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Genetic groups, also called unknown or phantom parents groups, are often used in dairy cattle genetic evaluations to account for selection that cannot be accounted for by known genetic relationships. With the advent of genomic evaluations, the theory of genetic groups was extended to the so-called single-step genomic BLUP (ssGBLUP). In short, genetic groups can be fitted in ssGBLUP through regression effects, or by including them in the pedigree and computing the adequate combined pedigree and genomic relationship matrix. In this study, we applied the so-called Quaas and Pollak transformation to a system of equations for single-step SNP BLUP (ssSNPBLUP), such that genetic groups can thereafter be included in the pedigree. The example in this study showed that including the genetic groups in the pedigree for ssSNPBLUP allowed reduced memory burden and computational costs in comparison to genetic groups fitted as covariates.

Aim of study: To assess selection methods via introgression to improve litter size in native and synthetic sheep breeds.Area of study: Sanandaj, Kurdistan, Iran.Material and methods: Selection approaches were performed using classical, genomic, gene-assisted classical (GasClassical) and gene-assisted genomic (GasGenomic) selection. Litter size trait with heritability of 0.1 including two chromosomes was simulated. On chromosome 1, a single QTL as the major gene was created to explain 40% of the total additive genetic variance. After simulation of a historical population, the animals from the last historical population were split into two populations. For the next 7 generations, animals were selected for favorable or unfavorable alleles to create distinct breeds of A or B, respectively. Then from the last generation, both males and females from breed B were selected to create a native population. On the other hand, males from breed A and females from breed B were mated to simulate a synthetic population. Finally, intra-population selections were carried out based on high breeding values during the last five generations.Main results: The genetic gain in the synthetic breed was higher than that of the native breed under all selection methods. The frequencies of favorable alleles after five generations in the classical, genomic, GasClassical and GasGenoimc selection approaches in the synthetic breed were 0.623, 0.730, 0.850 and 0.848, respectively.Research highlights: Combining gene-assisted selection with classical or genomic selection has the potential to improve genetic gain and increase the frequencies of favorable allele for litter size in sheep.

Aim of study: To assess selection methods via introgression to improve litter size in native and synthetic sheep breeds.Area of study: Sanandaj, Kurdistan, Iran.Material and methods: Selection approaches were performed using classical, genomic, gene-assisted classical (GasClassical) and gene-assisted genomic (GasGenomic) selection. Litter size trait with heritability of 0.1 including two chromosomes was simulated. On chromosome 1, a single QTL as the major gene was created to explain 40% of the total additive genetic variance. After simulation of a historical population, the animals from the last historical population were split into two populations. For the next 7 generations, animals were selected for favorable or unfavorable alleles to create distinct breeds of A or B, respectively. Then from the last generation, both males and females from breed B were selected to create a native population. On the other hand, males from breed A and females from breed B were mated to simulate a synthetic population. Finally, intra-population selections were carried out based on high breeding values during the last five generations.Main results: The genetic gain in the synthetic breed was higher than that of the native breed under all selection methods. The frequencies of favorable alleles after five generations in the classical, genomic, GasClassical and GasGenoimc selection approaches in the synthetic breed were 0.623, 0.730, 0.850 and 0.848, respectively.Research highlights: Combining gene-assisted selection with classical or genomic selection has the potential to improve genetic gain and increase the frequencies of favorable allele for litter size in sheep.

