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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.

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 [Formula: see text] and no effect with probability (1 - [Formula: see text]). 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.

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. [Formula: see text] and a matrix based on linkage disequilibrium (LD), i.e. [Formula: see text], using genomic and phenotypic data collected on 5416 broiler chickens. Furthermore, the effects of regressing the coefficients of [Formula: see text] back to A (LDA) and to [Formula: see text] (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 [Formula: see text]. For the analysed dataset, the best results were obtained when [Formula: see text] was combined with relationships in A or [Formula: see text], 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.

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.

Background: Multi-marker methods, which fit all markers simultaneously, were originally tailored for genomic selection purposes, but have proven to be useful also in association analyses, especially the so-called BayesC Bayesian methods. In a recent study, BayesD extended BayesC towards accounting for dominance effects and improved prediction accuracy and persistence in genomic selection. The current study investigated the power and precision of BayesC and BayesD in genome-wide association studies by means of stochastic simulations and applied these methods to a dairy cattle dataset., Methods: The simulation protocol was designed to mimic the genetic architecture of quantitative traits as realistically as possible. Special emphasis was put on the joint distribution of the additive and dominance effects of causative mutations. Additive marker effects were estimated by BayesC and additive and dominance effects by BayesD. The dependencies between additive and dominance effects were modelled in BayesD by choosing appropriate priors. A sliding-window approach was used. For each window, the R. Fernando window posterior probability of association was calculated and this was used for inference purpose. The power to map segregating causal effects and the mapping precision were assessed for various marker densities up to full sequence information and various window sizes., Results: Power to map a QTL increased with higher marker densities and larger window sizes. This held true for both methods. Method BayesD had improved power compared to BayesC. The increase in power was between -2 and 8% for causative genes that explained more than 2.5% of the genetic variance. In addition, inspection of the estimates of genomic window dominance variance allowed for inference about the magnitude of dominance at significant associations, which remains hidden in BayesC analysis. Mapping precision was not substantially improved by BayesD., Conclusions: BayesD improved power, but precision only slightly. Application of BayesD needs large datasets with genotypes and own performance records as phenotypes. Given the current efforts to establish cow reference populations in dairy cattle genomic selection schemes, such datasets are expected to be soon available, which will enable the application of BayesD for association mapping and genomic prediction purposes.

Background: Rare breeds represent a valuable resource for future market demands. These populations are usually well-adapted, but their low census compromises the genetic diversity and future of these breeds. Since improvement of a breed for commercial traits may also confer higher probabilities of survival for the breed, it is important to achieve good responses to artificial selection. Therefore, efficient genetic management of these populations is essential to ensure that they respond adequately to genetic selection in possible future artificial selection scenarios. Scenarios that maximize the maximum genetic variance in a unique population could be a valuable option. The aim of this work was to study the effect of the maximization of genetic variance to increase selection response and improve the capacity of a population to adapt to a new environment/production system., Results: We simulated a random scenario (A), a full-sib scenario (B), a scenario applying the maximum variance total (MVT) method (C), a MVT scenario with a restriction on increases in average inbreeding (D), a MVT scenario with a restriction on average individual increases in inbreeding (E), and a minimum coancestry scenario (F). Twenty replicates of each scenario were simulated for 100 generations, followed by 10 generations of selection. Effective population size was used to monitor the outcomes of these scenarios. Although the best response to selection was achieved in scenarios B and C, they were discarded because they are unpractical. Scenario A was also discarded because of its low response to selection. Scenario D yielded less response to selection and a smaller effective population size than scenario E, for which response to selection was higher during early generations because of the moderately structured population. In scenario F, response to selection was slightly higher than in Scenario E in the last generations., Conclusions: Application of MVT with a restriction on individual increases in inbreeding resulted in the largest response to selection during early generations, but if inbreeding depression is a concern, a minimum coancestry scenario is then a valuable alternative, in particular for a long-term response to selection.

