Performance of genomic selection under a single-step approach in autochthonous Spanish beef cattle populations.

This study evaluated different strategies for implementing a single-step genomic selection programme in two autochthonous Spanish beef cattle populations (Pirenaica-Pi and Rubia Gallega-RG). The strategies were compared in terms of accuracy attained under different scenarios by simulating genomic data over the known genealogy. Several genotyping approaches were tested, as well as, other factors like marker density, effective population size, mutation rate and heritability of the trait. The results obtained showed gains in accuracy with respect to pedigree BLUP evaluation in all cases. The greatest benefit was obtained when the candidates to selection had their genotypes included in the evaluation. Moreover, genotyping the individuals with the most accurate predictions maximized the gains but other suboptimal strategies also yielded satisfactory results. Furthermore, the gains in accuracy increased with the marker density reaching a plateau at around 50,000 markers. Likewise, the effective population size and the mutation rate have also shown an effect, both increasing the accuracy with decreasing values of these population parameters. Finally, the results obtained for the RG population showed greater gains compared to the Pi population, probably attributed to the wider implantation of artificial insemination.

Beyond genomic selection: The animal model strikes back (one generation)!

Genome inheritance is by segments of DNA rather than by independent loci. We introduce the ancestral regression (AR) as a recursive system of simultaneous equations, with grandparental path coefficients as novel parameters. The information given by the pedigree in the AR is complementary with that provided by a dense set of genomic markers, such that the resulting linear function of grandparental BV is uncorrelated to the average of parental BV in the absence of inbreeding. AR is then connected to segmental inheritance by a causal multivariate Gaussian density for BV. The resulting covariance structure (Σ) is Markovian, meaning that conditional on the BV of parents and grandparents, the BV of the animal is independent of everything else. Thus, an algorithm is presented to invert the resulting covariance structure, with a computing effort that is linear in the number of animals as in the case of the inverse additive relationship matrix.

Estimates of the actual relationship between half-sibs in a pig population.

Genomic relationships based on markers capture the actual instead of the expected (based on pedigree) proportion of genome shared identical by descent (IBD). Several methods exist to estimate genomic relationships. In this research, we compare four such methods that were tested looking at the empirical distribution of the estimated relationships across 6704 pairs of half-sibs from a cross-bred pig population. The first method based on multiple marker linkage analysis displayed a mean and standard deviation (SD) in close agreement with the expected ones and was robust to changes in the minor allele frequencies (MAF). A single marker method that accounts for linkage disequilibrium (LD) and inbreeding came second, showing more sensitivity to changes in the MAF. Another single marker method that considers neither inbreeding nor LD showed the smallest empirical SD and was the most sensible to changes in MAF. A higher mean and SD were displayed by VanRaden's method, which was not sensitive to changes in MAF. Therefore, the method based on multiple marker linkage analysis and the single marker method that considers LD and inbreeding performed closer to theoretical values and were consistent with the estimates reported in literature for human half-sibs.

Polynomial order selection in random regression models via penalizing adaptively the likelihood.

Orthogonal Legendre polynomials (LP) are used to model the shape of additive genetic and permanent environmental effects in random regression models (RRM). Frequently, the Akaike (AIC) and the Bayesian (BIC) information criteria are employed to select LP order. However, it has been theoretically shown that neither AIC nor BIC is simultaneously optimal in terms of consistency and efficiency. Thus, the goal was to introduce a method, 'penalizing adaptively the likelihood' (PAL), as a criterion to select LP order in RRM. Four simulated data sets and real data (60,513 records, 6675 Colombian Holstein cows) were employed. Nested models were fitted to the data, and AIC, BIC and PAL were calculated for all of them. Results showed that PAL and BIC identified with probability of one the true LP order for the additive genetic and permanent environmental effects, but AIC tended to favour over parameterized models. Conversely, when the true model was unknown, PAL selected the best model with higher probability than AIC. In the latter case, BIC never favoured the best model. To summarize, PAL selected a correct model order regardless of whether the 'true' model was within the set of candidates.

Accounting for unknown foster dams in the genetic evaluation of embryo transfer progeny.