In Chapter one a method was developed to separate the genomic relationship matrix into two independent covariance matrices. Here, the base group component describes the covariance that results from systematic differences in allele frequencies between groups at the pedigree base. The remaining segregation component describes the genomic relationship that is corrected for the differences between base populations. To investigate the proposed decomposition three different models were tested on six traits, where the covariance between animals was described either only by the segregation component or by a combination of the two components. An additional variant examining the effect of a fixed modeling of the group effects was included. In total, 7965 genotyped Fleckvieh and 4257 genotyped Brown Swiss and 143 genotyped Original Braunvieh bulls were available for this study. The proposed decomposition of the genomic relationship matrix helped to examine the relative importance of the effects of base groups and segregation component in a given population. It was possible to estimate significant differences between the means of base groups in most cases for both breeds and for the traits analyzed. Analysis of the matrix of base group contributions to the populations investigated revealed several general breed-specific aspects. Comparing the three models, it was concluded that the segregation component is not sufficient to describe the covariance completely. However, it also was found that the model applied has no strong impact on predictive power if the animals used for validation show no differences in their genetic composition with respect to the base groups and if the majority of them have complete pedigrees of sufficient depth. The subject of the chapter two was investigation to systematically increase the reliability of genomic breeding values by integrating cows into the reference population of genomic breeding value estimation. For this purpose a dataset was generated, In Kapitel 1 wurde eine Methode entwickelt, die die Verwandtschaftsmatrix in zwei unabhängige Kovarianzmatrizen trennt. Dabei beschreibt die eine Matrix die Basisgruppenkomponente, eine Kovarianzkomponente die auf Allelfrequenzunterschiede zwischen Gruppen der Basispopulation zurückzuführen ist. Die Segregationskomponente beschreibt die genomische Verwandtschaft, welche um diese Unterschiede zwischen verschiedenen Basispopulationen korrigiert wurde. Die Zerlegung wurde anhand drei verschiedener Modelle für sechs Merkmale untersucht. Dabei wurde die Kovarianz zwischen Tieren entweder nur durch die Segregationskomponente oder über eine Kombination beider Komponenten beschrieben. Eine zusätzliche Variante untersuchte den Effekt einer fixen Modellierung der Gruppeneffekte. Zur Verfügung standen für diese Studie die Genotypen von 7965 Fleckviehbullen sowie von 4257 Braunvieh- und 143 Original Braunviehbullen. Mit dieser Methode war es möglich, den Umfang der Basisgruppeneffekte und der Segregationskomponente in den beiden untersuchten Populationen sichtbar zu machen. Es konnten signifikante Unterschiede zwischen den mittleren Basisgruppeneffekten in den meisten Fällen für beide Rassen und für die sechs Merkmale gefunden werden. Die Analyse der Genanteile der diversen Basisgruppen an den untersuchten Populationen machte zudem einige rassetypische Aspekte sichtbar. Es wurde festgestellt, dass die Segregationskomponente nicht ausreicht die Kovarianz vollständig zu beschreiben. Allerdings wurde auch festgestellt, dass das verwendete Modell keinen starken Einfluss auf die Vorhersagekraft hat, wenn die Validierungstiere in ihrer genetischen Zusammensetzung weitgehend homogen sind und die Mehrheit von ihnen ein vollständiges und tiefes Pedigree aufweist. Kapitel 2 umfasst Berechnungen zur systematischen Steigerung der Sicherheiten genomischer Zuchtwerte durch die Aufnahme von Kühen in die Lernstichprobe der genomischen Zuchtwertschätzung. Hierfür wurde eine Simulationsstudie du

Genomic evaluations have been proposed as a mean to improve the reliabilities of the estimation of breeding values. This hypothesis has been tested using 50,649 lactation records from 19,067 Florida goats, daughters of 4397 dams and 500 sires. A sample of 538 dams and 87 sires from the formerly described population were genotyped with the Illumina 55 K Goat Bead-Chip (53,347 SNP). Genetic parameters were estimated using the animal model and REML methodology comparing two approaches: (i) a classical approach with the BLUP methodology; and (ii) a single step (ss) approach with the single step genomic BLUP (ssGBLUP) methodology. The BLUPF90 software was used to obtain the genomic relationship matrix (G) and to estimate genetic parameters and breeding values. The results showed a correlation between A (pedigree relationship matrix) and G matrix of 0.826. When the full studied population was considered, no significant differences were observed between the estimations of the genetic parameters obtained with A and combined A and G matrices. The correlation between the EBV and GEBV was 0.989. An increment of 1.06% in the average reliability of the estimations was observed in the ssGBLUP vs. the traditional BLUP evaluation. When only the EBVs of the animals genotyped were compared, the correlation between the estimates obtained with both approaches decreased to 0.952, but with an increment of 5.86% of the average reliability of the GEBVs.

