Genetic mapping and genomic selection using recombination breakpoint data

Genome-wide association study and genomic selection of flax powdery mildew in Xinjiang Province

Flax powdery mildew (PM), caused by Oidium lini, is a globally distributed fungal disease of flax, and seriously impairs its yield and quality. To data, only three resistance genes and a few putative quantitative trait loci (QTL) have been reported for flax PM resistance. To dissect the resistance mechanism against PM and identify resistant genetic regions, based on four years of phenotypic datasets (2017, 2019 to 2021), a genome-wide association study (GWAS) was performed on 200 flax core accessions using 674,074 SNPs and 7 models. A total of 434 unique quantitative trait nucleotides (QTNs) associated with 331 QTL were detected. Sixty-four loci shared in at least two datasets were found to be significant in haplotype analyses, and 20 of these sites were shared by multiple models. Simultaneously, a large-effect locus (qDI 11.2) was detected repeatedly, which was present in the mapping study of flax pasmo resistance loci. Oil flax had more QTL with positive-effect or favorable alleles (PQTL) and showed higher PM resistance than fiber flax, indicating that effects of these QTL were mainly additive. Furthermore, an excellent resistant variety C120 was identified and can be used to promote planting. Based on 331 QTLs identified through GWAS and the statistical model GBLUP, a genomic selection (GS) model related to flax PM resistance was constructed, and the prediction accuracy rate was 0.96. Our results provide valuable insights into the genetic basis of resistance and contribute to the advancement of breeding programs.

An expression-directed linear mixed model discovering low-effect genetic variants

Detecting genetic variants with low-effect sizes using a moderate sample size is difficult, hindering downstream efforts to learn pathology and estimating heritability. In this work, by utilizing informative weights learned from training genetically predicted gene expression models, we formed an alternative approach to estimate the polygenic term in a linear mixed model. Our linear mixed model estimates the genetic background by incorporating their relevance to gene expression. Our protocol, expression-directed linear mixed model, enables the discovery of subtle signals of low-effect variants using moderate sample size. By applying expression-directed linear mixed model to cohorts of around 5,000 individuals with either binary (WTCCC) or quantitative (NFBC1966) traits, we demonstrated its power gain at the low-effect end of the genetic etiology spectrum. In aggregate, the additional low-effect variants detected by expression-directed linear mixed model substantially improved estimation of missing heritability. Expression-directed linear mixed model moves precision medicine forward by accurately detecting the contribution of low-effect genetic variants to human diseases.

Dissecting the genetic architecture of quantitative traits using genome-wide identity-by-descent sharing

Additive and dominance genetic variances underlying the expression of quantitative traits are important quantities for predicting short-term responses to selection, but they are notoriously challenging to estimate in most non-model wild populations. Specifically, large-sized or panmictic populations may be characterized by low variance in genetic relatedness among individuals which, in turn, can prevent accurate estimation of quantitative genetic parameters. We used estimates of genome-wide identity-by-descent (IBD) sharing from autosomal SNP loci to estimate quantitative genetic parameters for ecologically important traits in nine-spined sticklebacks (Pungitius pungitius) from a large, outbred population. Using empirical and simulated datasets, with varying sample sizes and pedigree complexity, we assessed the performance of different crossing schemes in estimating additive genetic variance and heritability for all traits. We found that low variance in relatedness characteristic of wild outbred populations with high migration rate can impair the estimation of quantitative genetic parameters and bias heritability estimates downwards. On the other hand, the use of a half-sib/full-sib design allowed precise estimation of genetic variance components and revealed significant additive variance and heritability for all measured traits, with negligible dominance contributions. Genome-partitioning and QTL mapping analyses revealed that most traits had a polygenic basis and were controlled by genes at multiple chromosomes. Furthermore, different QTL contributed to variation in the same traits in different populations suggesting heterogeneous underpinnings of parallel evolution at the phenotypic level. Our results provide important guidelines for future studies aimed at estimating adaptive potential in the wild, particularly for those conducted in outbred large-sized populations.

A genome-wide association study and genomic prediction for Phakopsora pachyrhizi resistance in soybean

Soybean brown rust (SBR), caused by Phakopsora pachyrhizi, is a devastating fungal disease that threatens global soybean production. This study conducted a genome-wide association study (GWAS) with seven models on a panel of 3,082 soybean accessions to identify the markers associated with SBR resistance by 30,314 high quality single nucleotide polymorphism (SNPs). Then five genomic selection (GS) models, including Ridge regression best linear unbiased predictor (rrBLUP), Genomic best linear unbiased predictor (gBLUP), Bayesian least absolute shrinkage and selection operator (Bayesian LASSO), Random Forest (RF), and Support vector machines (SVM), were used to predict breeding values of SBR resistance using whole genome SNP sets and GWAS-based marker sets. Four SNPs, namely Gm18_57,223,391 (LOD = 2.69), Gm16_29,491,946 (LOD = 3.86), Gm06_45,035,185 (LOD = 4.74), and Gm18_51,994,200 (LOD = 3.60), were located near the reported P. pachyrhizi R genes, Rpp1, Rpp2, Rpp3, and Rpp4, respectively. Other significant SNPs, including Gm02_7,235,181 (LOD = 7.91), Gm02_7234594 (LOD = 7.61), Gm03_38,913,029 (LOD = 6.85), Gm04_46,003,059 (LOD = 6.03), Gm09_1,951,644 (LOD = 10.07), Gm10_39,142,024 (LOD = 7.12), Gm12_28,136,735 (LOD = 7.03), Gm13_16,350,701(LOD = 5.63), Gm14_6,185,611 (LOD = 5.51), and Gm19_44,734,953 (LOD = 6.02), were associated with abundant disease resistance genes, such as Glyma.02G084100, Glyma.03G175300, Glyma.04g189500, Glyma.09G023800, Glyma.12G160400, Glyma.13G064500, Glyma.14g073300, and Glyma.19G190200. The annotations of these genes included but not limited to: LRR class gene, cytochrome 450, cell wall structure, RCC1, NAC, ABC transporter, F-box domain, etc. The GWAS based markers showed more accuracies in genomic prediction than the whole genome SNPs, and Bayesian LASSO model was the ideal model in SBR resistance prediction with 44.5% ~ 60.4% accuracies. This study aids breeders in predicting selection accuracy of complex traits such as disease resistance and can shorten the soybean breeding cycle by the identified markers.

Digitalizing breeding in plants: A new trend of next-generation breeding based on genomic prediction

As the world's population grows and food needs diversification, the demand for cereals and horticultural crops with beneficial traits increases. In order to meet a variety of demands, suitable cultivars and innovative breeding methods need to be developed. Breeding methods have changed over time following the advance of genetics. With the advent of new sequencing technology in the early 21st century, predictive breeding, such as genomic selection (GS), emerged when large-scale genomic information became available. GS shows good predictive ability for the selection of individuals with traits of interest even for quantitative traits by using various types of the whole genome-scanning markers, breaking away from the limitations of marker-assisted selection (MAS). In the current review, we briefly describe the history of breeding techniques, each breeding method, various statistical models applied to GS and methods to increase the GS efficiency. Consequently, we intend to propose and define the term digital breeding through this review article. Digital breeding is to develop a predictive breeding methods such as GS at a higher level, aiming to minimize human intervention by automatically proceeding breeding design, propagating breeding populations, and to make selections in consideration of various environments, climates, and topography during the breeding process. We also classified the phases of digital breeding based on the technologies and methods applied to each phase. This review paper will provide an understanding and a direction for the final evolution of plant breeding in the future.

