caa a22 4500 378925865 CHVBK 20180305123617.0 cr unu---uuuuu 161128e20041109xx s 000 0 eng 10.2202/1544-6115.1048 doi (NATIONALLICENCE)gruyter-10.2202/1544-6115.1048 Sparse Inverse of Covariance Matrix of QTL Effects with Incomplete Marker Data [Elektronische Daten] [R. Mark Thallman, Kathryn J Hanford, Stephen D Kachman, L. Dale Van Vleck] Gametic models for fitting breeding values at QTL as random effects in outbred populations have become popular because they require few assumptions about the number and distribution of QTL alleles segregating. The covariance matrix of the gametic effects has an inverse that is sparse and can be constructed rapidly by a simple algorithm, provided that all individuals have marker data, but not otherwise. An equivalent model, in which the joint distribution of QTL breeding values and marker genotypes is considered, was shown to generate a covariance matrix with a sparse inverse that can be constructed rapidly with a simple algorithm. This result makes more feasible including QTL as random effects in analyses of large pedigrees for QTL detection and marker assisted selection. Such analyses often use algorithms that rely upon sparseness of the mixed model equations and require the inverse of the covariance matrix, but not the covariance matrix itself. With the proposed model, each individual has two random effects for each possible unordered marker genotype for that individual. Therefore, individuals with marker data have two random effects, just as with the gametic model. To keep the notation and the derivation simple, the method is derived under the assumptions of a single linked marker and that the pedigree does not contain loops. The algorithm could be applied, as an approximate method, to pedigrees that contain loops. ©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston Computational Biology/Bioinformatics nationallicence QTL mapping nationallicence genetic relationships nationallicence marker assisted selection nationallicence Thallman R. Mark USDA, ARS, Roman L. Hruska U.S. Meat Animal Research Center aut Hanford Kathryn J. USDA, ARS, Roman L. Hruska U.S. Meat Animal Research Center, Lincoln aut Kachman Stephen D. Dept. of Statistics, University of Nebraska, Lincoln aut Van Vleck L. Dale USDA, ARS, Roman L. Hruska U.S. Meat Animal Research Center, Lincoln aut Statistical Applications in Genetics and Molecular Biology De Gruyter 3/1(2004-11-09), 1-21 3:1<1 2004 3 sagmb https://doi.org/10.2202/1544-6115.1048 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2202/1544-6115.1048 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Thallman R. Mark USDA, ARS, Roman L. Hruska U.S. Meat Animal Research Center aut NATIONALLICENCE 700 1- Hanford Kathryn J. USDA, ARS, Roman L. Hruska U.S. Meat Animal Research Center, Lincoln aut NATIONALLICENCE 700 1- Kachman Stephen D. Dept. of Statistics, University of Nebraska, Lincoln aut NATIONALLICENCE 700 1- Van Vleck L. Dale USDA, ARS, Roman L. Hruska U.S. Meat Animal Research Center, Lincoln aut NATIONALLICENCE 773 0- Statistical Applications in Genetics and Molecular Biology De Gruyter 3/1(2004-11-09), 1-21 3:1<1 2004 3 sagmb CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter