Causal inference for the covariance between breeding values under identity disequilibrium.

BACKGROUND: The covariance matrix of breeding values is at the heart of prediction methods. Prediction of breeding values can be formulated using either an "observed" or a theoretical covariance matrix, and a major argument for choosing one or the other is the reduction of the computational burden for inverting such a matrix. In this regard, covariance matrices that are derived from Markov causal models possess properties that deliver sparse inverses. RESULTS: By using causal Markov models, we express the breeding value of an individual as a linear regression on ancestral breeding values, plus a residual term, which we call residual breeding value (RBV). The latter is a noise term that accounts for the uncertainty in prediction due to lack of fit of the linear regression. A notable property of these models is the parental Markov condition, through which the multivariate distribution of breeding values is uniquely determined by the distribution of the mutually independent RBV. Animal breeders have long been relying on a causal Markov model, while using the additive relationship matrix as the covariance matrix structure of breeding values, which is calculated assuming gametic equilibrium. However, additional covariances among breeding values arise due to identity disequilibrium, which is defined as the difference between the covariance matrix under the multi-loci probability of identity-by-descent ([Formula: see text]) and its expectation under gametic phase equilibrium, i.e., A. The disequilibrium term [Formula: see text]-A is considered in the model for predicting breeding values called the "ancestral regression" (AR), a causal Markov model. Here, we introduce the "ancestral regression to parents" (PAR) causal Markov model, which reduces the computational burden of the AR approach. By taking advantage of the conditional independence property of the PAR Markov model, we derive covariances between the breeding values of grandparents and grand-offspring and between parents and offspring. In addition, we obtain analytical expressions for the covariance between collateral relatives under the PAR model, as well as for the inbreeding coefficient. CONCLUSIONS: We introduced the causal PAR Markov model that captures identity disequilibrium in the covariances among breeding values and produces a sparse inverse covariance matrix to build and solve a set of mixed model equations.

Genome-wide scan for signatures of selection in the Brangus cattle genome.

Brangus is a composite cattle breed developed with the objective of combining the advantages of Angus and Zebuine breeds (Brahman, mainly) in tropical climates. The aim of this work was to estimate breed composition both genome-wide and locally, at the chromosome level, and to uncover genomic regions evidencing positive selection in the Argentinean Brangus population/nucleus. To do so, we analysed marker data from 478 animals, including Brangus, Angus and Brahman. Average breed composition was 35.0% ± 9.6% of Brahman, lower than expected according to the theoretical fractions deduced by the usual cross-breeding practice in this breed. Local ancestry analysis evidenced that breed composition varies between chromosomes, ranging from 19.6% for BTA26 to 56.1% for BTA5. Using approaches based on allelic frequencies and linkage disequilibrium, genomic regions with putative selection signatures were identified in several chromosomes (BTA1, BTA5, BTA6 and BTA14). These regions harbour genes involved in horn development, growth, lipid metabolism, reproduction and immune response. We argue that the overlapping of a chromosome segment originated in one of the parental breeds and over-represented in the sample with the location of a signature of selection constitutes evidence of a selection process that has occurred in the breed since its take off in the 1950s. In this regard, our results could contribute to the understanding of the genetic mechanisms involved in cross-bred cattle adaptation and productivity in tropical environments.

Comparing Genomic Prediction Models by Means of Cross Validation.

In the two decades of continuous development of genomic selection, a great variety of models have been proposed to make predictions from the information available in dense marker panels. Besides deciding which particular model to use, practitioners also need to make many minor choices for those parameters in the model which are not typically estimated by the data (so called "hyper-parameters"). When the focus is placed on predictions, most of these decisions are made in a direction sought to optimize predictive accuracy. Here we discuss and illustrate using publicly available crop datasets the use of cross validation to make many such decisions. In particular, we emphasize the importance of paired comparisons to achieve high power in the comparison between candidate models, as well as the need to define notions of relevance in the difference between their performances. Regarding the latter, we borrow the idea of equivalence margins from clinical research and introduce new statistical tests. We conclude that most hyper-parameters can be learnt from the data by either minimizing REML or by using weakly-informative priors, with good predictive results. In particular, the default options in a popular software are generally competitive with the optimal values. With regard to the performance assessments themselves, we conclude that the paired k-fold cross validation is a generally applicable and statistically powerful methodology to assess differences in model accuracies. Coupled with the definition of equivalence margins based on expected genetic gain, it becomes a useful tool for breeders.

Single-step genomic prediction of Eucalyptus dunnii using different identity-by-descent and identity-by-state relationship matrices.

