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.

Meta-analysis of genome-wide association from genomic prediction models.

Genome-wide association (GWA) studies based on GBLUP models are a common practice in animal breeding. However, effect sizes of GWA tests are small, requiring larger sample sizes to enhance power of detection of rare variants. Because of difficulties in increasing sample size in animal populations, one alternative is to implement a meta-analysis (MA), combining information and results from independent GWA studies. Although this methodology has been used widely in human genetics, implementation in animal breeding has been limited. Thus, we present methods to implement a MA of GWA, describing the proper approach to compute weights derived from multiple genomic evaluations based on animal-centric GBLUP models. Application to real datasets shows that MA increases power of detection of associations in comparison with population-level GWA, allowing for population structure and heterogeneity of variance components across populations to be accounted for. Another advantage of MA is that it does not require access to genotype data that is required for a joint analysis. Scripts related to the implementation of this approach, which consider the strength of association as well as the sign, are distributed and thus account for heterogeneity in association phase between QTL and SNPs. Thus, MA of GWA is an attractive alternative to summarizing results from multiple genomic studies, avoiding restrictions with genotype data sharing, definition of fixed effects and different scales of measurement of evaluated traits.

A comparison of methods to estimate genomic relationships using pedigree and markers in livestock populations.

Accurate prediction of breeding values depends on capturing the variability in genome sharing of relatives with the same pedigree relationship. Here, we compare two approaches to set up genomic relationship matrices for precision of genomic relationships (GR) and accuracy of estimated breeding values (GEBV). Real and simulated data (pigs, 60k SNP) were analysed, and GR were estimated using two approaches: (i) identity by state, corrected with either the observed (GVR-O ) or the base population (GVR-B ) allele frequencies and (ii) identity by descent using linkage analysis (GIBD-L ). Estimators were evaluated for precision and empirical bias with respect to true pedigree IBD GR. All three estimators had very low bias. GIBD-L displayed the lowest sampling error and the highest correlation with true genome-shared values. GVR-B approximated GIBD-L 's correlation and had lower error than GVR-O . Accuracy of GEBV for selection candidates was significantly higher when GIBD-L was used and identical between GVR-O and GVR-B . In real data, GIBD-L 's sampling standard deviation was the closest to the theoretical value for each pedigree relationship. Use of pedigree to calculate GR improved the precision of estimates and the accuracy of GEBV.

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.

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.

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.

Multiple paternal origins of domestic cattle revealed by Y-specific interspersed multilocus microsatellites.

In this study, we show how Y-specific interspersed multilocus microsatellites, which are loci that yield several amplified bands differing in size from the same male individual and PCR reaction, are a powerful source of information for tracing the history of cattle. Our results confirm the existence of three main groups of sires, which are separated by evolutionary time and clearly predate domestication. These three groups are consistent with the haplogroups previously identified by Götherström et al. (2005) using five Y-specific segregating sites: Y1 and Y2 in taurine (Bos taurus) cattle and Y3 in zebu (Bos indicus) cattle. The zebu cattle cluster clearly originates from a domestication process that was geographically and temporally separated from that of taurine clusters. Our analyses further suggest that: (i) introgression of wild sire genetic material into domesticated herds may have a significant role in the formation of modern cattle, including the formation of the Y1 haplogroup; (ii) a putative domestication event in Africa probably included local Y2-like wild sires; (iii) the West African zebu cattle Y-chromosome may have partially originated from an ancient introgression of humped cattle into Africa; and (iv) the high genetic similarity among Asian zebu sires is consistent with a single domestication process.

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.

Shiga toxin-producing Escherichia coli (STEC) O22:H8 isolated from cattle reduces E. coli O157:H7 adherence in vitro and in vivo.