Animals born by embryo transfer (ET) are usually not included in the genetic evaluation of beef cattle for preweaning growth if the recipient dam is unknown. This is primarily to avoid potential bias in the estimation of the unknown age of dam. We present a method that allows including records of calves with unknown age of dam. Assumptions are as follows: (i) foster cows belong to the same breed being evaluated, (ii) there is no correlation between the breeding value (BV) of the calf and the maternal BV of the recipient cow, and (iii) cows of all ages are used as recipients. We examine the issue of bias for the fixed level of unknown age of dam (AOD) and propose an estimator of the effect based on classical measurement error theory (MEM) and a Bayesian approach. Using stochastic simulation under random mating or selection, the MEM estimating equations were compared with BLUP in two situations as follows: (i) full information (FI); (ii) missing AOD information on some dams. Predictions of breeding value (PBV) from the FI situation had the smallest empirical average bias followed by PBV obtained without taking measurement error into account. In turn, MEM displayed the highest bias, although the differences were small. On the other hand, MEM showed the smallest MSEP, for either random mating or selection, followed by FI, whereas ignoring measurement error produced the largest MSEP. As a consequence from the smallest MSEP with a relatively small bias, empirical accuracies of PBV were larger for MEM than those for full information, which in turn showed larger accuracies than the situation ignoring measurement error. It is concluded that MEM equations are a useful alternative for analysing weaning weight data when recipient cows are unknown, as it mitigates the effects of bias in AOD by decreasing MSEP.

Bayesian conjugate analysis using a generalized inverted Wishart distribution accounts for differential uncertainty among the genetic parameters--an application to the maternal animal model.

Consider the estimation of genetic (co)variance components from a maternal animal model (MAM) using a conjugated Bayesian approach. Usually, more uncertainty is expected a priori on the value of the maternal additive variance than on the value of the direct additive variance. However, it is not possible to model such differential uncertainty when assuming an inverted Wishart (IW) distribution for the genetic covariance matrix. Instead, consider the use of a generalized inverted Wishart (GIW) distribution. The GIW is essentially an extension of the IW distribution with a larger set of distinct parameters. In this study, the GIW distribution in its full generality is introduced and theoretical results regarding its use as the prior distribution for the genetic covariance matrix of the MAM are derived. In particular, we prove that the conditional conjugacy property holds so that parameter estimation can be accomplished via the Gibbs sampler. A sampling algorithm is also sketched. Furthermore, we describe how to specify the hyperparameters to account for differential prior opinion on the (co)variance components. A recursive strategy to elicit these parameters is then presented and tested using field records and simulated data. The procedure returned accurate estimates and reduced standard errors when compared with non-informative prior settings while improving the convergence rates. In general, faster convergence was always observed when a stronger weight was placed on the prior distributions. However, analyses based on the IW distribution have also produced biased estimates when the prior means were set to over-dispersed values.

Additive genetic variance and covariance between relatives in synthetic wheat crosses with variable parental ploidy levels.

Cultivated bread wheat (Triticum aestivum L.) is an allohexaploid species resulting from the natural hybridization and chromosome doubling of allotetraploid durum wheat (T. turgidum) and a diploid goatgrass Aegilops tauschii Coss (Ae. tauschii). Synthetic hexaploid wheat (SHW) was developed through the interspecific hybridization of Ae. tauschii and T. turgidum, and then crossed to T. aestivum to produce synthetic hexaploid wheat derivatives (SHWDs). Owing to this founding variability, one may infer that the genetic variances of native wild populations vs improved wheat may vary due to their differential origin and evolutionary history. In this study, we partitioned the additive variance of SHW and SHWD with respect to their breed origin by fitting a hierarchical Bayesian model with heterogeneous covariance structure for breeding values to estimate variance components for each breed category, and segregation variance. Two data sets were used to test the proposed hierarchical Bayesian model, one from a multi-year multi-location field trial of SHWD and the other comprising the two species of SHW. For the SHWD, the Bayesian estimates of additive variances of grain yield from each breed category were similar for T. turgidum and Ae. tauschii, but smaller for T. aestivum. Segregation variances between Ae. tauschii-T. aestivum and T. turgidum-T. aestivum populations explained a sizable proportion of the phenotypic variance. Bayesian additive variance components and the Best Linear Unbiased Predictors (BLUPs) estimated by two well-known software programs were similar for multi-breed origin and for the sum of the breeding values by origin for both data sets. Our results support the suitability of models with heterogeneous additive genetic variances to predict breeding values in wheat crosses with variable ploidy levels.

