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Imprinting is a phenomenon that alters the expression of genes according to the parental origin of their alleles. A quantitative form to evaluate the imprinting effect is known as parent-of-origin effect. Our aim with this work is to identify parent-of-origin effects that influence the number of oocytes and embryos in Gir dairy cattle. A dataset with 17,526 Ovum Pick Up observations from 1641 Gir donors was used to estimate parent-of-origin effects for the traits number of total oocytes (TO), number of viable oocytes (VO) and number of embryos (EM). To identify parent-of-origin effects, dam and sire gametic effects were included, individually or together, in an animal model for TO, VO and EM traits. For TO, inclusion of paternal origin effects in the model was significant (P < 0.05), and explained 6 % of the total phenotypic variance. For VO and EM no significant parent-of-origin effects were found for either parental line. In conclusion, paternal effects appear to influence the total oocyte production in the Gir cattle breed.

In the last decade, a number of methods have been suggested to deal with large amounts of genetic data in genomic predictions. Yet, steadily growing population sizes and the suboptimal use of computational resources are pushing the practical application of these approaches to their limits. As an extension to the C/CUDA library miraculix, we have developed tailored solutions for the computation of genotype matrix multiplications which is a critical bottleneck in the empirical evaluation of many statistical models. We demonstrate the benefits of our solutions at the example of single-step models which make repeated use of this kind of multiplication. Targeting modern Nvidia® GPUs as well as a broad range of CPU architectures, our implementation significantly reduces the time required for the estimation of breeding values in large population sizes. miraculix is released under the Apache 2.0 license and is freely available at https://github.com/alexfreudenberg/miraculix.

Background: Single-step genomic best linear unbiased prediction (ssGBLUP) models allow the combination of genomic, pedigree, and phenotypic data into a single model, which is computationally challenging for large genotyped populations. In practice, genotypes of animals without their own phenotype and progeny, so-called genotyped selection candidates, can become available after genomic breeding values have been estimated by ssGBLUP. In some breeding programmes, genomic estimated breeding values (GEBV) for these animals should be known shortly after obtaining genotype information but recomputing GEBV using the full ssGBLUP takes too much time. In this study, first we compare two equivalent formulations of ssGBLUP models, i.e. one that is based on the Woodbury matrix identity applied to the inverse of the genomic relationship matrix, and one that is based on marker equations. Second, we present computationally-fast approaches to indirectly compute GEBV for genotyped selection candidates, without the need to do the full ssGBLUP evaluation. Results: The indirect approaches use information from the latest ssGBLUP evaluation and rely on the decomposition of GEBV into its components. The two equivalent ssGBLUP models and indirect approaches were tested on a six-trait calving difficulty model using Irish dairy and beef cattle data that include 2.6 million genotyped animals of which about 500,000 were considered as genotyped selection candidates. When using the same computational approaches, the solving phase of the two equivalent ssGBLUP models showed similar requirements for memory and time per iteration. The computational differences between them were due to the preprocessing phase of the genomic information. Regarding the indirect approaches, compared to GEBV obtained from single-step evaluations including all genotypes, indirect GEBV had correlations higher than 0.99 for all traits while showing little dispersion and level bias. Conclusions: In conclusion, ssGBLUP predic

We have previously shown that single-step genomic best linear unbiased prediction (ssGBLUP) estimates breeding values of genomically preselected animals without preselection bias for widely recorded traits, that is traits recorded for the majority of animals in the breeding population. This study investigated the impact of genomic preselection (GPS) on accuracy and bias in ssGBLUP evaluation of genomically preselected animals for a scarcely recorded trait, that is a trait recorded for only a small proportion of the animals, which generally has a lower prediction accuracy than widely recorded traits, mainly due to having a much smaller number of phenotypes available. We used data from a commercial pig breeding program, considering feed intake as a scarcely recorded target trait, being available for ~30% of the animals with phenotypes for any trait, and average daily gain, backfat thickness and loin depth as widely recorded predictor traits, being available for >95% of the animals with phenotypes for any trait. The data contained the routine GPS implemented by commercial animal breeding programs, and we retrospectively implemented two scenarios with additional layers of GPS by discarding pedigree, genotypes and phenotypes of animals without progeny. The ssGBLUP evaluation following GPS used records only from the target trait, only from the predictor traits, or both. Accuracy for feed intake did not differ statistically across GPS scenarios, although it tended to decrease with more intense GPS. The accuracy had average values of 0.37, 0.44, and 0.45 across all GPS scenarios when, respectively, records from only the target trait, only the predictor traits, or both were used in the ssGBLUP evaluation. Considerable deflation of the genomic breeding values for feed intake was observed in the most stringent GPS scenario, due to the variance components being underestimated as a result of the limited amount of strongly preselected data. As long as (co)variance components were

