A new approach fits multivariate genomic prediction models efficiently.

BACKGROUND: Fast, memory-efficient, and reliable algorithms for estimating genomic estimated breeding values (GEBV) for multiple traits and environments are needed to make timely decisions in breeding. Multivariate genomic prediction exploits genetic correlations between traits and environments to increase accuracy of GEBV compared to univariate methods. These genetic correlations are estimated simultaneously with GEBV, because they are specific to year, environment, and management. However, estimating genetic parameters is computationally demanding with restricted maximum likelihood (REML) and Bayesian samplers, and canonical transformations or orthogonalizations cannot be used for unbalanced experimental designs. METHODS: We propose a multivariate randomized Gauss-Seidel algorithm for simultaneous estimation of model effects and genetic parameters. Two previously proposed methods for estimating genetic parameters were combined with a Gauss-Seidel (GS) solver, and were called Tilde-Hat-GS (THGS) and Pseudo-Expectation-GS (PEGS). Balanced and unbalanced experimental designs were simulated to compare runtime, bias and accuracy of GEBV, and bias and standard errors of estimates of heritabilities and genetic correlations of THGS, PEGS, and REML. Models with 10 to 400 response variables, 1279 to 42,034 genetic markers, and 5990 to 1.85 million observations were fitted. RESULTS: Runtime of PEGS and THGS was a fraction of REML. Accuracies of GEBV were slightly lower than those from REML, but higher than those from the univariate approach, hence THGS and PEGS exploited genetic correlations. For 500 to 600 observations per response variable, biases of estimates of genetic parameters of THGS and PEGS were small, but standard errors of estimates of genetic correlations were higher than for REML. Bias and standard errors decreased as sample size increased. For balanced designs, GEBV and estimates of genetic correlations from THGS were unbiased when only an intercept and eigenvectors of genotype scores were fitted. CONCLUSIONS: THGS and PEGS are fast and memory-efficient algorithms for multivariate genomic prediction for balanced and unbalanced experimental designs. They are scalable for increasing numbers of environments and genetic markers. Accuracy of GEBV was comparable to REML. Estimates of genetic parameters had little bias, but their standard errors were larger than for REML. More studies are needed to evaluate the proposed methods for datasets that contain selection.

Nested-association mapping (NAM)-based genetic dissection uncovers candidate genes for seed and pod weights in peanut (Arachis hypogaea).

Multiparental genetic mapping populations such as nested-association mapping (NAM) have great potential for investigating quantitative traits and associated genomic regions leading to rapid discovery of candidate genes and markers. To demonstrate the utility and power of this approach, two NAM populations, NAM_Tifrunner and NAM_Florida-07, were used for dissecting genetic control of 100-pod weight (PW) and 100-seed weight (SW) in peanut. Two high-density SNP-based genetic maps were constructed with 3341 loci and 2668 loci for NAM_Tifrunner and NAM_Florida-07, respectively. The quantitative trait locus (QTL) analysis identified 12 and 8 major effect QTLs for PW and SW, respectively, in NAM_Tifrunner, and 13 and 11 major effect QTLs for PW and SW, respectively, in NAM_Florida-07. Most of the QTLs associated with PW and SW were mapped on the chromosomes A05, A06, B05 and B06. A genomewide association study (GWAS) analysis identified 19 and 28 highly significant SNP-trait associations (STAs) in NAM_Tifrunner and 11 and 17 STAs in NAM_Florida-07 for PW and SW, respectively. These significant STAs were co-localized, suggesting that PW and SW are co-regulated by several candidate genes identified on chromosomes A05, A06, B05, and B06. This study demonstrates the utility of NAM population for genetic dissection of complex traits and performing high-resolution trait mapping in peanut.

bWGR: Bayesian Whole-Genome Regression.

MOTIVATION: Whole-genome regressions methods represent a key framework for genome-wide prediction, cross-validation studies, and association analysis. The bWGR offers a compendium of Bayesian methods with various priors available, allowing users to predict complex traits with different genetic architectures. RESULTS: Here we introduce bWGR, an R package that enables users to efficient fit and cross-validate Bayesian and likelihood whole-genome regression methods. It implements a series of methods referred to as the Bayesian alphabet under the traditional Gibbs sampling and optimized Expectation-Maximization. The package also enables fitting efficient multivariate models and complex hierarchical models. The package is user-friendly and computational efficient. AVAILABILITY AND IMPLEMENTATION: bWGR is an R package available in the CRAN repository. It can be installed in R by typing: install.packages("bWGR"). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Genomic prediction using subsampling.