Evaluation of the potential use of a meta-population for genomic selection in autochthonous beef cattle populations.

This study investigated the potential application of genomic selection under a multi-breed scheme in the Spanish autochthonous beef cattle populations using a simulation study that replicates the structure of linkage disequilibrium obtained from a sample of 25 triplets of sire/dam/offspring per population and using the BovineHD Beadchip. Purebred and combined reference sets were used for the genomic evaluation and several scenarios of different genetic architecture of the trait were investigated. The single-breed evaluations yielded the highest within-breed accuracies. Across breed accuracies were found low but positive on average confirming the genetic connectedness between the populations. If the same genotyping effort is split in several populations, the accuracies were lower when compared with single-breed evaluation, but showed a small advantage over small-sized purebred reference sets over the accuracies of subsequent generations. Besides, the genetic architecture of the trait did not show any relevant effect on the accuracy with the exception of rare variants, which yielded slightly lower results and higher loss of predictive ability over the generations.

Evidence of positive selection towards Zebuine haplotypes in the BoLA region of Brangus cattle.

The Brangus breed was developed to combine the superior characteristics of both of its founder breeds, Angus and Brahman. It combines the high adaptability to tropical and subtropical environments, disease resistance, and overall hardiness of Zebu cattle with the reproductive potential and carcass quality of Angus. It is known that the major histocompatibility complex (MHC, also known as bovine leucocyte antigen: BoLA), located on chromosome 23, encodes several genes involved in the adaptive immune response and may be responsible for adaptation to harsh environments. The objective of this work was to evaluate whether the local breed ancestry percentages in the BoLA locus of a Brangus population diverged from the estimated genome-wide proportions and to identify signatures of positive selection in this genomic region. For this, 167 animals (100 Brangus, 45 Angus and 22 Brahman) were genotyped using a high-density single nucleotide polymorphism array. The local ancestry analysis showed that more than half of the haplotypes (55.0%) shared a Brahman origin. This value was significantly different from the global genome-wide proportion estimated by cluster analysis (34.7% Brahman), and the proportion expected by pedigree (37.5% Brahman). The analysis of selection signatures by genetic differentiation (F st ) and extended haplotype homozygosity-based methods (iHS and Rsb) revealed 10 and seven candidate regions, respectively. The analysis of the genes located within these candidate regions showed mainly genes involved in immune response-related pathway, while other genes and pathways were also observed (cell surface signalling pathways, membrane proteins and ion-binding proteins). Our results suggest that the BoLA region of Brangus cattle may have been enriched with Brahman haplotypes as a consequence of selection processes to promote adaptation to subtropical environments.

Genomic differentiation between Asturiana de los Valles, Avileña-Negra Ibérica, Bruna dels Pirineus, Morucha, Pirenaica, Retinta and Rubia Gallega cattle breeds.

The Spanish local beef cattle breeds have most likely common origin followed by a process of differentiation. This particular historical evolution has most probably left detectable signatures in the genome. The objective of this study was to identify genomic regions associated with differentiation processes in seven Spanish autochthonous populations (Asturiana de los Valles (AV), Avileña-Negra Ibérica (ANI), Bruna dels Pirineus (BP), Morucha (Mo), Pirenaica (Pi), Retinta (Re) and Rubia Gallega (RG)). The BovineHD 777K BeadChip was used on 342 individuals (AV, n=50; ANI, n=48; BP, n=50; Mo, n=50; Pi, n=48; Re, n=48; RG, n=48) chosen to be as unrelated as possible. We calculated the fixation index (F ST ) and performed a Bayesian analysis named SelEstim. The output of both procedures was very similar, although the Bayesian analysis provided a richer inference and allowed us to calculate significance thresholds by generating a pseudo-observed data set from the estimated posterior distributions. We identified a very large number of genomic regions, but when a very restrictive significance threshold was applied these regions were reduced to only 10. Among them, four regions can be highlighted because they comprised a large number of single nucleotide polymorphisms and showed extremely high signals (Kullback-Leiber divergence (KLD)>6). They are located in BTA 2 (5 575 950 to 10 152 228 base pairs (bp)), BTA 5 (17 596 734 to 18 850 702 bp), BTA 6 (37 853 912 to 39 441 548 bp) and BTA 18 (13 345 515 to 15 243 838 bp) and harbor, among others, the MSTN (Myostatin), KIT-LG (KIT Ligand), LAP3 (leucine aminopeptidase 3), NAPCG (non-SMC condensing I complex, subunit G), LCORL (ligand dependent nuclear receptor corepressor-like) and MC1R (Melanocortin 1 receptor) genes. Knowledge on these genomic regions allows to identify potential targets of recent selection and helps to define potential candidate genes associated with traits of interest, such as coat color, muscle development, fertility, growth, carcass and immunological response.

