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Abstract Background Whole-genome sequence (WGS) data are increasingly available on large numbers of individuals in animal and plant breeding and in human genetics through second-generation resequencing technologies, 1000 genomes projects, and large-scale genotype imputation from lower marker densities. Here, we present a computationally fast implementation of a variable selection genomic prediction method, that could handle WGS data on more than 35,000 individuals, test its accuracy for across-breed predictions and assess its quantitative trait locus (QTL) mapping precision. Methods The Monte Carlo Markov chain (MCMC) variable selection model (Bayes GC) fits simultaneously a genomic best linear unbiased prediction (GBLUP) term, i.e. a polygenic effect whose correlations are described by a genomic relationship matrix (G), and a Bayes C term, i.e. a set of single nucleotide polymorphisms (SNPs) with large effects selected by the model. Computational speed is improved by a Metropolis–Hastings sampling that directs computations to the SNPs, which are, a priori, most likely to be included into the model. Speed is also improved by running many relatively short MCMC chains. Memory requirements are reduced by storing the genotype matrix in binary form. The model was tested on a WGS dataset containing Holstein, Jersey and Australian Red cattle. The data contained 4,809,520 genotypes on 35,549 individuals together with their milk, fat and protein yields, and fat and protein percentage traits. Results The prediction accuracies of the Jersey individuals improved by 1.5% when using across-breed GBLUP compared to within-breed predictions. Using WGS instead of 600 k SNP-chip data yielded on average a 3% accuracy improvement for Australian Red cows. QTL were fine-mapped by locating the SNP with the highest posterior probability of being included in the model. Various QTL known from the literature were rediscovered, and a new SNP affecting milk production was discovered on chromosome 20 at 34.501126 Mb. Due to the high mapping precision, it was clear that many of the discovered QTL were the same across the five dairy traits. Conclusions Across-breed Bayes GC genomic prediction improved prediction accuracies compared to GBLUP. The combination of across-breed WGS data and Bayesian genomic prediction proved remarkably effective for the fine-mapping of QTL.

Abstract Background Polyploidy is widespread in animals and especially in plants. Different kinds of ploidies exist, for example, hexaploidy in wheat, octaploidy in strawberries, and diploidy, triploidy, tetraploidy, and pseudo-tetraploidy (partly tetraploid) in fish. Triploid offspring from diploid parents occur frequently in the wild in Atlantic salmon (Salmo salar) and, as with triploidy in general, the triploid individuals are sterile. Induced triploidy in Atlantic salmon is common practice to produce sterile fish. In Norwegian aquaculture, production of sterile triploid fish is an attempt by government and industry to limit genetic introgression between wild and farmed fish. However, triploid fish may have traits and properties that differ from those of diploids. Investigating the genetics behind traits in triploids has proved challenging because genotype calling of genetic markers in triploids is not supported by standard software. Our aim was to develop a method that can be used for genotype calling of genetic markers in triploid individuals. Results Allele signals were produced for 381 triploid Atlantic salmon offspring using a 56 K Thermo Fisher GeneTitan genotyping platform. Genotypes were successfully called by applying finite normal mixture models to the (transformed) allele signals. Subsets of markers were filtered by quality control statistics for use with downstream analyses. The quality of the called genotypes was sufficient to allow for assignment of diploid parents to the triploid offspring and to discriminate between maternal and paternal parents from autosomal inheritance patterns. In addition, as the maternal inheritance in triploid offspring is identical to gynogenetic inheritance, the maternal recombination pattern for each chromosome could be mapped by using a similar approach as that used in gene-centromere mapping. Conclusions We show that calling of dense marker genotypes for triploid individuals is feasible. The resulting genotypes can be used in parentage assignment of triploid offspring to diploid parents, to discriminate between maternal and paternal parents using autosomal inheritance patterns, and to map the maternal recombination pattern using an approach similar to gene-centromere mapping. Genotyping of triploid individuals is important both for selective breeding programs and unravelling the underlying genetics of phenotypes recorded in triploids. In principle, the developed method can be used for genotype calling of other polyploid organisms.

Abstract Background The availability of both pedigree and genomic sources of information for animal breeding and genetics has created new challenges in understanding how they can be best used and interpreted. This study estimated genetic variance components based on genomic information and compared these to the variance components estimated from pedigree alone in a population generated to estimate non-additive genetic variance. Furthermore, the study examined the impact of the assumptions of Hardy–Weinberg equilibrium (HWE) on estimates of genetic variance components. For the first time, the magnitude of inbreeding depression for important commercial traits in Nile tilapia was estimated by using genomic data. Results The study estimated the non-additive genetic variance in a Nile tilapia population of full-sib families and, when present, it was almost entirely represented by additive-by-additive epistatic variance, although in pedigree studies this non-additive variance is commonly assumed to arise from dominance. For body depth (BD) and body weight at harvest (BWH), the proportion of additive-by-additive epistatic to phenotypic variance was estimated to be 0.15 and 0.17 using genomic data (P

Abstract Background The main aim of single-step genomic predictions was to facilitate optimal selection in populations consisting of both genotyped and non-genotyped individuals. However, in spite of intensive research, biases still occur, which make it difficult to perform optimal selection across groups of animals. The objective of this study was to investigate whether incomplete genotype datasets with errors could be a potential source of level-bias between genotyped and non-genotyped animals and between animals genotyped on different single nucleotide polymorphism (SNP) panels in single-step genomic predictions. Results Incomplete and erroneous genotypes of young animals caused biases in breeding values between groups of animals. Systematic noise or missing data for less than 1% of the SNPs in the genotype data had substantial effects on the differences in breeding values between genotyped and non-genotyped animals, and between animals genotyped on different chips. The breeding values of young genotyped individuals were biased upward, and the magnitude was up to 0.8 genetic standard deviations, compared with breeding values of non-genotyped individuals. Similarly, the magnitude of a small value added to the diagonal of the genomic relationship matrix affected the level of average breeding values between groups of genotyped and non-genotyped animals. Cross-validation accuracies and regression coefficients were not sensitive to these factors. Conclusions Because, historically, different SNP chips have been used for genotyping different parts of a population, fine-tuning of imputation within and across SNP chips and handling of missing genotypes are crucial for reducing bias. Although all the SNPs used for estimating breeding values are present on the chip used for genotyping young animals, incompleteness and some genotype errors might lead to level-biases in breeding values.

Abstract Background Two distinct populations have been extensively studied in Atlantic cod (Gadus morhua L.): the Northeast Arctic cod (NEAC) population and the coastal cod (CC) population. The objectives of the current study were to identify genomic islands of divergence and to propose an approach to quantify the strength of selection pressures using whole-genome single nucleotide polymorphism (SNP) data. After applying filtering criteria, information on 93 animals (9 CC individuals, 50 NEAC animals and 34 CC × NEAC crossbred individuals) and 3,123,434 autosomal SNPs were used. Results Four genomic islands of divergence were identified on chromosomes 1, 2, 7 and 12, which were mapped accurately based on SNP data and which extended in size from 11 to 18 Mb. These regions differed considerably between the two populations although the differences in the rest of the genome were small due to considerable gene flow between the populations. The estimates of selection pressures showed that natural selection was substantially more important than genetic drift in shaping these genomic islands. Our data confirmed results from earlier publications that suggested that genomic islands are due to chromosomal rearrangements that are under strong selection and reduce recombination between rearranged and non-rearranged segments. Conclusions Our findings further support the hypothesis that selection and reduced recombination in genomic islands may promote speciation between these two populations although their habitats overlap considerably and migrations occur between them.