Genomic selection based on the single-step genomic best linear unbiased prediction (ssGBLUP) approach is becoming an important tool in forest tree breeding. The quality of the variance components and the predictive ability of the estimated breeding values (GEBV) depends on how well marker-based genomic relationships describe the actual genetic relationships at unobserved causal loci. We investigated the performance of GEBV obtained when fitting models with genomic covariance matrices based on two identity-by-descent (IBD) and two identity-by-state (IBS) relationship measures. Multiple-trait multiple-site ssGBLUP models were fitted to diameter and stem straightness in five open-pollinated progeny trials of Eucalyptus dunnii, genotyped using the EUChip60K. We also fitted the conventional ABLUP model with a pedigree-based covariance matrix. Estimated relationships from the IBD estimators displayed consistently lower standard deviations than those from the IBS approaches. Although ssGBLUP based in IBS estimators resulted in higher trait-site heritabilities, the gain in accuracy of the relationships using IBD estimators has resulted in higher predictive ability and lower bias of GEBV, especially for low-heritability trait-site. ssGBLUP based on IBS and IBD approaches performed considerably better than the traditional ABLUP. In summary, our results advocate the use of the ssGBLUP approach jointly with the IBD relationship matrix in open-pollinated forest tree evaluation.

Phantom Epistasis in Genomic Selection: On the Predictive Ability of Epistatic Models.

Genomic selection uses whole-genome marker models to predict phenotypes or genetic values for complex traits. Some of these models fit interaction terms between markers, and are therefore called epistatic. The biological interpretation of the corresponding fitted effects is not straightforward and there is the threat of overinterpreting their functional meaning. Here we show that the predictive ability of epistatic models relative to additive models can change with the density of the marker panel. In more detail, we show that for publicly available Arabidopsis and rice datasets, an initial superiority of epistatic models over additive models, which can be observed at a lower marker density, vanishes when the number of markers increases. We relate these observations to earlier results reported in the context of association studies which showed that detecting statistical epistatic effects may not only be related to interactions in the underlying genetic architecture, but also to incomplete linkage disequilibrium at low marker density ("Phantom Epistasis"). Finally, we illustrate in a simulation study that due to phantom epistasis, epistatic models may also predict the genetic value of an underlying purely additive genetic architecture better than additive models, when the marker density is low. Our observations can encourage the use of genomic epistatic models with low density panels, and discourage their biological over-interpretation.

DMSO supplementation during in vitro maturation of bovine oocytes improves blastocyst rate and quality.

The molecule Dimethyl sulfoxide is widely used as drug solvent. However, its antioxidant property was poorly explored. In this study, we evaluated the effect of DMSO supplementation during oocyte in vitro maturation (IVM) on embryo development and quality. Bovine oocytes were matured with different DMSO concentrations (0, 0.1, 0.25, 0.5, 0.75, 1 and 10% v:v) followed by in vitro fertilization. Subsequently, quality indicators such as gene expression of SOX2, OCT4, CDX2, SOD1, oocyte and embryo redox status and DNA damage were evaluated. Polar body extrusion and blastocyst rates increased with 0.5% v:v DMSO. Moreover, first polar body extrusion and blastocyst rates did not increase with 1%, and 10% of DMSO reduced polar body extrusion and did not produce blastocyst. Optimal concentration of DMSO for the use on the maturation was estimated at around 0.45% v:v. Supplementation with 0.5% v:v DMSO has not affected mRNA abundance of genes key in blastocyst, however 0.75% increased gene expression of OCT4 and SOX2. Oocytes matured with 0.5% v:v DMSO and blastocyst from DMSO group showed reduced lipid peroxidation respect control. Total Glutathione concentrations increased in blastocyst stage in DMSO group. DMSO increased the total cell number of blastocysts but not TUNEL positive cells. In conclusion, our results suggest that low DMSO concentrations used during bovine oocytes in vitro maturation increases the maturation, as well as the blastocyst rate and its quality, without demonstrating deleterious effect on embryo cells.

Mapping Recombination Rate on the Autosomal Chromosomes Based on the Persistency of Linkage Disequilibrium Phase Among Autochthonous Beef Cattle Populations in Spain.

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 95th (or 5th) percentile throughout the autosomal genome.

The effect of the H-1 scaling factors τ and ω on the structure of H in the single-step procedure.

BACKGROUND: The single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text]. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text], which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text]. Since the definition of this blending is based on the equation describing [Formula: see text], its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text]. RESULTS: Here, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. CONCLUSION: Our results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text].

On the performance of tests for the detection of signatures of selection: a case study with the Spanish autochthonous beef cattle populations.

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.

Longitudinal data analysis of polymorphisms in the κ-casein and ß-lactoglobulin genes shows differential effects along the trajectory of the lactation curve in tropical dairy goats.