Genotyping marker density and prediction models effects in long-term breeding schemes of cross-pollinated crops

In genomic recurrent selection, the more markers, the better because they buffer the linkage disequilibrium losses caused by recombination over cycles, and consequently, provide higher responses to selection. Reductions of genotyping marker density have been extensively evaluated as potential strategies to reduce the genotyping costs of genomic selection (GS). Low-density marker panels are appealing in GS because they entail lower multicollinearity and computing time and allow more individuals to be genotyped for the same cost. However, statistical models used in GS are usually evaluated with empirical data, using "static" training sets and populations. This may be adequate for making predictions during a breeding program's initial cycles but not for the long-term. Moreover, studies that focus on long selective breeding cycles generally do not consider GS models with the effect of dominance, which is particularly important for breeding outcomes in cross-pollinated crops. Hence, dominance effects are important and unexplored in GS for long-term programs involving allogamous species. To address it, we employed two approaches: analysis of empirical maize datasets and simulations of long-term breeding applying phenotypic and genomic recurrent selection (intrapopulation and reciprocal schemes). In both schemes, we simulated twenty breeding cycles and assessed the effect of marker density reduction on the population mean, the best crosses, additive variance, selective accuracy, and response to selection with models [additive, additive-dominant, general (GCA), and this plus specific combining ability (GCA + SCA)]. Our results indicate that marker reduction based on linkage disequilibrium levels provides useful predictions only within a cycle, as accuracy significantly decreases over cycles. In the long-term, without training set updating, high-marker density provides the best responses to selection. The model to be used depends on the breeding scheme: additive for intrapopulation and additive-dominant or GCA + SCA for reciprocal.

Genetic Dissection of Phosphorus Use Efficiency and Genotype-by-Environment Interaction in Maize

Genotype-by-environment interaction (G-by-E) is a common but potentially problematic phenomenon in plant breeding. In this study, we investigated the genotypic performance and two measures of plasticity on a phenotypic and genetic level by assessing 234 maize doubled haploid lines from six populations for 15 traits in seven macro-environments with a focus on varying soil phosphorus levels. It was found intergenic regions contributed the most to the variation of phenotypic linear plasticity. For 15 traits, 124 and 31 quantitative trait loci (QTL) were identified for genotypic performance and phenotypic plasticity, respectively. Further, some genes associated with phosphorus use efficiency, such as Zm00001eb117170, Zm00001eb258520, and Zm00001eb265410, encode small ubiquitin-like modifier E3 ligase were identified. By significantly testing the main effect and G-by-E effect, 38 main QTL and 17 interaction QTL were identified, respectively, in which MQTL38 contained the gene Zm00001eb374120, and its effect was related to phosphorus concentration in the soil, the lower the concentration, the greater the effect. Differences in the size and sign of the QTL effect in multiple environments could account for G-by-E. At last, the superiority of G-by-E in genomic selection was observed. In summary, our findings will provide theoretical guidance for breeding P-efficient and broadly adaptable varieties.

Uncontrolled transposition following RNAi loss causes hypermutation and antifungal drug resistance in clinical isolates of Cryptococcus neoformans

Cryptococcus neoformans infections cause approximately 15% of AIDS-related deaths owing to a combination of limited antifungal therapies and drug resistance. A collection of clinical and environmental C. neoformans isolates were assayed for increased mutation rates via fluctuation analysis, and we identified two hypermutator C. neoformans clinical isolates with increased mutation rates when exposed to the combination of rapamycin and FK506. Sequencing of drug target genes found that Cnl1 transposon insertions conferred the majority of resistance to rapamycin and FK506 and could also independently cause resistance to 5-fluoroorotic acid and the clinically relevant antifungal 5-flucytosine. Whole-genome sequencing revealed both hypermutator genomes harbour a nonsense mutation in the RNA-interference component ZNF3 and hundreds of Cnl1 elements organized into massive subtelomeric arrays on each of the fourteen chromosomes. Quantitative trait locus mapping in 28 progeny derived from a cross between a hypermutator and wild-type identified a locus associated with hypermutation that included znf3. CRISPR editing of the znf3 nonsense mutation abolished hypermutation and restored small-interfering-RNA production. We conclude that hypermutation and drug resistance in these clinical isolates result from RNA-interference loss and accumulation of Cnl1 elements.

PIP-SNP: a pipeline for processing SNP data featured as linkage disequilibrium bin mapping, genotype imputing and marker synthesizing

Genome-wide association study data analyses often face two significant challenges: (i) high dimensionality of single-nucleotide polymorphism (SNP) genotypes and (ii) imputation of missing values. SNPs are not independent due to physical linkage and natural selection. The correlation of nearby SNPs is known as linkage disequilibrium (LD), which can be used for LD conceptual SNP bin mapping, missing genotype inferencing and SNP dimension reduction. We used a stochastic process to describe the SNP signals and proposed two types of autocorrelations to measure nearby SNPs' information redundancy. Based on the calculated autocorrelation coefficients, we constructed LD bins. We adopted a k-nearest neighbors algorithm (kNN) to impute the missing genotypes. We proposed several novel methods to find the optimal synthetic marker to represent the SNP bin. We also proposed methods to evaluate the information loss or information conservation between using the original genome-wide markers and using dimension-reduced synthetic markers. Our performance assessments on the real-life SNP data from a rice recombinant inbred line (RIL) population and a rice HapMap project show that the new methods produce satisfactory results. We implemented these functional modules in C/C++ and streamlined them into a web-based pipeline named PIP-SNP (https://bioinfo.noble.org/PIP_SNP/) for processing SNP data.

Integrated genomic selection for rapid improvement of crops

An increase in the rate of crop improvement is essential for achieving sustained food production and other needs of ever-increasing population. Genomic selection (GS) is a potential breeding tool that has been successfully employed in animal breeding and is being incorporated into plant breeding. GS promises accelerated breeding cycles through a rapid selection of superior genotypes. Numerous empirical and simulation studies on GS and realized impacts on improvement in the crop yields are recently being reported. For a holistic understanding of the technology, we briefly discuss the concept of genetic gain, GS methodology, its current status, advantages of GS over other breeding methods, prediction models, and the factors controlling prediction accuracy in GS. Also, integration of speed breeding and other novel technologies viz. high throughput genotyping and phenotyping technologies for enhancing the efficiency and pace of GS, followed by its prospective applications in varietal development programs is reviewed.