BACKGROUND: Genome-wide assisted selection is a critical tool for the genetic improvement of plants and animals. Whole-genome regression models in Bayesian framework represent the main family of prediction methods. Fitting such models with a large number of observations involves a prohibitive computational burden. We propose the use of subsampling bootstrap Markov chain in genomic prediction. Such method consists of fitting whole-genome regression models by subsampling observations in each round of a Markov Chain Monte Carlo. We evaluated the effect of subsampling bootstrap on prediction and computational parameters. RESULTS: Across datasets, we observed an optimal subsampling proportion of observations around 50% with replacement, and around 33% without replacement. Subsampling provided a substantial decrease in computation time, reducing the time to fit the model by half. On average, losses on predictive properties imposed by subsampling were negligible, usually below 1%. For each dataset, an optimal subsampling point that improves prediction properties was observed, but the improvements were also negligible. CONCLUSION: Combining subsampling with Gibbs sampling is an interesting ensemble algorithm. The investigation indicates that the subsampling bootstrap Markov chain algorithm substantially reduces computational burden associated with model fitting, and it may slightly enhance prediction properties.

NAM: association studies in multiple populations.

MOTIVATION: Mixed linear models provide important techniques for performing genome-wide association studies. However, current models have pitfalls associated with their strong assumptions. Here, we propose a new implementation designed to overcome some of these pitfalls using an empirical Bayes algorithm. RESULTS: Here we introduce NAM, an R package that allows user to take into account prior information regarding population stratification to relax the linkage phase assumption of current methods. It allows markers to be treated as a random effect to increase the resolution, and uses a sliding-window strategy to increase power and avoid double fitting markers into the model. AVAILABILITY AND IMPLEMENTATION: NAM is an R package available in the CRAN repository. It can be installed in R by typing install.packages ('NAM'). CONTACT: krainey@purdue.edu. SUPPLEMENTARY INFORMATION: Supplementary date are available at Bioinformatics online.

Walking through the statistical black boxes of plant breeding.

KEY MESSAGE: The main statistical procedures in plant breeding are based on Gaussian process and can be computed through mixed linear models. Intelligent decision making relies on our ability to extract useful information from data to help us achieve our goals more efficiently. Many plant breeders and geneticists perform statistical analyses without understanding the underlying assumptions of the methods or their strengths and pitfalls. In other words, they treat these statistical methods (software and programs) like black boxes. Black boxes represent complex pieces of machinery with contents that are not fully understood by the user. The user sees the inputs and outputs without knowing how the outputs are generated. By providing a general background on statistical methodologies, this review aims (1) to introduce basic concepts of machine learning and its applications to plant breeding; (2) to link classical selection theory to current statistical approaches; (3) to show how to solve mixed models and extend their application to pedigree-based and genomic-based prediction; and (4) to clarify how the algorithms of genome-wide association studies work, including their assumptions and limitations.

A marker weighting approach for enhancing within-family accuracy in genomic prediction.

Genomic selection is revolutionizing plant breeding. However, its practical implementation is still very challenging, since predicted values do not necessarily have high correspondence to the observed phenotypic values. When the goal is to predict within-family, it is not always possible to obtain reasonable accuracies, which is of paramount importance to improve the selection process. For this reason, in this research, we propose the Adversaria-Boruta (AB) method, which combines the virtues of the adversarial validation (AV) method and the Boruta feature selection method. The AB method operates primarily by minimizing the disparity between training and testing distributions. This is accomplished by reducing the weight assigned to markers that display the most significant differences between the training and testing sets. Therefore, the AB method built a weighted genomic relationship matrix that is implemented with the genomic best linear unbiased predictor (GBLUP) model. The proposed AB method is compared using 12 real data sets with the GBLUP model that uses a nonweighted genomic relationship matrix. Our results show that the proposed AB method outperforms the GBLUP by 8.6, 19.7, and 9.8% in terms of Pearson's correlation, mean square error, and normalized root mean square error, respectively. Our results support that the proposed AB method is a useful tool to improve the prediction accuracy of a complete family, however, we encourage other investigators to evaluate the AB method to increase the empirical evidence of its potential.