The κ-casein (CSN-3) and ß-lactoglobulin (BLG) genes are extensively polymorphic in ruminants. Several association studies have estimated the effects of polymorphisms in these genes on milk yield, milk composition, and cheese-manufacturing properties. Usually, these results are based on production integrated over the lactation curve or on cross-sectional studies at specific days in milk (DIM). However, as differential expression of milk protein genes occurs over lactation, the effect of the polymorphisms may change over time. In this study, we fitted a mixed-effects regression model to test-day records of milk yield and milk quality traits (fat, protein, and total solids yields) from Colombian tropical dairy goats. We used the well-characterized A/B polymorphisms in the CSN-3 and BLG genes. We argued that this approach provided more efficient estimators than cross-sectional designs, given the same number and pattern of observations, and allowed exclusion of between-subject variation from model error. The BLG genotype AA showed a greater performance than the BB genotype for all traits along the whole lactation curve, whereas the heterozygote showed an intermediate performance. We observed no such constant pattern for the CSN-3 gene between the AA homozygote and the heterozygote (the BB genotype was absent from the sample). The differences among the genotypic effects of the BLG and the CSN-3 polymorphisms were statistically significant during peak and mid lactation (around 40-160 DIM) for the BLG gene and only for mid lactation (80-145 DIM) for the CSN-3 gene. We also estimated the additive and dominant effects of the BLG locus. The locus showed a statistically significant additive behavior along the whole lactation trajectory for all quality traits, whereas for milk yield the effect was not significant at later stages. In turn, we detected a statistically significant dominance effect only for fat yield in the early and peak stages of lactation (at about 1-45 DIM). The longitudinal analysis of test-day records allowed us to estimate the differential effects of polymorphisms along the lactation curve, pointing toward stages that could be affected by the gene.

Consequences of paternally inherited effects on the genetic evaluation of maternal effects.

BACKGROUND: Mixed models are commonly used for the estimation of variance components and genetic evaluation of livestock populations. Some evaluation models include two types of additive genetic effects, direct and maternal. Estimates of variance components obtained with models that account for maternal effects have been the subject of a long-standing controversy about strong negative estimates of the covariance between direct and maternal effects. Genomic imprinting is known to be in some cases statistically confounded with maternal effects. In this study, we analysed the consequences of ignoring paternally inherited effects on the partitioning of genetic variance. RESULTS: We showed that the existence of paternal parent-of-origin effects can bias the estimation of variance components when maternal effects are included in the evaluation model. Specifically, we demonstrated that adding a constraint on the genetic parameters of a maternal model resulted in correlations between relatives that were the same as those obtained with a model that fits only paternally inherited effects for most pairs of individuals, as in livestock pedigrees. The main consequence is an upward bias in the estimates of the direct and maternal additive genetic variances and a downward bias in the direct-maternal genetic covariance. This was confirmed by a simulation study that investigated five scenarios, with the trait affected by (1) only additive genetic effects, (2) only paternally inherited effects, (3) additive genetic and paternally inherited effects, (4) direct and maternal additive genetic effects and (5) direct and maternal additive genetic plus paternally inherited effects. For each scenario, the existence of a paternally inherited effect not accounted for by the estimation model resulted in a partitioning of the genetic variance according to the predicted pattern. In addition, a model comparison test confirmed that direct and maternal additive models and paternally inherited models provided an equivalent fit. CONCLUSIONS: Ignoring paternally inherited effects in the maternal models for genetic evaluation can lead to a specific pattern of bias in variance component estimates, which may account for the unexpectedly strong negative direct-maternal genetic correlations that are typically reported in the literature.

A Bayesian model for the analysis of transgenerational epigenetic variation.

Epigenetics has become one of the major areas of biological research. However, the degree of phenotypic variability that is explained by epigenetic processes still remains unclear. From a quantitative genetics perspective, the estimation of variance components is achieved by means of the information provided by the resemblance between relatives. In a previous study, this resemblance was described as a function of the epigenetic variance component and a reset coefficient that indicates the rate of dissipation of epigenetic marks across generations. Given these assumptions, we propose a Bayesian mixed model methodology that allows the estimation of epigenetic variance from a genealogical and phenotypic database. The methodology is based on the development of a T: matrix of epigenetic relationships that depends on the reset coefficient. In addition, we present a simple procedure for the calculation of the inverse of this matrix ( T-1: ) and a Gibbs sampler algorithm that obtains posterior estimates of all the unknowns in the model. The new procedure was used with two simulated data sets and with a beef cattle database. In the simulated populations, the results of the analysis provided marginal posterior distributions that included the population parameters in the regions of highest posterior density. In the case of the beef cattle dataset, the posterior estimate of transgenerational epigenetic variability was very low and a model comparison test indicated that a model that did not included it was the most plausible.