Genetic population structure constrains local adaptation in sticklebacks

Repeated and independent adaptation to specific environmental conditions from standing genetic variation is common. However, if genetic variation is limited, the evolution of similar locally adapted traits may be restricted to genetically different and potentially less optimal solutions or prevented from happening altogether. Using a quantitative trait locus (QTL) mapping approach, we identified the genomic regions responsible for the repeated pelvic reduction (PR) in three crosses between nine-spined stickleback populations expressing full and reduced pelvic structures. In one cross, PR mapped to linkage group 7 (LG7) containing the gene Pitx1, known to control pelvic reduction also in the three-spined stickleback. In the two other crosses, PR was polygenic and attributed to 10 novel QTL, of which 90% were unique to specific crosses. When screening the genomes from 27 different populations for deletions in the Pitx1 regulatory element, these were only found in the population in which PR mapped to LG7, even though the morphological data indicated large-effect QTL for PR in several other populations as well. Consistent with the available theory and simulations parameterized on empirical data, we hypothesize that the observed variability in genetic architecture of PR is due to heterogeneity in the spatial distribution of standing genetic variation caused by >2× stronger population structuring among freshwater populations and >10× stronger genetic isolation by distance in the sea in nine-spined sticklebacks as compared to three-spined sticklebacks.

Deshrinking ridge regression for genome-wide association studies

MOTIVATION

Genome-wide association studies (GWAS) are still the primary steps toward gene discovery. The urgency is more obvious in the big data era when GWAS are conducted simultaneously for thousand traits, e.g. transcriptomic and metabolomic traits. Efficient mixed model association (EMMA) and genome-wide efficient mixed model association (GEMMA) are the widely used methods for GWAS. An algorithm with high computational efficiency is badly needed. It is interesting to note that the test statistics of the ordinary ridge regression (ORR) have the same patterns across the genome as those obtained from the EMMA method. However, ORR has never been used for GWAS due to its severe shrinkage on the estimated effects and the test statistics.

RESULTS

We introduce a degree of freedom for each marker effect obtained from ORR and use it to deshrink both the estimated effect and the standard error so that the Wald test of ORR is brought back to the same level as that of EMMA. The new method is called deshrinking ridge regression (DRR). By evaluating the methods under three different model sizes (small, medium and large), we demonstrate that DRR is more generalized for all model sizes than EMMA, which only works for medium and large models. Furthermore, DRR detect all markers in a simultaneous manner instead of scanning one marker at a time. As a result, the computational time complexity of DRR is much simpler than EMMA and about m (number of genetic variants) times simpler than that of GEMMA when the sample size is way smaller than the number of markers.

CONTACT

shizhong.xu@ucr.edu.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Pleiotropy and epistasis within and between signaling pathways defines the genetic architecture of fungal virulence

Cryptococcal disease is estimated to affect nearly a quarter of a million people annually. Environmental isolates of Cryptococcus deneoformans, which make up 15 to 30% of clinical infections in temperate climates such as Europe, vary in their pathogenicity, ranging from benign to hyper-virulent. Key traits that contribute to virulence, such as the production of the pigment melanin, an extracellular polysaccharide capsule, and the ability to grow at human body temperature have been identified, yet little is known about the genetic basis of variation in such traits. Here we investigate the genetic basis of melanization, capsule size, thermal tolerance, oxidative stress resistance, and antifungal drug sensitivity using quantitative trait locus (QTL) mapping in progeny derived from a cross between two divergent C. deneoformans strains. Using a "function-valued" QTL analysis framework that exploits both time-series information and growth differences across multiple environments, we identified QTL for each of these virulence traits and drug susceptibility. For three QTL we identified the underlying genes and nucleotide differences that govern variation in virulence traits. One of these genes, RIC8, which encodes a regulator of cAMP-PKA signaling, contributes to variation in four virulence traits: melanization, capsule size, thermal tolerance, and resistance to oxidative stress. Two major effect QTL for amphotericin B resistance map to the genes SSK1 and SSK2, which encode key components of the HOG pathway, a fungal-specific signal transduction network that orchestrates cellular responses to osmotic and other stresses. We also discovered complex epistatic interactions within and between genes in the HOG and cAMP-PKA pathways that regulate antifungal drug resistance and resistance to oxidative stress. Our findings advance the understanding of virulence traits among diverse lineages of Cryptococcus, and highlight the role of genetic variation in key stress-responsive signaling pathways as a major contributor to phenotypic variation.

Accelerating Tomato Breeding by Exploiting Genomic Selection Approaches

Genomic selection (GS) is a predictive approach that was built up to increase the rate of genetic gain per unit of time and reduce the generation interval by utilizing genome-wide markers in breeding programs. It has emerged as a valuable method for improving complex traits that are controlled by many genes with small effects. GS enables the prediction of the breeding value of candidate genotypes for selection. In this work, we address important issues related to GS and its implementation in the plant context with special emphasis on tomato breeding. Genomic constraints and critical parameters affecting the accuracy of prediction such as the number of markers, statistical model, phenotyping and complexity of trait, training population size and composition should be carefully evaluated. The comparison of GS approaches for facilitating the selection of tomato superior genotypes during breeding programs is also discussed. GS applied to tomato breeding has already been shown to be feasible. We illustrated how GS can improve the rate of gain in elite line selection, and descendent and backcross schemes. The GS schemes have begun to be delineated and computer science can provide support for future selection strategies. A new promising breeding framework is beginning to emerge for optimizing tomato improvement procedures.

A Gaussian process model and Bayesian variable selection for mapping function-valued quantitative traits with incomplete phenotypic data

Motivation

Recent advances in high dimensional phenotyping bring time as an extra dimension into the phenotypes. This promotes the quantitative trait locus (QTL) studies of function-valued traits such as those related to growth and development. Existing approaches for analyzing functional traits utilize either parametric methods or semi-parametric approaches based on splines and wavelets. However, very limited choices of software tools are currently available for practical implementation of functional QTL mapping and variable selection.

Results

We propose a Bayesian Gaussian process (GP) approach for functional QTL mapping. We use GPs to model the continuously varying coefficients which describe how the effects of molecular markers on the quantitative trait are changing over time. We use an efficient gradient based algorithm to estimate the tuning parameters of GPs. Notably, the GP approach is directly applicable to the incomplete datasets having even larger than 50% missing data rate (among phenotypes). We further develop a stepwise algorithm to search through the model space in terms of genetic variants, and use a minimal increase of Bayesian posterior probability as a stopping rule to focus on only a small set of putative QTL. We also discuss the connection between GP and penalized B-splines and wavelets. On two simulated and three real datasets, our GP approach demonstrates great flexibility for modeling different types of phenotypic trajectories with low computational cost. The proposed model selection approach finds the most likely QTL reliably in tested datasets.

Availability and implementation

Software and simulated data are available as a MATLAB package ‘GPQTLmapping’, and they can be downloaded from GitHub (https://github.com/jpvanhat/GPQTLmapping). Real datasets used in case studies are publicly available at QTL Archive.

Supplementary information

Supplementary data are available at Bioinformatics online.