Abstract Background In pigs, crossbreeding aims at exploiting heterosis, but heterosis is difficult to quantify. Heterozygosity at genetic markers is easier to measure and could potentially be used as an indicator of heterosis. The objective of this study was to investigate the effect of heterozygosity on various maternal and production traits in purebred and crossbred pigs. The proportion of heterozygosity at genetic markers across the genome for each individual was included in the prediction model as a fixed regression across or within breeds. Results Estimates of regression coefficients of heterozygosity showed large effects for some traits. For maternal traits, regression coefficient estimates were always in a favourable direction, while for production, meat and slaughter quality traits, they were both favourable and unfavourable. Traits with the largest estimated effects of heterozygosity were total number born, litter weight at 3 weeks, weight at 150 days, and age at 40 kg. Estimates of regression coefficients on heterozygosity differed between breeds. Traits with the largest effect of heterozygosity also showed a significant (P

Abstract Background Parentage assignment is usually based on a limited number of unlinked, independent genomic markers (microsatellites, low-density single nucleotide polymorphisms (SNPs), etc.). Classical methods for parentage assignment are exclusion-based (i.e. based on loci that violate Mendelian inheritance) or likelihood-based, assuming independent inheritance of loci. For true parent–offspring relations, genotyping errors cause apparent violations of Mendelian inheritance. Thus, the maximum proportion of such violations must be determined, which is complicated by variable call- and genotype error rates among loci and individuals. Recently, genotyping using high-density SNP chips has become available at lower cost and is increasingly used in genetics research and breeding programs. However, dense SNPs are not independently inherited, violating the assumptions of the likelihood-based methods. Hence, parentage assignment usually assumes a maximum proportion of exclusions, or applies likelihood-based methods on a smaller subset of independent markers. Our aim was to develop a fast and accurate trio parentage assignment method for dense SNP data without prior genotyping error- or call rate knowledge among loci and individuals. This genomic relationship likelihood (GRL) method infers parentage by using genomic relationships, which are typically used in genomic prediction models. Results Using 50 simulated datasets with 53,427 to 55,517 SNPs, genotyping error rates of 1–3% and call rates of ~ 80 to 98%, GRL was found to be fast and highly (~ 99%) accurate for parentage assignment. An iterative approach was developed for training using the evaluation data, giving similar accuracy. For comparison, we used the Colony2 software that assigns parentage and sibship simultaneously to increase the power of the likelihood-based method and found that it has considerably lower accuracy than GRL. We also compared GRL with an exclusion-based method in which one of the parameters was estimated using GRL assignments.This method was slightly more accurate than GRL. Conclusions We show that GRL is a fast and accurate method of parentage assignment that can use dense, non-independent SNPs, with variable call rates and unknown genotyping error rates. By offering an alternative way of assigning parents, GRL is also suitable for estimating the expected proportion of inconsistent parent–offspring genotypes for exclusion-based models.

Abstract Background The replacement of fish oil (FO) and fishmeal with plant ingredients in the diet of farmed Atlantic salmon has resulted in reduced levels of the health-promoting long-chain polyunsaturated omega-3 fatty acids (n-3 LC-PUFA) eicosapentaenoic (EPA; 20:5n-3) and docosahexaenoic acid (DHA; 22:6n-3) in their filets. Previous studies showed the potential of selective breeding to increase n-3 LC-PUFA levels in salmon tissues, but knowledge on the genetic parameters for individual muscle fatty acids (FA) and their relationships with other traits is still lacking. Thus, we estimated genetic parameters for muscle content of individual FA, and their relationships with lipid deposition traits, muscle pigmentation, sea lice and pancreas disease in slaughter-sized Atlantic salmon. Our aim was to evaluate the selection potential for increased n-3 LC-PUFA content and provide insight into FA metabolism in Atlantic salmon muscle. Results Among the n-3 PUFA, proportional contents of alpha-linolenic acid (ALA; 18:3n-3) and DHA had the highest heritability (0.26) and EPA the lowest (0.09). Genetic correlations of EPA and DHA proportions with muscle fat differed considerably, 0.60 and 0.01, respectively. The genetic correlation of DHA proportion with visceral fat was positive and high (0.61), whereas that of EPA proportion with lice density was negative. FA that are in close proximity along the bioconversion pathway showed positive correlations with each other, whereas the start (ALA) and end-point (DHA) of the pathway were negatively correlated (− 0.28), indicating active bioconversion of ALA to DHA in the muscle of fish fed high FO-diet. Conclusions Since contents of individual FA in salmon muscle show additive genetic variation, changing FA composition by selective breeding is possible. Taken together, our results show that the heritabilities of individual n-3 LC-PUFA and their genetic correlations with other traits vary, which indicates that they play different roles in muscle lipid metabolism, and that proportional muscle contents of EPA and DHA are linked to body fat deposition. Thus, different selection strategies can be applied in order to increase the content of healthy omega-3 FAin the salmon muscle. We recommend selection for the proportion of EPA + DHA in the muscle because they are both essential FA and because such selection has no clear detrimental effects on other traits.

Abstract Background For marker effect models and genomic animal models, computational requirements increase with the number of loci and the number of genotyped individuals, respectively. In the latter case, the inverse genomic relationship matrix (GRM) is typically needed, which is computationally demanding to compute for large datasets. Thus, there is a great need for dimensionality-reduction methods that can analyze massive genomic data. For this purpose, we developed reduced-dimension singular value decomposition (SVD) based models for genomic prediction. Methods Fast SVD is performed by analyzing different chromosomes/genome segments in parallel and/or by restricting SVD to a limited core of genotyped individuals, producing chromosome- or segment-specific principal components (PC). Given a limited effective population size, nearly all the genetic variation can be effectively captured by a limited number of PC. Genomic prediction can then be performed either by PC ridge regression (PCRR) or by genomic animal models using an inverse GRM computed from the chosen PC (PCIG). In the latter case, computation of the inverse GRM will be feasible for any number of genotyped individuals and can be readily produced row- or element-wise. Results Using simulated data, we show that PCRR and PCIG models, using chromosome-wise SVD of a core sample of individuals, are appropriate for genomic prediction in a larger population, and results in virtually identical predicted breeding values as the original full-dimension genomic model (r = 1.000). Compared with other algorithms (e.g. algorithm for proven and young animals, APY), the (chromosome-wise SVD-based) PCRR and PCIG models were more robust to size of the core sample, giving nearly identical results even down to 500 core individuals. The method was also successfully tested on a large multi-breed dataset. Conclusions SVD can be used for dimensionality reduction of large genomic datasets. After SVD, genomic prediction using dense genomic data and many genotyped individuals can be done in a computationally efficient manner. Using this method, the resulting genomic estimated breeding values were virtually identical to those computed from a full-dimension genomic model.

