The marker effects implied by the genomic breeding values of a single-step fit,
a = b (1 - w) Z' G*^-1 u / (2 sum p q) (VanRaden 2008; Wang et al. 2012), with Z the
genotypes centred by twice the allele frequency (a missing genotype at the marker mean),
u the breeding values of the genotyped animals, and G* the SAME matrix the fit
inverted: VanRaden's G brought to the scale of A22 by the affine adjustment a + b G,
blended with A22 by the weight w. Everything the fit used is read from the fit: the
blend, the APY core (the APY inverse is applied to u without forming any n x n
matrix) or the Vecchia k, and the metafounders. With metafounders the genomic matrix is
the G05 of Legarra et al. (2015), Z = M - 1 over all markers, monomorphic included, and
scale m / 2, with no affine adjustment (b = 1): the equivalent marker model is
u = (M - 1) a, and the same formula gives the expectation of a given u. A marker
with no observed genotype has no frequency and is left out, as in the fit. The G*
rebuilt from pedigree and genotypes is checked against the diagonal the fit stored,
before any n x n work: another genotype matrix, or a pedigree that changes the
inbreeding of the genotyped animals, is refused instead of backsolving another model.
The check cannot see every difference (a pedigree with the same inbreeding passes it),
so give exactly the pedigree and genotypes of the fit; with vecchia_k also in the same
row order, because the Vecchia inverse depends on it.
Arguments
- fit
result of
model()fitted withgenotypes=- pedigree
the same pedigree used in the fit
- genotypes
the same list
ids/mused in the fit- blend
leave
NULL: the blend is read from the fit. A value different from the fit's is refused.- group
covariance group of the genomic term ("animal" by default)
Value
vector of marker effects, in the units of the trait per allele dose, named by
the column names of m, with attributes freq (the allele frequencies that centre
each marker, named the same way; 0.5 under metafounders), denom (2 sum p q over the
markers used, or half their number under metafounders) and route ("exact",
"apy" or "vecchia")
Details
The exact route needs one n x n matrix (the genomic one, factored in place); the APY
route needs only the core rows; the Vecchia route rebuilds the dense pipeline of the fit,
about three n x n matrices.
References
VanRaden, P.M. (2008). Journal of Dairy Science 91:4414-4423.
Wang, H., Misztal, I., Aguilar, I., Legarra, A. & Muir, W.M. (2012). Genome-wide association mapping including phenotypes from relatives without genotypes. Genetics Research 94:73-83.
Legarra, A., Christensen, O.F., Vitezica, Z.G., Aguilar, I. & Misztal, I. (2015). Ancestral relationships using metafounders: finite ancestral populations and across population relationships. Genetics 200:455-468.