Current status of genomic evaluation

Early application of genomic selection relied on SNP estimation with phenotypes or de-regressed proofs (DRP). Chips of 50k SNP seemed sufficient for an accurate estimation of SNP effects. Genomic estimated breeding values (GEBV) were composed of an index with parent average, direct genomic value, and deduction of a parental index to eliminate double counting. Use of SNP selection or weighting increased accuracy with small data sets but had minimal to no impact with large data sets. Efforts to include potentially causative SNP derived from sequence data or high-density chips showed limited or no gain in accuracy. After the implementation of genomic selection, EBV by BLUP became biased because of genomic preselection and DRP computed based on EBV required adjustments, and the creation of DRP for females is hard and subject to double counting. Genomic selection was greatly simplified by single-step genomic BLUP (ssGBLUP). This method based on combining genomic and pedigree relationships automatically creates an index with all sources of information, can use any combination of male and female genotypes, and accounts for preselection. To avoid biases, especially under strong selection, ssGBLUP requires that pedigree and genomic relationships are compatible. Because the inversion of the genomic relationship matrix (G) becomes costly with more than 100k genotyped animals, large data computations in ssGBLUP were solved by exploiting limited dimensionality of genomic data due to limited effective population size. With such dimensionality ranging from 4k in chickens to about 15k in cattle, the inverse of G can be created directly (e.g., by the algorithm for proven and young) at a linear cost. Due to its simplicity and accuracy, ssGBLUP is routinely used for genomic selection by the major chicken, pig, and beef industries. Single step can be used to derive SNP effects for indirect prediction and for genome-wide association studies, including computations of the P-values. Alternative single-step formulations exist that use SNP effects for genotyped or for all animals. Although genomics is the new standard in breeding and genetics, there are still some problems that need to be solved. This involves new validation procedures that are unaffected by selection, parameter estimation that accounts for all the genomic data used in selection, and strategies to address reduction in genetic variances after genomic selection was implemented.

A Bayesian Framework for Robust Quantitative Trait Locus Mapping and Outlier Detection

We introduce a Bayesian framework for simultaneous feature selection and outlier detection in sparse high-dimensional regression models, with a focus on quantitative trait locus (QTL) mapping in experimental crosses. More specifically, we incorporate the robust mean shift outlier handling mechanism into the multiple QTL mapping regression model and apply LASSO regularization concurrently to the genetic effects and the mean-shift terms through the flexible extended Bayesian LASSO (EBL) prior structure, thereby combining QTL mapping and outlier detection into a single sparse model representation problem. The EBL priors on the mean-shift terms prevent outlying phenotypic values from distorting the genotype-phenotype association and allow their detection as cases with outstanding mean shift values following the LASSO shrinkage. Simulation results demonstrate the effectiveness of our new methodology at mapping QTLs in the presence of outlying phenotypic values and simultaneously identifying the potential outliers, while maintaining a comparable performance to the standard EBL on outlier-free data.

Novel Bayesian Networks for Genomic Prediction of Developmental Traits in Biomass Sorghum

The ability to connect genetic information between traits over time allow Bayesian networks to offer a powerful probabilistic framework to construct genomic prediction models. In this study, we phenotyped a diversity panel of 869 biomass sorghum (Sorghum bicolor (L.) Moench) lines, which had been genotyped with 100,435 SNP markers, for plant height (PH) with biweekly measurements from 30 to 120 days after planting (DAP) and for end-of-season dry biomass yield (DBY) in four environments. We evaluated five genomic prediction models: Bayesian network (BN), Pleiotropic Bayesian network (PBN), Dynamic Bayesian network (DBN), multi-trait GBLUP (MTr-GBLUP), and multi-time GBLUP (MTi-GBLUP) models. In fivefold cross-validation, prediction accuracies ranged from 0.46 (PBN) to 0.49 (MTr-GBLUP) for DBY and from 0.47 (DBN, DAP120) to 0.75 (MTi-GBLUP, DAP60) for PH. Forward-chaining cross-validation further improved prediction accuracies of the DBN, MTi-GBLUP and MTr-GBLUP models for PH (training slice: 30-45 DAP) by 36.4-52.4% relative to the BN and PBN models. Coincidence indices (target: biomass, secondary: PH) and a coincidence index based on lines (PH time series) showed that the ranking of lines by PH changed minimally after 45 DAP. These results suggest a two-level indirect selection method for PH at harvest (first-level target trait) and DBY (second-level target trait) could be conducted earlier in the season based on ranking of lines by PH at 45 DAP (secondary trait). With the advance of high-throughput phenotyping technologies, our proposed two-level indirect selection framework could be valuable for enhancing genetic gain per unit of time when selecting on developmental traits.

Identification of Quantitative Trait Loci for Component Traits of Flowering Capacity Across Temperature in Petunia

For ornamental annual bedding plants, flowering performance is critical. Flowering performance includes the length of the flowering period, the longevity of individual flowers, and the number of flowers produced during the flowering period, or flowering capacity. Flowering capacity is a function of several component traits, including the number of branches producing flowers, the number of inflorescences per flowering branch, and the number of flower buds per inflorescence. We employed an F₇Petunia axillaris × P. exserta recombinant inbred line population to identify QTL for flowering capacity component traits. The population was phenotyped at 14, 17, and 20° over two years. Fifteen robust QTL (rQTL; QTL detected in two or more temperatures/years) were identified across six of the seven Petunia chromosomes (Chr) for total flower bud number (FlBud), branch number (Branch), flowering branch number (FlBranch), and primary shoot flower bud number (FlBudPS). The largest effect QTL explained up to 28.8, 34.9, 36, and 23.1% of the phenotypic variation for FlBub, FlBudPS, Branch, and FlBranch, respectively. rQTL for FlBud and FlBranch co-localized on Chr 1, and rQTL for FlBud, FlBudPS, and FlBranch co-localized on Chr 4. These regions in particular should be useful for identifying genes controlling flowering capacity of this important ornamental plant.

A coordinate descent approach for sparse Bayesian learning in high dimensional QTL mapping and genome-wide association studies

MOTIVATION

Genomic scanning approaches that detect one locus at a time are subject to many problems in genome-wide association studies and quantitative trait locus mapping. The problems include large matrix inversion, over-conservativeness for tests after Bonferroni correction and difficulty in evaluation of the total genetic contribution to a trait's variance. Targeting these problems, we take a further step and investigate a multiple locus model that detects all markers simultaneously in a single model.

RESULTS

We developed a sparse Bayesian learning (SBL) method for quantitative trait locus mapping and genome-wide association studies. This new method adopts a coordinate descent algorithm to estimate parameters (marker effects) by updating one parameter at a time conditional on current values of all other parameters. It uses an L2 type of penalty that allows the method to handle extremely large sample sizes (>100 000). Simulation studies show that SBL often has higher statistical powers and the simulated true loci are often detected with extremely small P-values, indicating that SBL is insensitive to stringent thresholds in significance testing.

AVAILABILITY AND IMPLEMENTATION

An R package (sbl) is available on the comprehensive R archive network (CRAN) and https://github.com/MeiyueComputBio/sbl/tree/master/R%20packge.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Functional models in genome-wide selection

The development of sequencing technologies has enabled the discovery of markers that are abundantly distributed over the whole genome. Knowledge about the marker locations in reference genomes provides further insights in the search for causal regions and the prediction of genomic values. The present study proposes a Bayesian functional approach for incorporating the marker locations into genomic analysis using stochastic methods to search causal regions and predict genotypic values. For this, three scenarios were analyzed: F2 population with 300 individuals and three different heritability levels (0.2, 0.5, and 0.8), along with 12,150 SNP markers that were distributed through ten linkage groups; F∞ populations with 320 individuals and three different heritability levels (0.2, 0.5, and 0.8), along with 10,020 SNP markers that were distributed through ten linkage groups; and data related to Eucalyptus spp. to measure the model performance in a real LD setting, with 611 individuals whose phenotypes were simulated from QTLs distributed through a panel of 36,812 SNPs with known positions. The performance of the proposed method was compared with those of other genome selection models, namely, RR-BLUP, Bayes B and Bayesian Lasso. The Bayesian functional model presented higher or similar predictive ability when compared with those classical regressions methods in simulated and real scenarios on different LD structures. In general, the Bayesian functional model also achieved higher computational efficiency, using 12 SNPs per MCMC round. The model was efficient in the identification of causal regions and showed high flexibility of analysis, as it is easily adaptable to any genomic selection model.

