Heritable microbiome variation is correlated with source environment in locally adapted maize varieties

Beneficial interactions with microorganisms are pivotal for crop performance and resilience. However, it remains unclear how heritable the microbiome is with respect to the host plant genotype and to what extent host genetic mechanisms can modulate plant-microbiota interactions in the face of environmental stresses. Here we surveyed 3,168 root and rhizosphere microbiome samples from 129 accessions of locally adapted Zea, sourced from diverse habitats and grown under control and different stress conditions. We quantified stress treatment and host genotype effects on the microbiome. Plant genotype and source environment were predictive of microbiome abundance. Genome-wide association analysis identified host genetic variants linked to both rhizosphere microbiome abundance and source environment. We identified transposon insertions in a candidate gene linked to both the abundance of a keystone bacterium Massilia in our controlled experiments and total soil nitrogen in the source environment. Isolation and controlled inoculation of Massilia alone can contribute to root development, whole-plant biomass production and adaptation to low nitrogen availability. We conclude that locally adapted maize varieties exert patterns of genetic control on their root and rhizosphere microbiomes that follow variation in their home environments, consistent with a role in tolerance to prevailing stress.

Genomic prediction reveals unexplored variation in grain protein and lysine content across a vast winter wheat genebank collection

Globally, wheat (Triticum aestivum L.) is a major source of proteins in human nutrition despite its unbalanced amino acid composition. The low lysine content in the protein fraction of wheat can lead to protein-energy-malnutrition prominently in developing countries. A promising strategy to overcome this problem is to breed varieties which combine high protein content with high lysine content. Nevertheless, this requires the incorporation of yet undefined donor genotypes into pre-breeding programs. Genebank collections are suspected to harbor the needed genetic diversity. In the 1970s, a large-scale screening of protein traits was conducted for the wheat genebank collection in Gatersleben; however, this data has been poorly mined so far. In the present study, a large historical dataset on protein content and lysine content of 4,971 accessions was curated, strictly corrected for outliers as well as for unreplicated data and consolidated as the corresponding adjusted entry means. Four genomic prediction approaches were compared based on the ability to accurately predict the traits of interest. High-quality phenotypic data of 558 accessions was leveraged by engaging the best performing prediction model, namely EG-BLUP. Finally, this publication incorporates predicted phenotypes of 7,651 accessions of the winter wheat collection. Five accessions were proposed as donor genotypes due to the combination of outstanding high protein content as well as lysine content. Further investigation of the passport data suggested an association of the adjusted lysine content with the elevation of the collecting site. This publicly available information can facilitate future pre-breeding activities.

Genetic control and prospects of predictive breeding for European winter wheat's Zeleny sedimentation values and Hagberg-Perten falling number

KEY MESSAGE

Sedimentation values and falling number in the last decades have helped maintain high baking quality despite rigorous selection for grain yield in wheat. Allelic combinations of major loci sustained the bread-making quality while improving grain yield. Glu-D1, Pinb-D1, and non-gluten proteins are associated with sedimentation values and falling number in European wheat. Zeleny sedimentation values (ZSV) and Hagberg-Perten falling number (HFN) are among the most important parameters that help determine the baking quality classes of wheat and, thus, influence the monetary benefits for growers. We used a published data set of 372 European wheat varieties evaluated in replicated field trials in multiple environments. ZSV and HFN traits hold a wide and significant genotypic variation and high broad-sense heritability. The genetic correlations revealed positive and significant associations of ZSV and HFN with each other, grain protein content (GPC) and grain hardness; however, they were all significantly negatively correlated with grain yield. Besides, GPC appeared to be the major predictor for ZSV and HFN. Our genome-wide association analyses based on high-quality SSR, SNP, and candidate gene markers revealed a strong quantitative genetic nature of ZSV and HFN by explaining their total genotypic variance as 41.49% and 38.06%, respectively. The association of known Glutenin (Glu-1) and Puroindoline (Pin-1) with ZSV provided positive analytic proof of our studies. We report novel candidate loci associated with globulins and albumins-the non-gluten monomeric proteins in wheat. In addition, predictive breeding analyses for ZSV and HFN suggest using genomic selection in the early stages of breeding programs with an average prediction accuracy of 81 and 59%, respectively.

