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Abstract The implementation of genetic groups in BLUP evaluations accounts for different expectations of breeding values in base animals. Notwithstanding, many feasible structures of genetic groups exist and there are no analytical tools described to compare them easily. In this sense, the recent development of a simple and stable procedure to calculate the Bayes factor between nested competing models allowed us to develop a new approach of that method focused on compared models with different structures of random genetic groups. The procedure is based on a reparameterization of the model in terms of intraclass correlation of genetic groups. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null intraclass correlation. It compares two nested models, a model with a given structure of genetic groups against a model without genetic groups. The calculation of the Bayes factor between different structures of genetic groups can be quickly and easily obtained from the Bayes factor between the nested models. We applied this approach to a weaning weight data set of the Bruna dels Pirineus beef cattle, comparing several structures of genetic groups, and the final results showed that the preferable structure was an only group for unknown dams and different groups for unknown sires for each year of calving.

Abstract The estimation of genetic correlations between a nonlinear trait such as longevity and linear traits is computationally difficult on large datasets. A two-step approach was proposed and was checked via simulation. First, univariate analyses were performed to get genetic variance estimates and to compute pseudo-records and their associated weights. These pseudo-records were virtual performances free of all environmental effects that can be used in a BLUP animal model, leading to the same breeding values as in the (possibly nonlinear) initial analyses. By combining these pseudo-records in a multiple trait model and fixing the genetic and residual variances to their values computed during the first step, we obtained correlation estimates by AI-REML and approximate MT-BLUP predicted breeding values that blend direct and indirect information on longevity. Mean genetic correlations and reliabilities obtained on simulated data confirmed the suitability of this approach in a wide range of situations. When nonzero residual correlations exist between traits, a sire model gave nearly unbiased estimates of genetic correlations, while the animal model estimates were biased upwards. Finally, when an incorrect genetic trend was simulated to lead to biased pseudo-records, a joint analysis including a time effect could adequately correct for this bias.

Abstract The genetic structure of eight Spanish autochthonous populations (breeds) of beef cattle were studied from pedigree records. The populations studied were: Alistana and Sayaguesa (minority breeds), Avileña – Negra Ibérica and Morucha ("dehesa" breeds, with a scarce incidence of artificial insemination), and mountain breeds, including Asturiana de los Valles, Asturiana de la Montaña and Pirenaica, with extensive use of AI. The Bruna dels Pirineus breed possesses characteristics which make its classification into one of the former groups difficult. There was a large variation between breeds both in the census and the number of herds. Generation intervals ranged from 3.7 to 5.5 years, tending to be longer as the population size was larger. The effective numbers of herds suggest that a small number of herds behaves as a selection nucleus for the rest of the breed. The complete generation equivalent has also been greatly variable, although in general scarce, with the exception of the Pirenaica breed, with a mean of 3.8. Inbreeding effective population sizes were actually small (21 to 127), especially in the mountain-type breeds. However, the average relatedness computed for these breeds suggests that a slight exchange of animals between herds will lead to a much more favourable evolution of inbreeding. The effective number of founders and ancestors were also variable among breeds, although in general the breeds behaved as if they were founded by a small number of animals (25 to 163).

Abstract Background Beef carcass conformation and fat cover scores are measured by subjective grading performed by trained technicians. The discrete nature of these scores is taken into account in genetic evaluations using a threshold model, which assumes an underlying continuous distribution called liability that can be modelled by different methods. Methods Five threshold models were compared in this study: three threshold linear models, one including slaughterhouse and sex effects, along with other systematic effects, with homogeneous thresholds and two extensions with heterogeneous thresholds that vary across slaughterhouses and across slaughterhouse and sex and a generalised linear model with reverse extreme value errors. For this last model, the underlying variable followed a Weibull distribution and was both a log-linear model and a grouped data model. The fifth model was an extension of grouped data models with score-dependent effects in order to allow for heterogeneous thresholds that vary across slaughterhouse and sex. Goodness-of-fit of these models was tested using the bootstrap methodology. Field data included 2,539 carcasses of the Bruna dels Pirineus beef cattle breed. Results Differences in carcass conformation and fat cover scores among slaughterhouses could not be totally captured by a systematic slaughterhouse effect, as fitted in the threshold linear model with homogeneous thresholds, and different thresholds per slaughterhouse were estimated using a slaughterhouse-specific threshold model. This model fixed most of the deficiencies when stratification by slaughterhouse was done, but it still failed to correctly fit frequencies stratified by sex, especially for fat cover, as 5 of the 8 current percentages were not included within the bootstrap interval. This indicates that scoring varied with sex and a specific sex per slaughterhouse threshold linear model should be used in order to guarantee the goodness-of-fit of the genetic evaluation model. This was also observed in grouped data models that avoided fitting deficiencies when slaughterhouse and sex effects were score-dependent. Conclusions Both threshold linear models and grouped data models can guarantee the goodness-of-fit of the genetic evaluation for carcass conformation and fat cover, but our results highlight the need for specific thresholds by sex and slaughterhouse in order to avoid fitting deficiencies.

