Simulation of dual-purpose chicken breeding programs implementing gene editing.

BACKGROUND: In spite of being controversial and raising ethical concerns, the application of gene editing is more likely to be accepted when it contributes to improving animal welfare. One of the animal welfare and ethical issues in chicken breeding is chick culling, the killing of the male layer chicks after hatching due to the poor fattening performance. Although establishing dual-purpose chicken lines could solve this problem, unfavorable genetic correlations between egg and meat production traits hindered their competitiveness. Although it is also controversial in ethical terms, gene editing may accelerate genetic progress in dual-purpose chicken and alleviate the ethical concerns from chick culling. RESULTS: The simulation compared the utility improvement in dual-purpose use under two breeding schemes: one consisting in the improvement of the laying hens, and the second in the improvement of a synthetic line obtained from a layer broiler cross. In each breeding scheme, the breeding programs were simulated with and without gene editing. Polygenic breeding values and 500 simulated quantitative trait loci (QTL) with different levels of pleiotropy caused negative correlations between egg production, meat production, and overall health. The results of the simulation demonstrated that genetic gain could be accelerated by at most 81% for several generations if gene editing was used. The actual increase in genetic gain depended on the number of single nucleotide polymorphisms (SNPs) being edited per animal. The rate of genetic improvement became equal in scenarios with and without gene editing after 20 generations. This is because the remaining segregating QTL had small effects and their edition would have negative overall health effects from potential off-target edits. Although gene editing can improve genetic gain in quantitative traits, it can only be recommended as long as QTL with reasonable effect sizes are segregating and detectable. CONCLUSIONS: This simulation demonstrates the potential of gene editing to accelerate the simultaneous improvement of negatively correlated traits. When the risk of negative consequences from gene editing persists, the number of SNPs to be edited should be chosen carefully to obtain the optimal genetic gain.

Economic benefits of herd genotyping and using sexed semen for pure and beef-on-dairy breeding in dairy herds.

The cost benefits of herd genotyping and the benefits of using sexed semen have been affected by recent improvements in sexing technologies, incorporation of direct health traits in the German total merit index for Holstein cattle, deteriorating prices for purebred heifer calves and bull calves, and introduction of herd genotyping programs. Inseminating genetically superior dams with female-sexed Holstein semen increases the mean breeding value of heifer calves and can produce more Holstein heifer calves than are needed for replacement. This provides an opportunity to increase the selection response in health and production traits at the farm level. A deterministic model is introduced that predicts the increase or decrease in net profit when a farmer takes part in a herd genotyping program and follows a certain insemination strategy. The types of semen allocated to cows and heifers may be sexed or unsexed and Holstein or beef breed. Genetically superior heifers and cows are inseminated with female-sexed Holstein semen, intermediate dams with unsexed Holstein semen, and genetically inferior dams with unsexed or male-sexed beef breed semen. In general, participating in a herd genotyping program is beneficial for German Holstein breeders. The optimum proportions of cows and heifers that should be inseminated with a certain type of semen are sensitive to farm-specific peculiarities. A small price difference between crossbred bull calves and crossbred heifer calves often makes the use of male-sexed beef breed semen uneconomic. Under the conditions considered, it was found to be advantageous to inseminate approximately 50% of heifers and 10% of cows with the highest genetic merit with female-sexed Holstein semen. The optimum proportion of cows that should be inseminated with unsexed beef breed semen was found to be approximately 40%. In a herd with a low replacement rate, the selected heifers can exhibit their genetic superiority over a longer period of time, and a larger proportion of cows can be inseminated with beef breed semen. Participation in a herd genotyping program is, therefore, particularly beneficial for herds with low replacement rates.

Selection index theory for populations under directional and stabilizing selection.

