Genomic prediction of synthetic hexaploid wheat upon tetraploid durum and diploid Aegilops parental pools.

Bread wheat (Triticum aestivum L.) is a globally important food crop, which was domesticated about 8-10,000 years ago. Bread wheat is an allopolyploid, and it evolved from two hybridization events of three species. To widen the genetic base in breeding, bread wheat has been re-synthesized by crossing durum wheat (Triticum turgidum ssp. durum) and goat grass (Aegilops tauschii Coss), leading to so-called synthetic hexaploid wheat (SHW). We applied the quantitative genetics tools of "hybrid prediction"-originally developed for the prediction of wheat hybrids generated from different heterotic groups - to a situation of allopolyploidization. Our use-case predicts the phenotypes of SHW for three quantitatively inherited global wheat diseases, namely tan spot (TS), septoria nodorum blotch (SNB), and spot blotch (SB). Our results revealed prediction abilities comparable to studies in 'traditional' elite or hybrid wheat. Prediction abilities were highest using a marker model and performing random cross-validation, predicting the performance of untested SHW (0.483 for SB to 0.730 for TS). When testing parents not necessarily used in SHW, combination prediction abilities were slightly lower (0.378 for SB to 0.718 for TS), yet still promising. Despite the limited phenotypic data, our results provide a general example for predictive models targeting an allopolyploidization event and a method that can guide the use of genetic resources available in gene banks.

Multispectral and thermal infrared data, visual scores for severity of common rust symptoms, and genotypic single nucleotide polymorphism data of three F2-derived biparental doubled-haploid maize populations.

Three F2-derived biparental doubled haploid (DH) maize populations were generated for genetic mapping of resistance to common rust. Each of the three populations has the same susceptible parent, but a different resistance donor parent. Population 1 and 3 consist of 320 lines each, population 2 consists of 260 lines. The DH lines were evaluated for their susceptibility to common rust in two years and with two replications in each year. For phenotyping, a visual score (VS) for susceptibility was assigned. Additionally, unmanned aerial vehicle (UAV) derived multispectral and thermal infrared data was recorded and combined in different vegetation indices ("remote sensing", RS). The DH lines were genotyped with the DarTseq method, to obtain data on single nucleotide polymorphisms (SNPs). After quality control, 9051 markers remained. Missing values were "imputed" by the empirical mean of the marker scores of the respective locus. We used the data for comparison of genome-wide association studies and genomic prediction when based on different phenotyping methods, that is either VS or RS data. The data may be interesting for reuse for instance for benchmarking genomic prediction models, for phytopathological studies addressing common rust, or for specifications of vegetation indices.

Modeling within and between Sub-Genomes Epistasis of Synthetic Hexaploid Wheat for Genome-Enabled Prediction of Diseases.

Common wheat (Triticum aestivum) is a hexaploid crop comprising three diploid sub-genomes labeled A, B, and D. The objective of this study is to investigate whether there is a discernible influence pattern from the D sub-genome with epistasis in genomic models for wheat diseases. Four genomic statistical models were employed; two models considered the linear genomic relationship of the lines. The first model (G) utilized all molecular markers, while the second model (ABD) utilized three matrices representing the A, B, and D sub-genomes. The remaining two models incorporated epistasis, one (GI) using all markers and the other (ABDI) considering markers in sub-genomes A, B, and D, including inter- and intra-sub-genome interactions. The data utilized pertained to three diseases: tan spot (TS), septoria nodorum blotch (SNB), and spot blotch (SB), for synthetic hexaploid wheat (SHW) lines. The results (variance components) indicate that epistasis makes a substantial contribution to explaining genomic variation, accounting for approximately 50% in SNB and SB and only 29% for TS. In this contribution of epistasis, the influence of intra- and inter-sub-genome interactions of the D sub-genome is crucial, being close to 50% in TS and higher in SNB (60%) and SB (60%). This increase in explaining genomic variation is reflected in an enhancement of predictive ability from the G model (additive) to the ABDI model (additive and epistasis) by 9%, 5%, and 1% for SNB, SB, and TS, respectively. These results, in line with other studies, underscore the significance of the D sub-genome in disease traits and suggest a potential application to be explored in the future regarding the selection of parental crosses based on sub-genomes.

Use of remote sensing for linkage mapping and genomic prediction for common rust resistance in maize.

