rlpsi: Restricted Linear Phenotypic Selection Index (RLPSI)

In selection.index: Analysis of Selection Index in Plant Breeding

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)

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.

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

Examples

## Not run: 
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)

## End(Not run)

selection.index documentation built on March 9, 2026, 1:06 a.m.