The relation between the genetic architecture of quantitative traits and long-term genetic response

The genetic architecture of a quantitative trait refers to the number of genetic variants, allele frequencies, and effect sizes of variants that affect a trait and their mode of gene action. This study was conducted to investigate the effect of four shapes of allelic frequency distributions (constant, uniform, L-shaped and U-shaped) and different number of trait-affecting loci (50, 100, 200, 500) on allelic frequency changes, long term genetic response, and maintaining genetic variance. To this end, a population of 440 individuals composed of 40 males and 400 females as well as a genome of 200 cM consisting of two chromosomes and with a mutation rate of 2.5?×?10^?5 per locus was simulated. Selection of superior animals was done using best linear unbiased prediction (BLUP) with assumption of infinitesimal model. Selection intensity was constant over 30 generations of selection. The highest genetic progress obtained when the allelic frequency had L-shaped distribution and number of trait-affecting loci was high (500). Although quantitative genetic theories predict the extinction of genetic variance due to artificial selection in long time, our results showed that under L- and U-shapped allelic frequency distributions, the additive genetic variance is persistent after 30 generations of selection. Further, presence or absence of selection limit can be an indication of low (<50) or high (>100) number of trait-affecting loci, respectively. It was concluded that the genetic architecture of complex traits is an important subject which should be considered in studies concerning long-term response to selection.     

Using whole-genome sequence data to predict quantitative trait phenotypes in Drosophila melanogaster

Predicting organismal phenotypes from genotype data is important for plant and animal breeding, medicine, and evolutionary biology. Genomic-based phenotype prediction has been applied for single-nucleotide polymorphism (SNP) genotyping platforms, but not using complete genome sequences. Here, we report genomic prediction for starvation stress resistance and startle response in Drosophila melanogaster, using ～2.5 million SNPs determined by sequencing the Drosophila Genetic Reference Panel population of inbred lines. We constructed a genomic relationship matrix from the SNP data and used it in a genomic best linear unbiased prediction (GBLUP) model. We assessed predictive ability as the correlation between predicted genetic values and observed phenotypes by cross-validation, and found a predictive ability of 0.239±0.008 (0.230±0.012) for starvation resistance (startle response). The predictive ability of BayesB, a Bayesian method with internal SNP selection, was not greater than GBLUP. Selection of the 5% SNPs with either the highest absolute effect or variance explained did not improve predictive ability. Predictive ability decreased only when fewer than 150,000 SNPs were used to construct the genomic relationship matrix. We hypothesize that predictive power in this population stems from the SNP-based modeling of the subtle relationship structure caused by long-range linkage disequilibrium and not from population structure or SNPs in linkage disequilibrium with causal variants. We discuss the implications of these results for genomic prediction in other organisms.     

A method to optimize selection on multiple identified quantitative trait loci

A mathematical approach was developed to model and optimize selection on multiple known quantitative trait loci (QTL) and polygenic estimated breeding values in order to maximize a weighted sum of responses to selection over multiple generations. The model allows for linkage between QTL with multiple alleles and arbitrary genetic effects, including dominance, epistasis, and gametic imprinting. Gametic phase disequilibrium between the QTL and between the QTL and polygenes is modeled but polygenic variance is assumed constant. Breeding programs with discrete generations, differential selection of males and females and random mating of selected parents are modeled. Polygenic EBV obtained from best linear unbiased prediction models can be accommodated. The problem was formulated as a multiple-stage optimal control problem and an iterative approach was developed for its solution. The method can be used to develop and evaluate optimal strategies for selection on multiple QTL for a wide range of situations and genetic models.     

A fast genomic selection approach for large genomic data

Key message

We propose a novel computational method for genomic selection that combines identical-by-state (IBS)-based Haseman–Elston (HE) regression and best linear prediction (BLP), called HE-BLP.