Breeding for disease resistance is a central component of strategies implemented to mitigate biotic stress impacts on crop yield. Conventionally, genotypes of a plant population are evaluated through a labor-intensive process of assigning visual scores (VS) of susceptibility (or resistance) by specifically trained staff, which limits manageable volumes and repeatability of evaluation trials. Remote sensing (RS) tools have the potential to streamline phenotyping processes and to deliver more standardized results at higher through-put. Here, we use a two-year evaluation trial of three newly developed biparental populations of maize doubled haploid lines (DH) to compare the results of genomic analyses of resistance to common rust (CR) when phenotyping is either based on conventional VS or on RS-derived (vegetation) indices. As a general observation, for each population × year combination, the broad sense heritability of VS was greater than or very close to the maximum heritability across all RS indices. Moreover, results of linkage mapping as well as of genomic prediction (GP), suggest that VS data was of a higher quality, indicated by higher -logp values in the linkage studies and higher predictive abilities for genomic prediction. Nevertheless, despite the qualitative differences between the phenotyping methods, each successfully identified the same genomic region on chromosome 10 as being associated with disease resistance. This region is likely related to the known CR resistance locus Rp1. Our results indicate that RS technology can be used to streamline genetic evaluation processes for foliar disease resistance in maize. In particular, RS can potentially reduce costs of phenotypic evaluations and increase trialing capacities.

Genome and Environment Based Prediction Models and Methods of Complex Traits Incorporating Genotype × Environment Interaction.

Genomic-enabled prediction models are of paramount importance for the successful implementation of genomic selection (GS) based on breeding values. As opposed to animal breeding, plant breeding includes extensive multienvironment and multiyear field trial data. Hence, genomic-enabled prediction models should include genotype × environment (G × E) interaction, which most of the time increases the prediction performance when the response of lines are different from environment to environment. In this chapter, we describe a historical timeline since 2012 related to advances of the GS models that take into account G × E interaction. We describe theoretical and practical aspects of those GS models, including the gains in prediction performance when including G × E structures for both complex continuous and categorical scale traits. Then, we detailed and explained the main G × E genomic prediction models for complex traits measured in continuous and noncontinuous (categorical) scale. Related to G × E interaction models this review also examine the analyses of the information generated with high-throughput phenotype data (phenomic) and the joint analyses of multitrait and multienvironment field trial data that is also employed in the general assessment of multitrait G × E interaction. The inclusion of nongenomic data in increasing the accuracy and biological reliability of the G × E approach is also outlined. We show the recent advances in large-scale envirotyping (enviromics), and how the use of mechanistic computational modeling can derive the crop growth and development aspects useful for predicting phenotypes and explaining G × E.

Incorporating Omics Data in Genomic Prediction.

In this chapter, we discuss the motivation for integrating other types of omics data into genomic prediction methods. We give an overview of literature investigating the performance of omics-enhanced predictions, and highlight potential pitfalls when applying these methods in breeding. We emphasize that the statistical methods available for genomic data can be transferred to the general omics case. However, when using a framework of omic relationship matrices, the standardization of the variables may be more relevant than it is for a genomic relationship matrix based on single-nucleotide polymorphisms.

Accounting for epistasis improves genomic prediction of phenotypes with univariate and bivariate models across environments.

KEY MESSAGE: The accuracy of genomic prediction of phenotypes can be increased by including the top-ranked pairwise SNP interactions into the prediction model. We compared the predictive ability of various prediction models for a maize dataset derived from 910 doubled haploid lines from two European landraces (Kemater Landmais Gelb and Petkuser Ferdinand Rot), which were tested at six locations in Germany and Spain. The compared models were Genomic Best Linear Unbiased Prediction (GBLUP) as an additive model, Epistatic Random Regression BLUP (ERRBLUP) accounting for all pairwise SNP interactions, and selective Epistatic Random Regression BLUP (sERRBLUP) accounting for a selected subset of pairwise SNP interactions. These models have been compared in both univariate and bivariate statistical settings for predictions within and across environments. Our results indicate that modeling all pairwise SNP interactions into the univariate/bivariate model (ERRBLUP) is not superior in predictive ability to the respective additive model (GBLUP). However, incorporating only a selected subset of interactions with the highest effect variances in univariate/bivariate sERRBLUP can increase predictive ability significantly compared to the univariate/bivariate GBLUP. Overall, bivariate models consistently outperform univariate models in predictive ability. Across all studied traits, locations and landraces, the increase in prediction accuracy from univariate GBLUP to univariate sERRBLUP ranged from 5.9 to 112.4 percent, with an average increase of 47 percent. For bivariate models, the change ranged from -0.3 to + 27.9 percent comparing the bivariate sERRBLUP to the bivariate GBLUP, with an average increase of 11 percent. This considerable increase in predictive ability achieved by sERRBLUP may be of interest for "sparse testing" approaches in which only a subset of the lines/hybrids of interest is observed at each location.

