Smith_Hazel: Smith-Hazel index

View source: R/Smith_Hazel.R

Smith_HazelR Documentation

Smith-Hazel index



Computes the Smith (1936) and Hazel (1943) index given economic weights and phenotypic and genotypic variance-covariance matrices. The Smith-Hazel index is computed as follows: \loadmathjax \mjsdeqn\bfb = P^-1Aw

where \mjseqn\bfP and \mjseqn\bfG are phenotypic and genetic covariance matrices, respectively, and \mjseqn\bfb and \mjseqn\bfw are vectors of index coefficients and economic weightings, respectively.

The genetic worth \mjseqnI of an individual genotype based on traits x, y, ..., n, is calculated as:


I = b_xG_x + b_yG_y + ... + b_nG_n

where b the index coefficient for the traits x, y, ..., n, respectively, and G is the individual genotype BLUPs for the traits x, y, ..., n, respectively.


  use_data = "blup",
  pcov = NULL,
  gcov = NULL,
  SI = 15,
  weights = NULL



The input data. It can be either a two-way table with genotypes in rows and traits in columns, or an object fitted with the function gamem(). Please, see Details for more details.


Define which data to use If .data is an object of class gamem. Defaults to "blup" (the BLUPs for genotypes). Use "pheno" to use phenotypic means instead BLUPs for computing the index.

pcov, gcov

The phenotypic and genotypic variance-covariance matrix, respectively. Defaults to NULL. If a two-way table is informed in .data these matrices are mandatory.


The selection intensity (percentage). Defaults to 20


The vector of economic weights. Defaults to a vector of 1s with the same length of the number of traits.


When using the phenotypic means in .data, be sure the genotype's code are in rownames. If .data is an object of class gamem them the BLUPs for each genotype are used to compute the index. In this case, the genetic covariance components are estimated by mean cross products.


An object of class hz containing:

  • b: the vector of index coefficient.

  • index: The genetic worth.

  • sel_dif_trait: The selection differencial.

  • sel_gen: The selected genotypes.

  • gcov: The genotypic variance-covariance matrix

  • pcov: The phenotypic variance-covariance matrix


Tiago Olivoto


Smith, H.F. 1936. A discriminant function for plant selection. Ann. Eugen. 7:240-250. doi: 10.1111/j.1469-1809.1936.tb02143.x

Hazel, L.N. 1943. The genetic basis for constructing selection indexes. Genetics 28:476-90.

See Also

mtsi(), mgidi(), fai_blup()


vcov <- covcor_design(data_g, GEN, REP, everything())
means <- as.matrix(vcov$means)
pcov <- vcov$phen_cov
gcov <- vcov$geno_cov

index <- Smith_Hazel(means, pcov = pcov, gcov = gcov, weights = rep(1, 15))

metan documentation built on March 7, 2023, 5:34 p.m.