BACKGROUND: The purpose of a selection index is that its use to select animals for breeding maximizes the profit of a breed in future generations. The profit of a breed is in general a quantity that predicts the satisfaction of future owners with their breed, and the satisfaction of the consumers with the products that are produced by the breed. Many traits, such as conformation traits and product quality traits have intermediate optima. Traditional selection index theory applies only to directional selection and cannot achieve any further improvement once the trait means have reached their optima. A well-founded theory is needed that extends the established selection index theory to cover directional as well as stabilizing selection as limiting cases, and that can be applied to maximize the profit of a breed in both situations. RESULTS: The optimum selection index shifts the trait means towards the optima and, in the case of stabilizing selection, decreases the phenotypic variance, which causes the phenotypes to be closer to the optimum. The optimum index depends not only on the breeding values, but also on the squared breeding values, the allele contents of major quantitative trait loci (QTL), the QTL heterozygosities, the inbreeding coefficient of the animal, and the kinship of the animal with the population. CONCLUSION: The optimum selection index drives the alleles of major QTL to fixation when the trait mean approaches the optimum because decreasing the phenotypic variance shifts the trait values closer to the optimum, which increases the profit of the breed. The index weight on the kinship coefficient balances the increased genetic gain that can be achieved in future generations by outcrossing, and the increased genetic gain that can be achieved under stabilizing selection by reducing the phenotypic variance. In a model with dominance variance, it can also account for the effect of inbreeding depression. The combining ability between potential mating partners, which predicts the total merit of their offspring, could become an important parameter for mate allocation that could be used to further shift the phenotypes towards their optimum values.

Defining valid breeding goals for animal breeds.

BACKGROUND: The objective of any valid breeding program is to increase the suitability of a breed for its future purposes. The approach most often followed in animal breeding for optimizing breeding goals assumes that the sole desire of the owners is profit maximization. As this assumption is often violated, a generalized approach is needed that does not rely on this assumption. RESULTS: The generalized approach is based on the niche concept. The niche of a breed is a set of environments in which a small population of the breed would have a positive population growth rate. Its growth rate depends on demand from prospective consumers and supply from producers. The approach involves defining the niche that is envisaged for the breed and identifying the trait optima that maximize the breed's adaptation to its envisaged niche within the set of permissible breeding goals. The set of permissible breeding goals is the set of all potential breeding goals that are compatible with animal welfare and could be reached within the planning horizon of the breeding program. In general, the breed's adaptation depends on the satisfaction of the producers with the animals and on the satisfaction of the consumers with the products produced by the animals. When consumers buy live animals, then the breed needs to adapt to both the environments provided by the producers, and the environments provided by the consumers. The profit function is replaced by a more general adaptedness function that measures the breed's adaptation to its envisaged niche. CONCLUSIONS: The proposed approach coincides with the traditional approach if the producers have the sole desire to maximize their income, and if consumer preferences are well reflected by the product prices. If these assumptions are not met, then the traditional approach to breeding goal optimization is unlikely to result in a valid breeding goal. Using the example of companion breeds, this paper shows that the proposed approach has the potential to fill the gap.

Genomic rotational crossbreeding with advanced optimum contribution selection methods applied to simulated German Angler and German Holstein dairy cattle populations.

Many local dairy cattle breeds are facing genetic extinction due to a large proportion of foreign genes, which have been introgressed in the past. In addition, the performance gap to popular high-yielding breeds is increasing, resulting in a risk of numeric extinction. In the present simulation study, a genomic rotational crossbreeding scheme with the high-yielding German Holstein breed and the numerically small German Angler breed was analysed with the aim to utilize heterosis effects in the crossbred animals. Simultaneously inbreeding was controlled, and the amount of Holstein introgression observed in the Angler breed was reduced. Different scenarios of implementing OCS methods for Angler individuals were evaluated, which differed in their restrictions regarding kinship, native kinship, as well as the amount of genetic contributions from German Holstein. The results showed that rotational crossbreeding can result in superior crossbred offspring compared to the purebred parental lines, whereby OCS methods can simultaneously restrict the increase in inbreeding and keep the Holstein contributions at their current level. However, reducing the amount of migrant contributions while restricting the increase in the native kinship in Angler turned out to be a costly restriction. The reason was that Angler with low genetic contributions from Holsteins tended to have similar Angler ancestors. Consequently, reducing Holstein contributions would considerably increase the native kinship in Angler if it were not constrained. The constraint on the native kinship made a constraint on the conventional kinship superfluous and caused it to increase at a much lower rate than envisaged. This led to both, a high genetic diversity and a low genetic gain. The high genetic diversity in Angler also resulted in lower and oscillating heterosis effects in the crossbred animals. Thus, the reduction of migrant contribution did not increase heterosis effects in the crossbred offspring, and did not result in superior crossbred offspring in general.

