Smith_Hazel  R Documentation 
Computes the Smith (1936) and Hazel (1943) index given economic weights and phenotypic and genotypic variancecovariance matrices. The SmithHazel 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:
\mjsdeqnI = 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.
Smith_Hazel( .data, use_data = "blup", pcov = NULL, gcov = NULL, SI = 15, weights = NULL )
.data 
The input data. It can be either a twoway table with genotypes
in rows and traits in columns, or an object fitted with the function

use_data 
Define which data to use If 
pcov, gcov 
The phenotypic and genotypic variancecovariance matrix,
respectively. Defaults to 
SI 
The selection intensity (percentage). Defaults to 
weights 
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 variancecovariance matrix
pcov: The phenotypic variancecovariance matrix
Tiago Olivoto tiagoolivoto@gmail.com
Smith, H.F. 1936. A discriminant function for plant selection. Ann. Eugen. 7:240250. doi: 10.1111/j.14691809.1936.tb02143.x
Hazel, L.N. 1943. The genetic basis for constructing selection indexes. Genetics 28:47690. https://www.genetics.org/content/28/6/476.short
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))
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