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


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 (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 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 G-1. The indirect method can also be applied to construct an approximate G-1 for populations with incomplete marker data, providing approximate probabilities of descent for QTL alleles for individuals with incomplete marker data.

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Correspondence to Mehdi Sargolzaei.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sargolzaei, M., Iwaisaki, H. & Colleau, JJ. Efficient computation of the inverse of gametic relationship matrix for a marked QTL. Genet Sel Evol 38, 253 (2006).

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  • BLUP
  • indirect method
  • inverse of gametic relationship matrix
  • marked QTL
  • tabular method