In Chapter one a method was developed to separate the genomic relationship matrix into two independent covariance matrices. Here, the base group component describes the covariance that results from systematic differences in allele frequencies between groups at the pedigree base. The remaining segregation component describes the genomic relationship that is corrected for the differences between base populations. To investigate the proposed decomposition three different models were tested on six traits, where the covariance between animals was described either only by the segregation component or by a combination of the two components. An additional variant examining the effect of a fixed modeling of the group effects was included. In total, 7965 genotyped Fleckvieh and 4257 genotyped Brown Swiss and 143 genotyped Original Braunvieh bulls were available for this study. The proposed decomposition of the genomic relationship matrix helped to examine the relative importance of the effects of base groups and segregation component in a given population. It was possible to estimate significant differences between the means of base groups in most cases for both breeds and for the traits analyzed. Analysis of the matrix of base group contributions to the populations investigated revealed several general breed-specific aspects. Comparing the three models, it was concluded that the segregation component is not sufficient to describe the covariance completely. However, it also was found that the model applied has no strong impact on predictive power if the animals used for validation show no differences in their genetic composition with respect to the base groups and if the majority of them have complete pedigrees of sufficient depth. The subject of the chapter two was investigation to systematically increase the reliability of genomic breeding values by integrating cows into the reference population of genomic breeding value estimation. For this purpose a dataset was generated, In Kapitel 1 wurde eine Methode entwickelt, die die Verwandtschaftsmatrix in zwei unabhängige Kovarianzmatrizen trennt. Dabei beschreibt die eine Matrix die Basisgruppenkomponente, eine Kovarianzkomponente die auf Allelfrequenzunterschiede zwischen Gruppen der Basispopulation zurückzuführen ist. Die Segregationskomponente beschreibt die genomische Verwandtschaft, welche um diese Unterschiede zwischen verschiedenen Basispopulationen korrigiert wurde. Die Zerlegung wurde anhand drei verschiedener Modelle für sechs Merkmale untersucht. Dabei wurde die Kovarianz zwischen Tieren entweder nur durch die Segregationskomponente oder über eine Kombination beider Komponenten beschrieben. Eine zusätzliche Variante untersuchte den Effekt einer fixen Modellierung der Gruppeneffekte. Zur Verfügung standen für diese Studie die Genotypen von 7965 Fleckviehbullen sowie von 4257 Braunvieh- und 143 Original Braunviehbullen. Mit dieser Methode war es möglich, den Umfang der Basisgruppeneffekte und der Segregationskomponente in den beiden untersuchten Populationen sichtbar zu machen. Es konnten signifikante Unterschiede zwischen den mittleren Basisgruppeneffekten in den meisten Fällen für beide Rassen und für die sechs Merkmale gefunden werden. Die Analyse der Genanteile der diversen Basisgruppen an den untersuchten Populationen machte zudem einige rassetypische Aspekte sichtbar. Es wurde festgestellt, dass die Segregationskomponente nicht ausreicht die Kovarianz vollständig zu beschreiben. Allerdings wurde auch festgestellt, dass das verwendete Modell keinen starken Einfluss auf die Vorhersagekraft hat, wenn die Validierungstiere in ihrer genetischen Zusammensetzung weitgehend homogen sind und die Mehrheit von ihnen ein vollständiges und tiefes Pedigree aufweist. Kapitel 2 umfasst Berechnungen zur systematischen Steigerung der Sicherheiten genomischer Zuchtwerte durch die Aufnahme von Kühen in die Lernstichprobe der genomischen Zuchtwertschätzung. Hierfür wurde eine Simulationsstudie du