Genome-wide association studies using binned genotypes

Linear mixed models (LMM) that tests trait association one marker at a time have been the most popular methods for genome-wide association studies. However, this approach has potential pitfalls: over conservativeness after Bonferroni correction, ignorance of linkage disequilibrium (LD) between neighboring markers, and power reduction due to overfitting SNP effects. So, multiple locus models that can simultaneously estimate and test all markers in the genome are more appropriate. Based on the multiple locus models, we proposed a bin model that combines markers into bins based on their LD relationships. A bin is treated as a new synthetic marker and we detect the associations between bins and traits. Since the number of bins can be substantially smaller than the number of markers, a penalized multiple regression method can be adopted by fitting all bins to a single model. We developed an innovative method to bin the neighboring markers and used the least absolute shrinkage and selection operator (LASSO) method. We compared BIN-Lasso with SNP-Lasso and Q + K-LMM in a simulation experiment, and showed that the new method is more powerful with less Type I error than the other two methods. We also applied the bin model to a Chinese Simmental beef cattle population for bone weight association study. The new method identified more significant associations than the classical LMM. The bin model is a new dimension reduction technique that takes advantage of biological information (i.e., LD). The new method will be a significant breakthrough in associative genomics in the big data era.

Mapping quantitative trait loci using binned genotypes

Precise mapping of quantitative trait loci (QTLs) is critical for assessing genetic effects and identifying candidate genes for quantitative traits. Interval and composite interval mappings have been the methods of choice for several decades, which have provided tools for identifying genomic regions harboring causal genes for quantitative traits. Historically, the concept was developed on the basis of sparse marker maps where genotypes of loci within intervals could not be observed. Currently, genomes of many organisms have been saturated with markers due to the new sequencing technologies. Genotyping by sequencing usually generates hundreds of thousands of single nucleotide polymorphisms (SNPs), which often include the causal polymorphisms. The concept of interval no longer exists, prompting the necessity of a norm change in QTL mapping technology to make use of the high-volume genomic data. Here we developed a statistical method and a software package to map QTLs by binning markers into haplotype blocks, called bins. The new method detects associations of bins with quantitative traits. It borrows the mixed model methodology with a polygenic control from genome-wide association studies (GWAS) and can handle all kinds of experimental populations under the linear mixed model (LMM) framework. We tested the method using both simulated data and data from populations of rice. The results showed that this method has higher power than the current methods. An R package named binQTL is available from GitHub.

Evaluation of GBLUP, BayesB and elastic net for genomic prediction in Chinese Simmental beef cattle

Chinese Simmental beef cattle are the most economically important cattle breed in China. Estimated breeding values for growth, carcass, and meat quality traits are commonly used as selection criteria in animal breeding. The objective of this study was to evaluate the accuracy of alternative statistical methods for the estimation of genomic breeding values. Analyses of the accuracy of genomic best linear unbiased prediction (GBLUP), BayesB, and elastic net (EN) were performed with an Illumina BovineHD BeadChip on 1,217 animals by applying 5-fold cross-validation. Overall, the accuracies ranged from 0.17 to 0.296 for ten traits, and the heritability estimates ranged from 0.36 to 0.63. The EN (alpha = 0.001) model provided the most accurate prediction, which was also slightly higher (0.2–2%) than that of GBLUP for most traits, such as average daily weight gain (ADG) and carcass weight (CW). BayesB was less accurate for each trait than were EN (alpha = 0.001) and GBLUP. These findings indicate the importance of using an appropriate variable selection method for the genomic selection of traits and suggest the influence of the genetic architecture of the traits we analyzed.

Analysis of phenotypic- and Estimated Breeding Values (EBV) to dissect the genetic architecture of complex traits in a Scots pine three-generation pedigree design

In forest tree breeding, family-based Quantitative Trait Loci (QTL) studies are valuable as methods to dissect the complexity of a trait and as a source of candidate genes. In the field of conifer research, our study contributes to the evaluation of phenotypic and predicted breeding values for the identification of QTL linked to complex traits in a three-generation pedigree population in Scots pine (Pinus sylvestris L.). A total of 11 470 open pollinated F₂-progeny trees established at three different locations, were measured for growth and adaptive traits. Breeding values were predicted for their 360 mothers, originating from a single cross of two grand-parents. A multilevel LASSO association analysis was conducted to detect QTL using genotypes of the mothers with the corresponding phenotypes and Estimated Breeding Values (EBV). Different levels of genotype-by-environment (G × E) effects among sites at different years, were detected for survival and height. Moderate-to-low narrow sense heritabilities and EBV accuracies were found for all traits and all sites. We identified 18 AFLPs and 12 SNPs to be associated with QTL for one or more traits. 62 QTL were significant with percentages of variance explained ranging from 1.7 to 18.9%. In those cases where the same marker was associated to a phenotypic or an ebvQTL, the ebvQTL always explained higher proportion of the variance, maybe due to the more accurate nature of Estimated Breeding Values (EBV). Two SNP-QTL showed pleiotropic effects for traits related with hardiness, seed, cone and flower production. Furthermore, we detected several QTL with significant effects across multiple ages, which could be considered as strong candidate loci for early selection. The lack of reproducibility of some QTL detected across sites may be due to environmental heterogeneity reflected by the genotype- and QTL-by-environment effects.

Recursive Algorithms for Modeling Genomic Ancestral Origins in a Fixed Pedigree

The study of gene flow in pedigrees is of strong interest for the development of quantitative trait loci (QTL) mapping methods in multiparental populations. We developed a Markovian framework for modeling ancestral origins along two homologous chromosomes within individuals in fixed pedigrees. A highly beneficial property of our method is that the size of state space depends linearly or quadratically on the number of pedigree founders, whereas this increases exponentially with pedigree size in alternative methods. To calculate the parameter values of the Markov process, we describe two novel recursive algorithms that differ with respect to the pedigree founders being assumed to be exchangeable or not. Our algorithms apply equally to autosomes and sex chromosomes, another desirable feature of our approach. We tested the accuracy of the algorithms by a million simulations on a pedigree. We demonstrated two applications of the recursive algorithms in multiparental populations: design a breeding scheme for maximizing the overall density of recombination breakpoints and thus the QTL mapping resolution, and incorporate pedigree information into hidden Markov models in ancestral inference from genotypic data; the conditional probabilities and the recombination breakpoint data resulting from ancestral inference can facilitate follow-up QTL mapping. The results show that the generality of the recursive algorithms can greatly increase the application range of genetic analysis such as ancestral inference in multiparental populations.

A multi-parent advanced generation inter-cross (MAGIC) population for genetic analysis and improvement of cowpea (Vigna unguiculata L. Walp.)