Abstract Background A procedure to measure connectedness among herds was applied to a beef cattle population bred by natural service. It consists of two steps: (a) computing coefficients of determination (CDs) of comparisons among herds; and (b) building sets of connected herds. Methods The CDs of comparisons among herds were calculated using a sampling-based method that estimates empirical variances of true and predicted breeding values from a simulated n-sample. Once the CD matrix was estimated, a clustering method that can handle a large number of comparisons was applied to build compact clusters of connected herds of the Bruna dels Pirineus beef cattle. Since in this breed, natural service is predominant and there are almost no links with reference sires, to estimate CDs, an animal model was used taking into consideration all pedigree information and, especially, the connections with dams. A sensitivity analysis was performed to contrast single-trait sire and animal model evaluations with different heritabilities, multiple-trait animal model evaluations with different degrees of genetic correlations and models with maternal effects. Results Using a sire model, the percentage of connected herds was very low even for highly heritable traits whereas with an animal model, most of the herds of the breed were well connected and high CD values were obtained among them, especially for highly heritable traits (the mean of average CD per herd was 0.535 for a simulated heritability of 0.40). For the lowly heritable traits, the average CD increased from 0.310 in the single-trait evaluation to 0.319 and 0.354 in the multi-trait evaluation with moderate and high genetic correlations, respectively. In models with maternal effects, the average CD per herd for the direct effects was similar to that from single-trait evaluations. For the maternal effects, the average CD per herd increased if the maternal effects had a high genetic correlation with the direct effects, but the percentage of connected herds for maternal effects was very low, less than 12%. Conclusions The degree of connectedness in a bovine population bred by natural service mating, such as Bruna del Pirineus beef cattle, measured as the CD of comparisons among herds, is high. It is possible to define a pool of animals for which estimated breeding values can be compared after an across-herds genetic evaluation, especially for highly heritable traits.

In organisms with sexual reproduction, genetic diversity, and genome evolution are governed by meiotic recombination caused by crossing-over, which is known to vary within the genome. In this study, we propose a simple method to estimate the recombination rate that makes use of the persistency of linkage disequilibrium (LD) phase among closely related populations. The biological material comprised 171 triplets (sire/dam/offspring) from seven populations of autochthonous beef cattle in Spain (Asturiana de los Valles, Avileña-Negra Ibérica, Bruna dels Pirineus, Morucha, Pirenaica, Retinta, and Rubia Gallega), which were genotyped for 777,962 SNPs with the BovineHD BeadChip. After standard quality filtering, we reconstructed the haplotype phases in the parental individuals and calculated the LD by the correlation - r - between each pair of markers that had a genetic distance < 1 Mb. Subsequently, these correlations were used to calculate the persistency of LD phase between each pair of populations along the autosomal genome. Therefore, the distribution of the recombination rate along the genome can be inferred since the effect of the number of generations of divergence should be equivalent throughout the genome. In our study, the recombination rate was highest in the largest chromosomes and at the distal portion of the chromosomes. In addition, the persistency of LD phase was highly heterogeneous throughout the genome, with a ratio of 25.4 times between the estimates of the recombination rates from the genomic regions that had the highest (BTA18-7.1 Mb) and the lowest (BTA12-42.4 Mb) estimates. Finally, an overrepresentation enrichment analysis (ORA) showed differences in the enriched gene ontology (GO) terms between the genes located in the genomic regions with estimates of the recombination rate over (or below) the 95 th (or 5 th ) percentile throughout the autosomal genome., (Copyright © 2019 Mouresan, González-Rodríguez, Cañas-Álvarez, Munilla, Altarriba, Díaz, Baró, Molina, Lopez-Buesa, Piedrafita and Varona.)

