TAILIEUCHUNG - Báo cáo sinh học: " Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học quốc tế đề tài: Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse | Genetics Selection Evolution BioMed Central Open Access Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse Takuro Oikawa and Kazuhiro Yasuda Address Graduate School of Natural Science and Technology Okayama University Okayama-shi 700-8530 Japan Email Takuro Oikawa - toikawa@ KazuhiroYasuda-ky_0911@ Corresponding author Published 3 March 2009 Received 28 January 2009 Genetics Selection Evolution 2009 41 25 doi 1297-9686-41 -25 Accepted 3 March 2009 This article is available from http content 41 1 25 2009 Oikawa and Yasuda licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Abstract In the field of animal breeding estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix NRM into a mixed model has made these analyses possible. However a method including a genetically identical animal GIA in NRM if genetic relationships between pairs of GIAs are not perfect is still lacking. Here we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to off-diagonal elements between pairs of GIAs to 1-x and the other elements to 0 where x is a constant less than . The inverse of the K matrix is then calculated directly by a simple formula. Thus the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual its transpose matrix the inverse of the K matrix and the inverse of diagonal matrix D in which the diagonal elements comprise a number of known parents

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