Multi-parent advanced generation inter-cross (MAGIC) populations are an emerging type of resource for dissecting the genetic structure of traits and improving breeding populations. We developed a MAGIC population for cowpea (Vigna unguiculata L. Walp.) from eight founder parents. These founders were genetically diverse and carried many abiotic and biotic stress resistance, seed quality and agronomic traits relevant to cowpea improvement in the United States and sub-Saharan Africa, where cowpea is vitally important in the human diet and local economies. The eight parents were inter-crossed using structured matings to ensure that the population would have balanced representation from each parent, followed by single-seed descent, resulting in 305 F₈ recombinant inbred lines each carrying a mosaic of genome blocks contributed by all founders. This was confirmed by single nucleotide polymorphism genotyping with the Illumina Cowpea Consortium Array. These lines were on average 99.74% homozygous but also diverse in agronomic traits across environments. Quantitative trait loci (QTLs) were identified for several parental traits. Loci with major effects on photoperiod sensitivity and seed size were also verified by biparental genetic mapping. The recombination events were concentrated in telomeric regions. Due to its broad genetic base, this cowpea MAGIC population promises breakthroughs in genetic gain, QTL and gene discovery, enhancement of breeding populations and, for some lines, direct releases as new varieties.

Controlling the Overfitting of Heritability in Genomic Selection through Cross Validation

In genomic selection (GS), all the markers across the entire genome are used to conduct marker-assisted selection such that each quantitative trait locus of complex trait is in linkage disequilibrium with at least one marker. Although GS improves estimated breeding values and genetic gain, in most GS models genetic variance is estimated from training samples with many trait-irrelevant markers, which leads to severe overfitting in the calculation of trait heritability. In this study, we demonstrated overfitting heritability due to the inclusion of trait-irrelevant markers using a series of simulations, and such overfitting can be effectively controlled by cross validation experiment. In the proposed method, the genetic variance is simply the variance of the genetic values predicted through cross validation, the residual variance is the variance of the differences between the observed phenotypic values and the predicted genetic values, and these two resultant variance components are used for calculating the unbiased heritability. We also demonstrated that the heritability calculated through cross validation is equivalent to trait predictability, which objectively reflects the applicability of the GS models. The proposed method can be implemented with the Mixed Procedure in SAS or with our R package “GSMX” which is publically available at https://cran.r-project.org/web/packages/GSMX/index.html.

Prediction and association mapping of agronomic traits in maize using multiple omic data

Genomic selection holds a great promise to accelerate plant breeding via early selection before phenotypes are measured, and it offers major advantages over marker-assisted selection for highly polygenic traits. In addition to genomic data, metabolome and transcriptome are increasingly receiving attention as new data sources for phenotype prediction. We used data available from maize as a model to compare the predictive abilities of three different omic data sources using eight representative methods for six traits. We found that the best linear unbiased prediction overall performs better than other methods across different traits and different omic data, and genomic prediction performs better than transcriptomic and metabolomic predictions. For the same maize data, we also conducted genome-wide association study, transcriptome-wide association studies and metabolome-wide association studies for the six agronomic traits using both the genome-wide efficient mixed model association (GEMMA) method and a modified least absolute shrinkage and selection operator (LASSO) method. The new LASSO method has the ability to perform statistical tests. Simulation studies show that the modified LASSO performs better than GEMMA in terms of high power and low Type 1 error.

High Density Linkage Map Construction and Mapping of Yield Trait QTLs in Maize (Zea mays) Using the Genotyping-by-Sequencing (GBS) Technology

Increasing grain yield is the ultimate goal for maize breeding. High resolution quantitative trait loci (QTL) mapping can help us understand the molecular basis of phenotypic variation of yield and thus facilitate marker assisted breeding. The aim of this study is to use genotyping-by-sequencing (GBS) for large-scale SNP discovery and simultaneous genotyping of all F₂ individuals from a cross between two varieties of maize that are in clear contrast in yield and related traits. A set of 199 F₂ progeny derived from the cross of varieties SG-5 and SG-7 were generated and genotyped by GBS. A total of 1,046,524,604 reads with an average of 5,258,918 reads per F₂ individual were generated. This number of reads represents an approximately 0.36-fold coverage of the maize reference genome Zea_mays.AGPv3.29 for each F₂ individual. A total of 68,882 raw SNPs were discovered in the F₂ population, which, after stringent filtering, led to a total of 29,927 high quality SNPs. Comparative analysis using these physically mapped marker loci revealed a higher degree of synteny with the reference genome. The SNP genotype data were utilized to construct an intra-specific genetic linkage map of maize consisting of 3,305 bins on 10 linkage groups spanning 2,236.66 cM at an average distance of 0.68 cM between consecutive markers. From this map, we identified 28 QTLs associated with yield traits (100-kernel weight, ear length, ear diameter, cob diameter, kernel row number, corn grains per row, ear weight, and grain weight per plant) using the composite interval mapping (CIM) method and 29 QTLs using the least absolute shrinkage selection operator (LASSO) method. QTLs identified by the CIM method account for 6.4% to 19.7% of the phenotypic variation. Small intervals of three QTLs (qCGR-1, qKW-2, and qGWP-4) contain several genes, including one gene (GRMZM2G139872) encoding the F-box protein, three genes (GRMZM2G180811, GRMZM5G828139, and GRMZM5G873194) encoding the WD40-repeat protein, and one gene (GRMZM2G019183) encoding the UDP-Glycosyltransferase. The work will not only help to understand the mechanisms that control yield traits of maize, but also provide a basis for marker-assisted selection and map-based cloning in further studies.

Dissection of Recombination Attributes for Multiple Maize Populations Using a Common SNP Assay

Recombination is a vital characteristic for quantitative trait loci mapping and breeding to enhance the yield potential of maize. However, recombination characteristics in globally used segregating populations have never been evaluated at similar genetic marker densities. This study aimed to divulge the characteristics of recombination events, recombinant chromosomal segments, and recombination frequency for four dissimilar populations. These populations were doubled haploid (DH), recombination inbred line (RIL), intermated B73xMo17 (IBM), and multi-parent advanced generation inter-cross (MAGIC), using the Illumina MaizeSNP50 BeadChip to provide markers. Our results revealed that the average number of recombination events was 16, 41, 72, and 86 per line in DH, RIL, IBM, and MAGIC populations, respectively. Accordingly, the average length of recombinant chromosomal segments was 84.8, 47.3, 29.2, and 20.4 Mb in DH, RIL, IBM, and MAGIC populations, respectively. Furtherly, the recombination frequency varied in different genomic regions and population types [DH (0-12.7 cM/Mb), RIL (0-15.5 cM/Mb), IBM (0-24.1 cM/Mb), MAGIC (0-42.3 cM/Mb)]. Utilizing different sub-sets of lines, the recombination bin number and size were analyzed in each population. Additionally, different sub-sets of markers and lines were employed to estimate the recombination bin number and size via formulas for relationship in these populations. The relationship between recombination events and recombination bin length was also examined. Our results contribute to determining the most suitable number of genetic markers, lines in each population, and population type for successful mapping and breeding.

