As the living standard of people rises, quality and safety traits of agricultural plants have received growing attentions by consumers and breeders alike. Quality traits are known as traits that offer better appearance, flavor, taste, nutrition, longer shelf life and less damage to plant products, while safety traits can be defined as plant traits that are directly or indirectly linked to human health, such as the content of antioxidant compounds in horticultural products. Typical quality and safety traits include, but are not limited to, appearance, texture, taste, flavor and aroma of plant products; nutritional, anti-nutritional or allergic component contents; uptake, accumulation and degradation of exogenous toxic substances by plants; synthesis and transformation of endogenous harmful substances in plants; post-harvest quality change and shelf life. Some quality and safety traits are more closely related to the environment or human activities, such as the accumulation of heavy metals, antibiotic residues and the novel artificial nanoparticles in plants. Tremendous efforts are being put into breeding programs to synergistically improve quality and safety traits, which, however, are in some cases impeded by the trade-offs among target traits. For example, plants may contain certain components, for instance, stone cells, anti-nutritional factors and allergens, which are beneficial to their own but unfavorable for human consumption or detrimental to health  and dietary fiber. Tea plant has huge health benefits and economic values. Tea contains many secondary metabolites such as flavonoids, theanine and alkaloids, which play many health benefits in human body  and fruit firmness based on hyperspectral images and deep learning regression, which offers a new solution for non-destructive assessment of cherry tomato fruit quality .Accurate acquisition of the phenotypic data is prerequisite for trait improvement. The past decades have witnessed big progress in phenotyping techniques and methods, covering a wide range of traits from morphological, biochemical to the physiological levels. For example, advanced mathematical algorithm such as Elliptic Fourier equation was employed in precise and comprehensive quantification of fruit shape in cucurbit crops , recombinant inbred lines (RILs) or double haploids (DHs); genome-wide association studies (GWAS) based on natural populations; and faster approaches using bulked-segregant analysis sequencing (BSA-seq) or quantitative trait locus sequencing (QTL-seq) have been mostly applied. For example, a locus strongly associated with firmness and harvest date of fruit was identified in apple by GWAS and the causal gene was found to encode the transcription factor NAC18.1. Single nucleotide polymorphisms (SNPs) were found in both the CDS and promoter regions of NAC18.1, leading to the differential ripening programs among the apple accessions  and “M4-7” (yellow stigma), Lv et al. detected two stable QTLs (SC2.1 and SC8.1) related to stigma color. Apart from melon, the formation mechanism and determinants of fruit quality in cucumber was reviewed by Zhang et al. highlighting the importance of integrating the methods of traditional breeding, molecular markers and bio-technologies. Other than quality traits, studies on diseases resistances of cucumber were summarized by Miao et al., where recent discoveries on the inheritance, molecular markers and QTL mapping of various diseases were reviewed, which sheds lights on the strategy for resistance breeding in this crop.As the genomic technologies burst in the recent decades, genetic dissection of a large number of quality and safety traits have become feasible in many horticultural plants, which solidifies the basis of genetic improvement of the traits. Particularly, pedigree-based genetic mapping using bi-parental populations such as second filial generation  genes in tea. In pepper, 158 carotenoid cleavage oxygenase (CCO) genes were identified by Yao et al. and 10 CONSTANS-like (COL) genes were characteized by Huang et al. and Wang et al. reported the identification of 32 terpene synthases (TPS) genes in Cymbidium faberi. In short, the elucidation of genetic architectures of many important quality and safety traits and the systemic identification of gene families responsible for the trait regulation have laid a foundation for breeding-by-molecular-design.The completeness of genome sequencing in many horticultural plants have allowed genome-wide identification of genes involve in quality and safety traits. Integrative biology features the integration and intersection of multiple disciplines to study the laws of living organisms at the systems level  have great diversity among populations of Brassica wild species  and aquaporin  genes were upregulated by selenite while transporter genes SULTR1;1 and SULTR2;1 were responsive to selenate. Using tissue culture and transcriptomic profiling, Chen et al. showed that activated carbon promoted the development of peony roots into seedlings by stimulating the processes of phenylpropanoid biosynthesis and biosynthesis of stratum cutin and suberin. In addition to omics, research paradigm integrating physiological, biochemical and molecular biological methods are also