Genomic selection uses genome-wide dense SNP marker genotyping for the prediction of genetic values, and consists of two steps: (1) estimation of SNP effects, and (2) prediction of genetic value based on SNP genotypes and estimates of their effects. For the former step, BayesB type of estimators have been proposed, which assume a priori that many markers have no effects, and some have an effect coming from a gamma or exponential distribution, i.e. a fat-tailed distribution. Whilst such estimators have been developed using Monte Carlo Markov chain (MCMC), here we derive a much faster non-MCMC based estimator by analytically performing the required integrations. The accuracy of the genome-wide breeding value estimates was 0.011 (s.e. 0.005) lower than that of the MCMC based BayesB predictor, which may be because the integrations were performed one-byone instead of for all SNPs simultaneously. The bias of the new method was opposite to that of the MCMC based BayesB, in that the new method underestimates the breeding values of the best selection candidates, whereas MCMC-BayesB overestimated their breeding values. The new method was computationally several orders of magnitude faster than MCMC based BayesB, which will mainly be advantageous in computer simulations of entire breeding schemes, in cross-validation testing, and practical schemes with frequent re-estimation of breeding values.

BackgroundThe information provided by dense genome-wide markers using high throughput technology is of considerable potential in human disease studies and livestock breeding programs. Genome-wide association studies relate individual single nucleotide polymorphisms (SNP) from dense SNP panels to individual measurements of complex traits, with the underlying assumption being that any association is caused by linkage disequilibrium (LD) between SNP and quantitative trait loci (QTL) affecting the trait. Often SNP are in genomic regions of no trait variation. Whole genome Bayesian models are an effective way of incorporating this and other important prior information into modelling. However a full Bayesian analysis is often not feasible due to the large computational time involved.ResultsThis article proposes an expectation-maximization (EM) algorithm called emBayesB which allows only a proportion of SNP to be in LD with QTL and incorporates prior information about the distribution of SNP effects. The posterior probability of being in LD with at least one QTL is calculated for each SNP along with estimates of the hyperparameters for the mixture prior. A simulated example of genomic selection from an international workshop is used to demonstrate the features of the EM algorithm. The accuracy of prediction is comparable to a full Bayesian analysis but the EM algorithm is considerably faster. The EM algorithm was accurate in locating QTL which explained more than 1% of the total genetic variation. A computational algorithm for very large SNP panels is described.ConclusionsemBayesB is a fast and accurate EM algorithm for implementing genomic selection and predicting complex traits by mapping QTL in genome-wide dense SNP marker data. Its accuracy is similar to Bayesian methods but it takes only a fraction of the time.

Mating activity in a southern Queensland population of S. serrata was at a maximum level in mid-spring and late summer-early autumn. Spawning activity, as indicated by the incidence of spent females, began early in spring and ended in early autumn while water temperatures exceeded approximately 22�C. Nevertheless, ovary condition was apparently held constant during the colder non-spawning half of the year. Ovary condition was not correlated with either ovary coloui or crab size.

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The productive performance of progeny by Bonsmara and Belmont Red sires was compared in contemporarily reared groups in South Africa. Measurements on 4279 pedigreed progeny of 96 Bonsmara sires and 18 Belmont Red sires were recorded over 15 years in 4 diverse climatic regions of South Africa. Growth traits were measured on growing stock from birth to 18 months at pasture. Weight gain, feed conversion rate, frame size, scrotal circumference and visually assessed ‘functional efficiency’ scores were recorded on male progeny fed high protein rations. Carcass traits were measured on a subset of the male progeny. Age at first calving, and repeated measurements of calving date and calving interval were recorded on breeding females as indicators of reproductive performance. Tick counts were made on males and females across a range of ages during times of heavy field infestation. There were differences in progeny performance for some traits. Bonsmara sired animals generally scored higher than Belmont Red progeny for functional efficiency. Belmont Red sired calves were lighter at birth (35.9 v. 37.3; P0.05) and cows by Belmont Red sires had a shorter average calving interval (440 v. 455; P<0.05). Sire breed by region interaction was not important. The differences in scored and measured traits generally reflected differences in selection policies adopted by the breed societies. Variation in growth and fertility traits due to sire was greater than variation due to breed and demonstrated the potential for identifying superior individuals. The performance of the sire breeds for the range of traits and environments studied advocated that selected Bonsmara and Belmont Red animals from South African herds would be suitable for inclusion in breeding programs in Australian Belmont Red herds.