Genomic dominance variance analysis of health and milk production traits in German Holstein cattle.

Genomic analyses commonly explore the additive genetic variance of traits. The non-additive variance, however, is usually small but often significant in dairy cattle. This study aimed at dissecting the genetic variance of eight health traits that recently entered the total merit index in Germany and the somatic cell score (SCS), as well as four milk production traits by analysing additive and dominance variance components. The heritabilities were low for all health traits (between 0.033 for mastitis and 0.099 for SCS), and moderate for the milk production traits (between 0.261 for milk energy yield and 0.351 for milk yield). For all traits, the contribution of dominance variance to the phenotypic variance was low, varying between 0.018 for ovarian cysts and 0.078 for milk yield. Inbreeding depression, inferred from the SNP-based observed homozygosity, was significant only for the milk production traits. The contribution of dominance variance to the genetic variance was larger for the health traits, ranging from 0.233 for ovarian cysts to 0.551 for mastitis, encouraging further studies that aim at discovering QTLs based on their additive and dominance effects.

Selecting the hologenome to breed for an improved feed efficiency in pigs-A novel selection index.

Most traits in animal breeding, including feed efficiency traits in pigs, are affected by many genes with small effect and have a moderately high heritability between 0.1 and 0.5, which enables efficient selection. Since the microbiota composition in the gastrointestinal tract is also partly heritable and was shown to have a substantial effect on feed efficiency, the host genes affect the phenotype not only directly by altering metabolic pathways, but also indirectly by changing the microbiota composition. The effect m i of the microbiota composition on the breeding value g i of an animal i is the conditional expectation of its breeding value, given the vector φ i with microbiota frequencies, that is m i = E g i | φ i . The breeding value g i of an animal can therefore be decomposed into a heritable contribution m i that arises from an altered microbiota composition and a heritable contribution p i that arises from altered metabolic pathways within the animal, so g i = m i + p i . Instead of selecting for breeding value g ^ i , an index comprising the two components m ^ i and p ^ i with appropriate weights, that is I i = λ 1 m ^ i + λ 2 p ^ i , can be used. The present study shows how this breeding strategy can be applied in pig genomic selection breeding scheme for two feed efficiency traits and daily gain.

Optimum contribution selection for animal breeding and conservation: the R package optiSel.

BACKGROUND: Selecting animals for breeding in the optimum way plays an essential role for the management of genetic resources and in selective breeding of livestock species. It requires to compute the optimum genetic contribution of each selection candidate to the next generation. Current software packages for optimum contribution selection (OCS) are not able to handle the main conflicting objectives of animal breeding programs simultaneously, which includes to increase genetic gain, to increase or to maintain genetic diversity, to recover the original genetic background of endangered breeds with historic introgression, and to maintain or increase genetic diversity at native alleles. RESULTS: The free R package optiSel offers functions for estimating the above mentioned parameters from pedigree and marker data, and for solving OCS problems. One parameter can be optimized, whereas the remaining ones can be constrained. The results reveal the optimum numbers of offspring of all selection candidates, and can subsequently be used for mate allocation. Different solvers can be used. Solver slsqp was superior when the genetic diversity at native alleles was to be maximized, whereas solvers cccp and cccp2 were superior for all other OCS problems. CONCLUSION: Optimum contribution selection applied to local breeds requires special attention due to the conflicting objectives of their breeding programs. The free R package optiSel is an easy-to-use software taking these conflicting objectives into account.

Managing genomes of conserved livestock breeds with historical introgression to decrease genetic overlap with other breeds.

Recovering the native genetic background of a breed and increasing the founder genome equivalent (FGE) that is contributed by a breed to the gene pool of the species can increase its value for conservation. The suitability of several strategies was compared, whereby a hypothetical multi-breed population, the core set, was used to approximate the genetic diversity of the species. Twenty-five generations of management were simulated based on genotypes of German Angler cattle. The scenarios were compared when the kinship reached 0.10. The native contribution (NC) increased in a population with 400 births per generation from 0.317 to 0.706, whereas 1,000 births enabled to reach 0.894. This scenario maximized the NC, constrained the native kinship, and the kinship of the core set so that its genetic diversity could not decrease. It increased the proportions of mainstream breeds because their genes were removed from the target breed. A substantial increase of the FGE was achieved in some other scenarios, which arose from reduced genetic overlap and from increased diversity within the breed. The latter factor is especially important for breeds with high contributions to the core set.