Background: The management of genetic variation in a breeding scheme relies very much on the control of the average relationship between selected parents. Optimum contribution selection is a method that seeks the optimum way to select for genetic improvement while controlling the rate of inbreeding., Methods: A novel iterative algorithm, Gencont2, for calculating optimum genetic contributions was developed. It was validated by comparing it with a previous program, Gencont, on three datasets that were obtained from practical breeding programs in three species (cattle, pig and sheep). The number of selection candidates was 2929, 3907 and 6875 for the pig, cattle and sheep datasets, respectively., Results: In most cases, both algorithms selected the same candidates and led to very similar results with respect to genetic gain for the cattle and pig datasets. In cases, where the number of animals to select varied, the contributions of the additional selected candidates ranged from 0.006 to 0.08 %. The correlations between assigned contributions were very close to 1 in all cases; however, the iterative algorithm decreased the computation time considerably by 90 to 93 % (13 to 22 times faster) compared to Gencont. For the sheep dataset, only results from the iterative algorithm are reported because Gencont could not handle a large number of selection candidates., Conclusions: Thus, the new iterative algorithm provides an interesting alternative for the practical implementation of optimal contribution selection on a large scale in order to manage inbreeding and increase the sustainability of animal breeding programs.

Background: Currently, genomic prediction in cattle is largely based on panels of about 54k single nucleotide polymorphisms (SNPs). However with the decreasing costs of and current advances in next-generation sequencing technologies, whole-genome sequence (WGS) data on large numbers of individuals is within reach. Availability of such data provides new opportunities for genomic selection, which need to be explored., Methods: This simulation study investigated how much predictive ability is gained by using WGS data under scenarios with QTL (quantitative trait loci) densities ranging from 45 to 132 QTL/Morgan and heritabilities ranging from 0.07 to 0.30, compared to different SNP densities, with emphasis on divergent dairy cattle breeds with small populations. The relative performances of best linear unbiased prediction (SNP-BLUP) and of a variable selection method with a mixture of two normal distributions (MixP) were also evaluated. Genomic predictions were based on within-population, across-population, and multi-breed reference populations., Results: The use of WGS data for within-population predictions resulted in small to large increases in accuracy for low to moderately heritable traits. Depending on heritability of the trait, and on SNP and QTL densities, accuracy increased by up to 31 %. The advantage of WGS data was more pronounced (7 to 92 % increase in accuracy depending on trait heritability, SNP and QTL densities, and time of divergence between populations) with a combined reference population and when using MixP. While MixP outperformed SNP-BLUP at 45 QTL/Morgan, SNP-BLUP was as good as MixP when QTL density increased to 132 QTL/Morgan., Conclusions: Our results show that, genomic predictions in numerically small cattle populations would benefit from a combination of WGS data, a multi-breed reference population, and a variable selection method.

Background: In dairy cattle, current genomic predictions are largely based on sire models that analyze daughter yield deviations of bulls, which are derived from pedigree-based animal model evaluations (in a two-step approach). Extension to animal model genomic predictions (AMGP) is not straightforward, because most of the animals that are involved in the genetic evaluation are not genotyped. In single-step genomic best linear unbiased prediction (SSGBLUP), the pedigree-based relationship matrix A and the genomic relationship matrix G are combined in a matrix H, which allows for AMGP. However, as the number of genotyped animals increases, imputation of the genotypes for all animals in the pedigree may be considered. Our aim was to impute genotypes for all animals in the pedigree, construct alternative relationship matrices based on the imputation results, and evaluate the accuracy of the resulting AMGP by cross-validation in the national Norwegian Red dairy cattle population., Results: A large-scale national dataset was effectively handled by splitting it into two sets: (1) genotyped animals and their ancestors (i.e. GA set with 20,918 animals) and (2) the descendants of the genotyped animals (i.e. D set with 4,022,179 animals). This allowed restricting genomic computations to a relatively small set of animals (GA set), whereas the majority of the animals (D set) were added to the animal model equations using Henderson's rules, in order to make optimal use of the D set information. Genotypes were imputed by segregation analysis of a large pedigree with relatively few genotyped animals (3285 out of 20,918). Among the AMGP models, the linkage and linkage disequilibrium based G matrix (G LDLA0 ) yielded the highest accuracy, which on average was 0.06 higher than with SSGBLUP and 0.07 higher than with two-step sire genomic evaluations., Conclusions: AMGP methods based on genotype imputation on a national scale were developed, and the most accurate method, GLDLA0BLUP, combined linkage and linkage disequilibrium information. The advantage of AMGP over a sire model based on two-step genomic predictions is expected to increase as the number of genotyped cows increases and for species, with smaller sire families and more dam relationships.

