Efficient computation of the inverse of gametic relationship matrix for a marked QTL

Mehdi Sargolzaei; Hiroaki Iwaisaki; Jean-Jacques Colleau

doi:doi:10.1051/gse:2006002

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Volume 38 / No 3 (May-June 2006)

Genet. Sel. Evol., 38 3 (2006) 253-264

Abstract

Free Access

Issue		Genet. Sel. Evol. Volume 38, Number 3, May-June 2006


Page(s)		253 - 264
DOI		https://doi.org/10.1051/gse:2006002
Published online		26 April 2006

Genet. Sel. Evol. 38 (2006) 253-264
DOI: 10.1051/gse:2006002

Efficient computation of the inverse of gametic relationship matrix for a marked QTL

Mehdi Sargolzaei^a, Hiroaki Iwaisaki^{a, b} and Jean-Jacques Colleau^c

^a Course of Environmental Management Science, Graduate School of Science and Technology, Niigata 950-2181, Japan
^b Department of Agro-biology, Faculty of Agriculture, Niigata University, Niigata 950-2181, Japan
^c Station de génétique quantitative et appliquée, Institut national de la recherche agronomique, 78352 Jouy-en-Josas Cedex, France

(Received 27 May 2005; accepted 1 December 2005 ; published online 26 April 2006)

Abstract - Best linear unbiased prediction of genetic merits for a marked quantitative trait locus (QTL) using mixed model methodology includes the inverse of conditional gametic relationship matrix ( ${\rm {\bf G}}^{-1}$ ) for a marked QTL. When accounting for inbreeding, the conditional gametic relationships between two parents of individuals for a marked QTL are necessary to build ${\rm {\bf G}}^{-1}$ directly. Up to now, the tabular method and its adaptations have been used to compute these relationships. In the present paper, an indirect method was implemented at the gametic level to compute these few relationships. Simulation results showed that the indirect method can perform faster with significantly less storage requirements than adaptation of the tabular method. The efficiency of the indirect method was mainly due to the use of the sparseness of ${\rm {\bf G}}^{-1}$ . The indirect method can also be applied to construct an approximate ${\rm {\bf G}}^{-1}$ for populations with incomplete marker data, providing approximate probabilities of descent for QTL alleles for individuals with incomplete marker data.

Key words: BLUP / indirect method / inverse of gametic relationship matrix / marked QTL / tabular method

Correspondence and reprints: f03m301f@mail.cc.niigata-u.ac.jp

© INRA, EDP Sciences 2006