Incorporating Prior Knowledge of Principal Components in Genomic Prediction.

Genomic prediction using a large number of markers is challenging, due to the curse of dimensionality as well as multicollinearity arising from linkage disequilibrium between markers. Several methods have been proposed to solve these problems such as Principal Component Analysis (PCA) that is commonly used to reduce the dimension of predictor variables by generating orthogonal variables. Usually, the knowledge from PCA is incorporated in genomic prediction, assuming equal variance for the PCs or a variance proportional to the eigenvalues, both treat variances as fixed. Here, three prior distributions including normal, scaled-t and double exponential were assumed for PC effects in a Bayesian framework with a subset of PCs. These developed PCR models (dPCRm) were compared to routine genomic prediction models (RGPM) i.e., ridge and Bayesian ridge regression, BayesA, BayesB, and PC regression with a subset of PCs but PC variances predefined as proportional to the eigenvalues (PCR-Eigen). The performance of methods was compared by simulating a single trait with heritability of 0.25 on a genome consisted of 3,000 SNPs on three chromosomes and QTL numbers of 15, 60, and 105. After 500 generations of random mating as the historical population, a population was isolated and mated for another 15 generations. The generations 8 and 9 of recent population were used as the reference population and the next six generations as validation populations. The accuracy and bias of predictions were evaluated within the reference population, and each of validation populations. The accuracies of dPCRm were similar to RGPM (0.536 to 0.664 vs. 0.542 to 0.671), and higher than the accuracies of PCR-Eigen (0.504 to 0.641) within reference population over different QTL numbers. Decline in accuracies in validation populations were from 0.633 to 0.310, 0.639 to 0.313, and 0.617 to 0.298 using dPCRm, RGPM and PCR-Eigen, respectively. Prediction biases of dPCRm and RGPM were similar and always much less than biases of PCR-Eigen. In conclusion assuming PC variances as random variables via prior specification yielded higher accuracy than PCR-Eigen and same accuracy as RGPM, while fewer predictors were used.

A two step Bayesian approach for genomic prediction of breeding values.

BACKGROUND: In genomic models that assign an individual variance to each marker, the contribution of one marker to the posterior distribution of the marker variance is only one degree of freedom (df), which introduces many variance parameters with only little information per variance parameter. A better alternative could be to form clusters of markers with similar effects where markers in a cluster have a common variance. Therefore, the influence of each marker group of size p on the posterior distribution of the marker variances will be p df. METHODS: The simulated data from the 15th QTL-MAS workshop were analyzed such that SNP markers were ranked based on their effects and markers with similar estimated effects were grouped together. In step 1, all markers with minor allele frequency more than 0.01 were included in a SNP-BLUP prediction model. In step 2, markers were ranked based on their estimated variance on the trait in step 1 and each 150 markers were assigned to one group with a common variance. In further analyses, subsets of 1500 and 450 markers with largest effects in step 2 were kept in the prediction model. RESULTS: Grouping markers outperformed SNP-BLUP model in terms of accuracy of predicted breeding values. However, the accuracies of predicted breeding values were lower than Bayesian methods with marker specific variances. CONCLUSIONS: Grouping markers is less flexible than allowing each marker to have a specific marker variance but, by grouping, the power to estimate marker variances increases. A prior knowledge of the genetic architecture of the trait is necessary for clustering markers and appropriate prior parameterization.

Comparison of linear mixed model analysis and genealogy-based haplotype clustering with a Bayesian approach for association mapping in a pedigreed population.

BACKGROUND: Despite many success stories of genome wide association studies (GWAS), challenges exist in QTL detection especially in datasets with many levels of relatedness. In this study we compared four methods of GWA on a dataset simulated for the 15th QTL-MAS workshop. The four methods were 1) Mixed model analysis (MMA), 2) Random haplotype model (RHM), 3) Genealogy-based mixed model (GENMIX), and 4) Bayesian variable selection (BVS). The data consisted of phenotypes of 2000 animals from 20 sire families and were genotyped with 9990 SNPs on five chromosomes. RESULTS: Out of the eight simulated QTL, these four methods MMA, RHM, GENMIX and BVS identified 6, 6, 8 and 7 QTL respectively and 4 QTL were common across the methods. GENMIX had the highest power to detect QTL however it also produced 4 false positives. BVS was the second best method in terms of power, detecting all QTL except the one on chromosome 5 with epistatic interaction. Two spurious associations were obtained across methods. Though all the methods considered the full pedigree in the analyses, it was not sufficient to avoid all the spurious associations arising due to family structure. CONCLUSIONS: Using several methods with divergent approaches for GWAS can be useful in gaining confidence on the QTL identified. In our comparison, GENMIX was found to be the best method in terms of power but it needs appropriate correction for multiple testing to avoid the false positives. This study shows that the issues of multiple testing and the relatedness among study samples need special attention in GWAS.