The algorithm for proven and young animals (APY) efficiently computes an approximated inverse of the genomic relationship matrix, by dividing genotyped animals in the so-called core and noncore animals. The APY leads to computationally feasible single-step genomic Best Linear Unbiased Prediction (ssGBLUP) with a large number of genotyped animals and was successfully applied to real single-breed or line datasets. This study aimed to assess the quality of genomic estimated breeding values (GEBV) when using the APY (GEBVAPY), in comparison to GEBV when using the directly inverted genomic relationship matrix (GEBVDIRECT), for situations based on crossbreeding schemes, including F1 and F2 crosses, such as the ones for pigs and chickens. Based on simulations of a 3-way crossbreeding program, we compared different approximated inverses of a genomic relationship matrix, by varying the size and the composition of the core group. We showed that GEBVAPY were accurate approximations of GEBVDIRECT for multivariate ssGBLUP involving different breeds and their crosses. GEBVAPY as accurate as GEBVDIRECT were obtained when the core groups included animals from different breed compositions and when the core groups had a size between the numbers of the largest eigenvalues explaining 98% and 99% of the variation in the raw genomic relationship matrix.

In Chapter one a method was developed to separate the genomic relationship matrix into two independent covariance matrices. Here, the base group component describes the covariance that results from systematic differences in allele frequencies between groups at the pedigree base. The remaining segregation component describes the genomic relationship that is corrected for the differences between base populations. To investigate the proposed decomposition three different models were tested on six traits, where the covariance between animals was described either only by the segregation component or by a combination of the two components. An additional variant examining the effect of a fixed modeling of the group effects was included. In total, 7965 genotyped Fleckvieh and 4257 genotyped Brown Swiss and 143 genotyped Original Braunvieh bulls were available for this study. The proposed decomposition of the genomic relationship matrix helped to examine the relative importance of the effects of base groups and segregation component in a given population. It was possible to estimate significant differences between the means of base groups in most cases for both breeds and for the traits analyzed. Analysis of the matrix of base group contributions to the populations investigated revealed several general breed-specific aspects. Comparing the three models, it was concluded that the segregation component is not sufficient to describe the covariance completely. However, it also was found that the model applied has no strong impact on predictive power if the animals used for validation show no differences in their genetic composition with respect to the base groups and if the majority of them have complete pedigrees of sufficient depth. The subject of the chapter two was investigation to systematically increase the reliability of genomic breeding values by integrating cows into the reference population of genomic breeding value estimation. For this purpose a dataset was generated, In Kapitel 1 wurde eine Methode entwickelt, die die Verwandtschaftsmatrix in zwei unabhängige Kovarianzmatrizen trennt. Dabei beschreibt die eine Matrix die Basisgruppenkomponente, eine Kovarianzkomponente die auf Allelfrequenzunterschiede zwischen Gruppen der Basispopulation zurückzuführen ist. Die Segregationskomponente beschreibt die genomische Verwandtschaft, welche um diese Unterschiede zwischen verschiedenen Basispopulationen korrigiert wurde. Die Zerlegung wurde anhand drei verschiedener Modelle für sechs Merkmale untersucht. Dabei wurde die Kovarianz zwischen Tieren entweder nur durch die Segregationskomponente oder über eine Kombination beider Komponenten beschrieben. Eine zusätzliche Variante untersuchte den Effekt einer fixen Modellierung der Gruppeneffekte. Zur Verfügung standen für diese Studie die Genotypen von 7965 Fleckviehbullen sowie von 4257 Braunvieh- und 143 Original Braunviehbullen. Mit dieser Methode war es möglich, den Umfang der Basisgruppeneffekte und der Segregationskomponente in den beiden untersuchten Populationen sichtbar zu machen. Es konnten signifikante Unterschiede zwischen den mittleren Basisgruppeneffekten in den meisten Fällen für beide Rassen und für die sechs Merkmale gefunden werden. Die Analyse der Genanteile der diversen Basisgruppen an den untersuchten Populationen machte zudem einige rassetypische Aspekte sichtbar. Es wurde festgestellt, dass die Segregationskomponente nicht ausreicht die Kovarianz vollständig zu beschreiben. Allerdings wurde auch festgestellt, dass das verwendete Modell keinen starken Einfluss auf die Vorhersagekraft hat, wenn die Validierungstiere in ihrer genetischen Zusammensetzung weitgehend homogen sind und die Mehrheit von ihnen ein vollständiges und tiefes Pedigree aufweist. Kapitel 2 umfasst Berechnungen zur systematischen Steigerung der Sicherheiten genomischer Zuchtwerte durch die Aufnahme von Kühen in die Lernstichprobe der genomischen Zuchtwertschätzung. Hierfür wurde eine Simulationsstudie du