Abstract

Genomic best linear unbiased prediction (GBLUP) has been widely used in whole-genome prediction for breeding programs. To determine the total genetic variance of a training population, a linear mixed model (LMM) should be solved via restricted maximum likelihood (REML), whose computational complexity is the cube of the sample size. We proposed a novel computational method combining identical-by-state (IBS)-based Haseman–Elston (HE) regression and best linear prediction (BLP), called HE-BLP. With this method, the total genetic variance can be estimated by solving a simple HE linear regression, which has a computational complex of the sample size squared; therefore, it is suitable for large-scale genomic data, except those with which environmental effects need to be estimated simultaneously, because it does not allow for this estimation. In Monte Carlo simulation studies, the estimated heritability based on HE was identical to that based on REML, and the prediction accuracy via HE-BLP and traditional GBLUP was also quite similar when quantitative trait loci (QTLs) were randomly distributed along the genome and their effects followed a normal distribution. In addition, the kernel row number (KRN) trait in a maize IBM population was used to evaluate the performance of the two methods; the results showed similar prediction accuracy of breeding values despite slightly different estimated heritability via HE and REML, probably due to the underlying genetic architecture. HE-BLP can be a future genomic selection method choice for even larger sets of genomic data in certain special cases where environmental effects can be ignored. The software for HE regression and the simulation program is available online in the Genetic Analysis Repository (GEAR; https://github.com/gc5k/GEAR/wiki).

     

Mixed Model Methods for Genomic Prediction and Variance Component Estimation of Additive and Dominance Effects Using SNP Markers

We established a genomic model of quantitative trait with genomic additive and dominance relationships that parallels the traditional quantitative genetics model, which partitions a genotypic value as breeding value plus dominance deviation and calculates additive and dominance relationships using pedigree information. Based on this genomic model, two sets of computationally complementary but mathematically identical mixed model methods were developed for genomic best linear unbiased prediction (GBLUP) and genomic restricted maximum likelihood estimation (GREML) of additive and dominance effects using SNP markers. These two sets are referred to as the CE and QM sets, where the CE set was designed for large numbers of markers and the QM set was designed for large numbers of individuals. GBLUP and associated accuracy formulations for individuals in training and validation data sets were derived for breeding values, dominance deviations and genotypic values. Simulation study showed that GREML and GBLUP generally were able to capture small additive and dominance effects that each accounted for 0.00005–0.0003 of the phenotypic variance and GREML was able to differentiate true additive and dominance heritability levels. GBLUP of the total genetic value as the summation of additive and dominance effects had higher prediction accuracy than either additive or dominance GBLUP, causal variants had the highest accuracy of GREML and GBLUP, and predicted accuracies were in agreement with observed accuracies. Genomic additive and dominance relationship matrices using SNP markers were consistent with theoretical expectations. The GREML and GBLUP methods can be an effective tool for assessing the type and magnitude of genetic effects affecting a phenotype and for predicting the total genetic value at the whole genome level.     

Pre-selecting markers based on fixation index scores improved the power of genomic evaluations in a combined Yorkshire pig population

Combining different swine populations in genomic prediction can be an important tool, leading to an increased accuracy of genomic prediction using single nucleotide polymorphism (SNP) chip data compared with within-population genomic. However, the expected higher accuracy of multi-population genomic prediction has not been realized. This may be due to an inconsistent linkage disequilibrium (LD) between SNPs and quantitative trait loci (QTL) across populations, and the weak genetic relationships across populations. In this study, we determined the impact of different genomic relationship matrices, SNP density and pre-selected variants on prediction accuracy using a combined Yorkshire pig population. Our objective was to provide useful strategies for improving the accuracy of genomic prediction within a combined population. Results showed that the accuracy of genomic best linear unbiased prediction (GBLUP) using imputed whole-genome sequencing (WGS) data in the combined population was always higher than that within populations. Furthermore, the use of imputed WGS data always resulted in a higher accuracy of GBLUP than the use of 80K chip data for the combined population. Additionally, the accuracy of GBLUP with a non-linear genomic relationship matrix was markedly increased (0.87% to 15.17% for 80K chip data, and 0.43% to 4.01% for imputed WGS data) compared with that obtained with a linear genomic relationship matrix, except for the prediction of XD population in the combined population using imputed WGS data. More importantly, the application of pre-selected variants based on fixation index (Fst) scores improved the accuracy of multi-population genomic prediction, especially for 80K chip data. For BLUP|GA (BLUP approach given the genetic architecture), the use of a linear method with an appropriate weight to build a weight-relatedness matrix led to a higher prediction accuracy compared with the use of only pre-selected SNPs for genomic evaluations, especially for the total number of piglets born. However, for the non-linear method, BLUP|GA showed only a small increase or even a decrease in prediction accuracy compared with the use of only pre-selected SNPs. Overall, the best genomic evaluation strategy for reproduction-related traits for a combined population was found to be GBLUP performed with a non-linear genomic relationship matrix using variants pre-selected from the 80K chip data based on Fst scores.     

