Builds the matrix \(H\) that combines pedigree and genomic information, so that genotyped and ungenotyped individuals can be analysed in a single model. This is the relationship structure behind single-step genomic prediction (ssGBLUP).
Usage
Hmatrix(x, ...)
# S4 method for class 'BreedingExperiment'
Hmatrix(x, blend = 0.05, tune = TRUE, min_maf = 0, impute = TRUE, ...)Arguments
- x
A BreedingExperiment object with both a pedigree and genotypes.
- ...
Unused.
- blend
Weight \(w\) given to \(A_{22}\) when blending, between 0 and 1. The default, 0.05, is a common choice.
- tune
Rescale \(G\) to the scale of \(A_{22}\) before blending.
- min_maf, impute
Passed to
Gmatrix().
Value
A symmetric numeric matrix over every individual in the pedigree,
ungenotyped individuals first, with an attribute genotyped giving the
identifiers of the genotyped group.
Details
Real breeding programmes genotype only part of the population. Using only \(G\) throws away every ungenotyped relative; using only \(A\) throws away the markers. \(H\) keeps both: relationships among genotyped individuals come from the markers, relationships among ungenotyped individuals are those from the pedigree corrected by what the markers reveal about their genotyped relatives, and the two groups are connected through the pedigree.
Writing 1 for ungenotyped and 2 for genotyped individuals, $$H_{22} = G^{*}$$ $$H_{12} = A_{12} A_{22}^{-1} G^{*}$$ $$H_{11} = A_{11} + A_{12} A_{22}^{-1} (G^{*} - A_{22}) A_{22}^{-1} A_{21}$$
Because \(G\) and \(A_{22}\) are estimated on different scales, \(G\) is first made compatible with \(A_{22}\) in two standard steps. Tuning rescales \(G\) so that its mean diagonal and mean off-diagonal match those of \(A_{22}\). Blending then mixes in a small share of \(A_{22}\), \(G^{*} = (1-w)G + wA_{22}\), which also makes the result invertible when markers are fewer than individuals.
References
Legarra, A., Aguilar, I. & Misztal, I. (2009) "A relationship matrix including full pedigree and genomic information." Journal of Dairy Science 92, 4656-4663. doi:10.3168/jds.2009-2061
Christensen, O. F. & Lund, M. S. (2010) "Genomic prediction when some animals are not genotyped." Genetics Selection Evolution 42, 2. doi:10.1186/1297-9686-42-2
Aguilar, I., Misztal, I., Johnson, D. L., Legarra, A., Tsuruta, S. & Lawlor, T. J. (2010) "Hot topic: A unified approach to utilize phenotypic, full pedigree, and genomic information for genetic evaluation of Holstein final score." Journal of Dairy Science 93, 743-752. doi:10.3168/jds.2009-2730
Examples
# only some of the individuals are genotyped
set.seed(1)
be <- simulateBreeding(n_ind = 30, n_marker = 300, genotyped = 20)
H <- Hmatrix(be)
dim(H)
#> [1] 30 30
attr(H, "genotyped")
#> [1] "ind011" "ind013" "ind019" "ind024" "ind027" "ind030" "ind012" "ind014"
#> [9] "ind020" "ind022" "ind026" "ind015" "ind016" "ind017" "ind018" "ind021"
#> [17] "ind023" "ind025" "ind028" "ind029"