High-throughput characterization, correlation, and mapping of leaf photosynthetic and functional traits in the soybean (Glycine max) nested association mapping population.

Photosynthesis is a key target to improve crop production in many species including soybean [Glycine max (L.) Merr.]. A challenge is that phenotyping photosynthetic traits by traditional approaches is slow and destructive. There is proof-of-concept for leaf hyperspectral reflectance as a rapid method to model photosynthetic traits. However, the crucial step of demonstrating that hyperspectral approaches can be used to advance understanding of the genetic architecture of photosynthetic traits is untested. To address this challenge, we used full-range (500-2,400 nm) leaf reflectance spectroscopy to build partial least squares regression models to estimate leaf traits, including the rate-limiting processes of photosynthesis, maximum Rubisco carboxylation rate, and maximum electron transport. In total, 11 models were produced from a diverse population of soybean sampled over multiple field seasons to estimate photosynthetic parameters, chlorophyll content, leaf carbon and leaf nitrogen percentage, and specific leaf area (with R2 from 0.56 to 0.96 and root mean square error approximately <10% of the range of calibration data). We explore the utility of these models by applying them to the soybean nested association mapping population, which showed variability in photosynthetic and leaf traits. Genetic mapping provided insights into the underlying genetic architecture of photosynthetic traits and potential improvement in soybean. Notably, the maximum Rubisco carboxylation rate mapped to a region of chromosome 19 containing genes encoding multiple small subunits of Rubisco. We also mapped the maximum electron transport rate to a region of chromosome 10 containing a fructose 1,6-bisphosphatase gene, encoding an important enzyme in the regeneration of ribulose 1,5-bisphosphate and the sucrose biosynthetic pathway. The estimated rate-limiting steps of photosynthesis were low or negatively correlated with yield suggesting that these traits are not influenced by the same genetic mechanisms and are not limiting yield in the soybean NAM population. Leaf carbon percentage, leaf nitrogen percentage, and specific leaf area showed strong correlations with yield and may be of interest in breeding programs as a proxy for yield. This work is among the first to use hyperspectral reflectance to model and map the genetic architecture of the rate-limiting steps of photosynthesis.

Two decades of association mapping: Insights on disease resistance in major crops.

Climate change across the globe has an impact on the occurrence, prevalence, and severity of plant diseases. About 30% of yield losses in major crops are due to plant diseases; emerging diseases are likely to worsen the sustainable production in the coming years. Plant diseases have led to increased hunger and mass migration of human populations in the past, thus a serious threat to global food security. Equipping the modern varieties/hybrids with enhanced genetic resistance is the most economic, sustainable and environmentally friendly solution. Plant geneticists have done tremendous work in identifying stable resistance in primary genepools and many times other than primary genepools to breed resistant varieties in different major crops. Over the last two decades, the availability of crop and pathogen genomes due to advances in next generation sequencing technologies improved our understanding of trait genetics using different approaches. Genome-wide association studies have been effectively used to identify candidate genes and map loci associated with different diseases in crop plants. In this review, we highlight successful examples for the discovery of resistance genes to many important diseases. In addition, major developments in association studies, statistical models and bioinformatic tools that improve the power, resolution and the efficiency of identifying marker-trait associations. Overall this review provides comprehensive insights into the two decades of advances in GWAS studies and discusses the challenges and opportunities this research area provides for breeding resistant varieties.

Impact of Genomic Prediction Model, Selection Intensity, and Breeding Strategy on the Long-Term Genetic Gain and Genetic Erosion in Soybean Breeding.