Application of multi-trait Bayesian decision theory for parental genomic selection.

In all breeding programs, the decision about which individuals to select and intermate to form the next selection cycle is crucial. The improvement of genetic stocks requires considering multiple traits simultaneously, given that economic value and net genetic merits depend on many traits; therefore, with the advance of computational and statistical tools and genomic selection (GS), researchers are focusing on multi-trait selection. Selection of the best individuals is difficult, especially in traits that are antagonistically correlated, where improvement in one trait might imply a reduction in other(s). There are approaches that facilitate multi-trait selection, and recently a Bayesian decision theory (BDT) has been proposed. Parental selection using BDT has the potential to be effective in multi-trait selection given that it summarizes all relevant quantitative genetic concepts such as heritability, response to selection and the structure of dependence between traits (correlation). In this study, we applied BDT to provide a treatment for the complexity of multi-trait parental selection using three multivariate loss functions (LF), Kullback-Leibler (KL), Energy Score, and Multivariate Asymmetric Loss (MALF), to select the best-performing parents for the next breeding cycle in two extensive real wheat data sets. Results show that the high ranking lines in genomic estimated breeding value (GEBV) for certain traits did not always have low values for the posterior expected loss (PEL). For both data sets, the KL LF gave similar importance to all traits including grain yield. In contrast, the Energy Score and MALF gave a better performance in three of four traits that were different than grain yield. The BDT approach should help breeders to decide based not only on the GEBV per se of the parent to be selected, but also on the level of uncertainty according to the Bayesian paradigm.

A review of deep learning applications for genomic selection.

BACKGROUND: Several conventional genomic Bayesian (or no Bayesian) prediction methods have been proposed including the standard additive genetic effect model for which the variance components are estimated with mixed model equations. In recent years, deep learning (DL) methods have been considered in the context of genomic prediction. The DL methods are nonparametric models providing flexibility to adapt to complicated associations between data and output with the ability to adapt to very complex patterns. MAIN BODY: We review the applications of deep learning (DL) methods in genomic selection (GS) to obtain a meta-picture of GS performance and highlight how these tools can help solve challenging plant breeding problems. We also provide general guidance for the effective use of DL methods including the fundamentals of DL and the requirements for its appropriate use. We discuss the pros and cons of this technique compared to traditional genomic prediction approaches as well as the current trends in DL applications. CONCLUSIONS: The main requirement for using DL is the quality and sufficiently large training data. Although, based on current literature GS in plant and animal breeding we did not find clear superiority of DL in terms of prediction power compared to conventional genome based prediction models. Nevertheless, there are clear evidences that DL algorithms capture nonlinear patterns more efficiently than conventional genome based. Deep learning algorithms are able to integrate data from different sources as is usually needed in GS assisted breeding and it shows the ability for improving prediction accuracy for large plant breeding data. It is important to apply DL to large training-testing data sets.

On Hadamard and Kronecker products in covariance structures for genotype × environment interaction.

When including genotype × environment interactions (G × E) in genomic prediction models, Hadamard or Kronecker products have been used to model the covariance structure of interactions. The relation between these two types of modeling has not been made clear in genomic prediction literature. Here, we demonstrate that a certain model based on a Hadamard formulation and another using the Kronecker product lead to exactly the same statistical model. Moreover, we illustrate how a multiplication of entries of covariance matrices is related to modeling locus × environmental-variable interactions explicitly. Finally, we use a wheat and a maize data set to illustrate that the environmental covariance E can be specified easily, also if no information on environmental variables - such as temperature or precipitation - is available. Given that lines have been tested in different environments, the corresponding environmental covariance can simply be estimated from the training set as phenotypic covariance between environments. To achieve a high level of increase in predictive ability, the environmental covariance has to be defined appropriately and records on the performance of the lines of the test set under different environmental conditions have to be included in the training set.

Cooperativity, absolute interaction, and algebraic optimization.

We consider a measure of cooperativity based on the minimal interaction required to generate an observed titration behavior. We describe the corresponding algebraic optimization problem and show how it can be solved using the nonlinear algebra tool SCIP. Moreover, we compute the minimal interactions and minimal molecules for several binding polynomials that describe the oxygen binding of various hemoglobins under different conditions. We compare their minimal interaction with the maximal slope of the Hill plot, and discuss similarities and discrepancies with a view towards the shapes of the binding curves.

Phantom Epistasis in Genomic Selection: On the Predictive Ability of Epistatic Models.