Power and precision of QTL mapping in simulated multiple porcine F2 crosses using whole-genome sequence information.

BACKGROUND: During the last two decades, many QTL (quantitative trait locus) mapping experiments in pigs have been conducted using F2 crosses established from two outbred founder breeds. The founder breeds were frequently chosen from the Asian and European type breeds. A combination of next-generation sequencing, SNP (single nucleotide polymorphism) genotyping technology using SNP-chips, and genotype imputation techniques, can be used to infer the sequence information of all F2 individuals in a cost-effective way. The aim of the present simulation study was to analyze the power and precision of genome-wide association studies (GWASs) with whole-genome sequence data in several types of F2 crosses, including pooled crosses. METHODS: Based on a common historical population, three breeds representing two European type breeds (EU1 and EU2) and one Asian type breed (AS) were simulated. Two F2 designs of 500 individuals each were simulated. The cross EU1xEU2 (ASxEU2) was simulated using the phylogenetically closely related breeds EU1 and EU2 (or distantly related breeds AS and EU2) as the founder breeds. The simulated genomes comprised ten chromosomes, each with a length of 1 Morgan and whole-genome sequence information. A polygenic trait with a heritability of 0.5, which was affected by approximately 20 QTL per Morgan, was simulated. GWASs were conducted using single marker mixed linear models, either within the crosses or in their pooled datasets. Additionally, the studies were conducted in the breed EU2, which was a founder breed in both simulated crosses. RESULTS: The power to map QTL was high (low) in the ASxEU2 (EU1xEU2) cross and was highest when the data of both crosses were analyzed jointly. By contrast, the mapping precision was the highest in the EU1xEU2 cross. Pooling data led to a precision that was in between the precision of the EU1xEU2 cross and the ASxEU2 cross. A higher mapping precision was observed for QTL segregating within a founder breed. CONCLUSIONS: These results suggest that the existing F2 crosses are promising databases for QTL mapping when the founder breeds are closely related or several crosses can be pooled. This conclusion is particularly applicable for QTL that segregate in a founder breed.

Novel optimum contribution selection methods accounting for conflicting objectives in breeding programs for livestock breeds with historical migration.

BACKGROUND: Optimum contribution selection (OCS) is effective for increasing genetic gain, controlling the rate of inbreeding and enables maintenance of genetic diversity. However, this diversity may be caused by high migrant contributions (MC) in the population due to introgression of genetic material from other breeds, which can threaten the conservation of small local populations. Therefore, breeding objectives should not only focus on increasing genetic gains but also on maintaining genetic originality and diversity of native alleles. This study aimed at investigating whether OCS was improved by including MC and modified kinships that account for breed origin of alleles. Three objective functions were considered for minimizing kinship, minimizing MC and maximizing genetic gain in the offspring generation, and we investigated their effects on German Angler and Vorderwald cattle. RESULTS: In most scenarios, the results were similar for Angler and Vorderwald cattle. A significant positive correlation between MC and estimated breeding values of the selection candidates was observed for both breeds, thus traditional OCS would increase MC. Optimization was performed under the condition that the rate of inbreeding did not exceed 1% and at least 30% of the maximum progress was achieved for all other criteria. Although traditional OCS provided the highest breeding values under restriction of classical kinship, the magnitude of MC in the progeny generation was not controlled. When MC were constrained or minimized, the kinship at native alleles increased compared to the reference scenario. Thus, in addition to constraining MC, constraining kinship at native alleles is required to ensure that native genetic diversity is maintained. When kinship at native alleles was constrained, the classical kinship was automatically lowered in most cases and more sires were selected. However, the average breeding value in the next generation was also lower than that obtained with traditional OCS. CONCLUSIONS: For local breeds with historical introgressions, current breeding programs should focus on increasing genetic gain and controlling inbreeding, as well as maintaining the genetic originality of the breeds and the diversity of native alleles via the inclusion of MC and kinship at native alleles in the OCS process.

Application of a Bayesian dominance model improves power in quantitative trait genome-wide association analysis.

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.

Within- and across-breed genomic prediction using whole-genome sequence and single nucleotide polymorphism panels.

