selection.index (version 2.0.0)

base_index: 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
)

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

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

Examples

if (FALSE) {
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)
}