Abstract Background Non-linear Bayesian genomic prediction models such as BayesA/B/C/R involve iteration and mostly Markov chain Monte Carlo (MCMC) algorithms, which are computationally expensive, especially when whole-genome sequence (WGS) data are analyzed. Singular value decomposition (SVD) of the genotype matrix can facilitate genomic prediction in large datasets, and can be used to estimate marker effects and their prediction error variances (PEV) in a computationally efficient manner. Here, we developed, implemented, and evaluated a direct, non-iterative method for the estimation of marker effects for the BayesC genomic prediction model. Methods The BayesC model assumes a priori that markers have normally distributed effects with probability $$ \uppi $$ π and no effect with probability (1 − $$ \uppi $$ π ). Marker effects and their PEV are estimated by using SVD and the posterior probability of the marker having a non-zero effect is calculated. These posterior probabilities are used to obtain marker-specific effect variances, which are subsequently used to approximate BayesC estimates of marker effects in a linear model. A computer simulation study was conducted to compare alternative genomic prediction methods, where a single reference generation was used to estimate marker effects, which were subsequently used for 10 generations of forward prediction, for which accuracies were evaluated. Results SVD-based posterior probabilities of markers having non-zero effects were generally lower than MCMC-based posterior probabilities, but for some regions the opposite occurred, resulting in clear signals for QTL-rich regions. The accuracies of breeding values estimated using SVD- and MCMC-based BayesC analyses were similar across the 10 generations of forward prediction. For an intermediate number of generations (2 to 5) of forward prediction, accuracies obtained with the BayesC model tended to be slightly higher than accuracies obtained using the best linear unbiased prediction of SNP effects (SNP-BLUP model). When reducing marker density from WGS data to 30 K, SNP-BLUP tended to yield the highest accuracies, at least in the short term. Conclusions Based on SVD of the genotype matrix, we developed a direct method for the calculation of BayesC estimates of marker effects. Although SVD- and MCMC-based marker effects differed slightly, their prediction accuracies were similar. Assuming that the SVD of the marker genotype matrix is already performed for other reasons (e.g. for SNP-BLUP), computation times for the BayesC predictions were comparable to those of SNP-BLUP.

Abstract Background Molecular data is now commonly used to predict breeding values (BV). Various methods to calculate genomic relationship matrices (GRM) have been developed, with some studies proposing regression of coefficients back to the reference matrix of pedigree-based relationship coefficients (A). The objective was to compare the utility of two GRM: a matrix based on linkage analysis (LA) and anchored to the pedigree, i.e. $${\mathbf{G}}_{{{\mathbf{LA}}}} ,$$ G LA , and a matrix based on linkage disequilibrium (LD), i.e. $${\mathbf{G}}_{{{\mathbf{LD}}}}$$ G LD , using genomic and phenotypic data collected on 5416 broiler chickens. Furthermore, the effects of regressing the coefficients of $${\mathbf{G}}_{{{\mathbf{LD}}}}$$ G LD back to A (LDA) and to $${\mathbf{G}}_{{{\mathbf{LA}}}}$$ G LA (LDLA) were evaluated, using a range of weighting factors. The performance of the matrices and their composite products was assessed by the fit of the models to the data, and the empirical accuracy and bias of the BV that they predicted. The sensitivity to marker choice was examined by using two chips of equal density but including different single nucleotide polymorphisms (SNPs). Results The likelihood of models using GRM and composite matrices exceeded the likelihood of models based on pedigree alone and was highest with intermediate weighting factors for both the LDA and LDLA approaches. For these data, empirical accuracies were not strongly affected by the weighting factors, although they were highest when different sources of information were combined. The optimum weighting factors depended on the type of matrices used, as well as on the choice of SNPs from which the GRM were constructed. Prediction bias was strongly affected by the chip used and less by the form of the GRM. Conclusions Our findings provide an empirical comparison of the efficacy of pedigree and genomic predictions in broiler chickens and examine the effects of fitting GRM with coefficients regressed back to a reference anchored to the pedigree, either A or $${\mathbf{G}}_{{{\mathbf{LA}}}}$$ G LA . For the analysed dataset, the best results were obtained when $${\mathbf{G}}_{{{\mathbf{LD}}}}$$ G LD was combined with relationships in A or $${\mathbf{G}}_{{{\mathbf{LA}}}}$$ G LA , with optimum weighting factors that depended on the choice of SNPs used. The optimum weighting factor for broiler body weight differed from weighting factors that were based on the density of SNPs and theoretically derived using generalised assumptions.

Abstract Background The rapid adoption of genomic selection is due to two key factors: availability of both high-throughput dense genotyping and statistical methods to estimate and predict breeding values. The development of such methods is still ongoing and, so far, there is no consensus on the best approach. Currently, the linear and non-linear methods for genomic prediction (GP) are treated as distinct approaches. The aim of this study was to evaluate the implementation of an iterative method (called GBC) that incorporates aspects of both linear [genomic-best linear unbiased prediction (G-BLUP)] and non-linear (Bayes-C) methods for GP. The iterative nature of GBC makes it less computationally demanding similar to other non-Markov chain Monte Carlo (MCMC) approaches. However, as a Bayesian method, GBC differs from both MCMC- and non-MCMC-based methods by combining some aspects of G-BLUP and Bayes-C methods for GP. Its relative performance was compared to those of G-BLUP and Bayes-C. Methods We used an imputed 50 K single-nucleotide polymorphism (SNP) dataset based on the Illumina Bovine50K BeadChip, which included 48,249 SNPs and 3244 records. Daughter yield deviations for somatic cell count, fat yield, milk yield, and protein yield were used as response variables. Results GBC was frequently (marginally) superior to G-BLUP and Bayes-C in terms of prediction accuracy and was significantly better than G-BLUP only for fat yield. On average across the four traits, GBC yielded a 0.009 and 0.006 increase in prediction accuracy over G-BLUP and Bayes-C, respectively. Computationally, GBC was very much faster than Bayes-C and similar to G-BLUP. Conclusions Our results show that incorporating some aspects of G-BLUP and Bayes-C in a single model can improve accuracy of GP over the commonly used method: G-BLUP. Generally, GBC did not statistically perform better than G-BLUP and Bayes-C, probably due to the close relationships between reference and validation individuals. Nevertheless, it is a flexible tool, in the sense, that it simultaneously incorporates some aspects of linear and non-linear models for GP, thereby exploiting family relationships while also accounting for linkage disequilibrium between SNPs and genes with large effects. The application of GBC in GP merits further exploration.

Abstract Two previously described QTL mapping methods, which combine linkage analysis (LA) and linkage disequilibrium analysis (LD), were compared for their ability to detect and map multiple QTL. The methods were tested on five different simulated data sets in which the exact QTL positions were known. Every simulated data set contained two QTL, but the distances between these QTL were varied from 15 to 150 cM. The results show that the single QTL mapping method (LDLA) gave good results as long as the distance between the QTL was large (> 90 cM). When the distance between the QTL was reduced, the single QTL method had problems positioning the two QTL and tended to position only one QTL, i.e. a "ghost" QTL, in between the two real QTL positions. The multi QTL mapping method (MP-LDLA) gave good results for all evaluated distances between the QTL. For the large distances between the QTL (> 90 cM) the single QTL method more often positioned the QTL in the correct marker bracket, but considering the broader likelihood peaks of the single point method it could be argued that the multi QTL method was more precise. Since the distances were reduced the multi QTL method was clearly more accurate than the single QTL method. The two methods combine well, and together provide a good tool to position single or multiple QTL in practical situations, where the number of QTL and their positions are unknown.