Background: The short-term impact of using different genomic prediction (GP) models in genomic selection has been intensively studied, but their long-term impact is poorly understood. Furthermore, long-term genetic gain of genomic selection is expected to improve by using Jannink's weighting (JW) method, in which rare favourable marker alleles are upweighted in the selection criterion. In this paper, we extend the JW method by including an additional parameter to decrease the emphasis on rare favourable alleles over the time horizon, with the purpose of further improving the long-term genetic gain. We call this new method dynamic weighting (DW). The paper explores the long-term impact of different GP models with or without weighting methods., Methods: Different selection criteria were tested by simulating a population of 500 animals with truncation selection of five males and 50 females. Selection criteria included unweighted and weighted genomic estimated breeding values using the JW or DW methods, for which ridge regression (RR) and Bayesian lasso (BL) were used to estimate marker effects. The impacts of these selection criteria were compared under three genetic architectures, i.e. varying numbers of QTL for the trait and for two time horizons of 15 (TH15) or 40 (TH40) generations., Results: For unweighted GP, BL resulted in up to 21.4% higher long-term genetic gain and 23.5% lower rate of inbreeding under TH40 than RR. For weighted GP, DW resulted in 1.3 to 5.5% higher long-term gain compared to unweighted GP. JW, however, showed a 6.8% lower long-term genetic gain relative to unweighted GP when BL was used to estimate the marker effects. Under TH40, both DW and JW obtained significantly higher genetic gain than unweighted GP. With DW, the long-term genetic gain was increased by up to 30.8% relative to unweighted GP, and also increased by 8% relative to JW, although at the expense of a lower short-term gain., Conclusions: Irrespective of the number of QTL simulated, BL is superior to RR in maintaining genetic variance and therefore results in higher long-term genetic gain. Moreover, DW is a promising method with which high long-term genetic gain can be expected within a fixed time frame.

Background: GBLUP (genomic best linear unbiased prediction) uses high-density single nucleotide polymorphism (SNP) markers to construct genomic identity-by-state (IBS) relationship matrices. However, identity-by-descent (IBD) relationships can be accurately calculated for extremely sparse markers. Here, we compare the accuracy of prediction of genome-wide breeding values (GW-BV) for a sib-evaluated trait in a typical aquaculture population, assuming either IBS or IBD genomic relationship matrices, and by varying marker density and size of the training dataset., Methods: A simulation study was performed, assuming a population with strong family structure over three subsequent generations. Traditional and genomic BLUP were used to estimate breeding values, the latter using either IBS or IBD genomic relationship matrices, with marker densities ranging from 10 to ~1200 SNPs/Morgan (M). Heritability ranged from 0.1 to 0.8, and phenotypes were recorded on 25 to 45 sibs per full-sib family (50 full-sib families). Models were compared based on their predictive ability (accuracy) with respect to true breeding values of unphenotyped (albeit genotyped) sibs in the last generation., Results: As expected, genomic prediction had greater accuracy compared to pedigree-based prediction. At the highest marker density, genomic prediction based on IBS information (IBS-GS) was slightly superior to that based on IBD information (IBD-GS), while at lower densities (≤100 SNPs/M), IBD-GS was more accurate. At the lowest densities (10 to 20 SNPs/M), IBS-GS was even outperformed by the pedigree-based model. Accuracy of IBD-GS was stable across marker densities performing well even down to 10 SNPs/M (2.5 to 6.1% reduction in accuracy compared to ~1200 SNPs/M). Loss of accuracy due to reduction in the size of training datasets was moderate and similar for both genomic prediction models. The relative superiority of (high-density) IBS-GS over IBD-GS was more pronounced for traits with a low heritability., Conclusions: Using dense markers, GBLUP based on either IBD or IBS relationship matrices proved to perform better than a pedigree-based model. However, accuracy of IBS-GS declined rapidly with decreasing marker densities, and was even outperformed by a traditional pedigree-based model at the lowest densities. In contrast, the accuracy of IBD-GS was very stable across marker densities.

As extinction of local domestic breeds and of isolated subpopulations of wild species continues, and the resources available for conservation programs are limited, prioritizing subpopulations for conservation is of high importance to halt the erosion of genetic diversity observed in endangered species. Current approaches usually only take neutral genetic diversity into account. However, adaptation of subpopulations to different environments also contributes to the diversity found in the species. This paper introduces two notions of adaptive variation. The adaptive diversity in a trait is the excess of variance found in genotypic values relative to the variance that would have been expected in the absence of selection. The adaptivity coverage of a set of subpopulations quantifies how well the subpopulations could adapt to a large range of environments within a limited time span. Additionally, genome-based notions of neutral diversities were obtained that correspond to well known pedigree-based definitions. The values of subpopulations for conservation of adaptivity coverage were compared with their conservation values for adaptive diversity and neutral diversities using simulated data. Conservation values for adaptive diversity and neutral diversities were only slightly correlated, but the values for conservation of adaptivity coverage showed a reasonable correlation with both kinds if the time span was chosen appropriately. Hence, maintaining adaptivity coverage is a promising approach to prioritize subpopulations for conservation decisions.