Unraveling Additive from Nonadditive Effects Using Genomic Relationship Matrices

The application of quantitative genetics in plant and animal breeding has largely focused on additive models, which may also capture dominance and epistatic effects. Partitioning genetic variance into its additive and nonadditive components using pedigree-based models (P-genomic best linear unbiased predictor) (P-BLUP) is difficult with most commonly available family structures. However, the availability of dense panels of molecular markers makes possible the use of additive- and dominance-realized genomic relationships for the estimation of variance components and the prediction of genetic values (G-BLUP). We evaluated height data from a multifamily population of the tree species Pinus taeda with a systematic series of models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance), using either pedigree- or marker-based information. We show that, compared with the pedigree, use of realized genomic relationships in marker-based models yields a substantially more precise separation of additive and nonadditive components of genetic variance. We conclude that the marker-based relationship matrices in a model including additive and nonadditive effects performed better, improving breeding value prediction. Moreover, our results suggest that, for tree height in this population, the additive and nonadditive components of genetic variance are similar in magnitude. This novel result improves our current understanding of the genetic control and architecture of a quantitative trait and should be considered when developing breeding strategies.     

Partitioning of genetic variation across the genome using multimarker methods in a wild bird population

The underlying basis of genetic variation in quantitative traits, in terms of the number of causal variants and the size of their effects, is largely unknown in natural populations. The expectation is that complex quantitative trait variation is attributable to many, possibly interacting, causal variants, whose effects may depend upon the sex, age and the environment in which they are expressed. A recently developed methodology in animal breeding derives a value of relatedness among individuals from high‐density genomic marker data, to estimate additive genetic variance within livestock populations. Here, we adapt and test the effectiveness of these methods to partition genetic variation for complex traits across genomic regions within ecological study populations where individuals have varying degrees of relatedness. We then apply this approach for the first time to a natural population and demonstrate that genetic variation in wing length in the great tit (Parus major) reflects contributions from multiple genomic regions. We show that a polygenic additive mode of gene action best describes the patterns observed, and we find no evidence of dosage compensation for the sex chromosome. Our results suggest that most of the genomic regions that influence wing length have the same effects in both sexes. We found a limited amount of genetic variance in males that is attributed to regions that have no effects in females, which could facilitate the sexual dimorphism observed for this trait. Although this exploratory work focuses on one complex trait, the methodology is generally applicable to any trait for any laboratory or wild population, paving the way for investigating sex‐, age‐ and environment‐specific genetic effects and thus the underlying genetic architecture of phenotype in biological study systems.     

Enhancing Genome-Enabled Prediction by Bagging Genomic BLUP

We examined whether or not the predictive ability of genomic best linear unbiased prediction (GBLUP) could be improved via a resampling method used in machine learning: bootstrap aggregating sampling (“bagging”). In theory, bagging can be useful when the predictor has large variance or when the number of markers is much larger than sample size, preventing effective regularization. After presenting a brief review of GBLUP, bagging was adapted to the context of GBLUP, both at the level of the genetic signal and of marker effects. The performance of bagging was evaluated with four simulated case studies including known or unknown quantitative trait loci, and an application was made to real data on grain yield in wheat planted in four environments. A metric aimed to quantify candidate-specific cross-validation uncertainty was proposed and assessed; as expected, model derived theoretical reliabilities bore no relationship with cross-validation accuracy. It was found that bagging can ameliorate predictive performance of GBLUP and make it more robust against over-fitting. Seemingly, 25–50 bootstrap samples was enough to attain reasonable predictions as well as stable measures of individual predictive mean squared errors.     