In this paper, we consider a block Jacobi preconditioner and various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving a sparse system of linear equations derived from a statistical linear mixed model that analyses simultaneously phenotypic and pedigree information of genotyped and ungenotyped animals with Single Polymorphism Nucleotide genotypes of genotyped animals. In livestock production systems, evaluating the genetic merit of the animals through such a model is a key process to ensure an improvement of animals for some characteristics of interest at each generation. First, we propose to define the deflation vectors using a subdomain deflation approach that considers some biological properties of the genotypes. Using simulated data, this approach reduces the number of iterations by up to 87% in comparison to a Preconditioned Conjugate Gradient method with a Jacobi preconditioner. Furthermore, compared to a DPCG method with same number of subdomains but defined randomly, this approach reduces the number of iterations by up to 20% for the same computational costs of one DPCG iteration. The properties of the resulting systems show that this approach annihilates the largest eigenvalues of the preconditioned coefficient matrix. Second, we propose the use of solution vectors of 12 systems of equations that include between 0.25% and 3% less data, as deflation vectors. For reducing the computational costs, we also consider a Proper Orthogonal Decomposition-reduced set of these 12 vectors. The properties of the resulting systems show that this recycling information approach annihilates the smallest eigenvalues of the preconditioned coefficient matrix, and results in a reduction of up to 39% in comparison to the PCG method. Finally, based on our experiment, the combination of the subdomain deflation approach relying on biological properties and of the POD-based approach to recycle previous solution vectors, for defin

In this paper, we consider a block Jacobi preconditioner and various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving a sparse system of linear equations derived from a statistical linear mixed model that analyses simultaneously phenotypic and pedigree information of genotyped and ungenotyped animals with Single Polymorphism Nucleotide genotypes of genotyped animals. In livestock production systems, evaluating the genetic merit of the animals through such a model is a key process to ensure an improvement of animals for some characteristics of interest at each generation. First, we propose to define the deflation vectors using a subdomain deflation approach that considers some biological properties of the genotypes. Using simulated data, this approach reduces the number of iterations by up to 87% in comparison to a Preconditioned Conjugate Gradient method with a Jacobi preconditioner. Furthermore, compared to a DPCG method with same number of subdomains but defined randomly, this approach reduces the number of iterations by up to 20% for the same computational costs of one DPCG iteration. The properties of the resulting systems show that this approach annihilates the largest eigenvalues of the preconditioned coefficient matrix. Second, we propose the use of solution vectors of 12 systems of equations that include between 0.25% and 3% less data, as deflation vectors. For reducing the computational costs, we also consider a Proper Orthogonal Decomposition-reduced set of these 12 vectors. The properties of the resulting systems show that this recycling information approach annihilates the smallest eigenvalues of the preconditioned coefficient matrix, and results in a reduction of up to 39% in comparison to the PCG method. Finally, based on our experiment, the combination of the subdomain deflation approach relying on biological properties and of the POD-based approach to recycle previous solution vectors, for de, Numerical Analysis

This archive contains all datasets and scripts to reproduce the results of our study. In this paper, we consider various deflation techniques applied in the Deflated Preconditioned Conjugate Gradient (DPCG) method for solving a sparse system of linear equations derived from a statistical linear mixed model that analyses simultaneously phenotypic and pedigree information of genotyped and ungenotyped animals with Single Polymorphism Nucleotide genotypes of genotyped animals.

Simulated SNP genotype data for 3-way crossbred animals and their purebred ancestors, mimicking chromosomes 1 and 18 of the pig genome. Parental lines are closely related, distantly related or unrelated to each other. For each dataset, 10 replicates are available.

In animal breeding, parents of the next generation are usually selected in multiple stages, and the initial stages of this selection are called preselection. Preselection reduces the information available for subsequent evaluation of preselected animals and this sometimes leads to bias. The objective of this study was to establish the minimum information required to subsequently evaluate genomically preselected animals without bias arising from preselection, with single-step genomic best linear unbiased prediction (ssGBLUP). We simulated a nucleus of a breeding program in which a recent population of 15 generations was produced. In each generation, parents of the next generation were selected in a single-stage selection based on pedigree BLUP. However, in generation 15, 10% of male and 15% of female offspring were preselected on their genomic estimated breeding values (GEBV). These GEBV were estimated using ssGBLUP, including the pedigree of all animals in generations 0–15, genotypes of all animals in generations 13–15 and phenotypes of all animals in generations 11–14. In subsequent ssGBLUP evaluation of these preselected animals, genotypes and phenotypes from various groups of animals were excluded one after another. We found that GEBV of the preselected animals were only estimated without preselection bias when genotypes and phenotypes of all animals in generations 13 and 14 and of the preselected animals were included in the subsequent evaluation. We also found that genotypes of the animals discarded at preselection only helped in reducing preselection bias in GEBV of their preselected sibs when genotypes of their parents were absent or excluded from the subsequent evaluation. We concluded that to prevent preselection bias in subsequent ssGBLUP evaluation of genomically preselected animals, information representative of the reference data used in the evaluation at preselection and genotypes and phenotypes of the preselected animals are needed in the subsequent e