Application of a Bayesian non-linear model hybrid scheme to sequence data for genomic prediction and QTL mapping.

Using whole genome sequence data might improve genomic prediction accuracy, when compared with high-density SNP arrays, and could lead to identification of casual mutations affecting complex traits. For some traits, the most accurate genomic predictions are achieved with non-linear Bayesian methods. However, as the number of variants and the size of the reference population increase, the computational time required to implement these Bayesian methods (typically with Monte Carlo Markov Chain sampling) becomes unfeasibly long. Here, we applied a new method, HyB_BR (for Hybrid BayesR), which implements a mixture model of normal distributions and hybridizes an Expectation-Maximization (EM) algorithm followed by Markov Chain Monte Carlo (MCMC) sampling, to genomic prediction in a large dairy cattle population with imputed whole genome sequence data. The imputed whole genome sequence data included 994,019 variant genotypes of 16,214 Holstein and Jersey bulls and cows. Traits included fat yield, milk volume, protein kg, fat% and protein% in milk, as well as fertility and heat tolerance. HyB_BR achieved genomic prediction accuracies as high as the full MCMC implementation of BayesR, both for predicting a validation set of Holstein and Jersey bulls (multi-breed prediction) and a validation set of Australian Red bulls (across-breed prediction). HyB_BR had a ten fold reduction in compute time, compared with the MCMC implementation of BayesR (48 hours versus 594 hours). We also demonstrate that in many cases HyB_BR identified sequence variants with a high posterior probability of affecting the milk production or fertility traits that were similar to those identified in BayesR. For heat tolerance, both HyB_BR and BayesR found variants in or close to promising candidate genes associated with this trait and not detected by previous studies. The results demonstrate that HyB_BR is a feasible method for simultaneous genomic prediction and QTL mapping with whole genome sequence in large reference populations.

Wang T ，Chen YP ，MacLeod IM ，Pryce JE ，Goddard ME ，Hayes BJ ... -  《BMC GENOMICS》

A hybrid expectation maximisation and MCMC sampling algorithm to implement Bayesian mixture model based genomic prediction and QTL mapping.

Bayesian mixture models in which the effects of SNP are assumed to come from normal distributions with different variances are attractive for simultaneous genomic prediction and QTL mapping. These models are usually implemented with Monte Carlo Markov Chain (MCMC) sampling, which requires long compute times with large genomic data sets. Here, we present an efficient approach (termed HyB_BR), which is a hybrid of an Expectation-Maximisation algorithm, followed by a limited number of MCMC without the requirement for burn-in. To test prediction accuracy from HyB_BR, dairy cattle and human disease trait data were used. In the dairy cattle data, there were four quantitative traits (milk volume, protein kg, fat% in milk and fertility) measured in 16,214 cattle from two breeds genotyped for 632,002 SNPs. Validation of genomic predictions was in a subset of cattle either from the reference set or in animals from a third breeds that were not in the reference set. In all cases, HyB_BR gave almost identical accuracies to Bayesian mixture models implemented with full MCMC, however computational time was reduced by up to 1/17 of that required by full MCMC. The SNPs with high posterior probability of a non-zero effect were also very similar between full MCMC and HyB_BR, with several known genes affecting milk production in this category, as well as some novel genes. HyB_BR was also applied to seven human diseases with 4890 individuals genotyped for around 300 K SNPs in a case/control design, from the Welcome Trust Case Control Consortium (WTCCC). In this data set, the results demonstrated again that HyB_BR performed as well as Bayesian mixture models with full MCMC for genomic predictions and genetic architecture inference while reducing the computational time from 45 h with full MCMC to 3 h with HyB_BR. The results for quantitative traits in cattle and disease in humans demonstrate that HyB_BR can perform equally well as Bayesian mixture models implemented with full MCMC in terms of prediction accuracy, but with up to 17 times faster than the full MCMC implementations. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in large genomic data sets.

Wang T ，Chen YP ，Bowman PJ ，Goddard ME ，Hayes BJ ... -  《BMC GENOMICS》

Improved precision of QTL mapping using a nonlinear Bayesian method in a multi-breed population leads to greater accuracy of across-breed genomic predictions.

Genomic selection is increasingly widely practised, particularly in dairy cattle. However, the accuracy of current predictions using GBLUP (genomic best linear unbiased prediction) decays rapidly across generations, and also as selection candidates become less related to the reference population. This is likely caused by the effects of causative mutations being dispersed across many SNPs (single nucleotide polymorphisms) that span large genomic intervals. In this paper, we hypothesise that the use of a nonlinear method (BayesR), combined with a multi-breed (Holstein/Jersey) reference population will map causative mutations with more precision than GBLUP and this, in turn, will increase the accuracy of genomic predictions for selection candidates that are less related to the reference animals. BayesR improved the across-breed prediction accuracy for Australian Red dairy cattle for five milk yield and composition traits by an average of 7% over the GBLUP approach (Australian Red animals were not included in the reference population). Using the multi-breed reference population with BayesR improved accuracy of prediction in Australian Red cattle by 2 - 5% compared to using BayesR with a single breed reference population. Inclusion of 8478 Holstein and 3917 Jersey cows in the reference population improved accuracy of predictions for these breeds by 4 and 5%. However, predictions for Holstein and Jersey cattle were similar using within-breed and multi-breed reference populations. We propose that the improvement in across-breed prediction achieved by BayesR with the multi-breed reference population is due to more precise mapping of quantitative trait loci (QTL), which was demonstrated for several regions. New candidate genes with functional links to milk synthesis were identified using differential gene expression in the mammary gland. QTL detection and genomic prediction are usually considered independently but persistence of genomic prediction accuracies across breeds requires accurate estimation of QTL effects. We show that accuracy of across-breed genomic predictions was higher with BayesR than with GBLUP and that BayesR mapped QTL more precisely. Further improvements of across-breed accuracy of genomic predictions and QTL mapping could be achieved by increasing the size of the reference population, including more breeds, and possibly by exploiting pleiotropic effects to improve mapping efficiency for QTL with small effects.