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.

Genetic parameters and signatures of selection in two divergent laying hen lines selected for feather pecking behaviour.

BACKGROUND: Feather pecking (FP) in laying hens is a well-known and multi-factorial behaviour with a genetic background. In a selection experiment, two lines were developed for 11 generations for high (HFP) and low (LFP) feather pecking, respectively. Starting with the second generation of selection, there was a constant difference in mean number of FP bouts between both lines. We used the data from this experiment to perform a quantitative genetic analysis and to map selection signatures. METHODS: Pedigree and phenotypic data were available for the last six generations of both lines. Univariate quantitative genetic analyses were conducted using mixed linear and generalized mixed linear models assuming a Poisson distribution. Selection signatures were mapped using 33,228 single nucleotide polymorphisms (SNPs) genotyped on 41 HFP and 34 LFP individuals of generation 11. For each SNP, we estimated Wright's fixation index (FST). We tested the null hypothesis that FST is driven purely by genetic drift against the alternative hypothesis that it is driven by genetic drift and selection. RESULTS: The mixed linear model failed to analyze the LFP data because of the large number of 0s in the observation vector. The Poisson model fitted the data well and revealed a small but continuous genetic trend in both lines. Most of the 17 genome-wide significant SNPs were located on chromosomes 3 and 4. Thirteen clusters with at least two significant SNPs within an interval of 3 Mb maximum were identified. Two clusters were mapped on chromosomes 3, 4, 8 and 19. Of the 17 genome-wide significant SNPs, 12 were located within the identified clusters. This indicates a non-random distribution of significant SNPs and points to the presence of selection sweeps. CONCLUSIONS: Data on FP should be analysed using generalised linear mixed models assuming a Poisson distribution, especially if the number of FP bouts is small and the distribution is heavily peaked at 0. The FST-based approach was suitable to map selection signatures that need to be confirmed by linkage or association mapping.

A unified approach to characterize and conserve adaptive and neutral genetic diversity in subdivided populations.

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.

Genomic selection using low density marker panels with application to a sire line in pigs.

BACKGROUND: Genomic selection has become a standard tool in dairy cattle breeding. However, for other animal species, implementation of this technology is hindered by the high cost of genotyping. One way to reduce the routine costs is to genotype selection candidates with an SNP (single nucleotide polymorphism) panel of reduced density. This strategy is investigated in the present paper. Methods are proposed for the approximation of SNP positions, for selection of SNPs to be included in the low-density panel, for genotype imputation, and for the estimation of the accuracy of genomic breeding values. The imputation method was developed for a situation in which selection candidates are genotyped with an SNP panel of reduced density but have high-density genotyped sires. The dams of selection candidates are not genotyped. The methods were applied to a sire line pig population with 895 German Piétrain boars genotyped with the PorcineSNP60 BeadChip. RESULTS: Genotype imputation error rates were 0.133 for a 384 marker panel, 0.079 for a 768 marker panel, and 0.022 for a 3000 marker panel. Error rates for markers with approximated positions were slightly larger. Availability of high-density genotypes for close relatives of the selection candidates reduced the imputation error rate. The estimated decrease in the accuracy of genomic breeding values due to imputation errors was 3% for the 384 marker panel and negligible for larger panels, provided that at least one parent of the selection candidates was genotyped at high-density.Genomic breeding values predicted from deregressed breeding values with low reliabilities were more strongly correlated with the estimated BLUP breeding values than with the true breeding values. This was not the case when a shortened pedigree was used to predict BLUP breeding values, in which the parents of the individuals genotyped at high-density were considered unknown. CONCLUSIONS: Genomic selection with imputation from very low- to high-density marker panels is a promising strategy for the implementation of genomic selection at acceptable costs. A panel size of 384 markers can be recommended for selection candidates of a pig breeding program if at least one parent is genotyped at high-density, but this appears to be the lower bound.

Bayesian models with dominance effects for genomic evaluation of quantitative traits.