PROBLEM ADDRESSED: Shiga toxin-producing Escherichia coli (STEC) are a group of bacteria responsible for food-associated diseases. Clinical features include a wide range of symptoms such as diarrhea, hemorrhagic colitis and the hemolytic uremic syndrome (HUS), a life-threatening condition. OBJECTIVE: Our group has observed that animals naturally colonized with STEC strains of unknown serotype were not efficiently colonized with E. coli O157:H7 after experimental infection. In order to assess the basis of the interference, three STEC strains were isolated from STEC persistently-colonized healthy cattle from a dairy farm in Buenos Aires, Argentina. METHODS AND RESULTS: The three isolated strains are E. coli O22:H8 and carry the stx1 and stx2d genes. The activatable activity of Stx2d was demonstrated in vitro. The three strains carry the adhesins iha, ehaA and lpfO113. E. coli O22:H8 formed stronger biofilms in abiotic surface than E. coli O157:H7 (eae+, stx2+) and displayed a more adherent phenotype in vitro towards HeLa cells. Furthermore, when both serotypes were cultured together O22:H8 could reduce O157:H7 adherence in vitro. When calves were intragastrically pre-challenged with 108 CFU of a mixture of the three STEC strains and two days later challenged with the same dose of the strain E. coli O157:H7 438/99, the shedding of the pathogen was significantly reduced. CONCLUSIONS: These results suggest that E. coli O22:H8, a serotype rarely associated with human illness, might compete with O157:H7 at the bovine recto-anal junction, making non-O157 carrying-calves less susceptible to O157:H7 colonization and shedding of the bacteria to the environment.

Refining genomewide association for growth and fat deposition traits in an F pig population.

The identification of genomic regions that affect additive genetic variation and contain genes involved in controlling growth and fat deposition has enormous impact in the farm animal industry (e.g., carcass merit and meat quality). Therefore, a genomewide association study was implemented in an F pig population using a 60,000 SNP marker panel for traits related to growth and fat deposition. Estimated genomic EBV were linearly transformed to calculate SNP effects and to identify genomic positions possibly associated with the genetic variability of each trait. Genomic segments were then defined considering the markers included in a region 1 Mb up- and downstream from the SNP with the smallest -value and a false discovery rate < 0.05 for each trait. The significance for each 2-Mb segment was tested using the Bonferroni correction. Significant SNP were detected on SSC2, SSC3, SSC5, and SSC6, but 2-Mb segment significant effects were observed on SSC3 for weight at birth (wt_birth) and on SSC6 for 10th-rib backfat and last-rib backfat measured by ultrasound at different ages. Furthermore, a 6-Mb segment on SSC6 was also considered because the 2-Mb segments for 10 different fat deposition traits were overlapped. Although the segment effects for each trait remain significant, the proportion of additive variance explained by this larger segment was slightly smaller in some traits. In general, the results confirm the presence of genetic variability for wt_birth on SSC3 (18.0-20.2 Mb) and for fat deposition traits on SSC6 (133.8-136.0 Mb). Within these regions, fibrosin () and myosin light chain, phosphorylatable, fast skeletal muscle () genes could be considered as candidates for the wt_birth signal on SSC3, and the SERPINE1 mRNAbinding protein 1 gene () may be a candidate for the fat deposition trait signals on SSC6.

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.

Impact of Infection Dose and Previous Serum Antibodies against the Locus of Enterocyte Effacement Proteins on Escherichia coli O157:H7 Shedding in Calves following Experimental Infection.

Escherichia coli O157:H7 is the main causative agent of haemolytic uremic syndrome. Cattle are the main reservoir of these bacteria, and have been shown to develop immune response to colonization. Our aim was to investigate the faecal shedding pattern of E. coli O157:H7 in calves challenged intragastrically with either 10(8) or 10(10) CFU, as well as the ability of specific preexisting antibodies to reduce shedding of the pathogen. Shedding was analysed by direct counting as well as enrichment of rectoanal mucosal swabs. Statistical analysis was performed using a linear model for repeated measures with and without the inclusion of preexisting antibodies against the carboxy-terminal fraction of intimin-γ (γ-intimin C280) as a covariable. Results suggest that there is a statistical difference in the area under the shedding curves between both doses for 14 as well as 28 days after challenge (p = 0.0069 and 0.0209, resp.). This difference is increased when the prechallenge antibodies are taken into account (p = 0.0056 and 0.0185). We concluded that the bacterial dose influences shedding on calves experimentally challenged and that preexisting antibodies against E. coli O157:H7 γ-intimin C280 could partially reduce faecal excretion.