Genomic predictions to leverage phenotypic data across genebanks

Genome-wide prediction is a powerful tool in breeding. Initial results suggest that genome-wide approaches are also promising for enhancing the use of the genebank material: predicting the performance of plant genetic resources can unlock their hidden potential and fill the information gap in genebanks across the world and, hence, underpin prebreeding programs. As a proof of concept, we evaluated the power of across-genebank prediction for extensive germplasm collections relying on historical data on flowering/heading date, plant height, and thousand kernel weight of 9,344 barley (Hordeum vulgare L.) plant genetic resources from the German Federal Ex situ Genebank for Agricultural and Horticultural Crops (IPK) and of 1,089 accessions from the International Center for Agriculture Research in the Dry Areas (ICARDA) genebank. Based on prediction abilities for each trait, three scenarios for predictive characterization were compared: 1) a benchmark scenario, where test and training sets only contain ICARDA accessions, 2) across-genebank predictions using IPK as training and ICARDA as test set, and 3) integrated genebank predictions that include IPK with 30% of ICARDA accessions as a training set to predict the rest of ICARDA accessions. Within the population of ICARDA accessions, prediction abilities were low to moderate, which was presumably caused by a limited number of accessions used to train the model. Interestingly, ICARDA prediction abilities were boosted up to ninefold by using training sets composed of IPK plus 30% of ICARDA accessions. Pervasive genotype × environment interactions (GEIs) can become a potential obstacle to train robust genome-wide prediction models across genebanks. This suggests that the potential adverse effect of GEI on prediction ability was counterbalanced by the augmented training set with certain connectivity to the test set. Therefore, across-genebank predictions hold the promise to improve the curation of the world's genebank collections and contribute significantly to the long-term development of traditional genebanks toward biodigital resource centers.

Maximization through optimization? On the relationship between hybrid performance and parental genetic distance

Heterosis is the improved performance of hybrids compared with their parental components and is widely exploited in agriculture. According to quantitative genetic theory, genetic distance between parents at heterotic quantitative trait loci is required for heterosis, but how heterosis varies with genetic distance has remained elusive, despite intensive research on the topic. Experimental studies have often found a positive association between heterosis and genetic distance that, however, varied in strength. Most importantly, it has remained unclear whether heterosis increases continuously with genetic distance or whether there is an optimum genetic distance after which heterosis declines again. Here, we revisit the relationship between heterosis and genetic distance and provide perspectives on how to maximize heterosis and hybrid performance in breeding, as well as the consequences for the design of heterotic groups and the utilization of more exotic material and genetic resources.

Deciphering the genetic basis of resistance to soybean cyst nematode combining IBD and association mapping

IBD analysis clarified the dynamics of chromosomal recombination during the ZP pedigree breeding process and identified ten genomic regions resistant to SCN race3 combining association mapping. Soybean cyst nematode (SCN, Heterodera glycines Ichinohe) is one of the most devastating pathogens for soybean production worldwide. The cultivar Zhongpin03-5373 (ZP), derived from SCN-resistant progenitor parents, Peking, PI 437654 and Huipizhi Heidou, is an elite line with high resistance to SCN race3. In the current study, a pedigree variation map was generated for ZP and its ten progenitors using 3,025,264 high-quality SNPs identified from an average of 16.2 × re-sequencing for each genome. Through identity by decent (IBD) tracking, we showed the dynamic change of genome and detected important IBD fragments, which revealed the comprehensively artificial selection of important traits during ZP breeding process. A total of 2,353 IBD fragments related to SCN resistance including SCN-resistant genes rhg1, rhg4 and NSF_RAN07 were identified based on the resistant-related genetic paths. Moreover, 23 genomic regions underlying resistance to SCN race3 were identified by genome-wide association study (GWAS) in 481 re-sequenced cultivated soybeans. Ten common loci were found by both IBD tracking and GWAS analysis. Haplotype analysis of 16 potential candidate genes suggested a causative SNP (C/T, - 1065) located in the promoter of Glyma.08G096500 and encoding a predicted TIFY5b-related protein on chr8 was highly correlated with SCN race3 resistance. Our results more thoroughly elucidated the dynamics of genomic fragments during ZP pedigree breeding and the genetic basis of SCN resistance, which will provide useful information for gene cloning and the development of resistant soybean cultivars using a marker-assisted selection approach.

