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An issue with single-step methods is compatibility between the marker-based relationship matrix for genotyped animals and the pedigree-based relationship matrix.
An issue with a single-step method is compatibility between the marker-based relationship matrix for genotyped animals and the pedigree-based relationship matrix [ 4- 6].
Studies on how to adjust the marker-based relationship matrix to be compatible with the submatrix of the pedigree-based relationship matrix for genotyped animals have been reported [ 4- 6].
A single-step method extends the usual pedigree-based method by replacing the additive relationship matrix constructed from pedigree by an additive relationship matrix that combines the marker-based relationship matrix for genotyped animals with the pedigree-based relationship matrix.
It also shows that only a part of the full genomic relationship matrix for genotyped animals is necessary to compute, since G w,33 = (1 - w) G(m other ) + wA33 does not enter into (12).
In the animal model, the inverse of the numerator relationship matrix (A-1) was replaced by H-1 that combines the pedigree and genomic information [ 5]: (1) H − 1 = A − 1 + [ 0 0 0 G − 1 − A 22 − 1 ], where G-1 is the inverse of the genomic relationship matrix and A 22 − 1 is the inverse of the pedigree-based relationship matrix for genotyped animals.
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The matrices G (m o ) = (m o − (2 ρ − 1 ) 1 T ) (m o − (2 ρ − 1 ) 1 T ) T / s and A11 are the marker-based relationship matrix for the genotyped animals and the submatrix of the pedigree-based relationship matrix corresponding to genotyped animals, respectively.
We used SSGBLUP as implemented in DMU [ 13], using the G-ADJUST option which adjusts elements in the genomic relationship so that the average of diagonal elements and the average of the off-diagonal elements equal their corresponding averages in the A matrix for the genotyped animals.
On the inverse scale, the elements of the matrix for non-genotyped animals do not depend on the marker genotypes.
Finally, with millions of genotyped animals, SSMi may become computationally infeasible because it requires full inversion of two very dense matrices for the genotyped animals.
Then, X is the matrix of genotyped variants, standardised such that is in correlation form.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com