Deterministic predictions of the accuracy of genomic breeding values in selection candidates with no phenotypes have been derived based on the heritability of the trait, number of phenotyped and genotyped animals in the reference population where the marker effects are estimated, the effective population size and the length of the genome. We assessed the value of these deterministic predictions given the results that have been achieved in Holstein and Jersey dairy cattle. We conclude that the deterministic predictions are useful guide for establishing the size of the reference populations which must be assembled in order to predict genomic breeding values at a desired level of accuracy in selection candidates.

Single step genomic BLUP (SS-GBLUP) for BREEDPLAN beef cattle evaluations is currently being tested for implementation across a number of breeds. A genomic data pipeline has been developed to enable efficient analysis of the industry-recorded SNP genotypes for incorporation in SS-GBLUP analyses. Complex data collection, along with format and/or naming convention inconsistencies challenges efficient data processing. This pipeline includes quality control of variable formatted data, and imputation of genotypes, for building the genomic relationship matrix required for implementation into single step evaluation.

The genetics of reproduction is poorly understood because the heritabilities of traits currently recorded are low. To elucidate the genetics underlying reproduction in beef cattle, we performed a genome-wide association study using the bovine SNP50 chip in 2 tropically adapted beef cattle breeds, Brahman and Tropical Composite. Here we present the results for 3 female reproduction traits: 1) age at puberty, defined as age in days at first observed corpus luteum (CL) after frequent ovarian ultrasound scans (AGECL); 2) the postpartum anestrous interval, measured as the number of days from calving to first ovulation postpartum (first rebreeding interval, PPAI); and 3) the occurrence of the first postpartum ovulation before weaning in the first rebreeding period (PW), defined from PPAI. In addition, correlated traits such as BW, height, serum IGF1 concentration, condition score, and fatness were also examined. In the Brahman and Tropical Composite cattle, 169 [false positive rate (FPR) = 0.262] and 84 (FPR = 0.581) SNP, respectively, were significant (P < 0.001) for AGECL. In Brahman, 41% of these significant markers mapped to a single chromosomal region on BTA14. In Tropical Composites, 16% of these significant markers were located on BTA5. For PPAI, 66 (FPR = 0.67) and 113 (FPR = 0.432) SNP were significant (P < 0.001) in Brahman and Tropical Composite, respectively, whereas for PW, 68 (FPR = 0.64) and 113 (FPR = 0.432) SNP were significant (P < 0.01). In Tropical Composites, the largest concentration of PPAI markers were located on BTA5 [19% (PPAI) and 23% (PW)], and BTA16 [17% (PPAI) and 18% (PW)]. In Brahman cattle, the largest concentration of markers for postpartum anestrus was located on BTA3 (14% for PPAI and PW) and BTA14 (17% PPAI). Very few of the significant markers for female reproduction traits for the Brahman and Tropical Composite breeds were located in the same chromosomal regions. However, fatness and BW traits as well as serum IGF1 concentration were found to be associated with similar genome regions within and between breeds. Clusters of SNP associated with multiple traits were located on BTA14 in Brahman and BTA5 in Tropical Composites.

Mixed models incorporating the inverse of a numerator relationship matrix (NRM) are widely used to estimate genetic parameters and to predict breeding values in animal breeding. A simple and quick method to directly calculate the inverse of the NRM has been historically developed for diploid animal species. Mixed models are less used in plant breeding partly because the existing method for diploids is not applicable to autopolyploid species. This is because of the phenomenon of double reduction and the possibility that gametes carry alleles which are identical by descent. This paper generalises the NRM and its inverse for autopolyploid species, so it can be easily incorporated into their genetic analysis. The technique proposed is to first calculate the kinship coefficient matrix and its inverse as a precursor to calculating the NRM and its inverse. This allows the NRM to be calculated for populations containing individuals of mixed ploidy levels. This generalization can also accommodate uncertain parentage by generating the "average" relationship matrix. The possibility that non-inbred parents can produce inbred progeny (double reduction) is also discussed. Rules are outlined that are applicable for any level of ploidy.