Genomic selection uses whole-genome marker models to predict phenotypes or genetic values for complex traits. Some of these models fit interaction terms between markers, and are therefore called epistatic. The biological interpretation of the corresponding fitted effects is not straightforward and there is the threat of overinterpreting their functional meaning. Here we show that the predictive ability of epistatic models relative to additive models can change with the density of the marker panel. In more detail, we show that for publicly available Arabidopsis and rice datasets, an initial superiority of epistatic models over additive models, which can be observed at a lower marker density, vanishes when the number of markers increases. We relate these observations to earlier results reported in the context of association studies which showed that detecting statistical epistatic effects may not only be related to interactions in the underlying genetic architecture, but also to incomplete linkage disequilibrium at low marker density ("Phantom Epistasis"). Finally, we illustrate in a simulation study that due to phantom epistasis, epistatic models may also predict the genetic value of an underlying purely additive genetic architecture better than additive models, when the marker density is low. Our observations can encourage the use of genomic epistatic models with low density panels, and discourage their biological over-interpretation.

Genomic Prediction Enhanced Sparse Testing for Multi-environment Trials.

"Sparse testing" refers to reduced multi-environment breeding trials in which not all genotypes of interest are grown in each environment. Using genomic-enabled prediction and a model embracing genotype × environment interaction (GE), the non-observed genotype-in-environment combinations can be predicted. Consequently, the overall costs can be reduced and the testing capacities can be increased. The accuracy of predicting the unobserved data depends on different factors including (1) how many genotypes overlap between environments, (2) in how many environments each genotype is grown, and (3) which prediction method is used. In this research, we studied the predictive ability obtained when using a fixed number of plots and different sparse testing designs. The considered designs included the extreme cases of (1) no overlap of genotypes between environments, and (2) complete overlap of the genotypes between environments. In the latter case, the prediction set fully consists of genotypes that have not been tested at all. Moreover, we gradually go from one extreme to the other considering (3) intermediates between the two previous cases with varying numbers of different or non-overlapping (NO)/overlapping (O) genotypes. The empirical study is built upon two different maize hybrid data sets consisting of different genotypes crossed to two different testers (T1 and T2) and each data set was analyzed separately. For each set, phenotypic records on yield from three different environments are available. Three different prediction models were implemented, two main effects models (M1 and M2), and a model (M3) including GE. The results showed that the genome-based model including GE (M3) captured more phenotypic variation than the models that did not include this component. Also, M3 provided higher prediction accuracy than models M1 and M2 for the different allocation scenarios. Reducing the size of the calibration sets decreased the prediction accuracy under all allocation designs with M3 being the less affected model; however, using the genome-enabled models (i.e., M2 and M3) the predictive ability is recovered when more genotypes are tested across environments. Our results indicate that a substantial part of the testing resources can be saved when using genome-based models including GE for optimizing sparse testing designs.

On the approximation of interaction effect models by Hadamard powers of the additive genomic relationship.

Whole genome epistasis models with interactions between different loci can be approximated by genomic relationship models based on Hadamard powers of the additive genomic relationship. We illustrate that the quality of this approximation reduces when the degree of interaction d increases. Moreover, considering relationship models defined as weighted sum of interactions of different degree, we investigate the impact of this decreasing quality of approximation of the summands on the approximation of the weighted sum. Our results indicate that these approximations remain on a reliable level, but their quality reduces when the weights of interactions of higher degrees do not decrease quickly.

Integrating Gene Expression Data Into Genomic Prediction.

Gene expression profiles potentially hold valuable information for the prediction of breeding values and phenotypes. In this study, the utility of transcriptome data for phenotype prediction was tested with 185 inbred lines of Drosophila melanogaster for nine traits in two sexes. We incorporated the transcriptome data into genomic prediction via two methods: GTBLUP and GRBLUP, both combining single nucleotide polymorphisms (SNPs) and transcriptome data. The genotypic data was used to construct the common additive genomic relationship, which was used in genomic best linear unbiased prediction (GBLUP) or jointly in a linear mixed model with a transcriptome-based linear kernel (GTBLUP), or with a transcriptome-based Gaussian kernel (GRBLUP). We studied the predictive ability of the models and discuss a concept of "omics-augmented broad sense heritability" for the multi-omics era. For most traits, GRBLUP and GBLUP provided similar predictive abilities, but GRBLUP explained more of the phenotypic variance. There was only one trait (olfactory perception to Ethyl Butyrate in females) in which the predictive ability of GRBLUP (0.23) was significantly higher than the predictive ability of GBLUP (0.21). Our results suggest that accounting for transcriptome data has the potential to improve genomic predictions if transcriptome data can be included on a larger scale.