Abstract Two random regression models, where the effect of a putative QTL was regressed on an environmental gradient, are described. The first model estimates the correlation between intercept and slope of the random regression, while the other model restricts this correlation to 1 or -1, which is expected under a bi-allelic QTL model. The random regression models were compared to a model assuming no gene by environment interactions. The comparison was done with regards to the models ability to detect QTL, to position them accurately and to detect possible QTL by environment interactions. A simulation study based on a granddaughter design was conducted, and QTL were assumed, either by assigning an effect independent of the environment or as a linear function of a simulated environmental gradient. It was concluded that the random regression models were suitable for detection of QTL effects, in the presence and absence of interactions with environmental gradients. Fixing the correlation between intercept and slope of the random regression had a positive effect on power when the QTL effects re-ranked between environments.

Abstract Extinction of breeds threatens genetic diversity of livestock species. The need to conserve genetic diversity is widely accepted but involves in general two questions: (i) is the expected loss of diversity in a set of breeds within a defined future time horizon large enough to establish a conservation plan, and if so (ii) which breeds should be prioritised for such a conservation plan? The present study uses a marker assisted methodology to address these questions. The methodology combines core set diversity measures with a stochastic method for the estimation of expected future diversity and breed marginal diversities. The latter is defined as the change in the total diversity of all breeds caused by a one unit decrease in extinction probability of a particular breed. The stochastic method was validated by means of simulations. A large field data set consisting of 44 North Eurasian cattle breeds was analysed using simplified determined extinction probabilities. The results show that the expected loss of diversity in this set within the next 20 to 50 years is between 1 and 3% of the actual diversity, provided that the extinction probabilities which were used are approximately valid. If this loss is to be reduced, it is sufficient to include those three to five breeds with the highest marginal diversity in a conservation scheme.

Abstract This study was designed to reveal any differences in effects of fast created versus total inbreeding on reproduction and body weights in mice. A line selected for large litter size for 124 generations (H) and a control line (K) maintained without selection for the same number of generations were crossed (HK) and used as a basis for the experiment. Within the HK cross, full sib, cousin or random mating were practised for two generations in order to create new inbreeding (IBF) at a fast rate. In the first generation of systematic mating, old inbreeding was regenerated in addition to creation of new inbreeding from the mating design giving total inbreeding (IBT). The number of pups born alive (NBA) and body weights of the animals were then analysed by a model including both IBT and IBF. The IBT of the dam was in the present study found to reduce the mean NBA with -0.48 (± 0.22) (p < 0.05) pups per 10% increase in the inbreeding coefficient, while the additional effect of IBF was -0.42 (± 0.27). For the trait NBA per female mated, the effect of IBT was estimated to be -0.45 (± 0.29) per 10% increase in the inbreeding coefficient and the effect of IBF was -0.90 (± 0.37) (p < 0.05) pups. In the present study, only small or non-significant effects of IBF of the dam could be found on sex-ratio and body weights at three and six weeks of age in a population already adjusted for IBT.

Abstract The need for conservation of farm animal genetic resources is widely accepted. A key question is the choice of breeds to be conserved. For this purpose, a core set of breeds was introduced in that the total genetic variance of a hypothetical quantitative trait was maximised (MVT core set). For each breed the relative contribution to the core set was estimated and the breeds were ranked for conservation priority according to their relative contribution. The method was based on average kinships between and within breeds and these can be estimated using genetic marker data. The method was compared to a recently published core set method that maximises the variance of a hypothetical population that could be obtained by interbreeding the conserved breeds (MVO core set). The results show that the MVT (MVO) core set favours breeds with a high (low) within breed kinship that are not related to other breeds. Following this, the MVT core set method suggests conserving breeds that show a large difference in the respective population mean of a hypothetical quantitative trait. This maximises the speed of achieving selection response for this hypothetical selection direction. Additionally, bootstrap based methods for the estimation of the breed's contribution to the core sets were introduced, substantially improving the accuracy of the contribution estimates.

Abstract A multi-locus QTL mapping method is presented, which combines linkage and linkage disequilibrium (LD) information and uses multitrait data. The method assumed a putative QTL at the midpoint of each marker bracket. Whether the putative QTL had an effect or not was sampled using Markov chain Monte Carlo (MCMC) methods. The method was tested in dairy cattle data on chromosome 14 where the DGAT1 gene was known to be segregating. The DGAT1 gene was mapped to a region of 0.04 cM, and the effects of the gene were accurately estimated. The fitting of multiple QTL gave a much sharper indication of the QTL position than a single QTL model using multitrait data, probably because the multi-locus QTL mapping reduced the carry over effect of the large DGAT1 gene to adjacent putative QTL positions. This suggests that the method could detect secondary QTL that would, in single point analyses, remain hidden under the broad peak of the dominant QTL. However, no indications for a second QTL affecting dairy traits were found on chromosome 14.

Abstract The ordinary-, penalized-, and bootstrap t-test, least squares and best linear unbiased prediction were compared for their false discovery rates (FDR), i.e. the fraction of falsely discovered genes, which was empirically estimated in a duplicate of the data set. The bootstrap-t-test yielded up to 80% lower FDRs than the alternative statistics, and its FDR was always as good as or better than any of the alternatives. Generally, the predicted FDR from the bootstrapped P-values agreed well with their empirical estimates, except when the number of mRNA samples is smaller than 16. In a cancer data set, the bootstrap-t-test discovered 200 differentially regulated genes at a FDR of 2.6%, and in a knock-out gene expression experiment 10 genes were discovered at a FDR of 3.2%. It is argued that, in the case of microarray data, control of the FDR takes sufficient account of the multiple testing, whilst being less stringent than Bonferoni-type multiple testing corrections. Extensions of the bootstrap simulations to more complicated test-statistics are discussed.

Abstract We studied different genetic models and evaluation systems to select against a genetic disease with additive, recessive or polygenic inheritance in genetic conservation schemes. When using optimum contribution selection with a restriction on the rate of inbreeding (ΔF) to select against a disease allele, selection directly on DNA-genotypes is, as expected, the most efficient strategy. Selection for BLUP or segregation analysis breeding value estimates both need 1–2 generations more to halve the frequency of the disease allele, while these methods do not require knowledge of the disease mutation at the DNA level. BLUP and segregation analysis methods were equally efficient when selecting against a disease with single gene or complex polygene inheritance, i.e. knowledge about the mode of inheritance of the disease was not needed for efficient selection against the disease. Smaller schemes or schemes with a more stringent restriction on ΔF needed more generations to halve the frequency of the disease alleles or the fraction of diseased animals. Optimum contribution selection maintained ΔF at its predefined level, even when selection of females was at random. It is argued that in the investigated small conservation schemes with selection against a genetic defect, control of ΔF is very important.