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.

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.

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.

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.

The combination of a sire model and a random regression term describing genotype by environment interactions may lead to biased estimates of genetic variance components because of heterogeneous residual variance. In order to test different models, simulated data with genotype by environment interactions, and dairy cattle data assumed to contain such interactions, were analyzed. Two animal models were compared to four sire models. Models differed in their ability to handle heterogeneous variance from different sources. Including an individual effect with a (co)variance matrix restricted to three times the sire (co)variance matrix permitted the modeling of the additive genetic variance not covered by the sire effect. This made the ability of sire models to handle heterogeneous genetic variance approximately equivalent to that of animal models. When residual variance was heterogeneous, a different approach to account for the heterogeneity of variance was needed, for example when using dairy cattle data in order to prevent overestimation of genetic heterogeneity of variance. Including environmental classes can be used to account for heterogeneous residual variance.

Genomic selection uses genome-wide dense SNP marker genotyping for the prediction of genetic values, and consists of two steps: (1) estimation of SNP effects, and (2) prediction of genetic value based on SNP genotypes and estimates of their effects. For the former step, BayesB type of estimators have been proposed, which assume a priori that many markers have no effects, and some have an effect coming from a gamma or exponential distribution, i.e. a fat-tailed distribution. Whilst such estimators have been developed using Monte Carlo Markov chain (MCMC), here we derive a much faster non-MCMC based estimator by analytically performing the required integrations. The accuracy of the genome-wide breeding value estimates was 0.011 (s.e. 0.005) lower than that of the MCMC based BayesB predictor, which may be because the integrations were performed one-by-one instead of for all SNPs simultaneously. The bias of the new method was opposite to that of the MCMC based BayesB, in that the new method underestimates the breeding values of the best selection candidates, whereas MCMC-BayesB overestimated their breeding values. The new method was computationally several orders of magnitude faster than MCMC based BayesB, which will mainly be advantageous in computer simulations of entire breeding schemes, in cross-validation testing, and practical schemes with frequent re-estimation of breeding values.

A novel multipoint method, based on an approximate coalescence approach, to analyze multiple linked markers is presented. Unlike other approximate coalescence methods, it considers all markers simultaneously but only two haplotypes at a time. We demonstrate the use of this method for linkage disequilibrium (LD) mapping of QTL and estimation of effective population size. The method estimates identity-by-descent (IBD) probabilities between pairs of marker haplotypes. Both LD and combined linkage and LD mapping rely on such IBD probabilities. The method is approximate in that it considers only the information on a pair of haplotypes, whereas a full modeling of the coalescence process would simultaneously consider all haplotypes. However, full coalescence modeling is computationally feasible only for few linked markers. Using simulations of the coalescence process, the method is shown to give almost unbiased estimates of the effective population size. Compared to direct marker and haplotype association analyses, IBD-based QTL mapping showed clearly a higher power to detect a QTL and a more realistic confidence interval for its position. The modeling of LD could be extended to estimate other LD-related parameters such as recombination rates.

Background: Genetic variation explains a considerable part of observed phenotypic variation in gene expression networks. This variation has been shown to be located both locally (cis) and distally (trans) to the genes being measured. Here we explore to which degree the phenotypic manifestation of local and distant polymorphisms is a dynamic feature of regulatory design., Results: By combining mathematical models of gene expression networks with genetic maps and linkage analysis we find that very different network structures and regulatory motifs give similar cis/trans linkage patterns. However, when the shape of the cis-regulatory input functions is more nonlinear or threshold-like, we observe for all networks a dramatic increase in the phenotypic expression of distant compared to local polymorphisms under otherwise equal conditions., Conclusion: Our findings indicate that genetic variation affecting the form of cis-regulatory input functions may reshape the genotype-phenotype map by changing the relative importance of cis and trans variation. Our approach combining nonlinear dynamic models with statistical genetics opens up for a systematic investigation of how functional genetic variation is translated into phenotypic variation under various systemic conditions.

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.

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.