High-throughput imaging of powdery mildew resistance of the winter wheat collection hosted at the German Federal ex situ Genebank for Agricultural and Horticultural Crops

BACKGROUND

Genebanks worldwide are transforming into biodigital resource centers, providing access not only to the plant material itself but also to its phenotypic and genotypic information. Adding information for relevant traits will help boost plant genetic resources' usage in breeding and research. Resistance traits are vital for adapting our agricultural systems to future challenges.

FINDINGS

Here we provide phenotypic data for the resistance against Blumeria graminis f. sp. tritici, the causal agent of wheat powdery mildew-a substantial risk to our agricultural production. Using a modern high-throughput phenotyping system, we infected and photographed a total of 113,638 wheat leaves of 7,320 winter wheat (Triticum aestivum L.) plant genetic resources of the German Federal ex situ Genebank for Agricultural and Horticultural Crops and 154 commercial genotypes. We quantified the resistance reaction captured by images and provide them here, along with the raw images.

CONCLUSION

This massive amount of phenotypic data, combined with already published genotypic data, also provides a valuable and unique training dataset for the development of novel genotype-based predictions as well as mapping methods.

Large-scale genotyping and phenotyping of a worldwide winter wheat genebank for its use in pre-breeding

Plant genetic resources (PGR) stored at genebanks are humanity's crop diversity savings for the future. Information on PGR contrasted with modern cultivars is key to select PGR parents for pre-breeding. Genotyping-by-sequencing was performed for 7,745 winter wheat PGR samples from the German Federal ex situ genebank at IPK Gatersleben and for 325 modern cultivars. Whole-genome shotgun sequencing was carried out for 446 diverse PGR samples and 322 modern cultivars and lines. In 19 field trials, 7,683 PGR and 232 elite cultivars were characterized for resistance to yellow rust - one of the major threats to wheat worldwide. Yield breeding values of 707 PGR were estimated using hybrid crosses with 36 cultivars - an approach that reduces the lack of agronomic adaptation of PGR and provides better estimates of their contribution to yield breeding. Cross-validations support the interoperability between genomic and phenotypic data. The here presented data are a stepping stone to unlock the functional variation of PGR for European pre-breeding and are the basis for future breeding and research activities.

Choosing the right tool: Leveraging of plant genetic resources in wheat (Triticum aestivum L.) benefits from selection of a suitable genomic prediction model

Genomic prediction of genebank accessions benefits from the consideration of additive-by-additive epistasis and subpopulation-specific marker effects. Wheat (Triticum aestivum L.) and other species of the Triticum genus are well represented in genebank collections worldwide. The substantial genetic diversity harbored by more than 850,000 accessions can be explored for their potential use in modern plant breeding. Characterization of these large number of accessions is constrained by the required resources, and this fact limits their use so far. This limitation might be overcome by engaging genomic prediction. The present study compared ten different genomic prediction approaches to the prediction of four traits, namely flowering time, plant height, thousand grain weight, and yellow rust resistance, in a diverse set of 7745 accession samples from Germany's Federal ex situ genebank at the Leibniz Institute of Plant Genetics and Crop Plant Research in Gatersleben. Approaches were evaluated based on prediction ability and robustness to the confounding influence of strong population structure. The authors propose the wide application of extended genomic best linear unbiased prediction due to the observed benefit of incorporating additive-by-additive epistasis. General and subpopulation-specific additive ridge regression best linear unbiased prediction, which accounts for subpopulation-specific marker-effects, was shown to be a good option if contrasting clusters are encountered in the analyzed collection. The presented findings reaffirm that the trait's genetic architecture as well as the composition and relatedness of the training set and test set are major driving factors for the accuracy of genomic prediction.