Abstract The quantitative assessment of genetic diversity within and between populations is important for decision making in genetic conservation plans. In this paper we define the genetic diversity of a set of populations, S, as the maximum genetic variance that can be obtained in a random mating population that is bred from the set of populations S. First we calculated the relative contribution of populations to a core set of populations in which the overlap of genetic diversity was minimised. This implies that the mean kinship in the core set should be minimal. The above definition of diversity differs from Weitzman diversity in that it attempts to conserve the founder population (and thus minimises the loss of alleles), whereas Weitzman diversity favours the conservation of many inbred lines. The former is preferred in species where inbred lines suffer from inbreeding depression. The application of the method is illustrated by an example involving 45 Dutch poultry breeds. The calculations used were easy to implement and not computer intensive. The method gave a ranking of breeds according to their contributions to genetic diversity. Losses in genetic diversity ranged from 2.1% to 4.5% for different subsets relative to the entire set of breeds, while the loss of founder genome equivalents ranged from 22.9% to 39.3%.

Abstract Minimum coancestry mating with a maximum of one offspring per mating pair (MC1) is compared with random mating schemes for populations with overlapping generations. Optimum contribution selection is used, whereby ΔF is restricted. For schemes with ΔF restricted to 0.25% per year, 256 animals born per year and heritability of 0.25, genetic gain increased with 18% compared with random mating. The effect of MC1 on genetic gain decreased for larger schemes and schemes with a less stringent restriction on inbreeding. Breeding schemes hardly changed when omitting the iteration on the generation interval to find an optimum distribution of parents over age-classes, which saves computer time, but inbreeding and genetic merit fluctuated more before the schemes had reached a steady-state. When bulls were progeny tested, these progeny tested bulls were selected instead of the young bulls, which led to increased generation intervals, increased selection intensity of bulls and increased genetic gain (35% compared to a scheme without progeny testing for random mating). The effect of MC1 decreased for schemes with progeny testing. MC1 mating increased genetic gain from 11–18% for overlapping and 1–4% for discrete generations, when comparing schemes with similar genetic gain and size.

Abstract The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.

Abstract The effect of non-random mating on genetic response was compared for populations with discrete generations. Mating followed a selection step where the average coancestry of selected animals was constrained, while genetic response was maximised. Minimum coancestry (MC), Minimum coancestry with a maximum of one offspring per mating pair (MC1) and Minimum variance of the relationships of offspring (MVRO) mating schemes resulted in a delay in inbreeding of about two generations compared with Random, Random factorial and Compensatory mating. In these breeding schemes where selection constrains the rate of inbreeding, ΔF, the improved family structure due to non-random mating increased genetic response. For schemes with ΔF constrained to 1.0% and 100 selection candidates, genetic response was 22% higher for the MC1 and MVRO schemes compared with Random mating schemes. For schemes with a less stringent constraint on ΔF or more selection candidates, the superiority of the MC1 and MVRO schemes was smaller (5–6%). In general, MC1 seemed to be the preferred mating method, since it almost always yielded the highest genetic response. MC1 mainly achieved these high genetic responses by avoiding extreme relationships among the offspring, i.e. fullsib offspring are avoided, and by making the contributions of ancestors to offspring more equal by mating least related animals.

Abstract Background Simulation studies have shown that accuracy and genetic gain are increased in genomic selection schemes compared to traditional aquaculture sib-based schemes. In genomic selection, accuracy of selection can be maximized by increasing the precision of the estimation of SNP effects and by maximizing the relationships between test sibs and candidate sibs. Another means of increasing the accuracy of the estimation of SNP effects is to create individuals in the test population with extreme genotypes. The latter approach was studied here with creation of double haploids and use of non-random mating designs. Methods Six alternative breeding schemes were simulated in which the design of the test population was varied: test sibs inherited maternal (Mat), paternal (Pat) or a mixture of maternal and paternal (MatPat) double haploid genomes or test sibs were obtained by maximum coancestry mating (MaxC), minimum coancestry mating (MinC), or random (RAND) mating. Three thousand test sibs and 3000 candidate sibs were genotyped. The test sibs were recorded for a trait that could not be measured on the candidates and were used to estimate SNP effects. Selection was done by truncation on genome-wide estimated breeding values and 100 individuals were selected as parents each generation, equally divided between both sexes. Results Results showed a 7 to 19% increase in selection accuracy and a 6 to 22% increase in genetic gain in the MatPat scheme compared to the RAND scheme. These increases were greater with lower heritabilities. Among all other scenarios, i.e. Mat, Pat, MaxC, and MinC, no substantial differences in selection accuracy and genetic gain were observed. Conclusions In conclusion, a test population designed with a mixture of paternal and maternal double haploids, i.e. the MatPat scheme, increases substantially the accuracy of selection and genetic gain. This will be particularly interesting for traits that cannot be recorded on the selection candidates and require the use of sib tests, such as disease resistance and meat quality.

Abstract Background In the past, pedigree relationships were used to control and monitor inbreeding because genomic relationships among selection candidates were not available until recently. The aim of this study was to understand the consequences for genetic variability across the genome when genomic information is used to estimate breeding values and in managing the inbreeding generated in the course of selection on genome-enhanced estimated breeding values. Methods These consequences were measured by genetic gain, pedigree- and genome-based rates of inbreeding, and local inbreeding across the genome. Breeding schemes were compared by simulating truncation selection or optimum contribution selection with a restriction on pedigree- or genome-based inbreeding, and with selection using estimated breeding values based on genome- or pedigree-based BLUP. Trait information was recorded on full-sibs of the candidates. Results When the information used to estimate breeding values and to constrain rates of inbreeding were either both pedigree-based or both genome-based, rates of genomic inbreeding were close to the desired values and the identical-by-descent profiles were reasonably uniform across the genome. However, with a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding were much higher than expected. With pedigree-instead of genome-based estimated breeding values, the impact of the largest QTL on the breeding values was much smaller, resulting in a more uniform genome-wide identical-by-descent profile but genomic rates of inbreeding were still higher than expected based on pedigree relationships, because they measure the inbreeding at a neutral locus not linked to any QTL. Neutral loci did not exist here, where there were 100 QTL on each chromosome. With a pedigree-based inbreeding constraint and genome-based estimated breeding values, genomic rates of inbreeding substantially exceeded the value of its constraint. In contrast, with a genome-based inbreeding constraint and genome-based estimated breeding values, marker frequencies changed, but this change was limited by the inbreeding constraint at the marker position. Conclusions To control inbreeding, it is necessary to account for it on the same basis as what is used to estimate breeding values, i.e. pedigree-based inbreeding control with traditional pedigree-based BLUP estimated breeding values and genome-based inbreeding control with genome-based estimated breeding values.

