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14 th QTL-MAS Workshop, Poznań University of Life Sciences, Poland 2010Genomic breeding value estimation and QTL detection using univariateand bivariate modelsMario P.L. Calus 1∗ , Han. A. Mulder 1 , Roel F. Veerkamp 11 Animal Breeding and Genomics Centre, Wageningen UR Livestock Research, Lelystad, Netherlands∗ Presenting author: Mario Calus, email: mario.calus@wur.nlBackground. The provided simulated dataset, including a quantitative and a binary trait, wasanalyzed with four univariate and bivariate linear models to predict breeding values foranimals without phenotypes. Two models were used that estimated variance components withREML using a numerator relationship matrix (A), or a SNP based genomic relationshipmatrix (G), as well as two SNP based Bayesian models with one (BayesA) or twodistributions (BayesC) for estimated SNP effects. The bivariate BayesC model sampled QTLprobabilities for each SNP conditional on both traits. Genotypes were permutated 2000 timesagainst the phenotype and pedigree data, to obtain significance thresholds for the posteriorQTL probabilities.Results. Estimated breeding values had correlations with phenotypes in the referencepopulation ranging from 0.75 and 0.89 for the quantitative trait, and from 0.58 to 0.67 for thebinary trait.Correlations were calculated between all different estimated breeding values, across modelsand traits, for animals without phenotypes. Correlations between the different SNP basedmodels were greater than 0.93 (0.87) for the quantitative (binary) trait. Correlations betweenboth traits ranged from 0.48 to 0.77 for the SNP based models, and from 0.36 to 0.61 formodel A. Correlations between both traits were on average 0.78 (0.55) for the bivariate(univariate) models. Estimated genetic correlations were 0.71 (0.66) for model G (A).The bivariate BayesC model detected 17 significant SNPs at the genome-wide level and 24significant SNPs chromosome-wide. Those SNPs clustered into 14 different windows of2Mb, suggesting that 14 QTLs were detected.Conclusions. Estimated breeding values of three different SNP based models, both in theirunivariate and bivariate forms, were in good agreement. Correlations between estimatedbreeding values of both traits indicated that bivariate models made better use of the data.Permutating the genotypes against phenotype and pedigree data in the BayesC modelprovided an effective way to derive significance thresholds for the posterior QTLprobabilities.18
14 th QTL-MAS Workshop, Poznań University of Life Sciences, Poland 2010Hierarchical likelihood opens a new way of estimating genetic values usinggenome-wide dense marker mapsXia Shen 1,2∗ , Lars Rönnegård 2,3 , Örjan Carlborg 1,31The Linnaeus Centre for Bioinformatics, Uppsala University, Uppsala, Sweden2Statistics Group, Dalarna University, Borlänge, Sweden.3Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Uppsala, Sweden.∗ Presenting author: Xia Shen, email: xia.shen@lcb.uu.seBackground. Genome-wide dense markers can be used to detect genes and estimatepolygenic effects. Among many methods, Bayesian techniques have been shown to bepowerful in genome-wide breeding value estimation and association studies. However,computation is known to be intensive in the Bayesian framework, and specifying a suitableprior distribution for each parameter is difficult. We propose to use hierarchical likelihood asan alternative statistical approach to map genes and estimate genomic breeding values indatasets with dense marker maps, to solve such problems. Using double hierarchicalgeneralized linear models, estimation of marker-specific variance is unified in one model andestimated using a fast iterative algorithm solely based on weighted least squares.Results. We analyzed the dataset distributed for the QTL-MAS conference 2010 using doublehierarchical generalized linear models and report breeding value estimates and detected QTL.The estimated breeding values obtained using double hierarchical generalized linear modelswere quite similar to those obtained using generalized linear mixed models (Pearsoncorrelation of 0.990 for the quantitative trait and 0.987 for the binary trait). Using a smoothedversion of the double hierarchical generalized linear model that we propose, QTL were clearlymapped by estimating marker-specific variances.Conclusions. Hierarchical likelihood enables estimating marker-specific variances under anon-Bayesian framework. Double hierarchical generalized linear models can be estimatedusing an iterative algorithm, which greatly shortens the execution time comparing to theBayesian computation. There is furthermore no need to specify any priors. Smoothing bydefining spatial correlation reduces noises at zero-effect markers and is powerful in localizingQTL. Estimating epistatic effects is also possible by such a unified analysis via hierarchicallikelihood.19
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