The Potential of Genome-Wide Prediction to Support Parental Selection, Evaluated with Data from a Commercial Barley Breeding Program

Parental selection is at the beginning and contributes significantly to the success of any breeding work. The value of a cross is reflected in the potential of its progeny population. Breeders invest substantial resources in evaluating progeny to select the best performing genotypes as candidates for variety development. Several proposals have been made to use genomics to support parental selection. These have mostly been evaluated using theoretical considerations or simulation studies. However, evaluations using experimental data have rarely been conducted. In this study, we tested the potential of genomic prediction for predicting the progeny mean, variance, and usefulness criterion using data from an applied breeding population for winter barley. For three traits with genetic architectures at varying levels of complexity, ear emergence, plant height, and grain yield, progeny mean, variance, and usefulness criterion were predicted and validated in scenarios resembling situations in which the described tools shall be used in plant breeding. While the population mean could be predicted with moderate to high prediction abilities amounting to 0.64, 0.21, and 0.39 in ear emergence, plant height, and grain yield, respectively, the prediction of family variance appeared difficult, as reflected in low prediction abilities of 0.41, 0.11, and 0.14, for ear emergence, plant height, and grain yield, respectively. We have shown that identifying superior crosses remains a challenging task and suggest that the success of predicting the usefulness criterion depends strongly on the complexity of the underlying trait.

Gabi wheat a panel of European elite lines as central stock for wheat genetic research

In plant sciences, curation and availability of interoperable phenotypic and genomic data is still in its infancy and represents an obstacle to rapid scientific discoveries in this field. To that end, supplementing the efforts being made to generate open access wheat genome, pan wheat genome and other bioinformatic resources, we present the GABI-WHEAT panel of elite European cultivars comprising 358 winter and 14 summer wheat varieties released between 1975 to 2007. The panel has been genotyped with SNP arrays of increasing density to investigate several important agronomic, quality and disease resistance traits. The robustness of investigated traits and interoperability of genomic and phenotypic data was assessed in the current publication with the aim to transform this panel into a public data resource for future genetic research in wheat. Consecutively, the phenotypic data was formatted to comply with FAIR principles and linked to online databases to substantiate panel origin information and quality. Thus, we were able to make a valuable resource available for plant science in a sustainable way.

Measurement(s)	agronomic, quality and disease traits
Technology Type(s)	manual measurement in the field
Sample Characteristic - Organism	Triticum aestivum L.

A catalogue of resistance gene homologs and a chromosome-scale reference sequence support resistance gene mapping in winter wheat

A resistance gene atlas is an integral component of the breeder's arsenal in the fight against evolving pathogens. Thanks to high-throughput sequencing, catalogues of resistance genes can be assembled even in crop species with large and polyploid genomes. Here, we report on capture sequencing and assembly of resistance gene homologs in a diversity panel of 907 winter wheat genotypes comprising ex situ genebank accessions and current elite cultivars. In addition, we use accurate long-read sequencing and chromosome conformation capture sequencing to construct a chromosome-scale genome sequence assembly of cv. Attraktion, an elite variety representative of European winter wheat. We illustrate the value of our resource for breeders and geneticists by (i) comparing the resistance gene complements in plant genetic resources and elite varieties and (ii) conducting genome-wide associations scans (GWAS) for the fungal diseases yellow rust and leaf rust using reference-based and reference-free GWAS approaches. The gene content under GWAS peaks was scrutinized in the assembly of cv. Attraktion.

Heterosis and Responses to Selection in Orange-Fleshed Sweetpotato (Ipomoea batatas L.) Improved Using Reciprocal Recurrent Selection

