Issue |
Genet. Sel. Evol.
Volume 33, Number 2, March-April 2001
|
|
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Page(s) | 153 - 173 | |
DOI | https://doi.org/10.1051/gse:2001114 |
Genet. Sel. Evol. 33 (2001) 153-173
A rapid method for computing the inverse of the gametic covariance matrix between relatives for a marked Quantitative Trait Locus
Gamal Abdel-Azim and Albert E. FreemanDepartment of Animal Science, Iowa State University, Ames, IA 50011, USA
(Received 23 December 1999; accepted 15 November 2000)
Abstract
The inverse of the gametic covariance matrix between relatives,
, for a marked quantitative trait locus (QTL) is
required in best linear unbiased prediction (BLUP) of breeding
values if marker data are available on a QTL. A rapid method for
computing the inverse of a gametic relationship matrix for a marked
QTL without building
itself is presented. The algorithm
is particularly useful due to the approach taken in computing inbreeding
coefficients by having to compute only few elements of
.
Numerical techniques for determining, storing, and computing the
required elements of
and the nonzero elements of the
inverse are discussed. We show that the subset of
required for computing the inbreeding coefficients and hence the inverse
is a tiny proportion of the whole matrix and can be easily stored in
computer memory using sparse matrix storage techniques. We also introduce
an algorithm to determine the maximum set of nonzero elements that can be
found in
and a strategy to efficiently store and access
them. Finally, we demonstrate that the inverse can be efficiently built
using the present techniques for very large and inbred populations.
Key words: gametic relationship / marker-assisted selection / best linear unbiased / prediction
Correspondence and reprints: Gamal Abdel-Azim gaazim@iastate.edu
© INRA, EDP Sciences 2001