widely used. For example, exogenous application of 5-Aminolevulinic acid and melatonin enhanced the nutritional quality and changed mature period in tomato  and baby mustard , respectively. Zhu et al. employed high-performance liquid chromatography (HPLC) analysis, comparative transcriptome sequencing and transient expression assay to investigate the regulation of floral pigmentation in orchids. CkCHS-1, CkDFR, and CkANS were identified as putative key genes regulating floral coloration. Another study by Wen et al. analyzed CcERF2, an ethylene-inducible transcription factor that preferentially expressed in the placenta of pepper fruit. Silencing CcERF2 reduced the content of capsaicinoids in pepper, suggesting that the gene involved in the regulation of capsaicinoids biosynthetic pathway. In a review article, Wang et al. summarized the recent research on the evolution and biological functions of the S1-bZIP transcription factors in plants, highlighting their role as signaling hubs through dimerization with cofactors to coordinate the expression of downstream genes. Undoubtedly, integrative biology approaches have been critical for understanding how the many quality and safety traits are determined in horticultural plants.A typical example of integrative biological study of quality and safety traits in horticultural plants is the dissection and manipulation of the bitterness trait in cucumber. Through large-scale phenotyping and genetic mapping, genomic regions governing fruit and leaf bitterness were delimited. Further facilitated by biochemical and molecular approaches, nine genes involved in the cucurbitacin C biosynthesis pathway were identified, and two transcription factors, Bl and Bt, were ultimately determined as the causal gene of leaf and fruit bitterness, respectively  phenotyping of quality and safety traits is generally more difficult; and (2) many of these traits are governed by multiple genes that are more prone to be affected by the environment. In order to accelerate the improvement of these traits, the research community may need to first fully digest and utilize the recent fundamental discoveries in the biology of quality and safety traits in horticultural plants. Particular attentions may be paid to latest research progresses in the innovative phenotyping techniques, exploration of genetic variations, important genes/QTLs that were identified as controlling the interested traits, molecular markers that were developed to tag the target traits, and the gene regulatory mechanisms underlying traits formation. In addition, In summary, the series of researches here describe the latest progresses on quality and safety traits studies in horticultural crops and highlight the combination of phenotyping and genetic methods in this field. In the future, researches on plant quality and safety traits will benefit more from integrative or systems biology strategies to achieve the goal of comprehensively understanding the gene-gene network and the gene-environment interaction. More specifically, focuses will be on: (1) unifying phenomics and genomics to identify the genes controlling traits of interest, which can manifest the power of both high-throughput phenotyping and genotyping technologies; (2) unifying bioinformatics, bioengineering and synthetic biology to design new routes for genetic manipulation; (3) combining traditional and modernized breeding techniques such as marker-assisted backcrossing (MAB), marker-assisted recurrent selection (MARC) and genomic selection (GS) for more efficient and precise development of new varieties with desired traits. Such multi-dimensional efforts are expected to solidify the theoretical foundation as well as provide rich genetic resources for the improvement of quality and safety traits in horticultural plants.All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Genotype imputation is a foundational tool for population genetics. Standard statistical imputation approaches rely on the co-location of large whole-genome sequencing-based reference panels, powerful computing environments, and potentially sensitive genetic study data. This results in computational resource and privacy-risk barriers to access to cutting-edge imputation techniques. Moreover, the accuracy of current statistical approaches is known to degrade in regions of low and complex linkage disequilibrium. Artificial neural network-based imputation approaches may overcome these limitations by encoding complex genotype relationships in easily portable inference models. Here, we demonstrate an autoencoder-based approach for genotype imputation, using a large, commonly used reference panel, and spanning the entirety of human chromosome 22. Our autoencoder-based genotype imputation strategy achieved superior imputation accuracy across the allele-frequency spectrum and across genomes of diverse ancestry, while delivering at least fourfold faster inference run time relative to standard imputation tools. The human genome is inherited in large blocks from parental genomes, generated through a DNA-sequence-dependent shuffling process called recombination. The non-uniform nature of recombination breakpoints producing these genomic blocks results in correlative genotype