The D of Cockerham (1954), Eqn 13.1 of Mrode & Pocrnic (4th ed., p.226): between
animal x with parents s, d and animal y with parents f, m,
d_xy = 0.25 (a_sf a_dm + a_sd a_fm), with a the additive relationship and the
diagonal equal to 1. The formula assumes a non-inbred population; with inbreeding in
the pedigree the off-diagonals are the classic approximation, not an exact identity.
Arguments
- ped
data.frame with animal, sire and dam, as in
model(); unknown parent 0 or NA
Value
dominance relationship matrix, rows and columns named by animal in the
topological order of pedigree(), ready for kernel(id, K = )
Details
The matrix is DENSE and is built from the full tabular A, so this is for pedigrees of
moderate size. For a large pedigree use dominance_inverse(), the sparse inverse of
the same D by sire x dam subclasses (Hoeschele & VanRaden, 1991, generalized to
inbreeding and overlapping generations), which enters the model as
kernel(id, Kinv = dominance_inverse(ped)) with the same likelihood as
kernel(id, K = dominance_matrix(ped)) whenever that representation exists (see
its page).
Examples
ped <- data.frame(animal = c("1", "2", "3", "4"),
sire = c("0", "0", "1", "1"),
dam = c("0", "0", "2", "2"))
dominance_matrix(ped)["3", "4"] # full sibs: 0.25
#> [1] 0.25