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: \[\bf{b = P^{-1}Aw}\]
where \(\bf{P}\) and \(\bf{G}\) are phenotypic and genetic covariance matrices, respectively, and \(\bf{b}\) and \(\bf{w}\) are vectors of index coefficients and economic weightings, respectively.
The genetic worth \(I\) 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.
Arguments
- .data
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.- use_data
Define which data to use If
.data
is an object of classgamem
. 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.- SI
The selection intensity (percentage). Defaults to
20
- weights
The vector of economic weights. Defaults to a vector of 1s with the same length of the number of traits.
Value
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
Details
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.
References
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. https://www.genetics.org/content/28/6/476.short
Author
Tiago Olivoto tiagoolivoto@gmail.com
Examples
# \donttest{
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))
# }