Single-step genomic prediction of Eucalyptus dunnii using different identity-by-descent and identity-by-state relationship matrices

Genomic selection based on the single-step genomic best linear unbiased prediction (ssGBLUP) approach is becoming an important tool in forest tree breeding. The quality of the variance components and the predictive ability of the estimated breeding values (GEBV) depends on how well marker-based genomic relationships describe the actual genetic relationships at unobserved causal loci. We investigated the performance of GEBV obtained when fitting models with genomic covariance matrices based on two identity-by-descent (IBD) and two identity-by-state (IBS) relationship measures. Multiple-trait multiple-site ssGBLUP models were fitted to diameter and stem straightness in five open-pollinated progeny trials of Eucalyptus dunnii, genotyped using the EUChip60K. We also fitted the conventional ABLUP model with a pedigree-based covariance matrix. Estimated relationships from the IBD estimators displayed consistently lower standard deviations than those from the IBS approaches. Although ssGBLUP based in IBS estimators resulted in higher trait-site heritabilities, the gain in accuracy of the relationships using IBD estimators has resulted in higher predictive ability and lower bias of GEBV, especially for low-heritability trait-site. ssGBLUP based on IBS and IBD approaches performed considerably better than the traditional ABLUP. In summary, our results advocate the use of the ssGBLUP approach jointly with the IBD relationship matrix in open-pollinated forest tree evaluation.Subject terms: Plant breeding, Genomics     

Application of Genomics Tools to Animal Breeding

The main goal in animal breeding is to select individuals that have high breeding values for traits of interest as parents to produce the next generation and to do so as quickly as possible. To date, most programs rely on statistical analysis of large data bases with phenotypes on breeding populations by linear mixed model methodology to estimate breeding values on selection candidates. However, there is a long history of research on the use of genetic markers to identify quantitative trait loci and their use in marker-assisted selection but with limited implementation in practical breeding programs. The advent of high-density SNP genotyping, combined with novel statistical methods for the use of this data to estimate breeding values, has resulted in the recent extensive application of genomic or whole-genome selection in dairy cattle and research to implement genomic selection in other livestock species is underway. The high-density SNP data also provides opportunities to detect QTL and to encover the genetic architecture of quantitative traits, in terms of the distribution of the size of genetic effects that contribute to trait differences in a population. Results show that this genetic architecture differs between traits but that for most traits, over 50% of the genetic variation resides in genomic regions with small effects that are of the order of magnitude that is expected under a highly polygenic model of inheritance.     

Different models of genetic variation and their effect on genomic evaluation

Background

The theory of genomic selection is based on the prediction of the effects of quantitative trait loci (QTL) in linkage disequilibrium (LD) with markers. However, there is increasing evidence that genomic selection also relies on "relationships" between individuals to accurately predict genetic values. Therefore, a better understanding of what genomic selection actually predicts is relevant so that appropriate methods of analysis are used in genomic evaluations.

Methods

Simulation was used to compare the performance of estimates of breeding values based on pedigree relationships (Best Linear Unbiased Prediction, BLUP), genomic relationships (gBLUP), and based on a Bayesian variable selection model (Bayes B) to estimate breeding values under a range of different underlying models of genetic variation. The effects of different marker densities and varying animal relationships were also examined.

Results

This study shows that genomic selection methods can predict a proportion of the additive genetic value when genetic variation is controlled by common quantitative trait loci (QTL model), rare loci (rare variant model), all loci (infinitesimal model) and a random association (a polygenic model). The Bayes B method was able to estimate breeding values more accurately than gBLUP under the QTL and rare variant models, for the alternative marker densities and reference populations. The Bayes B and gBLUP methods had similar accuracies under the infinitesimal model.