relationships across genetic variants, known as linkage disequilibrium. Thus, genotypes for a small subset (1–10%) of observed common genetic variants can be used to infer the genotype status of unobserved but known genetic variation sites across the genome   distribuRecently, artificial neural networks, especially autoencoders, have attracted attention in functional genomics for their ability to fill-in missing data for image restoration and inpainting . AutoencHere, we present a generalized approach to unphased human genotype imputation using sparse, denoising autoencoders capable of highly accurate genotype imputation at genotype masking levels (98+%) appropriate for array-based genotyping and low-pass sequencing-based population genetics initiatives. We describe the initial training and implementation of autoencoders spanning all of human chromosome 22, achieving equivalent to superior accuracy relative to modern HMM-based methods, and dramatically improving computational efficiency at deployment without the need to distribute reference panels.Sparse, de-noising autoencoders spanning all bi-allelic SNPs observed in the Haplotype Reference Consortium were developed and optimized. Each autoencoder receives masked data as input and is trained to predict the original uncorrupted data as the output. Each bi-allelic SNP was encoded as two binary input nodes, representing the presence or absence of each allele . This enGenotypes for all bi-allelic SNPs were converted to binary values representing the presence (1) or absence (0) of the reference allele A and alternative allele B, respectively, as shown in x is a vector containing the two allele presence input nodes to the autoencoder and their encoded allele presence values derived from the original genotype, G, of variant i. The output nodes of the autoencoder are similarly rescaled to 0–1 by a sigmoid function, split into three genotype outputs , and normalized using the Softmax function. The normalized outputs can also be regarded as probabilities and can be combined for the calculation of alternative allele dosage and as a measure of imputation quality. This representation is extensible to other classes of genetic variation, and allows for the use of probabilistic loss functions.where Whole-genome sequence data from the Haplotype Reference Consortium (HRC) was used for training and as the reference panel for comparison to HMM-based imputation . The dat% East Asian, 4.99% Native American, 5.53% African, and 50.61% admixed. MESA, Wellderly, and HGDP are all independent datasets, not used for autoencoder training, nor model selection, whereas HRC and ARIC were utilized for training and model selection, respectively.A balanced (50%:50% European and African genetic ancestry) subset of 796 whole genome sequences from the Atherosclerosis Risk in Communities cohort (ARIC) , was useGRCh38 mapped cohorts (HGDP and MESA) were converted to hg19 using Picard v2.25 . All othnull case in We employed two strategies for data augmentation – random variant masking and simulating further recombination with offspring formation. During training, random masking of input genotypes was performed at escalating rates, starting with a relatively low masking rate (80% of variants) that is gradually incremented in subsequent training rounds until up to only five variants remain unmasked per autoencoder. Masked variants are encoded as the FL)  , shown itx) predicted probability (tp) is weighted by the class imbalance factor αt and a modulating factor (1 - tp)γ. t represents the index of each allele in a genomic segment. The modulating factor is the standard focal loss factor with hyperparameter, γ, which amplifies the focal loss effect by down-weighting the contributions of well-classified alleles to the overall loss  of the truth class (nt sites). αt is aThis base focal loss function is further penalized and regularized to encourage simple and sparse models in terms of edge-weight and hidden layer activation complexity. These additional penalties result in our final loss function as shown in L1 and L2 norms of the autoencoder weight matrix (W), with their contributions mediated by the hyperparameters λ1 and λ2. S is a sparsity penalty, with its contribution mediated by the hyperparameter β, which penalizes deviation from a target hidden node activation set by the hyperparameter vs the observed mean activation j summed over total batches n, as shown in where n x n matrix of pairwise SNP correlations using all common genetic variation  from HRC. Correlation values were thresholded at 0.45, which is the threshold that returns the minimum number of segments spanning chromosome 22 with an average size per segment that fits into the video memory of GPUs. While developing the tiling algorithm, we tested lower thresholds, which made the segments smaller and more abundant, and thus made the GPU memory workload less efficient . Due to the obstacles related to computational inefficiency, CPU-GPU communication overhangs, and GPU memory limits, we did not proceed with model training on segments generated with other correlation thresholds. For each SNP, we calculated a box count of all pairwise SNP correlations spanning 500 common SNPs upstream and downstream of the index