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 (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.
Highlights
A marked quantitative trait locus (QTL) between relatives. This approach requires the inverse of conditional gametic relationship matrix (G−1) for the marked QTL of interest
Ruane and Colleau [8] constructed G−1 following the rules of Fernando and Grossman [3] except that as an approximation, inbreeding coefficients of parents based on pedigree information were used. van Arendonk et al [14] showed how partitioned matrix theory can be applied to directly compute G−1 for a marked QTL
In constructing G−1 directly by the methods of Wang et al [15] and Abdel-Azim and Freeman [1], accounting for inbreeding, the only nontrivial task is to compute a matrix which is proportional to the conditional Mendelian sampling covariance matrix for a marked QTL (D)
Summary
In constructing G−1 directly by the methods of Wang et al [15] and Abdel-Azim and Freeman [1], accounting for inbreeding, the only nontrivial task is to compute a matrix which is proportional to the conditional Mendelian sampling covariance matrix for a marked QTL (D). Wang et al [15, 16] applied the tabular method to compute D, whereas Abdel-Azim and Freeman [1] applied an adaptation of the tabular method [12] in which a small portion of G is enough to compute D The latter method provides a great computational advantage for large populations, its efficiency depends on the size of the required portion of G
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