Weighting Strategies for Single-Step Genomic BLUP: An Iterative Approach for Accurate Calculation of GEBV and GWAS

Genomic Best Linear Unbiased Predictor (GBLUP) assumes equal variance for all single nucleotide polymorphisms (SNP). When traits are influenced by major SNP, Bayesian methods have the advantage of SNP selection. To overcome the limitation of GBLUP, unequal variance or weights for all SNP are applied in a method called weighted GBLUP (WGBLUP). If only a fraction of animals is genotyped, single-step WGBLUP (WssGBLUP) can be used. Default weights in WGBLUP or WssGBLUP are obtained iteratively based on single SNP effect squared (u²) and/or heterozygosity. When the weights are optimal, prediction accuracy, and ability to detect major SNP are maximized. The objective was to develop optimal weights for WGBLUP-based methods. We evaluated 5 new procedures that accounted for locus-specific or windows-specific variance to maximize accuracy of predicting genomic estimated breeding value (GEBV) and SNP effect. Simulated datasets consisted of phenotypes for 13,000 animals, including 1540 animals genotyped for 45,000 SNP. Scenarios with 5, 100, and 500 simulated quantitative trait loci (QTL) were considered. The 5 new procedures for SNP weighting were: (1) u² plus a constant equal to the weight of the top SNP; (2) from a heavy-tailed distribution (similar to BayesA); (3) for every 20 SNP in a window along the whole genome, the largest effect (u²) among them; (4) the mean effect of every 20 SNP; and (5) the summation of every 20 SNP. Those methods were compared to the default WssGBLUP, GBLUP, BayesB, and BayesC. WssGBLUP methods were evaluated over 10 iterations. The accuracy of predicting GEBV was the correlation between true and estimated genomic breeding values for 300 genotyped animals from the last generation. The ability to detect the simulated QTL was also investigated. For most of the QTL scenarios, the accuracies obtained with all WssGBLUP procedures were higher compared to those from BayesB and BayesC, partly due to automatic inclusion of parent average in the former. Manhattan plots had higher resolution with 5 and 100 QTL. Using a common weight for a window of 20 SNP that sums or averages the SNP variance enhances accuracy of predicting GEBV and provides accurate estimation of marker effects.

Assessing Predictive Properties of Genome-Wide Selection in Soybeans

Many economically important traits in plant breeding have low heritability or are difficult to measure. For these traits, genomic selection has attractive features and may boost genetic gains. Our goal was to evaluate alternative scenarios to implement genomic selection for yield components in soybean (Glycine max L. merr). We used a nested association panel with cross validation to evaluate the impacts of training population size, genotyping density, and prediction model on the accuracy of genomic prediction. Our results indicate that training population size was the factor most relevant to improvement in genome-wide prediction, with greatest improvement observed in training sets up to 2000 individuals. We discuss assumptions that influence the choice of the prediction model. Although alternative models had minor impacts on prediction accuracy, the most robust prediction model was the combination of reproducing kernel Hilbert space regression and BayesB. Higher genotyping density marginally improved accuracy. Our study finds that breeding programs seeking efficient genomic selection in soybeans would best allocate resources by investing in a representative training set.

High Resolution Genomic Scans Reveal Genetic Architecture Controlling Alcohol Preference in Bidirectionally Selected Rat Model

Investigations on the influence of nature vs. nurture on Alcoholism (Alcohol Use Disorder) in human have yet to provide a clear view on potential genomic etiologies. To address this issue, we sequenced a replicated animal model system bidirectionally-selected for alcohol preference (AP). This model is uniquely suited to map genetic effects with high reproducibility, and resolution. The origin of the rat lines (an 8-way cross) resulted in small haplotype blocks (HB) with a corresponding high level of resolution. We sequenced DNAs from 40 samples (10 per line of each replicate) to determine allele frequencies and HB. We achieved ~46X coverage per line and replicate. Excessive differentiation in the genomic architecture between lines, across replicates, termed signatures of selection (SS), were classified according to gene and region. We identified SS in 930 genes associated with AP. The majority (50%) of the SS were confined to single gene regions, the greatest numbers of which were in promoters (284) and intronic regions (169) with the least in exon's (4), suggesting that differences in AP were primarily due to alterations in regulatory regions. We confirmed previously identified genes and found many new genes associated with AP. Of those newly identified genes, several demonstrated neuronal function involved in synaptic memory and reward behavior, e.g. ion channels (Kcnf1, Kcnn3, Scn5a), excitatory receptors (Grin2a, Gria3, Grip1), neurotransmitters (Pomc), and synapses (Snap29). This study not only reveals the polygenic architecture of AP, but also emphasizes the importance of regulatory elements, consistent with other complex traits.

Alcohol Used Disorder (AUD) or Alcoholism extracts a great societal cost in terms of human suffering. Understanding the genetic basis is critical to comprehend, treat and prevent this disease, but difficult in humans, as choice is influenced by nature and nurture. To discover its genetic basis, we used an animal model system that controlled for genetic and non-genetic factors through randomization, study replication, long-term divergent selection, and a controlled environment. We conducted whole genome sequencing in breeds that were either compulsive excessive drinkers or completely abstinent. We discovered consistent alterations in several genes and neurological pathways previously unassociated with alcoholism. These results strengthened our understanding of the genetic basis of alcoholism and revealed potential genetic- and neurological-based treatments.

PEPIS: A Pipeline for Estimating Epistatic Effects in Quantitative Trait Locus Mapping and Genome-Wide Association Studies

The term epistasis refers to interactions between multiple genetic loci. Genetic epistasis is important in regulating biological function and is considered to explain part of the 'missing heritability,' which involves marginal genetic effects that cannot be accounted for in genome-wide association studies. Thus, the study of epistasis is of great interest to geneticists. However, estimating epistatic effects for quantitative traits is challenging due to the large number of interaction effects that must be estimated, thus significantly increasing computing demands. Here, we present a new web server-based tool, the Pipeline for estimating EPIStatic genetic effects (PEPIS), for analyzing polygenic epistatic effects. The PEPIS software package is based on a new linear mixed model that has been used to predict the performance of hybrid rice. The PEPIS includes two main sub-pipelines: the first for kinship matrix calculation, and the second for polygenic component analyses and genome scanning for main and epistatic effects. To accommodate the demand for high-performance computation, the PEPIS utilizes C/C++ for mathematical matrix computing. In addition, the modules for kinship matrix calculations and main and epistatic-effect genome scanning employ parallel computing technology that effectively utilizes multiple computer nodes across our networked cluster, thus significantly improving the computational speed. For example, when analyzing the same immortalized F2 rice population genotypic data examined in a previous study, the PEPIS returned identical results at each analysis step with the original prototype R code, but the computational time was reduced from more than one month to about five minutes. These advances will help overcome the bottleneck frequently encountered in genome wide epistatic genetic effect analysis and enable accommodation of the high computational demand. The PEPIS is publically available at http://bioinfo.noble.org/PolyGenic_QTL/.

Implementation of Genomic Prediction in Lolium perenne (L.) Breeding Populations

Perennial ryegrass (Lolium perenne L.) is one of the most widely grown forage grasses in temperate agriculture. In order to maintain and increase its usage as forage in livestock agriculture, there is a continued need for improvement in biomass yield, quality, disease resistance, and seed yield. Genetic gain for traits such as biomass yield has been relatively modest. This has been attributed to its long breeding cycle, and the necessity to use population based breeding methods. Thanks to recent advances in genotyping techniques there is increasing interest in genomic selection from which genomically estimated breeding values are derived. In this paper we compare the classical RRBLUP model with state-of-the-art machine learning techniques that should yield themselves easily to use in GS and demonstrate their application to predicting quantitative traits in a breeding population of L. perenne. Prediction accuracies varied from 0 to 0.59 depending on trait, prediction model and composition of the training population. The BLUP model produced the highest prediction accuracies for most traits and training populations. Forage quality traits had the highest accuracies compared to yield related traits. There appeared to be no clear pattern to the effect of the training population composition on the prediction accuracies. The heritability of the forage quality traits was generally higher than for the yield related traits, and could partly explain the difference in accuracy. Some population structure was evident in the breeding populations, and probably contributed to the varying effects of training population on the predictions. The average linkage disequilibrium between adjacent markers ranged from 0.121 to 0.215. Higher marker density and larger training population closely related with the test population are likely to improve the prediction accuracy.