Abstract Background It is commonly assumed that prediction of genome-wide breeding values in genomic selection is achieved by capitalizing on linkage disequilibrium between markers and QTL but also on genetic relationships. Here, we investigated the reliability of predicting genome-wide breeding values based on population-wide linkage disequilibrium information, based on identity-by-descent relationships within the known pedigree, and to what extent linkage disequilibrium information improves predictions based on identity-by-descent genomic relationship information. Methods The study was performed on milk, fat, and protein yield, using genotype data on 35 706 SNP and deregressed proofs of 1086 Italian Brown Swiss bulls. Genome-wide breeding values were predicted using a genomic identity-by-state relationship matrix and a genomic identity-by-descent relationship matrix (averaged over all marker loci). The identity-by-descent matrix was calculated by linkage analysis using one to five generations of pedigree data. Results We showed that genome-wide breeding values prediction based only on identity-by-descent genomic relationships within the known pedigree was as or more reliable than that based on identity-by-state, which implicitly also accounts for genomic relationships that occurred before the known pedigree. Furthermore, combining the two matrices did not improve the prediction compared to using identity-by-descent alone. Including different numbers of generations in the pedigree showed that most of the information in genome-wide breeding values prediction comes from animals with known common ancestors less than four generations back in the pedigree. Conclusions Our results show that, in pedigreed breeding populations, the accuracy of genome-wide breeding values obtained by identity-by-descent relationships was not improved by identity-by-state information. Although, in principle, genomic selection based on identity-by-state does not require pedigree data, it does use the available pedigree structure. Our findings may explain why the prediction equations derived for one breed may not predict accurate genome-wide breeding values when applied to other breeds, since family structures differ among breeds.

Abstract Background In classical pedigree-based analysis, additive genetic variance is estimated from between-family variation, which requires the existence of larger phenotyped and pedigreed populations involving numerous families (parents). However, estimation is often complicated by confounding of genetic and environmental family effects, with the latter typically occurring among full-sibs. For this reason, genetic variance is often inferred based on covariance among more distant relatives, which reduces the power of the analysis. This simulation study shows that genome-wide identity-by-descent sharing among close relatives can be used to quantify additive genetic variance solely from within-family variation using data on extremely small family samples. Methods Identity-by-descent relationships among full-sibs were simulated assuming a genome size similar to that of humans (effective number of loci ~80). Genetic variance was estimated from phenotypic data assuming that genomic identity-by-descent relationships could be accurately re-created using information from genome-wide markers. The results were compared with standard pedigree-based genetic analysis. Results For a polygenic trait and a given number of phenotypes, the most accurate estimates of genetic variance were based on data from a single large full-sib family only. Compared with classical pedigree-based analysis, the proposed method is more robust to selection among parents and for confounding of environmental and genetic effects. Furthermore, in some cases, satisfactory results can be achieved even with less ideal data structures, i.e., for selectively genotyped data and for traits for which the genetic variance is largely under the control of a few major genes. Conclusions Estimation of genetic variance using genomic identity-by-descent relationships is especially useful for studies aiming at estimating additive genetic variance of highly fecund species, using data from small populations with limited pedigree information and/or few available parents, i.e., parents originating from non-pedigreed or even wild populations.

Abstract Background The risk of long-term unequal contribution of mating pairs to the gene pool is that deleterious recessive genes can be expressed. Such consequences could be alleviated by appropriately designing and optimizing breeding schemes i.e. by improving selection and mating procedures. Methods We studied the effect of mating designs, random, minimum coancestry and minimum covariance of ancestral contributions on rate of inbreeding and genetic gain for schemes with different information sources, i.e. sib test or own performance records, different genetic evaluation methods, i.e. BLUP or genomic selection, and different family structures, i.e. factorial or pair-wise. Results Results showed that substantial differences in rates of inbreeding due to mating design were present under schemes with a pair-wise family structure, for which minimum coancestry turned out to be more effective to generate lower rates of inbreeding. Specifically, substantial reductions in rates of inbreeding were observed in schemes using sib test records and BLUP evaluation. However, with a factorial family structure, differences in rates of inbreeding due mating designs were minor. Moreover, non-random mating had only a small effect in breeding schemes that used genomic evaluation, regardless of the information source. Conclusions It was concluded that minimum coancestry remains an efficient mating design when BLUP is used for genetic evaluation or when the size of the population is small, whereas the effect of non-random mating is smaller in schemes using genomic evaluation.

Abstract Background A newly recognized type of genetic variation, Copy Number Variation (CNV), is detected in mammalian genomes, e.g. the cattle genome. This form of variation can potentially cause phenotypic variation. Our objective was to determine whether dense SNP (single nucleotide polymorphisms) panels can capture the genetic variation due to a simple bi-allelic CNV, with the prospect of including the effect of such structural variations into genomic predictions. Methods A deletion type CNV on bovine chromosome 6 was predicted from its neighboring SNP with a multiple regression model. Our dataset consisted of CNV genotypes of 1,682 cows, along with 100 surrounding SNP genotypes. A prediction model was fitted considering 10 to 100 surrounding SNP and the accuracy obtained directly from the model was confirmed by cross-validation. Results and conclusions The accuracy of prediction increased with an increasing number of SNP in the model and the predicted accuracies were similar to those obtained by cross-validation. A substantial increase in accuracy was observed when the number of SNP increased from 10 to 50 but thereafter the increase was smaller, reaching the highest accuracy (0.94) with 100 surrounding SNP. Thus, we conclude that the genotype of a deletion type CNV and its putative QTL effect can be predicted with a maximum accuracy of 0.94 from surrounding SNP. This high prediction accuracy suggests that genetic variation due to simple deletion CNV is well captured by dense SNP panels. Since genomic selection relies on the availability of a dense marker panel with markers in close linkage disequilibrium to the QTL in order to predict their genetic values, we also discuss opportunities for genomic selection to predict the effects of CNV by dense SNP panels, when CNV cause variation in quantitative traits.

Abstract Genome-wide breeding value (GWEBV) estimation methods can be classified based on the prior distribution assumptions of marker effects. Genome-wide BLUP methods assume a normal prior distribution for all markers with a constant variance, and are computationally fast. In Bayesian methods, more flexible prior distributions of SNP effects are applied that allow for very large SNP effects although most are small or even zero, but these prior distributions are often also computationally demanding as they rely on Monte Carlo Markov chain sampling. In this study, we adopted the Pareto principle to weight available marker loci, i.e., we consider that x% of the loci explain (100 - x)% of the total genetic variance. Assuming this principle, it is also possible to define the variances of the prior distribution of the 'big' and 'small' SNP. The relatively few large SNP explain a large proportion of the genetic variance and the majority of the SNP show small effects and explain a minor proportion of the genetic variance. We name this method MixP, where the prior distribution is a mixture of two normal distributions, i.e. one with a big variance and one with a small variance. Simulation results, using a real Norwegian Red cattle pedigree, show that MixP is at least as accurate as the other methods in all studied cases. This method also reduces the hyper-parameters of the prior distribution from 2 (proportion and variance of SNP with big effects) to 1 (proportion of SNP with big effects), assuming the overall genetic variance is known. The mixture of normal distribution prior made it possible to solve the equations iteratively, which greatly reduced computation loads by two orders of magnitude. In the era of marker density reaching million(s) and whole-genome sequence data, MixP provides a computationally feasible Bayesian method of analysis.