Implementing meta-analysis from genome-wide association studies for pork quality traits.

Pork quality plays an important role in the meat processing industry. Thus, different methodologies have been implemented to elucidate the genetic architecture of traits affecting meat quality. One of the most common and widely used approaches is to perform genome-wide association (GWA) studies. However, a limitation of many GWA in animal breeding is the limited power due to small sample sizes in animal populations. One alternative is to implement a meta-analysis of GWA (MA-GWA) combining results from independent association studies. The objective of this study was to identify significant genomic regions associated with meat quality traits by performing MA-GWA for 8 different traits in 3 independent pig populations. Results from MA-GWA were used to search for genes possibly associated with the set of evaluated traits. Data from 3 pig data sets (U.S. Meat Animal Research Center, commercial, and Michigan State University Pig Resource Population) were used. A MA was implemented by combining -scores derived for each SNP in every population and then weighting them using the inverse of estimated variance of SNP effects. A search for annotated genes retrieved genes previously reported as candidates for shear force (calpain-1 catalytic subunit [] and calpastatin []), as well as for ultimate pH, purge loss, and cook loss (protein kinase, AMP-activated, γ 3 noncatalytic subunit []). In addition, novel candidate genes were identified for intramuscular fat and cook loss (acyl-CoA synthetase family member 3 mitochondrial []) and for the objective measure of muscle redness, CIE a* (glycogen synthase 1, muscle [] and ferritin, light polypeptide []). Thus, implementation of MA-GWA allowed integration of results for economically relevant traits and identified novel genes to be tested as candidates for meat quality traits in pig populations.

Reduced animal model with differential genetic grouping for direct and maternal effects.

Mixed-model equations for the reduced animal model with maternal effects and different genetic grouping of unknown parents for additive direct and maternal effects are derived. The matrices that relate the expected value and the variance of the breeding values of non-parents to the parents, as well as the different contributions of parental and non-parental breeding values, to the resulting mixed-model equations are presented. Mis-specification of additive maternal variance and the additive covariance between direct and maternal effects, arising from missing information on the dams of known individuals with records, is discussed. To avoid an incorrect specification of the variance-covariance matrix of the records without having to invert a nondiagonal variance of the residual terms, the breeding values of the unknown dams of individuals with records are included in the equations. Breeding values of non-parents are back-solved after the solutions for genetic groups and breeding values of parents are computed as simply as in cases in which maternal effects are absent. A numerical example is included to illustrate the derivations.

Risk-adjusted expected return for selection decisions.

The results of genetic evaluation are predictions of breeding values for the selection candidates, and these involve uncertainty with regard to future returns from the use of those selected individuals. This uncertainty is due to differential variability in BLUP of breeding values and can be translated into risk: High fluctuations mean greater risk, which is not taken into account by just looking at expected return. In this research, the methodology of value at risk (VaR) and expected shortfall is introduced for animal breeding decisions as a means to adjust the expected return for the cost of uncertainty in prediction of breeding values. This methodology has recently received a great deal of attention from financial institutions. Given a specified probability alpha, VaR is the alpha-quantile of the distribution of economic returns. The conditional value at risk (CVaR), or expected shortfall, is the expectation of the economic returns, which are less or equal to the VaR. By subtracting the CVaR from the predicted aggregate genotype (muR), a risk-adjusted expected return (RAER) measure was obtained. The measures muR, VaR, and RAER were calculated for a data set with progeny of 161 Polled Hereford bulls belonging to a beef cattle company. The Pearson and Spearman correlations between muR and RAER were 0.89 (P < 0.001) and 0.90 (P < 0.001), respectively. Even though the latter correlation was high, some bulls ranked differently for muR compared with RAER. The Pearson correlation between muR and VaR was low (0.124) and nonsignificant (P > 0.05), whereas the correlation between VaR and RAER was -0.31 (P < 0.0001). The results indicate the need to take into account the adjustment for risk in expected return in order to alleviate the effects of possible losses when overrated animals are selected.