Conclusions

Our results suggest that Bayes B is superior to gBLUP to estimate breeding values from genomic data. The underlying model of genetic variation greatly affects the predictive ability of genomic selection methods, and the superiority of Bayes B over gBLUP is highly dependent on the presence of large QTL effects. The use of SNP sequence data will outperform the less dense marker panels. However, the size and distribution of QTL effects and the size of reference populations still greatly influence the effectiveness of using sequence data for genomic prediction.     

Multiple-Trait Genomic Selection Methods Increase Genetic Value Prediction Accuracy

Genetic correlations between quantitative traits measured in many breeding programs are pervasive. These correlations indicate that measurements of one trait carry information on other traits. Current single-trait (univariate) genomic selection does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e., GBLUP, BayesA, and BayesCπ) were presented and compared to univariate models using simulated and real quantitative traits controlled by different genetic architectures. We also extended BayesA with fixed hyperparameters to a full hierarchical model that estimated hyperparameters and BayesCπ to impute missing phenotypes. We found that optimal marker-effect variance priors depended on the genetic architecture of the trait so that estimating them was beneficial. We showed that the prediction accuracy for a low-heritability trait could be significantly increased by multivariate genomic selection when a correlated high-heritability trait was available. Further, multiple-trait genomic selection had higher prediction accuracy than single-trait genomic selection when phenotypes are not available on all individuals and traits. Additional factors affecting the performance of multiple-trait genomic selection were explored.     

Efficient weighting methods for genomic best linear-unbiased prediction (BLUP) adapted to the genetic architectures of quantitative traits

Genomic best linear-unbiased prediction (GBLUP) assumes equal variance for all marker effects, which is suitable for traits that conform to the infinitesimal model. For traits controlled by major genes, Bayesian methods with shrinkage priors or genome-wide association study (GWAS) methods can be used to identify causal variants effectively. The information from Bayesian/GWAS methods can be used to construct the weighted genomic relationship matrix (G). However, it remains unclear which methods perform best for traits varying in genetic architecture. Therefore, we developed several methods to optimize the performance of weighted GBLUP and compare them with other available methods using simulated and real data sets. First, two types of methods (marker effects with local shrinkage or normal prior) were used to obtain test statistics and estimates for each marker effect. Second, three weighted G matrices were constructed based on the marker information from the first step: (1) the genomic-feature-weighted G, (2) the estimated marker-variance-weighted G, and (3) the absolute value of the estimated marker-effect-weighted G. Following the above process, six different weighted GBLUP methods (local shrinkage/normal-prior GF/EV/AEWGBLUP) were proposed for genomic prediction. Analyses with both simulated and real data demonstrated that these options offer flexibility for optimizing the weighted GBLUP for traits with a broad spectrum of genetic architectures. The advantage of weighting methods over GBLUP in terms of accuracy was trait dependant, ranging from 14.8% to marginal for simulated traits and from 44% to marginal for real traits. Local-shrinkage prior EVWGBLUP is superior for traits mainly controlled by loci of a large effect. Normal-prior AEWGBLUP performs well for traits mainly controlled by loci of moderate effect. For traits controlled by some loci with large effects (explain 25–50% genetic variance) and a range of loci with small effects, GFWGBLUP has advantages. In conclusion, the optimal weighted GBLUP method for genomic selection should take both the genetic architecture and number of QTLs of traits into consideration carefully.Subject terms: Quantitative trait, Genome-wide association studies, Animal breeding, Quantitative trait, Genome-wide association studies     

