base_index: Base Index (Williams, 1962)

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

Base Index (Williams, 1962)

Description

Implements the Base Index where coefficients are set equal to economic weights. This is a simple, non-optimized approach that serves as a baseline comparison.

Unlike the Smith-Hazel index which requires matrix inversion, the Base Index is computationally trivial and robust when covariance estimates are unreliable.

Usage

base_index(
  pmat,
  gmat,
  wmat,
  wcol = 1,
  selection_intensity = 2.063,
  compare_to_lpsi = TRUE,
  GAY = NULL
)

Arguments

pmat	Phenotypic variance-covariance matrix (n_traits x n_traits)
gmat	Genotypic variance-covariance matrix (n_traits x n_traits)
wmat	Economic weights matrix (n_traits x k), or vector
wcol	Weight column to use if wmat has multiple columns (default: 1)
selection_intensity	Selection intensity constant (default: 2.063)
compare_to_lpsi	Logical. If TRUE, compares Base Index efficiency to optimal LPSI (default: TRUE)
GAY	Optional. Genetic advance of comparative trait for PRE calculation

Details

Mathematical Formulation:

Index coefficients: b = w

The Base Index is appropriate when: - Covariance estimates are unreliable - Computational simplicity is required - A baseline for comparison is needed

Value

List with:

• summary - Data frame with coefficients and metrics

• b - Vector of Base Index coefficients (equal to w)

• w - Named vector of economic weights

• Delta_G - Named vector of expected genetic gains per trait

• lpsi_comparison - Optional comparison with Smith-Hazel LPSI

Examples

## Not run: 
gmat <- gen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
pmat <- phen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
weights <- c(10, 8, 6, 4, 2, 1, 1)

result <- base_index(pmat, gmat, weights, compare_to_lpsi = TRUE)
print(result)

## End(Not run)

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