Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: A rapid method for computing the inverse of the gametic covariance matrix between relatives for a marked | Genet Sei. Evol. 33 2001 153-173 INRA EDP Sciences 2001 153 Original article a rapid method for computing the inverse of the gametic covariance matrix between relatives for a marked Quantitative Trait Locus Gamal Abdel-Azim Albert E. Freeman Department of Animal Science Iowa State UniversitY Ames lA 50011 USA Received 23 December 1999 accepted 15 November 2000 Abstract - The inverse of the gametic covariance matrix between relatives G 1 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 G 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 G. Numerical techniques for determining storing and computing the required elements of G and the nonzero elements of the inverse are discussed. We show that the subset of G 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 G 1 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. gametic relationship marker-assisted selection best linear unbiased prediction 1. introduction The utilization of marker quantitative trait loci associations in genetic evaluation is now possible and likely to be used more extensively in the future. Also many authors have estimated gain through marker-assisted selection . 6 7 9 14 . Marker information will not replace phenotypic records because a full prediction of phenotype from DNA sequence is still far from .
