Pedigree numerator relationship matrix

Builds the additive relationship matrix \(A\) from the pedigree using the tabular method. Element \(A_{ij}\) is twice the coefficient of kinship between individuals \(i\) and \(j\), so a diagonal entry is \(1 + F_i\) where \(F_i\) is the inbreeding coefficient.

Usage

Amatrix(x, ...)

# S4 method for class 'BreedingExperiment'
Amatrix(x, ids = NULL, ...)

Arguments

x

A BreedingExperiment object.

...

Unused.

ids

Optional character vector of identifiers to return, in that order. Defaults to every individual in the pedigree.

Value

A symmetric numeric matrix with dimnames taken from the pedigree.

Details

The matrix is built recursively over a pedigree sorted so that parents come first: an individual's relationship to an earlier individual is the average of its parents' relationships to that individual, and its diagonal is \(1 + \tfrac{1}{2}A_{sire,dam}\).

References

Henderson, C. R. (1976) "A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values." Biometrics 32, 69-83. doi:10.2307/2529339

See also

Gmatrix(), Hmatrix(), inbreeding()

Examples

set.seed(1)
be <- simulateBreeding(n_ind = 12, n_marker = 30)
A <- Amatrix(be)
round(A[1:5, 1:5], 3)
#>        ind001 ind002 ind003 ind004 ind005
#> ind001      1      0      0      0      0
#> ind002      0      1      0      0      0
#> ind003      0      0      1      0      0
#> ind004      0      0      0      1      0
#> ind005      0      0      0      0      1