Genome-wide association (GWA) studies play a key role in current genetics research, unravelling genomic regions linked to phenotypic traits of interest in multiple species. Nevertheless, the extent of linkage disequilibrium (LD) may provide confounding results when significant genetic markers span along several contiguous cM. In this study, we have adapted the composite interval mapping approach to the GWA framework (composite GWA), in order to evaluate the impact of including competing (possibly linked) genetic markers when testing for the additive allelic effect inherent to a given genetic marker. We tested model performance on simulated data sets under different scenarios (i.e., qualitative trait loci effects, LD between genetic markers and width of the genomic region involved in the analysis). Our results showed that the genomic region had a small impact on the number of competing single nucleotide polymorphisms (SNPs) as well as on the precision of the composite GWA analysis. A similar conclusion was derived from the preferable range of LD between the tested SNP and competing SNPs, although moderate-to-high LD seemed to attenuate the loss of statistical power. The composite GWA improved specificity and reduced the number of significant genetic markers. The composite GWA model contributes a novel point of view for GWA analyses where testing circumscribed to the genomic region flanking each SNP (delimited by the nearest competing SNPs) and conditioning on linked markers increases the precision to locate causal mutations, but possibly at the expense of power.

Background: Procedures for the detection of signatures of selection can be classified according to the source of information they use to reject the null hypothesis of absence of selection. Three main groups of tests can be identified that are based on: (1) the analysis of the site frequency spectrum, (2) the study of the extension of the linkage disequilibrium across the length of the haplotypes that surround the polymorphism, and (3) the differentiation among populations. The aim of this study was to compare the performance of a subset of these procedures by using a dataset on seven Spanish autochthonous beef cattle populations., Results: Analysis of the correlations between the logarithms of the statistics that were obtained by 11 tests for detecting signatures of selection at each single nucleotide polymorphism confirmed that they can be clustered into the three main groups mentioned above. A factor analysis summarized the results of the 11 tests into three canonical axes that were each associated with one of the three groups. Moreover, the signatures of selection identified with the first and second groups of tests were shared across populations, whereas those with the third group were more breed-specific. Nevertheless, an enrichment analysis identified the metabolic pathways that were associated with each group; they coincided with canonical axes and were related to immune response, muscle development, protein biosynthesis, skin and pigmentation, glucose metabolism, fat metabolism, embryogenesis and morphology, heart and uterine metabolism, regulation of the hypothalamic-pituitary-thyroid axis, hormonal, cellular cycle, cell signaling and extracellular receptors., Conclusions: We show that the results of the procedures used to identify signals of selection differed substantially between the three groups of tests. However, they can be classified using a factor analysis. Moreover, each canonical factor that coincided with a group of tests identified different signals of selection, which could be attributed to processes of selection that occurred at different evolutionary times. Nevertheless, the metabolic pathways that were associated with each group of tests were similar, which suggests that the selection events that occurred during the evolutionary history of the populations probably affected the same group of traits.

Background: Beef carcass conformation and fat cover scores are measured by subjective grading performed by trained technicians. The discrete nature of these scores is taken into account in genetic evaluations using a threshold model, which assumes an underlying continuous distribution called liability that can be modelled by different methods., Methods: Five threshold models were compared in this study: three threshold linear models, one including slaughterhouse and sex effects, along with other systematic effects, with homogeneous thresholds and two extensions with heterogeneous thresholds that vary across slaughterhouses and across slaughterhouse and sex and a generalised linear model with reverse extreme value errors. For this last model, the underlying variable followed a Weibull distribution and was both a log-linear model and a grouped data model. The fifth model was an extension of grouped data models with score-dependent effects in order to allow for heterogeneous thresholds that vary across slaughterhouse and sex. Goodness-of-fit of these models was tested using the bootstrap methodology. Field data included 2,539 carcasses of the Bruna dels Pirineus beef cattle breed., Results: Differences in carcass conformation and fat cover scores among slaughterhouses could not be totally captured by a systematic slaughterhouse effect, as fitted in the threshold linear model with homogeneous thresholds, and different thresholds per slaughterhouse were estimated using a slaughterhouse-specific threshold model. This model fixed most of the deficiencies when stratification by slaughterhouse was done, but it still failed to correctly fit frequencies stratified by sex, especially for fat cover, as 5 of the 8 current percentages were not included within the bootstrap interval. This indicates that scoring varied with sex and a specific sex per slaughterhouse threshold linear model should be used in order to guarantee the goodness-of-fit of the genetic evaluation model. This was also observed in grouped data models that avoided fitting deficiencies when slaughterhouse and sex effects were score-dependent., Conclusions: Both threshold linear models and grouped data models can guarantee the goodness-of-fit of the genetic evaluation for carcass conformation and fat cover, but our results highlight the need for specific thresholds by sex and slaughterhouse in order to avoid fitting deficiencies.