Estimation of the environmental dam-offspring correlation in beef cattle.

A long standing controversy in animal breeding is related to the strong negative estimates of the direct-maternal genetic correlation obtained when fitting data on maternally influenced traits. In this article, we focused on a model that introduces a new correlation parameter among dam-offspring records. The extant theory allows estimation of the parameter when dams have at most a single offspring. Our goal was to develop an inferential procedure in a more general setting. To do so, we applied a Bayesian approach and we showed that the estimation could be accomplished by introducing a Markov chain Monte Carlo (MCMC) step embedded into a regular Gibbs sampler program. The procedure was implemented by means of an MCMC algorithm known as the Griddy-Gibbs sampler, and a Fortran 90 library was created to accomplish the task. The computer program is available from http://www.agro.uba.ar/catedras/mg_animal/software/RDBLK. With this tool at hand, we applied the inferential procedure to weaning weight records on beef cattle calves from an Argentinean Hereford herd, and we estimated the marginal distribution of the environmental dam-offspring correlation parameter. The distribution was unimodal and symmetric with a mean value of -0.14 (±0.03) and a 95% high posterior density interval between -0.20 and -0.07, indicating that the model placed a huge mass on negative values of the parameter. Noticeably, the magnitude of the direct-maternal genetic correlation diminished from -0.61 to -0.37 with respect to the standard maternal animal model. This result reinforces the idea that environmental covariances among dam-offspring records may bias the estimate of the direct-maternal genetic correlation.

Genetic diversity and divergence among Spanish beef cattle breeds assessed by a bovine high-density SNP chip.

The availability of SNP chips for massive genotyping has proven to be useful to genetically characterize populations of domestic cattle and to assess their degree of divergence. In this study, the Illumina BovineHD BeadChip genotyping array was used to describe the genetic variability and divergence among 7 important autochthonous Spanish beef cattle breeds. The within-breed genetic diversity, measured as the marker expected heterozygosity, was around 0.30, similar to other European cattle breeds. The analysis of molecular variance revealed that 94.22% of the total variance was explained by differences within individuals whereas only 4.46% was the result of differences among populations. The degree of genetic differentiation was small to moderate as the pairwise fixation index of genetic differentiation among breeds (F) estimates ranged from 0.026 to 0.068 and the Nei's D genetic distances ranged from 0.009 to 0.016. A neighbor joining (N-J) phylogenetic tree showed 2 main groups of breeds: Pirenaica, Bruna dels Pirineus, and Rubia Gallega on the one hand and Avileña-Negra Ibérica, Morucha, and Retinta on the other. In turn, Asturiana de los Valles occupied an independent and intermediate position. A principal component analysis (PCA) applied to a distance matrix based on marker identity by state, in which the first 2 axes explained up to 17.3% of the variance, showed a grouping of animals that was similar to the one observed in the N-J tree. Finally, a cluster analysis for ancestries allowed assigning all the individuals to the breed they belong to, although it revealed some degree of admixture among breeds. Our results indicate large within-breed diversity and a low degree of divergence among the autochthonous Spanish beef cattle breeds studied. Both N-J and PCA groupings fit quite well to the ancestral trunks from which the Spanish beef cattle breeds were supposed to derive.