G = 0

Coefficient formula: $$b_r = [I - P^{-1}GC(C'GP^{-1}GC)^{-1}C'G]P^{-1}Gw$$

Where: - P = Phenotypic variance-covariance matrix - G = Genotypic variance-covariance matrix - C = Constraint matrix (each column enforces one restriction) - w = Economic weights

The constraint C'Delta_G = 0 ensures zero genetic gain for restricted traits.

Examples

if (FALSE) {
gmat <- gen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
pmat <- phen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
wmat <- weight_mat(weight)

# Easy way: Restrict traits 1 and 3 to zero gain
result <- rlpsi(pmat, gmat, wmat, wcol = 1, restricted_traits = c(1, 3))

# Advanced way: Provide custom constraint matrix
C <- diag(ncol(pmat))[, 1, drop = FALSE]
result <- rlpsi(pmat, gmat, wmat, wcol = 1, C = C)
}