Estimating genomic breeding values from the QTL-MAS Workshop Data using a single SNP and haplotype / IBD approach

Genomic breeding values were estimated using a Gibbs sampler that avoided the use of the Metropolis-Hastings step as implemented in the BayesB model of Meuwissen et al., Genetics 2001, 157:1819–1829. Two models that estimated genomic estimated breeding values (EBVs) were applied: one used constructed haplotypes (based on alleles of 20 markers) and IBD matrices, another used single SNP regression. Both models were applied with or without polygenic effect. A fifth model included only polygenic effects and no genomic information. The models needed to estimate 366,959 effects for the haplotype/IBD approach, but only 11,850 effects for the single SNP approach. The four genomic models identified 11 to 14 regions that had a posterior QTL probability >0.1. Accuracies of genomic selection breeding values for animals in generations 4–6 ranged from 0.84 to 0.87 (haplotype/IBD vs. SNP). It can be concluded that including a polygenic effect in the genomic model had no effect on the accuracy of the total EBVs or prediction of the QTL positions. The SNP model yielded slightly higher accuracies for the total EBVs, while both models were able to detect nearly all QTL that explained at least 0.5% of the total phenotypic variance. Background The applied models to estimate genomic breeding values described in this paper, are derived from a multiple QTL mapping model described by Meuwissen and Goddard [1]. The methods are implemented using variable (i.e. in this case presence of a QTL or not on a putative QTL position) selection via Gibbs sampling [2]. Thus, the applied Bayesian method avoids the computationally costly Metropolis-Hastings step that was implemented in the BayesB model of Meuwissen et al. [3]. from 12th European workshop on QTL mapping and marker assisted selection Uppsala, Sweden. 15–16 May 2008 Published: 23 February 2009 BMC Proceedings 2009, 3(Suppl 1):S10 <supplement> <title> <p>Proceedings of the 12th European workshop on QTL mapping and marker assisted selection</p> </title> <sponsor> <note>Publication of this supplement was supported by EADGENE (European Animal Disease Genomics Network of Excellence). </note> </sponsor> <note>Proceedings</note> <url>http://www.biomedcentral. com/content/pdf/1753-6561-3-S1-info.pdf</url> </supplement> This article is available from: http://www.biomedcentral. com/1753-6561/3/S1/S10 © 2009 Calus et al; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Page 1 of 4 (page number not for citation purposes) BMC Proceedings 2009, 3(Suppl 1):S10 http://www.biomedcentral. com/1753-6561/3/S1/S10 Methods Parameterization of the model The data were analyzed with five different models considering only additive genetic effects. The first model (called 'HAP_POL') was: where yi is the phenotype of animal i, μ is the overall mean, si is a fixed effect for sexe, ui is the polygenic effect of animal i, vj is the direction of the QTL effects of the haplotypes at putative QTL position j, qij1 (qij2) is the size of the QTL effect for the paternal (maternal) haplotype of animal i at putative QTL position j, and ei is the residual term for animal i [1]. Note that the total effect of a haplotype is modeled as qij. × vj, and that qij. and vj may have a positive or negative value. The covariance among polygenic effects (u.) was modeled as A × , where A is the relationship matrix which was based on the full pedigree and is the polygenic variance. The second model (called 'HAP_NOPOL') was the same as HAP_POL, but omitted the polygenic component. The HAP models assumed a putative QTL in the midpoint of each marker bracket. The covariances among haplotypes at bracket j (q.j.) were modeled as Hj, which is the matrix of estimated IBD probabilities among the haplotypes at the midpoint of bracket j. The variance of q.j . was assumed 1, while vj is a scale parameter that accommodates for a bracket to have a large (small) effect, if a QTL is (not) present. IBD probabilities between haplotypes were calculated using the algorithm of Meuwissen and Goddard [4], which combines linkage disequilibrium with linkage information and, for each bracket j, considers 20 surrounding markers and all available pedigree information. The effective population size was assumed 100 and the number of generations since an arbitrary founder population was also assumed 100, as in Meuwissen and Goddard [1]. All pairs of base haplotypes (i.e haplotypes of first generation of genotyped animals) with an IBD probability above 0.95 were clustered, using a hierarchical clustering algorithm. If the matrix of IBD probabilities among base haplotypes was not positive definite after clustering, the matrix was bended by adding |min_eigenval| + 0.01 to all the diagonal elements, where |min_eigenval| is the absolute value of the lowest (negative) eigenvalue. The matrix was subsequently inverted by LU denomposition. The elements in for the descendant haplotypes were then calculated using the algorithm of Fernando and Grossman (1989) [5]. When the IBD probability of descendant haplotypes with one of their parental haplotypes exceeded 0.95, the descendant haplotype was clustered with this parental haplotype. The third applied model called 'SNP_POL' was: where yi, si, μ, and ui are as in model 1, vj is the direction of the effects of the alleles at marker locus j, qij1 and qij2 are the sizes of the marker effects of animal i at marker locus j, and ei is the residual term for animal i. The fourth model (called 'SNP_NOPOL') was the same as SNP_POL, but omitted the polygenic component. For reasons of comparison, a fifth model was applied, which did include the polygenic effects, but omitted the SNP effects. This model was called 'POL'. Solving algorithm For all models, a Markov chain Monte Carlo method using Gibbs sampling was used to obtain posterior estimates for all the effects in the model [1]. The scale parameter of a putative QTL at locus j, vj, was sampled from a normal distribution N(0, ), if a QTL was present in γ μ i i i ij ij j j i s u q q v e = + + + + ( ) + = ∑ 1 2 1 5994