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Abstract A method that predicts the genetic composition and inbreeding (F) of the future dairy cow population using information on the current cow population, semen use and progeny test bulls is described. This is combined with information on genetic merit of bulls to compare bull selection methods that minimise F and maximise breeding value for profit (called APR in Australia). The genetic composition of the future cow population of Australian Holstein-Friesian (HF) and Jersey up to 6 years into the future was predicted. F in Australian HF and Jersey breeds is likely to increase by about 0.002 and 0.003 per year between 2002 and 2008, respectively. A comparison of bull selection methods showed that a method that selects the best bull from all available bulls for each current or future cow, based on its calf's APR minus F depression, is better than bull selection methods based on APR alone, APR adjusted for mean F of prospective progeny after random mating and mean APR adjusted for the relationship between the selected bulls. This method reduced F of prospective progeny by about a third to a half compared to the other methods when bulls are mated to current and future cows that will be available 5 to 6 years from now. The method also reduced the relationship between the bulls selected to nearly the same extent as the method that is aimed at maximising genetic gain adjusted for the relationship between bulls. The method achieves this because cows with different pedigree exist in the population and the method selects relatively unrelated bulls to mate to these different cows. Selecting the best bull for each current or future cow so that the calf's genetic merit minus F depression is maximised can slow the rate of increase in F in the population.

Abstract A multi-locus QTL mapping method is presented, which combines linkage and linkage disequilibrium (LD) information and uses multitrait data. The method assumed a putative QTL at the midpoint of each marker bracket. Whether the putative QTL had an effect or not was sampled using Markov chain Monte Carlo (MCMC) methods. The method was tested in dairy cattle data on chromosome 14 where the DGAT1 gene was known to be segregating. The DGAT1 gene was mapped to a region of 0.04 cM, and the effects of the gene were accurately estimated. The fitting of multiple QTL gave a much sharper indication of the QTL position than a single QTL model using multitrait data, probably because the multi-locus QTL mapping reduced the carry over effect of the large DGAT1 gene to adjacent putative QTL positions. This suggests that the method could detect secondary QTL that would, in single point analyses, remain hidden under the broad peak of the dominant QTL. However, no indications for a second QTL affecting dairy traits were found on chromosome 14.

Abstract The ordinary-, penalized-, and bootstrap t-test, least squares and best linear unbiased prediction were compared for their false discovery rates (FDR), i.e. the fraction of falsely discovered genes, which was empirically estimated in a duplicate of the data set. The bootstrap-t-test yielded up to 80% lower FDRs than the alternative statistics, and its FDR was always as good as or better than any of the alternatives. Generally, the predicted FDR from the bootstrapped P-values agreed well with their empirical estimates, except when the number of mRNA samples is smaller than 16. In a cancer data set, the bootstrap-t-test discovered 200 differentially regulated genes at a FDR of 2.6%, and in a knock-out gene expression experiment 10 genes were discovered at a FDR of 3.2%. It is argued that, in the case of microarray data, control of the FDR takes sufficient account of the multiple testing, whilst being less stringent than Bonferoni-type multiple testing corrections. Extensions of the bootstrap simulations to more complicated test-statistics are discussed.

Abstract The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.

Abstract Meta-analysis of information from quantitative trait loci (QTL) mapping experiments was used to derive distributions of the effects of genes affecting quantitative traits. The two limitations of such information, that QTL effects as reported include experimental error, and that mapping experiments can only detect QTL above a certain size, were accounted for. Data from pig and dairy mapping experiments were used. Gamma distributions of QTL effects were fitted with maximum likelihood. The derived distributions were moderately leptokurtic, consistent with many genes of small effect and few of large effect. Seventeen percent and 35% of the leading QTL explained 90% of the genetic variance for the dairy and pig distributions respectively. The number of segregating genes affecting a quantitative trait in dairy populations was predicted assuming genes affecting a quantitative trait were neutral with respect to fitness. Between 50 and 100 genes were predicted, depending on the effective population size assumed. As data for the analysis included no QTL of small effect, the ability to estimate the number of QTL of small effect must inevitably be weak. It may be that there are more QTL of small effect than predicted by our gamma distributions. Nevertheless, the distributions have important implications for QTL mapping experiments and Marker Assisted Selection (MAS). Powerful mapping experiments, able to detect QTL of 0.1σp, will be required to detect enough QTL to explain 90% the genetic variance for a quantitative trait.

Abstract Background Two key findings from genomic selection experiments are 1) the reference population used must be very large to subsequently predict accurate genomic estimated breeding values (GEBV), and 2) prediction equations derived in one breed do not predict accurate GEBV when applied to other breeds. Both findings are a problem for breeds where the number of individuals in the reference population is limited. A multi-breed reference population is a potential solution, and here we investigate the accuracies of GEBV in Holstein dairy cattle and Jersey dairy cattle when the reference population is single breed or multi-breed. The accuracies were obtained both as a function of elements of the inverse coefficient matrix and from the realised accuracies of GEBV. Methods Best linear unbiased prediction with a multi-breed genomic relationship matrix (GBLUP) and two Bayesian methods (BAYESA and BAYES_SSVS) which estimate individual SNP effects were used to predict GEBV for 400 and 77 young Holstein and Jersey bulls respectively, from a reference population of 781 and 287 Holstein and Jersey bulls, respectively. Genotypes of 39,048 SNP markers were used. Phenotypes in the reference population were de-regressed breeding values for production traits. For the GBLUP method, expected accuracies calculated from the diagonal of the inverse of coefficient matrix were compared to realised accuracies. Results When GBLUP was used, expected accuracies from a function of elements of the inverse coefficient matrix agreed reasonably well with realised accuracies calculated from the correlation between GEBV and EBV in single breed populations, but not in multi-breed populations. When the Bayesian methods were used, realised accuracies of GEBV were up to 13% higher when the multi-breed reference population was used than when a pure breed reference was used. However no consistent increase in accuracy across traits was obtained. Conclusion Predicting genomic breeding values using a genomic relationship matrix is an attractive approach to implement genomic selection as expected accuracies of GEBV can be readily derived. However in multi-breed populations, Bayesian approaches give higher accuracies for some traits. Finally, multi-breed reference populations will be a valuable resource to fine map QTL.