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Pedigree to additive-genetic relatedness matrix A

Source: R/animal-keyword.R
pedigree_to_A.Rd

Computes the dense numerator-relationship matrix \(\mathbf A\) from a 3-column pedigree (id, sire, dam) using Henderson's (1976) recursive formula:

Usage

pedigree_to_A(pedigree)

Arguments

pedigree

A data frame with one row per individual and columns identifying the individual, sire, and dam. Column names are resolved BY NAME (MCMCglmm-style) using these synonyms:

  • Individual ID column: id or animal.

  • Sire (father) column: sire or father.

  • Dam (mother) column: dam or mother.

If none of the named synonyms is present, the function falls back to positional access – column 1 = id, column 2 = sire, column 3 = dam – with a soft note. Unknown parents encoded as NA or 0 (both treated as missing).

Value

Dense numeric matrix \(n \times n\) with rownames / colnames equal to the individual IDs.

Details

  • \(A_{ii} = 1 + F_i\), where \(F_i\) is the inbreeding coefficient of individual \(i\).

  • \(A_{ij} = \tfrac{1}{2}(A_{i,\text{sire}(j)} + A_{i,\text{dam}(j)})\) for \(j\) younger than \(i\) (pedigree is sorted oldest first).

Founder individuals (both parents unknown) are assumed unrelated and non-inbred: \(A_{founder, founder} = 1\).

Users typically don't call pedigree_to_A() directly – pass pedigree = ped to an animal_scalar() / animal_latent() / animal_indep() / animal_dep() keyword in the formula, and the keyword's parser handles the conversion internally. This function is exported as a public helper for users who want the matrix for their own diagnostics (e.g. inspection of inbreeding coefficients or pre-computation for repeated fits).

For very large pedigrees (\(n > 5000\)) the cubic-time cost of constructing a dense \(\mathbf A\) can become noticeable. When a sparse precision is available, pass it directly with Ainv =; for comparison against established implementations, see nadiv::makeAinv().

See also

animal_scalar() and siblings.