Sweetpotato is a highly heterozygous hybrid, and populations of orange-fleshed sweetpotato (OFSP) have a considerable importance for food security and health. The objectives were to estimate heterosis increments and response to selection in three OFSP hybrid populations (H1) developed in Peru for different product profiles after one reciprocal recurrent selection cycle, namely, H1 for wide adaptation and earliness (O-WAE), H1 for no sweetness after cooking (O-NSSP), and H1 for high iron (O-HIFE). The H1 populations were evaluated at two contrasting locations together with parents, foundation (parents in H0), and two widely adapted checks. Additionally, O-WAE was tested under two environmental conditions of 90-day and a normal 120-day harvest. In each H1, the yield and selected quality traits were recorded. The data were analyzed using linear mixed models. The storage root yield traits exhibited population average heterosis increments of up to 43.5%. The quality traits examined have exhibited no heterosis increments that are worth exploiting. The storage root yield genetic gain relative to the foundation was remarkable: 118.8% for H1-O-WAE for early harvest time, 81.5% for H1-O-WAE for normal harvest time, 132.4% for H1-O-NSSP, and 97.1% for H1-O-HIFE. Population hybrid breeding is a tool to achieve large genetic gains in sweetpotato yield via more efficient population improvement and allows a rapid dissemination of globally true seed that is generated from reproducible elite crosses, thus, avoiding costly and time-consuming virus cleaning of elite clones typically transferred as vegetative plantlets. The population hybrid breeding approach is probably applicable to other clonally propagated crops, where potential for true seed production exists.

SoySNP618K array: A high-resolution single nucleotide polymorphism platform as a valuable genomic resource for soybean genetics and breeding

Innovations in genomics have enabled the development of low-cost, high-resolution, single nucleotide polymorphism (SNP) genotyping arrays that accelerate breeding progress and support basic research in crop science. Here, we developed and validated the SoySNP618K array (618,888 SNPs) for the important crop soybean. The SNPs were selected from whole-genome resequencing data containing 2,214 diverse soybean accessions; 29.34% of the SNPs mapped to genic regions representing 86.85% of the 56,044 annotated high-confidence genes. Identity-by-state analyses of 318 soybeans revealed 17 redundant accessions, highlighting the potential of the SoySNP618K array in supporting gene bank management. The patterns of population stratification and genomic regions enriched through domestication were highly consistent with previous findings based on resequencing data, suggesting that the ascertainment bias in the SoySNP618K array was largely compensated for. Genome-wide association mapping in combination with reported quantitative trait loci enabled fine-mapping of genes known to influence flowering time, E2 and GmPRR3b, and of a new candidate gene, GmVIP5. Moreover, genomic prediction of flowering and maturity time in 502 recombinant inbred lines was highly accurate (>0.65). Thus, the SoySNP618K array is a valuable genomic tool that can be used to address many questions in applied breeding, germplasm management, and basic crop research.

Mining for New Sources of Resistance to Powdery Mildew in Genetic Resources of Winter Wheat

Genetic pathogen control is an economical and sustainable alternative to the use of chemicals. In order to breed resistant varieties, information about potentially unused genetic resistance mechanisms is of high value. We phenotyped 8,316 genotypes of the winter wheat collection of the German Federal ex situ gene bank for Agricultural and Horticultural Crops, Germany, for resistance to powdery mildew (PM), Blumeria graminis f. sp. tritici, one of the most important biotrophic pathogens in wheat. To achieve this, we used a semi-automatic phenotyping facility to perform high-throughput detached leaf assays. This data set, combined with genotyping-by-sequencing (GBS) marker data, was used to perform a genome-wide association study (GWAS). Alleles of significantly associated markers were compared with SNP profiles of 171 widely grown wheat varieties in Germany to identify currently unexploited resistance conferring genes. We also used the Chinese Spring reference genome annotation and various domain prediction algorithms to perform a domain enrichment analysis and produced a list of candidate genes for further investigation. We identified 51 significantly associated regions. In most of these, the susceptible allele was fixed in the tested commonly grown wheat varieties. Eleven of these were located on chromosomes for which no resistance conferring genes have been previously reported. In addition to enrichment of leucine-rich repeats (LRR), we saw enrichment of several domain types so far not reported as relevant to PM resistance, thus, indicating potentially novel candidate genes for the disease resistance research and prebreeding in wheat.