Abstract Background Genetically, SNP that are in complete linkage disequilibrium with the causative SNP cannot be distinguished from the causative SNP. The Complete Linkage Disequilibrium (CLD) test presented here tests whether a SNP is in complete LD with the causative mutation or not. The performance of the CLD test is evaluated in 1000 simulated datasets. Methods The CLD test consists of two steps i.e. analysis I and analysis II. Analysis I consists of an association analysis of the investigated region. The log-likelihood values from analysis I are next ranked in descending order and in analysis II the CLD test evaluates differences in log-likelihood ratios between the best and second best markers. Under the null-hypothesis distribution, the best SNP is in greater LD with the QTL than the second best, while under the alternative-CLD-hypothesis, the best SNP is alike-in-state with the QTL. To find a significance threshold, the test was also performed on data excluding the causative SNP. The 5th, 10th and 50th highest TCLD value from 1000 replicated analyses were used to control the type-I-error rate of the test at p = 0.005, p = 0.01 and p = 0.05, respectively. Results In a situation where the QTL explained 48% of the phenotypic variance analysis I detected a QTL in 994 replicates (p = 0.001), where 972 were positioned in the correct QTL position. When the causative SNP was excluded from the analysis, 714 replicates detected evidence of a QTL (p = 0.001). In analysis II, the CLD test confirmed 280 causative SNP from 1000 simulations (p = 0.05), i.e. power was 28%. When the effect of the QTL was reduced by doubling the error variance, the power of the test reduced relatively little to 23%. When sequence data were used, the power of the test reduced to 16%. All SNP that were confirmed by the CLD test were positioned in the correct QTL position. Conclusions The CLD test can provide evidence for a causative SNP, but its power may be low in situations with closely linked markers. In such situations, also functional evidence will be needed to definitely conclude whether the SNP is causative or not.

Abstract Background In aquaculture breeding, resistance against infectious diseases is commonly assessed as time until death under exposure to a pathogen. For some diseases, a fraction of the individuals may appear as "cured" (non-susceptible), and the resulting survival time may thus be a result of two confounded underlying traits, i.e., endurance (individual hazard) and susceptibility (whether at risk or not), which may be accounted for by fitting a cure survival model. We applied a cure model to survival data of Pacific white shrimp (Penaeus vannamei) challenged with the Taura syndrome virus, which is one of the major pathogens of Panaeid shrimp species. Methods In total, 15,261 individuals of 513 full-sib families from three generations were challenge-tested in 21 separate tests (tanks). All challenge-tests were run until mortality naturally ceased. Time-until-event data were analyzed with a mixed cure survival model using Gibbs sampling, treating susceptibility and endurance as separate genetic traits. Results Overall mortality at the end of test was 28%, while 38% of the population was considered susceptible to the disease. The estimated underlying heritability was high for susceptibility (0.41 ± 0.07), but low for endurance (0.07 ± 0.03). Furthermore, endurance and susceptibility were distinct genetic traits (rg = 0.22 ± 0.25). Estimated breeding values for endurance and susceptibility were only moderately correlated (0.50), while estimated breeding values from classical models for analysis of challenge-test survival (ignoring the cured fraction) were closely correlated with estimated breeding values for susceptibility, but less correlated with estimated breeding values for endurance. Conclusions For Taura syndrome resistance, endurance and susceptibility are apparently distinct genetic traits. However, genetic evaluation of susceptibility based on the cure model showed clear associations with standard genetic evaluations that ignore the cure fraction for these data. Using the current testing design, genetic variation in observed survival time and absolute survival at the end of test were most likely dominated by genetic variation in susceptibility. If the aim is to reduce susceptibility, earlier termination of the challenge-test or back-truncation of the follow-up period should be avoided, as this may shift focus of selection towards endurance rather than susceptibility.

Abstract Background Traditional family-based aquaculture breeding programs, in which families are kept separately until individual tagging and most traits are measured on the sibs of the candidates, are costly and require a high level of reproductive control. The most widely used alternative is a selection scheme, where families are reared communally and the candidates are selected based on their own individual measurements of the traits under selection. However, in the latter selection schemes, inclusion of new traits depends on the availability of non-invasive techniques to measure the traits on selection candidates. This is a severe limitation of these schemes, especially for disease resistance and fillet quality traits. Methods Here, we present a new selection scheme, which was validated using computer simulations comprising 100 families, among which 1, 10 or 100 were reared communally in groups. Pooling of the DNA from 2000, 20000 or 50000 test individuals with the highest and lowest phenotypes was used to estimate 500, 5000 or 10000 marker effects. One thousand or 2000 out of 20000 candidates were preselected for a growth-like trait. These pre-selected candidates were genotyped, and they were selected on their genome-wide breeding values for a trait that could not be measured on the candidates. Results A high accuracy of selection, i.e. 0.60-0.88 was obtained with 20000-50000 test individuals but it was reduced when only 2000 test individuals were used. This shows the importance of having large numbers of phenotypic records to accurately estimate marker effects. The accuracy of selection decreased with increasing numbers of families per group. Conclusions This new selection scheme combines communal rearing of families, pre-selection of candidates, DNA pooling and genomic selection and makes multi-trait selection possible in aquaculture selection schemes without keeping families separately until individual tagging is possible. The new scheme can also be used for other farmed species, for which the cost of genotyping test individuals may be high, e.g. if trait heritability is low.

Abstract Background In the genetic analysis of binary traits with one observation per animal, animal threshold models frequently give biased heritability estimates. In some cases, this problem can be circumvented by fitting sire- or sire-dam models. However, these models are not appropriate in cases where individual records exist on parents. Therefore, the aim of our study was to develop a new Gibbs sampling algorithm for a proper estimation of genetic (co)variance components within an animal threshold model framework. Methods In the proposed algorithm, individuals are classified as either "informative" or "non-informative" with respect to genetic (co)variance components. The "non-informative" individuals are characterized by their Mendelian sampling deviations (deviance from the mid-parent mean) being completely confounded with a single residual on the underlying liability scale. For threshold models, residual variance on the underlying scale is not identifiable. Hence, variance of fully confounded Mendelian sampling deviations cannot be identified either, but can be inferred from the between-family variation. In the new algorithm, breeding values are sampled as in a standard animal model using the full relationship matrix, but genetic (co)variance components are inferred from the sampled breeding values and relationships between "informative" individuals (usually parents) only. The latter is analogous to a sire-dam model (in cases with no individual records on the parents). Results When applied to simulated data sets, the standard animal threshold model failed to produce useful results since samples of genetic variance always drifted towards infinity, while the new algorithm produced proper parameter estimates essentially identical to the results from a sire-dam model (given the fact that no individual records exist for the parents). Furthermore, the new algorithm showed much faster Markov chain mixing properties for genetic parameters (similar to the sire-dam model). Conclusions The new algorithm to estimate genetic parameters via Gibbs sampling solves the bias problems typically occurring in animal threshold model analysis of binary traits with one observation per animal. Furthermore, the method considerably speeds up mixing properties of the Gibbs sampler with respect to genetic parameters, which would be an advantage of any linear or non-linear animal model.