Genomic-assisted breeding has become an important tool in soybean breeding. However, the impact of different genomic selection (GS) approaches on short- and long-term gains is not well understood. Such gains are conditional on the breeding design and may vary with a combination of the prediction model, family size, selection strategies, and selection intensity. To address these open questions, we evaluated various scenarios through a simulated closed soybean breeding program over 200 breeding cycles. Genomic prediction was performed using genomic best linear unbiased prediction (GBLUP), Bayesian methods, and random forest, benchmarked against selection on phenotypic values, true breeding values (TBV), and random selection. Breeding strategies included selections within family (WF), across family (AF), and within pre-selected families (WPSF), with selection intensities of 2.5, 5.0, 7.5, and 10.0%. Selections were performed at the F4 generation, where individuals were phenotyped and genotyped with a 6K single nucleotide polymorphism (SNP) array. Initial genetic parameters for the simulation were estimated from the SoyNAM population. WF selections provided the most significant long-term genetic gains. GBLUP and Bayesian methods outperformed random forest and provided most of the genetic gains within the first 100 generations, being outperformed by phenotypic selection after generation 100. All methods provided similar performances under WPSF selections. A faster decay in genetic variance was observed when individuals were selected AF and WPSF, as 80% of the genetic variance was depleted within 28-58 cycles, whereas WF selections preserved the variance up to cycle 184. Surprisingly, the selection intensity had less impact on long-term gains than did the breeding strategies. The study supports that genetic gains can be optimized in the long term with specific combinations of prediction models, family size, selection strategies, and selection intensity. A combination of strategies may be necessary for balancing the short-, medium-, and long-term genetic gains in breeding programs while preserving the genetic variance.

Quantitative Genomic Dissection of Soybean Yield Components.

Soybean is a crop of major economic importance with low rates of genetic gains for grain yield compared to other field crops. A deeper understanding of the genetic architecture of yield components may enable better ways to tackle the breeding challenges. Key yield components include the total number of pods, nodes and the ratio pods per node. We evaluated the SoyNAM population, containing approximately 5600 lines from 40 biparental families that share a common parent, in 6 environments distributed across 3 years. The study indicates that the yield components under evaluation have low heritability, a reasonable amount of epistatic control, and partially oligogenic architecture: 18 quantitative trait loci were identified across the three yield components using multi-approach signal detection. Genetic correlation between yield and yield components was highly variable from family-to-family, ranging from -0.2 to 0.5. The genotype-by-environment correlation of yield components ranged from -0.1 to 0.4 within families. The number of pods can be utilized for indirect selection of yield. The selection of soybean for enhanced yield components can be successfully performed via genomic prediction, but the challenging data collections necessary to recalibrate models over time makes the introgression of QTL a potentially more feasible breeding strategy. The genomic prediction of yield components was relatively accurate across families, but less accurate predictions were obtained from within family predictions and predicting families not observed included in the calibration set.

Efficient Estimation of Marker Effects in Plant Breeding.

The evaluation of prediction machines is an important step for a successful implementation of genomic-enabled selection in plant breeding. Computation time and predictive ability constitute key metrics to determine the methodology utilized for the consolidation of genomic prediction pipeline. This study introduces two methods designed to couple high prediction accuracy with efficient computational performance: 1) a non-MCMC method to estimate marker effects with a Laplace prior; and 2) an iterative framework that allows solving whole-genome regression within mixed models with replicated observations in a single-stage. The investigation provides insights on predictive ability and marker effect estimates. Various genomic prediction techniques are compared based on cross-validation, assessing predictions across and within family. Properties of quantitative trait loci detection and single-stage method were evaluated on simulated plot-level data from unbalanced data structures. Estimation of marker effects by the new model is compared to a genome-wide association analysis and whole-genome regression methods. The single-stage approach is compared to a GBLUP fitted via restricted maximum likelihood, and a two-stages approaches where genetic values fit a whole-genome regression. The proposed framework provided high computational efficiency, robust prediction across datasets, and accurate estimation of marker effects.

Phenotypic Variation and Genetic Architecture for Photosynthesis and Water Use Efficiency in Soybean (Glycine max L. Merr).