Genomic prediction models trained with historical records enable populating the German ex situ genebank bio-digital resource center of barley (Hordeum sp.) with information on resistances to soilborne barley mosaic viruses

Genomic prediction with special weight of major genes is a valuable tool to populate bio-digital resource centers. Phenotypic information of crop genetic resources is a prerequisite for an informed selection that aims to broaden the genetic base of the elite breeding pools. We investigated the potential of genomic prediction based on historical screening data of plant responses against the Barley yellow mosaic viruses for populating the bio-digital resource center of barley. Our study includes dense marker data for 3838 accessions of winter barley, and historical screening data of 1751 accessions for Barley yellow mosaic virus (BaYMV) and of 1771 accessions for Barley mild mosaic virus (BaMMV). Linear mixed models were fitted by considering combinations for the effects of genotypes, years, and locations. The best linear unbiased estimations displayed a broad spectrum of plant responses against BaYMV and BaMMV. Prediction abilities, computed as correlations between predictions and observed phenotypes of accessions, were low for the marker-assisted selection approach amounting to 0.42. In contrast, prediction abilities of genomic best linear unbiased predictions were high, with values of 0.62 for BaYMV and 0.64 for BaMMV. Prediction abilities of genomic prediction were improved by up to ~ 5% using W-BLUP, in which more weight is given to markers with significant major effects found by association mapping. Our results outline the utility of historical screening data and W-BLUP model to predict the performance of the non-phenotyped individuals in genebank collections. The presented strategy can be considered as part of the different approaches used in genebank genomics to valorize genetic resources for their usage in disease resistance breeding and research.

Assessing the Suitability of Elite Lines for Hybrid Seed Production and as Testers in Wide Crosses With Wheat Genetic Resources

The use of genetic resources in breeding is considered critical to ensure future selection gain, but the absence of important adaptation genes often masks the breeding value of genetic resources for grain yield. Testing genetic resources in a hybrid background has been proposed as a solution to obtain unbiased estimates of breeding values for grain yield. In our study, we evaluated the suitability of European wheat elite lines for implementing this hybrid strategy, focusing on maximizing seed yield in hybrid production and reducing masking effects due to susceptibility to lodging, yellow rust, and leaf rust of genetic resources. Over a 3-year period, 63 wheat elite female lines were crossed with eight male plant genetic resources in a multi-environment field experiment to evaluate seed yield on the female side. Then, the resulting hybrids and their parents were tested for plant height, lodging, and susceptibility to yellow rust and leaf rust in a further field experiment at multiple locations. We found that seed yield was strongly influenced by the elite wheat line choice in addition to environment and observed substantial differences among elite tester lines in their ability to reduce susceptibility to lodging, yellow rust, and leaf rust when the hybrid strategy was implemented. Consequently, breeders can significantly increase the amount of hybrid seed produced in wide crosses through appropriate tester choice and adapt genetic resources of wheat with the hybrid strategy to the modern cropping system.

Genomics and breeding innovations for enhancing genetic gain for climate resilience and nutrition traits

KEY MESSAGE

Integrating genomics technologies and breeding methods to tweak core parameters of the breeder's equation could accelerate delivery of climate-resilient and nutrient rich crops for future food security. Accelerating genetic gain in crop improvement programs with respect to climate resilience and nutrition traits, and the realization of the improved gain in farmers' fields require integration of several approaches. This article focuses on innovative approaches to address core components of the breeder's equation. A prerequisite to enhancing genetic variance (σ2g) is the identification or creation of favorable alleles/haplotypes and their deployment for improving key traits. Novel alleles for new and existing target traits need to be accessed and added to the breeding population while maintaining genetic diversity. Selection intensity (i) in the breeding program can be improved by testing a larger population size, enabled by the statistical designs with minimal replications and high-throughput phenotyping. Selection priorities and criteria to select appropriate portion of the population too assume an important role. The most important component of breeder's equation is heritability (h2). Heritability estimates depend on several factors including the size and the type of population and the statistical methods. The present article starts with a brief discussion on the potential ways to enhance σ2g in the population. We highlight statistical methods and experimental designs that could improve trait heritability estimation. We also offer a perspective on reducing the breeding cycle time (t), which could be achieved through the selection of appropriate parents, optimizing the breeding scheme, rapid fixation of target alleles, and combining speed breeding with breeding programs to optimize trials for release. Finally, we summarize knowledge from multiple disciplines for enhancing genetic gains for climate resilience and nutritional traits.