In QTL mapping using linkage and/or linkage disequilibrium, an important process is to find the pattern of inheritance states and haplotype configurations, a process known as haplotype reconstruction. Haplotype reconstruction is routinely based upon observed pedigree information and marker genotypes for individuals in the pedigree. It is not feasible for the exact methods to use all such information for large complex pedigree especially when there are many missing genotypes. Markov Chain Monte Carlo (MCMC) approaches have been widely used to handle a complex pedigree with sparse genotypic data. However they often have reducibility problems or are slow to converge. Combining two different MCMC approaches results in improvement of computational speed and mixing properties. It allows obtaining reliable estimates such as identity by descent coefficients between individuals within a reasonable time.

A genome wide selection (GWS) platform was developed for prediction of genetic merit in dairy cattle. The critical components of the GWS platform included a genome wide SNP analysis assay representing 15,036 SNPs, 1546 progeny tested Holstein Friesian sires with EBV (ABV) for 42 lactation performance traits, and a series of complexity reduction methods with internal and external cross validation. Derived Molecular Breeding Values (MBV) using a fraction of the available SNP information, were shown to have high predictive value for genetic merit (r=0.65-0.87 with ABV) in bulls not used in the training data from which the SNP effects were derived. GWS can be used in the absence of SNP location and pedigree to make potentially highly accurate predictions of genetic merit at an early age from DNA analyses.

Background: Knowing the phase of marker genotype data can be useful in genome-wide association studies, because it makes it possible to use analysis frameworks that account for identity by descent or parent of origin of alleles and it can lead to a large increase in data quantities via genotype or sequence imputation. Long-range phasing and haplotype library imputation constitute a fast and accurate method to impute phase for SNP data. Methods: A long-range phasing and haplotype library imputation algorithm was developed. It combines information from surrogate parents and long haplotypes to resolve phase in a manner that is not dependent on the family structure of a dataset or on the presence of pedigree information. Results: The algorithm performed well in both simulated and real livestock and human datasets in terms of both phasing accuracy and computation efficiency. The percentage of alleles that could be phased in both simulated and real datasets of varying size generally exceeded 98% while the percentage of alleles incorrectly phased in simulated data was generally less than 0.5%. The accuracy of phasing was affected by dataset size, with lower accuracy for dataset sizes less than 1000, but was not affected by effective population size, family data structure, presence or absence of pedigree information, and SNP density. The method was computationally fast. In comparison to a commonly used statistical method (fastPHASE), the current method made about 8% less phasing mistakes and ran about 26 times faster for a small dataset. For larger datasets, the differences in computational time are expected to be even greater. A computer program implementing these methods has been made available. Conclusions: The algorithm and software developed in this study make feasible the routine phasing of high-density SNP chips in large datasets.

Since the 1990s many promises have been made about economic benefits available from genome scanning. We were assured that we would be able to look at an animal's genes and determine its genetic merit directly. Of course this included the assumption, generally implied, that we would have already determined the effects of all the (important) genes, at all times and under all circumstances. However, despite numerous 'in silico' proofs, it seems that ascertaining these effects is proving much more elusive than originally assumed. We did not comprehend how much data we would need. By mating the best to the best, we have been 'improving' domesticated species for millenia. We keep getting more sophisticated about determining what is 'best' but genetic improvement was achieved long before the mechanism of inheritance was understood. Despite shortcomings in our understanding of quantitative genetic variation (e.g. the search for the missing heritability), these methods are highly effective. Furthermore, these methods of genetic evaluation use no explicit knowledge of individual gene action. The question remains: 'Will such knowledge make predictions more accurate?'

Genomic information can accurately specify relationships among animals, including between those without known common ancestors. Genetic variances estimated with genomic data relate to unknown, more distant, founder populations than those defined by the pedigree. Starting from different sets of assumptions, the properties of some alternative genomic relationship matrices (G) are explored. Although the assumptions and matrices differ, the resulting sets of estimated breeding values predict the differences between animals identically, despite obtaining different estimates of the additive genetic variance - showing that there are many ways of building G that provide identical results. For some methods integer and logic, rather than floating point, operations will expedite building G many-fold.

A strategy to reduce computational demands of genome-wide association studies fitting a mixed model is presented. Improvements are achieved by utilizing a large proportion of calculations that remain constant across the multiple analyses for individual markers involved, with estimates obtained without inverting large matrices.