Genomic selection refers to the use of dense, genome-wide markers for the prediction of breeding values (BV) and subsequent selection of breeding individuals. It has become a standard tool in livestock and plant breeding for accelerating genetic gain. The core of genomic selection is the prediction of a large number of marker effects from a limited number of observations. Various Bayesian methods that successfully cope with this challenge are known. Until now, the main research emphasis has been on additive genetic effects. Dominance coefficients of quantitative trait loci (QTLs), however, can also be large, even if dominance variance and inbreeding depression are relatively small. Considering dominance might contribute to the accuracy of genomic selection and serve as a guide for choosing mating pairs with good combining abilities. A general hierarchical Bayesian model for genomic selection that can realistically account for dominance is introduced. Several submodels are proposed and compared with respect to their ability to predict genomic BV, dominance deviations and genotypic values (GV) by stochastic simulation. These submodels differ in the way the dependency between additive and dominance effects is modelled. Depending on the marker panel, the inclusion of dominance effects increased the accuracy of GV by about 17% and the accuracy of genomic BV by 2% in the offspring. Furthermore, it slowed down the decrease of the accuracies in subsequent generations. It was possible to obtain accurate estimates of GV, which enables mate selection programmes.

Optimum contribution selection for conserved populations with historic migration.

BACKGROUND: In recent decades, local varieties of domesticated animal species have been frequently crossed with economically superior breeds which has resulted in considerable genetic contributions from migrants. Optimum contribution selection by maximizing gene diversity while constraining breeding values of the offspring or vice versa could eventually lead to the extinction of local breeds with historic migration because maximization of gene diversity or breeding values would be achieved by maximization of migrant contributions. Therefore, other objective functions are needed for these breeds. RESULTS: Different objective functions and side constraints were compared with respect to their ability to reduce migrant contributions, to increase the genome equivalents originating from native founders, and to conserve gene diversity. Additionally, a new method for monitoring the development of effective size for breeds with incomplete pedigree records was applied. Approaches were compared for Vorderwald cattle, Hinterwald cattle, and Limpurg cattle. Migrant contributions could be substantially decreased for these three breeds, but the potential to increase the native genome equivalents is limited. CONCLUSIONS: The most promising approach was constraining migrant contributions while maximizing the conditional probability that two alleles randomly chosen from the offspring population are not identical by descent, given that both descend from native founders.

Improving the Accuracy of Multi-Breed Prediction in Admixed Populations by Accounting for the Breed Origin of Haplotype Segments.

Numerically small breeds have often been upgraded with mainstream breeds. This historic introgression predisposes the breeds for joint genomic evaluations with mainstream breeds. The linkage disequilibrium structure differs between breeds. The marker effects of a haplotype segment may, therefore, depend on the breed from which the haplotype segment originates. An appropriate method for genomic evaluation would account for this dependency. This study proposes a method for the computation of genomic breeding values for small admixed breeds that incorporate phenotypic and genomic information from large introgressed breeds by considering the breed origin of alleles (BOA) in the evaluation. The proposed BOA model classifies haplotype segments according to their origins and assumes different but correlated SNP effects for the different origins. The BOA model was compared in a simulation study to conventional within-breed genomic best linear unbiased prediction (GBLUP) and conventional multi-breed GBLUP models. The BOA model outperformed within-breed GBLUP as well as multi-breed GBLUP in most cases.

The contribution of dominance to the understanding of quantitative genetic variation.

Knowledge of the genetic architecture of a quantitative trait is useful to adjust methods for the prediction of genomic breeding values and to discover the extent to which common assumptions in quantitative trait locus (QTL) mapping experiments and breeding value estimation are violated. It also affects our ability to predict the long-term response of selection. In this paper, we focus on additive and dominance effects of QTL. We derive formulae that can be used to estimate the number of QTLs that affect a quantitative trait and parameters of the distribution of their additive and dominance effects from variance components, inbreeding depression and results from QTL mapping experiments. It is shown that a lower bound for the number of QTLs depends on the ratio of squared inbreeding depression to dominance variance. That is, high inbreeding depression must be due to a sufficient number of QTLs because otherwise the dominance variance would exceed the true value. Moreover, the second moment of the dominance coefficient depends only on the ratio of dominance variance to additive variance and on the dependency between additive effects and dominance coefficients. This has implications on the relative frequency of overdominant alleles. It is also demonstrated how the expected number of large QTLs determines the shape of the distribution of additive effects. The formulae are applied to milk yield and productive life in Holstein cattle. Possible sources for a potential bias of the results are discussed.