Unlocking big data doubled the accuracy in predicting the grain yield in hybrid wheat

The potential of big data to support businesses has been demonstrated in financial services, manufacturing, and telecommunications. Here, we report on efforts to enter a new data era in plant breeding by collecting genomic and phenotypic information from 12,858 wheat genotypes representing 6575 single-cross hybrids and 6283 inbred lines that were evaluated in six experimental series for yield in field trials encompassing ~125,000 plots. Integrating data resulted in twofold higher prediction ability compared with cases in which hybrid performance was predicted across individual experimental series. Our results suggest that combining data across breeding programs is a particularly appropriate strategy to exploit the potential of big data for predictive plant breeding. This paradigm shift can contribute to increasing yield and resilience, which is needed to feed the growing world population.

On the use of GBLUP and its extension for GWAS with additive and epistatic effects

Genomic best linear unbiased prediction (GBLUP) is the most widely used model for genome-wide predictions. Interestingly, it is also possible to perform genome-wide association studies (GWAS) based on GBLUP. Although the estimated marker effects in GBLUP are shrunken and the conventional test based on such effects has low power, it was observed that a modified test statistic can be produced and the result of test was identical to a standard GWAS model. Later, a mathematical proof was given for the special case that there is no fixed covariate in GBLUP. Since then, the new approach has been called “GWAS by GBLUP”. Nevertheless, covariates such as environmental and subpopulation effects are very common in GBLUP. Thus, it is necessary to confirm the equivalence in the general case. Recently, the concept was generalized to GWAS for epistatic effects and the new approach was termed rapid epistatic mixed-model association analysis (REMMA) because it greatly improved the computational efficiency. However, the relationship between REMMA and the standard GWAS model has not been investigated. In this study, we first provided a general mathematical proof of the equivalence between “GWAS by GBLUP” and the standard GWAS model for additive effects. Then, we compared REMMA with the standard GWAS model for epistatic effects by a theoretical investigation and by empirical data analyses. We hypothesized that the similarity of the two models is influenced by the relative contribution of additive and epistatic effects to the phenotypic variance, which was verified by empirical and simulation studies.

Genome-Wide Association Studies and Prediction of Tan Spot (Pyrenophora tritici-repentis) Infection in European Winter Wheat via Different Marker Platforms

Tan spot, caused by the fungus Pyrenophoratritici-repentis (Ptr), is a severe foliar disease of wheat (Triticumaestivum L.). Improving genetic resistance is a durable strategy to reduce Ptr-related losses. Here, we dissected Ptr-infection’s genetic basis in 372 European wheat varieties via simple sequence repeats (SSRs) plus 35k and 90k single nucleotide polymorphism (SNP) marker platforms. In our phenotypic data analyses, Ptr infection showed a significant genotypic variance and a significant negative correlation with plant height. Genome-wide association studies revealed a highly quantitative nature of Ptr infection and identified two quantitative trait loci (QTL), viz., QTs.ipk-7A and QTs.ipk-7B, which imparted 21.23 and 5.84% of the genotypic variance, respectively. Besides, the Rht-D1 gene showed a strong allelic influence on the infection scores. Due to the complex genetic nature of the Ptr infection, the potential of genome-wide prediction (GP) was assessed via three different genetic models on individual and combined marker platforms. The GP results indicated that the marker density and marker platforms do not considerably impact prediction accuracy (~40–42%) and that higher-order epistatic interactions may not be highly pervasive. Our results provide a further understanding of Ptr-infection’s genetic nature, serve as a resource for marker-assisted breeding, and highlight the potential of genome-wide selection for improved Ptr resistance.