Photosynthesis (A) and intrinsic water use efficiency (WUE) are physiological traits directly influencing biomass production, conversion efficiency, and grain yield. Though the influence of physiological process on yield is widely known, studies assessing improvement strategies are rare due to laborious phenotyping and specialized equipment needs. This is one of the first studies to assess the genetic architecture underlying A and intrinsic WUE, as well as to evaluate the feasibility of implementing genomic prediction. A panel of 383 soybean recombinant inbred lines were evaluated in a multi-environment yield trial that included measurements of A and intrinsic WUE, using an infrared gas analyzer during R4-R5 growth stages. Genetic variability was found to support the possibility of genetic improvement through breeding. High genetic correlation between grain yield (GY) and A (0.80) was observed, suggesting increases in GY can be achieved through the improvement of A. Genome-wide association analysis revealed quantitative trait loci (QTLs) for these physiological traits. Cross-validation studies indicated high predictive ability (>0.65) for the implementation of genomic prediction as a viable strategy to improve physiological efficiency while reducing field phenotyping. This work provides core knowledge to develop new soybean cultivars with enhanced photosynthesis and water use efficiency through conventional breeding and genomic techniques.

Genome-Wide Analysis of Grain Yield Stability and Environmental Interactions in a Multiparental Soybean Population.

Genetic improvement toward optimized and stable agronomic performance of soybean genotypes is desirable for food security. Understanding how genotypes perform in different environmental conditions helps breeders develop sustainable cultivars adapted to target regions. Complex traits of importance are known to be controlled by a large number of genomic regions with small effects whose magnitude and direction are modulated by environmental factors. Knowledge of the constraints and undesirable effects resulting from genotype by environmental interactions is a key objective in improving selection procedures in soybean breeding programs. In this study, the genetic basis of soybean grain yield responsiveness to environmental factors was examined in a large soybean nested association population. For this, a genome-wide association to performance stability estimates generated from a Finlay-Wilkinson analysis and the inclusion of the interaction between marker genotypes and environmental factors was implemented. Genomic footprints were investigated by analysis and meta-analysis using a recently published multiparent model. Results indicated that specific soybean genomic regions were associated with stability, and that multiplicative interactions were present between environments and genetic background. Seven genomic regions in six chromosomes were identified as being associated with genotype-by-environment interactions. This study provides insight into genomic assisted breeding aimed at achieving a more stable agronomic performance of soybean, and documented opportunities to exploit genomic regions that were specifically associated with interactions involving environments and subpopulations.

Genetic Architecture of Soybean Yield and Agronomic Traits.

Soybean is the world's leading source of vegetable protein and demand for its seed continues to grow. Breeders have successfully increased soybean yield, but the genetic architecture of yield and key agronomic traits is poorly understood. We developed a 40-mating soybean nested association mapping (NAM) population of 5,600 inbred lines that were characterized by single nucleotide polymorphism (SNP) markers and six agronomic traits in field trials in 22 environments. Analysis of the yield, agronomic, and SNP data revealed 23 significant marker-trait associations for yield, 19 for maturity, 15 for plant height, 17 for plant lodging, and 29 for seed mass. A higher frequency of estimated positive yield alleles was evident from elite founder parents than from exotic founders, although unique desirable alleles from the exotic group were identified, demonstrating the value of expanding the genetic base of US soybean breeding.

Genetic Architecture of Phenomic-Enabled Canopy Coverage in Glycine max.

Digital imagery can help to quantify seasonal changes in desirable crop phenotypes that can be treated as quantitative traits. Because limitations in precise and functional phenotyping restrain genetic improvement in the postgenomic era, imagery-based phenomics could become the next breakthrough to accelerate genetic gains in field crops. Whereas many phenomic studies focus on exploratory analysis of spectral data without obvious interpretative value, we used field images to directly measure soybean canopy development from phenological stage V2 to R5. Over 3 years, we collected imagery using ground and aerial platforms of a large and diverse nested association panel comprising 5555 lines. Genome-wide association analysis of canopy coverage across sampling dates detected a large quantitative trait locus (QTL) on soybean (Glycine max, L. Merr.) chromosome 19. This QTL provided an increase in yield of 47.3 kg ha-1 Variance component analysis indicated that a parameter, described as average canopy coverage, is a highly heritable trait (h2 = 0.77) with a promising genetic correlation with grain yield (0.87), enabling indirect selection of yield via canopy development parameters. Our findings indicate that fast canopy coverage is an early season trait that is inexpensive to measure and has great potential for application in breeding programs focused on yield improvement. We recommend using the average canopy coverage in multiple trait schemes, especially for the early stages of the breeding pipeline (including progeny rows and preliminary yield trials), in which the large number of field plots makes collection of grain yield data challenging.

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.