Genomic prediction of reproduction traits for Merino sheep

Economically important reproduction traits in sheep, such as number of lambs weaned and litter size, are expressed only in females and later in life after most selection decisions are made, which makes them ideal candidates for genomic selection. Accurate genomic predictions would lead to greater genetic gain for these traits by enabling accurate selection of young rams with high genetic merit. The aim of this study was to design and evaluate the accuracy of a genomic prediction method for female reproduction in sheep using daughter trait deviations (DTD) for sires and ewe phenotypes (when individual ewes were genotyped) for three reproduction traits: number of lambs born (NLB), litter size (LSIZE) and number of lambs weaned. Genomic best linear unbiased prediction (GBLUP), BayesR and pedigree BLUP analyses of the three reproduction traits measured on 5340 sheep (4503 ewes and 837 sires) with real and imputed genotypes for 510 174 SNPs were performed. The prediction of breeding values using both sire and ewe trait records was validated in Merino sheep. Prediction accuracy was evaluated by across sire family and random cross‐validations. Accuracies of genomic estimated breeding values (GEBVs) were assessed as the mean Pearson correlation adjusted by the accuracy of the input phenotypes. The addition of sire DTD into the prediction analysis resulted in higher accuracies compared with using only ewe records in genomic predictions or pedigree BLUP. Using GBLUP, the average accuracy based on the combined records (ewes and sire DTD) was 0.43 across traits, but the accuracies varied by trait and type of cross‐validations. The accuracies of GEBVs from random cross‐validations (range 0.17–0.61) were higher than were those from sire family cross‐validations (range 0.00–0.51). The GEBV accuracies of 0.41–0.54 for NLB and LSIZE based on the combined records were amongst the highest in the study. Although BayesR was not significantly different from GBLUP in prediction accuracy, it identified several candidate genes which are known to be associated with NLB and LSIZE. The approach provides a way to make use of all data available in genomic prediction for traits that have limited recording.     

Genomic Variation and Its Impact on Gene Expression in Drosophila melanogaster

Understanding the relationship between genetic and phenotypic variation is one of the great outstanding challenges in biology. To meet this challenge, comprehensive genomic variation maps of human as well as of model organism populations are required. Here, we present a nucleotide resolution catalog of single-nucleotide, multi-nucleotide, and structural variants in 39 Drosophila melanogaster Genetic Reference Panel inbred lines. Using an integrative, local assembly-based approach for variant discovery, we identify more than 3.6 million distinct variants, among which were more than 800,000 unique insertions, deletions (indels), and complex variants (1 to 6,000 bp). While the SNP density is higher near other variants, we find that variants themselves are not mutagenic, nor are regions with high variant density particularly mutation-prone. Rather, our data suggest that the elevated SNP density around variants is mainly due to population-level processes. We also provide insights into the regulatory architecture of gene expression variation in adult flies by mapping cis-expression quantitative trait loci (cis-eQTLs) for more than 2,000 genes. Indels comprise around 10% of all cis-eQTLs and show larger effects than SNP cis-eQTLs. In addition, we identified two-fold more gene associations in males as compared to females and found that most cis-eQTLs are sex-specific, revealing a partial decoupling of the genomic architecture between the sexes as well as the importance of genetic factors in mediating sex-biased gene expression. Finally, we performed RNA-seq-based allelic expression imbalance analyses in the offspring of crosses between sequenced lines, which revealed that the majority of strong cis-eQTLs can be validated in heterozygous individuals.     

Genetic Control of the Leaf Angle and Leaf Orientation Value as Revealed by Ultra-High Density Maps in Three Connected Maize Populations

Plant architecture is a key factor for high productivity maize because ideal plant architecture with an erect leaf angle and optimum leaf orientation value allow for more efficient light capture during photosynthesis and better wind circulation under dense planting conditions. To extend our understanding of the genetic mechanisms involved in leaf-related traits, three connected recombination inbred line (RIL) populations including 538 RILs were genotyped by genotyping-by-sequencing (GBS) method and phenotyped for the leaf angle and related traits in six environments. We conducted single population quantitative trait locus (QTL) mapping and joint linkage analysis based on high-density recombination bin maps constructed from GBS genotype data. A total of 45 QTLs with phenotypic effects ranging from 1.2% to 29.2% were detected for four leaf architecture traits by using joint linkage mapping across the three populations. All the QTLs identified for each trait could explain approximately 60% of the phenotypic variance. Four QTLs were located on small genomic regions where candidate genes were found. Genomic predictions from a genomic best linear unbiased prediction (GBLUP) model explained 45±9% to 68±8% of the variation in the remaining RILs for the four traits. These results extend our understanding of the genetics of leaf traits and can be used in genomic prediction to accelerate plant architecture improvement.     