Abstract Background Detecting a QTL is only the first step in genetic improvement programs. When a QTL with desirable characteristics is found, e.g. in a wild or unimproved population, it may be interesting to introgress the detected QTL into the commercial population. One approach to shorten the time needed for introgression is to combine both QTL identification and introgression, into a single step. This combines the strengths of fine mapping and backcrossing and paves the way for introgression of desirable but unknown QTL into recipient animal and plant lines. Methods The method consisting in combining QTL mapping and gene introgression has been extended from inbred to outbred populations in which QTL allele frequencies vary both in recipient and donor lines in different scenarios and for which polygenic effects are included in order to model background genes. The effectiveness of the combined QTL detection and introgression procedure was evaluated by simulation through four backcross generations. Results The allele substitution effect is underestimated when the favourable QTL allele is not fixed in the donor line. This underestimation is proportional to the frequency differences of the favourable QTL allele between the lines. In most scenarios, the estimates of the QTL location are unbiased and accurate. The retained donor chromosome segment and linkage drag are similar to expected values from other published studies. Conclusions In general, our results show that it is possible to combine QTL detection and introgression even in outbred species. Separating QTL mapping and introgression processes is often thought to be longer and more costly. However, using a combined process saves at least one generation. With respect to the linkage drag and obligatory drag, the results of the combined detection and introgression scheme are very similar to those of traditional introgression schemes.

Abstract Background When estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias. Methods Genomic selection using the Bayesian method, 'BayesB' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations. Results Accuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density. Conclusions Including a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.

Abstract Background Selection schemes aiming at introgressing genetic material from a donor into a recipient line may be performed by backcross-breeding programs combined with selection to preserve the favourable characteristics of the donor population. This stochastic simulation study investigated whether genomic selection can be effective in preserving a major quantitative trait locus (QTL) allele from a donor line during the backcrossing phase. Methods In a simulation study, two fish populations were generated: a recipient line selected for a production trait and a donor line characterized by an enhanced level of disease resistance. Both traits were polygenic, but one major QTL affecting disease resistance was segregating only within the donor line. Backcrossing was combined with three types of selection (for total merit index) among the crossbred individuals: classical selection, genomic selection using genome-wide dense marker maps, and gene-assisted genomic selection. It was assumed that production could be observed directly on the selection candidates, while disease resistance had to be inferred from tested sibs of the selection candidates. Results Classical selection was inefficient in preserving the target QTL through the backcrossing phase. In contrast, genomic selection (without specific knowledge of the target QTL) was usually effective in preserving the target QTL, and had higher genetic response to selection, especially for disease resistance. Compared with pure genomic selection, gene-assisted selection had an advantage with respect to disease resistance (28–40% increase in genetic gain) and acted as an extra precaution against loss of the target QTL. However, for total merit index the advantage of gene-assisted genomic selection over genomic selection was lower (4–5% increase in genetic gain). Conclusion Substantial differences between introgression programs using classical and genomic selection were observed, and the former was generally inferior with respect to both genetic gain and the ability to preserve the target QTL. Combining genomic selection with gene-assisted selection for the target QTL acted as an extra precaution against loss of the target QTL and gave additional genetic gain for disease resistance. However, the effect on total merit index was limited.

Abstract Background Genomic selection is a selection method where effects of dense genetic markers are first estimated in a test population and later used to predict breeding values of selection candidates. The aim of this paper was to investigate genetic gains, inbreeding and the accuracy of selection in a general genomic selection scheme for aquaculture, where the test population consists of sibs of the candidates. Methods The selection scheme started after simulating 4000 generations in a Fisher-Wright population with a size of 1000 to create a founder population. The basic scheme had 3000 selection candidates, 3000 tested sibs of the candidates, 100 full-sib families, a trait heritability of 0.4 and a marker density of 0.5Ne/M. Variants of this scheme were also analysed. Results The accuracy of selection in generation 5 was 0.823 for the basic scheme when the sib-testing was performed every generation. The accuracy was hardly reduced by selection, probably because the increased frequency of favourable alleles compensated for the Bulmer effect. When sib-testing was performed only in the first generation, in order to reduce costs, accuracy of selection in generation 5 dropped to 0.304, the main reduction occurring in the first generation. The genetic level in generation 5 was 6.35σa when sib-testing was performed every generation, which was 72%, 12% and 9% higher than when sib-testing was performed only in the first generation, only in the first three generations or every second generation, respectively. A marker density above 0.5Ne/M hardly increased accuracy of selection further. For the basic scheme, rates of inbreeding were reduced by 81% in these schemes compared to traditional selection schemes, due to within-family selection. Increasing the number of sibs to 6000 hardly affected the accuracy of selection, and increasing the number of candidates to 6000 increased genetic gain by 10%, mainly because of increased selection intensity. Conclusion Various strategies were evaluated to reduce the amount of sib-testing and genotyping, but all resulted in loss of selection accuracy and thus of genetic gain. Rates of inbreeding were reduced by 81% in genomic selection schemes compared to traditional selection schemes for the parameters of the basic scheme, due to within-family selection.

Abstract Background Recent developments in SNP discovery and high throughput genotyping technology have made the use of high-density SNP markers to predict breeding values feasible. This involves estimation of the SNP effects in a training data set, and use of these estimates to evaluate the breeding values of other 'evaluation' individuals. Simulation studies have shown that these predictions of breeding values can be accurate, when training and evaluation individuals are (closely) related. However, many general applications of genomic selection require the prediction of breeding values of 'unrelated' individuals, i.e. individuals from the same population, but not particularly closely related to the training individuals. Methods Accuracy of selection was investigated by computer simulation of small populations. Using scaling arguments, the results were extended to different populations, training data sets and genome sizes, and different trait heritabilities. Results Prediction of breeding values of unrelated individuals required a substantially higher marker density and number of training records than when prediction individuals were offspring of training individuals. However, when the number of records was 2*Ne*L and the number of markers was 10*Ne*L, the breeding values of unrelated individuals could be predicted with accuracies of 0.88 – 0.93, where Ne is the effective population size and L the genome size in Morgan. Reducing this requirement to 1*Ne*L individuals, reduced prediction accuracies to 0.73–0.83. Conclusion For livestock populations, 1NeL requires about ~30,000 training records, but this may be reduced if training and evaluation animals are related. A prediction equation is presented, that predicts accuracy when training and evaluation individuals are related. For humans, 1NeL requires ~350,000 individuals, which means that human disease risk prediction is possible only for diseases that are determined by a limited number of genes. Otherwise, genotyping and phenotypic recording need to become very common in the future.

Abstract Partial least square regression (PLSR) and principal component regression (PCR) are methods designed for situations where the number of predictors is larger than the number of records. The aim was to compare the accuracy of genome-wide breeding values (EBV) produced using PLSR and PCR with a Bayesian method, 'BayesB'. Marker densities of 1, 2, 4 and 8 Ne markers/Morgan were evaluated when the effective population size (Ne) was 100. The correlation between true breeding value and estimated breeding value increased with density from 0.611 to 0.681 and 0.604 to 0.658 using PLSR and PCR respectively, with an overall advantage to PLSR of 0.016 (s.e = 0.008). Both methods gave a lower accuracy compared to the 'BayesB', for which accuracy increased from 0.690 to 0.860. PLSR and PCR appeared less responsive to increased marker density with the advantage of 'BayesB' increasing by 17% from a marker density of 1 to 8Ne/M. PCR and PLSR showed greater bias than 'BayesB' in predicting breeding values at all densities. Although, the PLSR and PCR were computationally faster and simpler, these advantages do not outweigh the reduction in accuracy, and there is a benefit in obtaining relevant prior information from the distribution of gene effects.