[Background]Japanese Black cattle are a beef breed whose meat is well known to excel in meat quality, especially in marbling, and whose effective population size is relatively low in Japan. Unlike dairy cattle, the accuracy of genomic evaluation (GE) for carcass traits in beef cattle, including this breed, has been poorly studied. For carcass weight and marbling score in the breed, as well as the extent of whole genome linkage disequilibrium (LD), the effects of equally-spaced single nucleotide polymorphisms (SNPs) density on genomic relationship matrix (G matrix), genetic variance explained and GE were investigated using the genotype data of about 40, 000 SNPs and two statistical models. [Results]Using all pairs of two adjacent SNPs in the whole SNP set, the means of LD (r2) at ranges 0–0.1, 0.1–0.2, 0.2–0.5 and 0.5–1 Mb were 0.22, 0.13, 0.10 and 0.08, respectively, and 25.7, 13.9, 10.4 and 6.4% of the r2 values exceeded 0.3, respectively. While about 90% of the genetic variance for carcass weight estimated using all available SNPs was explained using 4, 000–6, 000 SNPs, the corresponding percentage for marbling score was consistently lower. With the conventional linear model incorporating the G matrix, correlation between the genomic estimated breeding values (GEBVs) obtained using 4, 000 SNPs and all available SNPs was 0.99 for carcass weight and 0.98 for marbling score, with an underestimation of the former GEBVs, especially for marbling score. [Conclusions]The Japanese Black is likely to be in a breed group with a relatively high extent of whole genome LD. The results indicated that the degree of marbling is controlled by only QTLs with relatively small effects, compared with carcass weight, and that using at least 4, 000 equally-spaced SNPs, there is a possibility of ranking animals genetically for these carcass traits in this breed.

In the next few years, with the advent of high-density single nucleotide polymorphism (SNP) arrays and genome sequencing, genomic evaluation methods will need to deal with a large number of genetic variants and an increasing sample size. The boosting algorithm is a machine-learning technique that may alleviate the drawbacks of dealing with such large data sets. This algorithm combines different predictors in a sequential manner with some shrinkage on them; each predictor is applied consecutively to the residuals from the committee formed by the previous ones to form a final prediction based on a subset of covariates. Here, a detailed description is provided and examples using a toy data set are included. A modification of the algorithm called " random boosting" was proposed to increase predictive ability and decrease computation time of genome-assisted evaluation in large data sets. Random boosting uses a random selection of markers to add a subsequent weak learner to the predictive model. These modifications were applied to a real data set composed of 1,797 bulls genotyped for 39,714 SNP. Deregressed proofs of 4 yield traits and 1 type trait from January 2009 routine evaluations were used as dependent variables. A 2-fold cross-validation scenario was implemented. Sires born before 2005 were used as a training sample (1,576 and 1,562 for production and type traits, respectively), whereas younger sires were used as a testing sample to evaluate predictive ability of the algorithm on yet-to-be-observed phenotypes. Comparison with the original algorithm was provided. The predictive ability of the algorithm was measured as Pearson correlations between observed and predicted responses. Further, estimated bias was computed as the average difference between observed and predicted phenotypes. The results showed that the modification of the original boosting algorithm could be run in 1% of the time used with the original algorithm and with negligible differences in accuracy a

