smith_hazel: Smith-Hazel Linear Phenotypic Selection Index

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

Smith-Hazel Linear Phenotypic Selection Index

Description

Implements the optimal Smith-Hazel selection index which maximizes the correlation between the index I = b'y and the breeding objective H = w'g.

This is the foundational selection index method from Chapter 2.

Usage

smith_hazel(
  pmat,
  gmat,
  wmat,
  wcol = 1,
  selection_intensity = 2.063,
  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 for 10% selection)
GAY	Optional. Genetic advance of comparative trait for PRE calculation

Details

Mathematical Formulation (Chapter 2):

Index coefficients: b = P^{-1}Gw

Where: - P = Phenotypic variance-covariance matrix - G = Genotypic variance-covariance matrix - w = Economic weights

Key metrics: - Variance of index: \sigma^2_I = b'Pb - Total genetic advance: R_H = i\sqrt{b'Pb} - Expected gains per trait: \Delta G = (i/\sigma_I)Gb - Heritability of index: h^2_I = b'Gb / b'Pb - Accuracy: r_{HI} = \sqrt{b'Gb / b'Pb}

Value

List with:

• summary - Data frame with coefficients and metrics

• b - Vector of Smith-Hazel index coefficients

• w - Named vector of economic weights

• Delta_G - Named vector of expected genetic gains per trait

• sigma_I - Standard deviation of the index

• GA - Total genetic advance

• PRE - Percent relative efficiency

• hI2 - Heritability of the index

• rHI - Accuracy (correlation with breeding objective)

Examples

## Not run: 
# Calculate variance-covariance matrices
gmat <- gen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])
pmat <- phen_varcov(seldata[, 3:9], seldata[, 2], seldata[, 1])

# Define economic weights
weights <- c(10, 8, 6, 4, 2, 1, 1)

# Build Smith-Hazel index
result <- smith_hazel(pmat, gmat, weights)
print(result)
summary(result)

## End(Not run)

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