Genetic Dissection of Hybrid Performance and Heterosis for Yield-Related Traits in Maize

Heterosis contributes a big proportion to hybrid performance in maize, especially for grain yield. It is attractive to explore the underlying genetic architecture of hybrid performance and heterosis. Considering its complexity, different from former mapping method, we developed a series of linear mixed models incorporating multiple polygenic covariance structures to quantify the contribution of each genetic component (additive, dominance, additive-by-additive, additive-by-dominance, and dominance-by-dominance) to hybrid performance and midparent heterosis variation and to identify significant additive and non-additive (dominance and epistatic) quantitative trait loci (QTL). Here, we developed a North Carolina II population by crossing 339 recombinant inbred lines with two elite lines (Chang7-2 and Mo17), resulting in two populations of hybrids signed as Chang7-2 × recombinant inbred lines and Mo17 × recombinant inbred lines, respectively. The results of a path analysis showed that kernel number per row and hundred grain weight contributed the most to the variation of grain yield. The heritability of midparent heterosis for 10 investigated traits ranged from 0.27 to 0.81. For the 10 traits, 21 main (additive and dominance) QTL for hybrid performance and 17 dominance QTL for midparent heterosis were identified in the pooled hybrid populations with two overlapping QTL. Several of the identified QTL showed pleiotropic effects. Significant epistatic QTL were also identified and were shown to play an important role in ear height variation. Genomic selection was used to assess the influence of QTL on prediction accuracy and to explore the strategy of heterosis utilization in maize breeding. Results showed that treating significant single nucleotide polymorphisms as fixed effects in the linear mixed model could improve the prediction accuracy under prediction schemes 2 and 3. In conclusion, the different analyses all substantiated the different genetic architecture of hybrid performance and midparent heterosis in maize. Dominance contributes the highest proportion to heterosis, especially for grain yield, however, epistasis contributes the highest proportion to hybrid performance of grain yield.

Haplotype-based genome-wide association increases the predictability of leaf rust (Puccinia triticina) resistance in wheat

Resistance breeding is crucial for sustainable control of wheat leaf rust and single nucleotide polymorphism (SNP)-based genome-wide association studies (GWAS) are widely used to dissect leaf rust resistance. Unfortunately, GWAS based on SNPs often explained only a small proportion of the genetic variation. We compared SNP-based GWAS with a method based on functional haplotypes (FH) considering epistasis in a comprehensive hybrid wheat mapping population composed of 133 parents plus their 1574 hybrids and characterized with 626 245 high-quality SNPs. In total, 2408 and 1 139 828 significant associations were detected in the mapping population by using SNP-based and FH-based GWAS, respectively. These associations mapped to 25 and 69 candidate regions, correspondingly. SNP-based GWAS highlighted two already-known resistance genes, Lr22a and Lr34-B, while FH-based GWAS detected associations not only on these genes but also on two additional genes, Lr10 and Lr1. As revealed by a second hybrid wheat population for independent validation, the use of detected associations from SNP-based and FH-based GWAS reached predictabilities of 11.72% and 22.86%, respectively. Therefore, FH-based GWAS is not only more powerful for detecting associations, but also improves the accuracy of marker-assisted selection compared with the SNP-based approach.

Efficient Algorithms for Calculating Epistatic Genomic Relationship Matrices

The genomic relationship matrix plays a key role in the analysis of genetic diversity, genomic prediction, and genome-wide association studies. The epistatic genomic relationship matrix is a natural generalization of the classic genomic relationship matrix in the sense that it implicitly models the epistatic effects among all markers. Calculating the exact form of the epistatic relationship matrix requires high computational load, and is hence not feasible when the number of markers is large, or when high-degree of epistasis is in consideration. Currently, many studies use the Hadamard product of the classic genomic relationship matrix as an approximation. However, the quality of the approximation is difficult to investigate in the strict mathematical sense. In this study, we derived iterative formulas for the precise form of the epistatic genomic relationship matrix for arbitrary degree of epistasis including both additive and dominance interactions. The key to our theoretical results is the observation of an interesting link between the elements in the genomic relationship matrix and symmetric polynomials, which motivated the application of the corresponding mathematical theory. Based on the iterative formulas, efficient recursive algorithms were implemented. Compared with the approximation by the Hadamard product, our algorithms provided a complete solution to the problem of calculating the exact epistatic genomic relationship matrix. As an application, we showed that our new algorithms easily relieved the computational burden in a previous study on the approximation behavior of two limit models.