A Random-Model Approach to QTL Mapping in Multiparent Advanced Generation Intercross (MAGIC) Populations

Most standard QTL mapping procedures apply to populations derived from the cross of two parents. QTL detected from such biparental populations are rarely relevant to breeding programs because of the narrow genetic basis: only two alleles are involved per locus. To improve the generality and applicability of mapping results, QTL should be detected using populations initiated from multiple parents, such as the multiparent advanced generation intercross (MAGIC) populations. The greatest challenges of QTL mapping in MAGIC populations come from multiple founder alleles and control of the genetic background information. We developed a random-model methodology by treating the founder effects of each locus as random effects following a normal distribution with a locus-specific variance. We also fit a polygenic effect to the model to control the genetic background. To improve the statistical power for a scanned marker, we release the marker effect absorbed by the polygene back to the model. In contrast to the fixed-model approach, we estimate and test the variance of each locus and scan the entire genome one locus at a time using likelihood-ratio test statistics. Simulation studies showed that this method can increase statistical power and reduce type I error compared with composite interval mapping (CIM) and multiparent whole-genome average interval mapping (MPWGAIM). We demonstrated the method using a public Arabidopsis thaliana MAGIC population and a mouse MAGIC population.

An efficient empirical Bayes method for genomewide association studies

Linear mixed model (LMM) is one of the most popular methods for genomewide association studies (GWAS). Numerous forms of LMM have been developed; however, there are two major issues in GWAS that have not been fully addressed before. The two issues are (i) the genomic background noise and (ii) low statistical power after Bonferroni correction. We proposed an empirical Bayes (EB) method by assigning each marker effect a normal prior distribution, resulting in shrinkage estimates of marker effects. We found that such a shrinkage approach can selectively shrink marker effects and reduce the noise level to zero for majority of non-associated markers. In the meantime, the EB method allows us to use an 'effective number of tests' to perform Bonferroni correction for multiple tests. Simulation studies for both human and pig data showed that EB method can significantly increase statistical power compared with the widely used exact GWAS methods, such as GEMMA and FaST-LMM-Select. Real data analyses in human breast cancer identified improved detection signals for markers previously known to be associated with breast cancer. We therefore believe that EB method is a valuable tool for identifying the genetic basis of complex traits.

Locally epistatic genomic relationship matrices for genomic association and prediction

In plant and animal breeding studies a distinction is made between the genetic value (additive plus epistatic genetic effects) and the breeding value (additive genetic effects) of an individual since it is expected that some of the epistatic genetic effects will be lost due to recombination. In this article, we argue that the breeder can take advantage of the epistatic marker effects in regions of low recombination. The models introduced here aim to estimate local epistatic line heritability by using genetic map information and combining local additive and epistatic effects. To this end, we have used semiparametric mixed models with multiple local genomic relationship matrices with hierarchical designs. Elastic-net postprocessing was used to introduce sparsity. Our models produce good predictive performance along with useful explanatory information.

Genomic selection: genome-wide prediction in plant improvement

Association analysis is used to measure relations between markers and quantitative trait loci (QTL). Their estimation ignores genes with small effects that trigger underpinning quantitative traits. By contrast, genome-wide selection estimates marker effects across the whole genome on the target population based on a prediction model developed in the training population (TP). Whole-genome prediction models estimate all marker effects in all loci and capture small QTL effects. Here, we review several genomic selection (GS) models with respect to both the prediction accuracy and genetic gain from selection. Phenotypic selection or marker-assisted breeding protocols can be replaced by selection, based on whole-genome predictions in which phenotyping updates the model to build up the prediction accuracy.

Constructing a dense genetic linkage map and mapping QTL for the traits of flower development in Brassica carinata

An integrated dense genetic linkage map was constructed in a B. carinata population and used for comparative genome analysis and QTL identification for flowering time. An integrated dense linkage map of Brassica carinata (BBCC) was constructed in a doubled haploid population based on DArT-Seq(TM) markers. A total of 4,031 markers corresponding to 1,366 unique loci were mapped including 639 bins, covering a genetic distance of 2,048 cM. We identified 136 blocks and islands conserved in Brassicaceae, which showed a feature of hexaploidisation representing the suggested ancestral crucifer karyotype. The B and C genome of B. carinata shared 85 % of commonly conserved blocks with the B genome of B. nigra/B. juncea and 80 % of commonly conserved blocks with the C genome of B. napus, and shown frequent structural rearrangements such as insertions and inversions. Up to 24 quantitative trait loci (QTL) for flowering and budding time were identified in the DH population. Of these QTL, one consistent QTL (qFT.B4-2) for flowering time was identified in all of the environments in the J block of the B4 linkage group, where a group of genes for flowering time were aligned in A. thaliana. Another major QTL for flowering time under a winter-cropped environment was detected in the E block of C6, where the BnFT-C6 gene was previously localised in B. napus. This high-density map would be useful not only to reveal the genetic variation in the species with QTL analysis and genome sequencing, but also for other applications such as marker-assisted selection and genomic selection, for the African mustard improvement.

Mapping quantitative trait loci by controlling polygenic background effects

A new mixed-model method was developed for mapping quantitative trait loci (QTL) by incorporating multiple polygenic covariance structures. First, we used genome-wide markers to calculate six different kinship matrices. We then partitioned the total genetic variance into six variance components, one corresponding to each kinship matrix, including the additive, dominance, additive × additive, dominance × dominance, additive × dominance, and dominance × additive variances. The six different kinship matrices along with the six estimated polygenic variances were used to control the genetic background of a QTL mapping model. Simulation studies showed that incorporating epistatic polygenic covariance structure can improve QTL mapping resolution. The method was applied to yield component traits of rice. We analyzed four traits (yield, tiller number, grain number, and grain weight) using 278 immortal F2 crosses (crosses between recombinant inbred lines) and 1619 markers. We found that the relative importance of each type of genetic variance varies across different traits. The total genetic variance of yield is contributed by additive × additive (18%), dominance × dominance (14%), additive × dominance (48%), and dominance × additive (15%) variances. Tiller number is contributed by additive (17%), additive × additive (22%), and dominance × additive (43%) variances. Grain number is mainly contributed by additive (42%), additive × additive (19%), and additive × dominance (31%) variances. Grain weight is almost exclusively contributed by the additive (73%) variance plus a small contribution from the additive × additive (10%) variance. Using the estimated genetic variance components to capture the polygenic covariance structure, we detected 39 effects for yield, 39 effects for tiller number, 24 for grain number, and 15 for grain weight. The new method can be directly applied to polygenic-effect-adjusted genome-wide association studies (GWAS) in human and other species.