Background: A procedure to measure connectedness among herds was applied to a beef cattle population bred by natural service. It consists of two steps: (a) computing coefficients of determination (CDs) of comparisons among herds; and (b) building sets of connected herds., Methods: The CDs of comparisons among herds were calculated using a sampling-based method that estimates empirical variances of true and predicted breeding values from a simulated n-sample. Once the CD matrix was estimated, a clustering method that can handle a large number of comparisons was applied to build compact clusters of connected herds of the Bruna dels Pirineus beef cattle. Since in this breed, natural service is predominant and there are almost no links with reference sires, to estimate CDs, an animal model was used taking into consideration all pedigree information and, especially, the connections with dams. A sensitivity analysis was performed to contrast single-trait sire and animal model evaluations with different heritabilities, multiple-trait animal model evaluations with different degrees of genetic correlations and models with maternal effects., Results: Using a sire model, the percentage of connected herds was very low even for highly heritable traits whereas with an animal model, most of the herds of the breed were well connected and high CD values were obtained among them, especially for highly heritable traits (the mean of average CD per herd was 0.535 for a simulated heritability of 0.40). For the lowly heritable traits, the average CD increased from 0.310 in the single-trait evaluation to 0.319 and 0.354 in the multi-trait evaluation with moderate and high genetic correlations, respectively. In models with maternal effects, the average CD per herd for the direct effects was similar to that from single-trait evaluations. For the maternal effects, the average CD per herd increased if the maternal effects had a high genetic correlation with the direct effects, but the percentage of connected herds for maternal effects was very low, less than 12%., Conclusions: The degree of connectedness in a bovine population bred by natural service mating, such as Bruna del Pirineus beef cattle, measured as the CD of comparisons among herds, is high. It is possible to define a pool of animals for which estimated breeding values can be compared after an across-herds genetic evaluation, especially for highly heritable traits.

The implementation of genetic groups in BLUP evaluations accounts for different expectations of breeding values in base animals. Notwithstanding, many feasible structures of genetic groups exist and there are no analytical tools described to compare them easily. In this sense, the recent development of a simple and stable procedure to calculate the Bayes factor between nested competing models allowed us to develop a new approach of that method focused on compared models with different structures of random genetic groups. The procedure is based on a reparameterization of the model in terms of intraclass correlation of genetic groups. The Bayes factor can be easily calculated from the output of a Markov chain Monte Carlo sampling by averaging conditional densities at the null intraclass correlation. It compares two nested models, a model with a given structure of genetic groups against a model without genetic groups. The calculation of the Bayes factor between different structures of genetic groups can be quickly and easily obtained from the Bayes factor between the nested models. We applied this approach to a weaning weight data set of the Bruna dels Pirineus beef cattle, comparing several structures of genetic groups, and the final results showed that the preferable structure was an only group for unknown dams and different groups for unknown sires for each year of calving.

The estimation of genetic correlations between a nonlinear trait such as longevity and linear traits is computationally difficult on large datasets. A two-step approach was proposed and was checked via simulation. First, univariate analyses were performed to get genetic variance estimates and to compute pseudo-records and their associated weights. These pseudo-records were virtual performances free of all environmental effects that can be used in a BLUP animal model, leading to the same breeding values as in the (possibly nonlinear) initial analyses. By combining these pseudo-records in a multiple trait model and fixing the genetic and residual variances to their values computed during the first step, we obtained correlation estimates by AI-REML and approximate MT-BLUP predicted breeding values that blend direct and indirect information on longevity. Mean genetic correlations and reliabilities obtained on simulated data confirmed the suitability of this approach in a wide range of situations. When nonzero residual correlations exist between traits, a sire model gave nearly unbiased estimates of genetic correlations, while the animal model estimates were biased upwards. Finally, when an incorrect genetic trend was simulated to lead to biased pseudo-records, a joint analysis including a time effect could adequately correct for this bias.