Genome-wide association studies and genomic evaluation using a dense set of genetic markers both require a large number of genotyped individuals. Collection of the respective samples contributes substantially to the cost of the approach. In dairy cattle research, the use of residues from routine milk recording would be a cost-saving alternative to obtain samples for an appropriate number of individuals with specific phenotypes in a very short time. To assess the suitability of milk recording residues, we concurrently investigated milk residues obtained after standardized milk recording procedures and blood samples from 115 cows originating from 3 farms with different milking systems by genotyping 15 microsatellite markers. We found that 4% of the milk samples were possibly assigned to the wrong animal (i.e., conflicts) and that at least 27% of the milk residues were contaminated, as indicated by an extra allele not present in the blood sample. These additional alleles primarily originated from a sample with a higher somatic cell score that went through the milk sample analyzer in the milk laboratory before the target sample. Furthermore, additional allele carryover was observed across more than one sample, when the difference in somatic cell count between samples exceeded 100,000 cells/mL. Finally, in several samples, the extra allele could not be traced back to previous samples passing through the milk sample analyzer. One source of those contaminations might be sample collection on-farm due to milk traces from the previously milked cow in the hose. No correlation was found between the farm management and conflicts or contaminations. We conclude that residues from routine milk recording are not suitable for genomic evaluation or genome-wide association studies because of the high prevalence of contamination generated at several steps during the collection and processing of milk residual samples.

Background Using SNP genotypes to apply genomic selection in breeding programs is becoming common practice. Tools to edit and check the quality of genotype data are required. Checking for Mendelian inconsistencies makes it possible to identify animals for which pedigree information and genotype information are not in agreement. Methods Straightforward tests to detect Mendelian inconsistencies exist that count the number of opposing homozygous marker (e.g. SNP) genotypes between parent and offspring (PAR-OFF). Here, we develop two tests to identify Mendelian inconsistencies between sibs. The first test counts SNP with opposing homozygous genotypes between sib pairs (SIBCOUNT). The second test compares pedigree and SNP-based relationships (SIBREL). All tests iteratively remove animals based on decreasing numbers of inconsistent parents and offspring or sibs. The PAR-OFF test, followed by either SIB test, was applied to a dataset comprising 2,078 genotyped cows and 211 genotyped sires. Theoretical expectations for distributions of test statistics of all three tests were calculated and compared to empirically derived values. Type I and II error rates were calculated after applying the tests to the edited data, while Mendelian inconsistencies were introduced by permuting pedigree against genotype data for various proportions of animals. Results Both SIB tests identified animal pairs for which pedigree and genomic relationships could be considered as inconsistent by visual inspection of a scatter plot of pairwise pedigree and SNP-based relationships. After removal of 235 animals with the PAR-OFF test, SIBCOUNT (SIBREL) identified 18 (22) additional inconsistent animals. Seventeen animals were identified by both methods. The numbers of incorrectly deleted animals (Type I error), were equally low for both methods, while the numbers of incorrectly non-deleted animals (Type II error), were considerably higher for SIBREL compared to SIBCOUNT. Conclusions Tests to remove Mendel

Background Using SNP genotypes to apply genomic selection in breeding programs is becoming common practice. Tools to edit and check the quality of genotype data are required. Checking for Mendelian inconsistencies makes it possible to identify animals for which pedigree information and genotype information are not in agreement. Methods Straightforward tests to detect Mendelian inconsistencies exist that count the number of opposing homozygous marker (e.g. SNP) genotypes between parent and offspring (PAR-OFF). Here, we develop two tests to identify Mendelian inconsistencies between sibs. The first test counts SNP with opposing homozygous genotypes between sib pairs (SIBCOUNT). The second test compares pedigree and SNP-based relationships (SIBREL). All tests iteratively remove animals based on decreasing numbers of inconsistent parents and offspring or sibs. The PAR-OFF test, followed by either SIB test, was applied to a dataset comprising 2,078 genotyped cows and 211 genotyped sires. Theoretical expectations for distributions of test statistics of all three tests were calculated and compared to empirically derived values. Type I and II error rates were calculated after applying the tests to the edited data, while Mendelian inconsistencies were introduced by permuting pedigree against genotype data for various proportions of animals. Results Both SIB tests identified animal pairs for which pedigree and genomic relationships could be considered as inconsistent by visual inspection of a scatter plot of pairwise pedigree and SNP-based relationships. After removal of 235 animals with the PAR-OFF test, SIBCOUNT (SIBREL) identified 18 (22) additional inconsistent animals. Seventeen animals were identified by both methods. The numbers of incorrectly deleted animals (Type I error), were equally low for both methods, while the numbers of incorrectly non-deleted animals (Type II error), were considerably higher for SIBREL compared to SIBCOUNT. Conclusions Tests to remove Mendel