Kemper KE ，Reich CM ，Bowman PJ ，Vander Jagt CJ ，Chamberlain AJ ，Mason BA ，Hayes BJ ，Goddard ME ... -  《-》

A multi-trait Bayesian method for mapping QTL and genomic prediction.

Genomic prediction and quantitative trait loci (QTL) mapping typically analyze one trait at a time but this may ignore the possibility that one polymorphism affects multiple traits. The aim of this study was to develop a multivariate Bayesian approach that could be used for simultaneously elucidating genetic architecture, QTL mapping, and genomic prediction. Our approach uses information from multiple traits to divide markers into 'unassociated' (no association with any trait) and 'associated' (associated with one or more traits). The effect of associated markers is estimated independently for each trait to avoid the assumption that QTL effects follow a multi-variate normal distribution. Using simulated data, our multivariate method (BayesMV) detected a larger number of true QTL (with a posterior probability > 0.9) and increased the accuracy of genomic prediction compared to an equivalent univariate method (BayesR). With real data, accuracies of genomic prediction in validation sets for milk yield traits with high-density genotypes were approximately equal to those from equivalent single-trait methods. BayesMV tended to select a similar number of single nucleotide polymorphisms (SNPs) per trait for genomic prediction compared to BayesR (i.e. those with non-zero effects), but BayesR selected different sets of SNPs for each trait, whereas BayesMV selected a common set of SNPs across traits. Despite these two dramatically different estimates of genetic architecture (i.e. different SNPs affecting each trait vs. pleiotropic SNPs), both models indicated that 3000 to 4000 SNPs are associated with a trait. The BayesMV approach may be advantageous when the aim is to develop a low-density SNP chip that works well for a number of traits. SNPs for milk yield traits identified by BayesMV and BayesR were also found to be associated with detailed milk composition. The BayesMV method simultaneously estimates the proportion of SNPs that are associated with a combination of traits. When applied to milk production traits, most of the identified SNPs were associated with all three traits (milk, fat and protein yield). BayesMV aims at exploiting pleiotropic QTL and selects a small number of SNPs that could be used to predict multiple traits.

Kemper KE ，Bowman PJ ，Hayes BJ ，Visscher PM ，Goddard ME ... -  《-》

On the use of whole-genome sequence data for across-breed genomic prediction and fine-scale mapping of QTL.

Whole-genome sequence (WGS) data are increasingly available on large numbers of individuals in animal and plant breeding and in human genetics through second-generation resequencing technologies, 1000 genomes projects, and large-scale genotype imputation from lower marker densities. Here, we present a computationally fast implementation of a variable selection genomic prediction method, that could handle WGS data on more than 35,000 individuals, test its accuracy for across-breed predictions and assess its quantitative trait locus (QTL) mapping precision. The Monte Carlo Markov chain (MCMC) variable selection model (Bayes GC) fits simultaneously a genomic best linear unbiased prediction (GBLUP) term, i.e. a polygenic effect whose correlations are described by a genomic relationship matrix (G), and a Bayes C term, i.e. a set of single nucleotide polymorphisms (SNPs) with large effects selected by the model. Computational speed is improved by a Metropolis-Hastings sampling that directs computations to the SNPs, which are, a priori, most likely to be included into the model. Speed is also improved by running many relatively short MCMC chains. Memory requirements are reduced by storing the genotype matrix in binary form. The model was tested on a WGS dataset containing Holstein, Jersey and Australian Red cattle. The data contained 4,809,520 genotypes on 35,549 individuals together with their milk, fat and protein yields, and fat and protein percentage traits. The prediction accuracies of the Jersey individuals improved by 1.5% when using across-breed GBLUP compared to within-breed predictions. Using WGS instead of 600 k SNP-chip data yielded on average a 3% accuracy improvement for Australian Red cows. QTL were fine-mapped by locating the SNP with the highest posterior probability of being included in the model. Various QTL known from the literature were rediscovered, and a new SNP affecting milk production was discovered on chromosome 20 at 34.501126 Mb. Due to the high mapping precision, it was clear that many of the discovered QTL were the same across the five dairy traits. Across-breed Bayes GC genomic prediction improved prediction accuracies compared to GBLUP. The combination of across-breed WGS data and Bayesian genomic prediction proved remarkably effective for the fine-mapping of QTL.

Meuwissen T ，van den Berg I ，Goddard M 《-》