Accuracy of genomic selection in European maize elite breeding populations

Genomic selection is a promising breeding strategy for rapid improvement of complex traits. The objective of our study was to investigate the prediction accuracy of genomic breeding values through cross validation. The study was based on experimental data of six segregating populations from a half-diallel mating design with 788 testcross progenies from an elite maize breeding program. The plants were intensively phenotyped in multi-location field trials and fingerprinted with 960 SNP markers. We used random regression best linear unbiased prediction in combination with fivefold cross validation. The prediction accuracy across populations was higher for grain moisture (0.90) than for grain yield (0.58). The accuracy of genomic selection realized for grain yield corresponds to the precision of phenotyping at unreplicated field trials in 3–4 locations. As for maize up to three generations are feasible per year, selection gain per unit time is high and, consequently, genomic selection holds great promise for maize breeding programs.     

Understanding the classics: the unifying concepts of transgressive segregation,inbreeding depression and heterosis and their central relevance for crop breeding

Transgressive segregation and heterosis are the reasons that plant breeding works. Molecular explanations for both phenomena have been suggested and play a contributing role. However, it is often overlooked by molecular genetic researchers that transgressive segregation and heterosis are most simply explained by dispersion of favorable alleles. Therefore, advances in molecular biology will deliver the most impact on plant breeding when integrated with sources of heritable trait variation – and this will be best achieved within a quantitative genetics framework. An example of the power of quantitative approaches is the implementation of genomic selection, which has recently revolutionized animal breeding. Genomic selection is now being applied to both hybrid and inbred crops and is likely to be the major source of improvement in plant breeding practice over the next decade. Breeders’ ability to efficiently apply genomic selection methodologies is due to recent technology advances in genotyping and sequencing. Furthermore, targeted integration of additional molecular data (such as gene expression, gene copy number and methylation status) into genomic prediction models may increase their performance. In this review, we discuss and contextualize a suite of established quantitative genetics themes relating to hybrid vigour, transgressive segregation and their central relevance to plant breeding, with the aim of informing crop researchers outside of the quantitative genetics discipline of their relevance and importance to crop improvement. Better understanding between molecular and quantitative disciplines will increase the potential for further improvements in plant breeding methodologies and so help underpin future food security.     

Accuracy of genomic prediction within and across populations for nematode resistance and body weight traits in sheep

Genomic prediction utilizes single nucleotide polymorphism (SNP) chip data to predict animal genetic merit. It has the advantage of potentially capturing the effects of the majority of loci that contribute to genetic variation in a trait, even when the effects of the individual loci are very small. To implement genomic prediction, marker effects are estimated with a training set, including individuals with marker genotypes and trait phenotypes; subsequently, genomic estimated breeding values (GEBV) for any genotyped individual in the population can be calculated using the estimated marker effects. In this study, we aimed to: (i) evaluate the potential of genomic prediction to predict GEBV for nematode resistance traits and BW in sheep, within and across populations; (ii) evaluate the accuracy of these predictions through within-population cross-validation; and (iii) explore the impact of population structure on the accuracy of prediction. Four data sets comprising 752 lambs from a Scottish Blackface population, 2371 from a Sarda×Lacaune backcross population, 1000 from a Martinik Black-Belly×Romane backcross population and 64 from a British Texel population were used in this study. Traits available for the analysis were faecal egg count for Nematodirus and Strongyles and BW at different ages or as average effect, depending on the population. Moreover, immunoglobulin A was also available for the Scottish Blackface population. Results show that GEBV had moderate to good within-population predictive accuracy, whereas across-population predictions had accuracies close to zero. This can be explained by our finding that in most cases the accuracy estimates were mostly because of additive genetic relatedness between animals, rather than linkage disequilibrium between SNP and quantitative trait loci. Therefore, our results suggest that genomic prediction for nematode resistance and BW may be of value in closely related animals, but that with the current SNP chip genomic predictions are unlikely to work across breeds.