SNP. This moving box count quantifies the overall local LD strength centered at each SNP. Local minima in this moving box count were used to split the genome into approximately independent genomic segments of two types – large segments of high LD interlaced with short segments of weak LD corresponding to recombination hotspot regions. Individual autoencoders were designed to span the entirety of a single high LD segment plus its adjacent upstream and downstream weak LD regions. Thus, adjacent autoencoders overlap at their weak LD ends. If an independent genomic segment exceeded the threshold number of SNPs amenable to deep learning given GPU memory limitations, internal local minima within the high LD regions were used to split the genomic segments further to a maximum of 6000 SNPs per autoencoder. Any remaining genomic segments still exceeding 6000 SNPs were further split into 6000 SNP segments with large overlaps of 2500 SNPs given the high degree of informative LD split across these regions. This tiling process resulted in 256 genomic segments spanning chromosome 22: 188 independent LD segments, 32 high LD segments resulting from internal local minima splits, and 36 segments further split due to GPU memory limitations.All model training tasks were distributed across a diversified set of NVIDIA graphical processing units (GPUs) with different video memory limits: 5 x Titan Vs (12 GB), 8x A100s (40 GB), 60x V100s (32 GB). Given computational complexity and GPU memory limitations, individual autoencoders were designed to span approximately independent genomic segments with boundaries defined by computationally identified recombination hotspots . These sWe first used a random grid search approach to define initial hyperparameter combinations producing generally accurate genotype imputation results. The hyperparameters and their potential starting values are listed in In order to avoid local optimal solutions and reduce the hyperparameter search space, we used an ensemble-based machine learning approach (Extreme Gradient Boosting–XGBoost) to predict the expected performance (r-squared) of each hyperparameter combination per genomic segment using the results of the coarse-grid search and predictive features calculated for each genomic segment. These features include the number of variants, average recombination rate and average pairwise Pearson correlation across all SNPs, proportion of rare and common variants across multiple minor allele frequency (MAF) bins, number of principal components necessary to explain at least 90% of variance, and the total variance explained by the first two principal components. The observed accuracies of the coarse-grid search, numbering 25,600 training inputs, were used to predict the accuracy of 500,000 new hyperparameter combinations selected from We then ranked all hyperparameter combinations by their predicted performance and selected the top 10 candidates per genomic segment along with the single best initially tested hyperparameter combination per genomic segments for further consideration. All other hyperparameter combinations were discarded. Genomic segments with sub-optimal performance relative to Minimac were subjected to tuning with simulated offspring formation. For tuning, the maximum number of epochs was increased  with automatic stop criteria: if there is no improvement in average loss value of the current masking/training cycle versus the previous one, the training is interrupted, otherwise training continues until the maximum epoch limit is reached. Each masking/training cycle consisted of 500 epochs. Final hyperparameter selection was based on performance on the validation dataset (ARIC).This process results in 256 unique autoencoders spanning the genomic segments of chromosome 22. Each genomic segment consists of a different number of input variables (genetic variants), sparsity, and correlation structure. Thus, 256 unique autoencoder models span the entirety of chromosome 22 .Performance was compared to Minimac4 , Beagle5We used the MESA cohort for inference runtime comparisons. Runtime was determined using the average and standard error of three imputation replicates. Two hardware configurations were used for the tests: (1) a low-end environment: 16-core Intel Xeon CPU (E5-2640 v2 2.00 GHz), 250 GB RAM, and one GPU (NVIDIA GTX 1080); (2) a high-end environment: 24-Core AMD CPU (EPYC 7352 2.3 GHz), 250 GB RAM, using one NVIDIA A100 GPU. We report computation time only, input/output (I/O) reading/writing times are excluded as separately optimized functions. Since the computational burden of training the models remains on the developer side, the runtime results refer to the task of imputing the missing genotypes given a pre-trained autoencoder set.https://github.com/TorkamaniLab/Imputation_Autoencoder/tree/master/autoencoder_tuning_pipeline; https://github.com/TorkamaniLab/imputation_accuracy_calculator; https://github.com/TorkamaniLab/imputator_inference, copy archived at swh:1:rev:2fbd203acf8aaf320a520c6374d6f4d57f068a7c; https://github.com/TorkamaniLab/imputator_inference; The data that support the findings of this study are available from dbGAP and European Genome-phenome Archive (EGA), but restrictions apply to the availability of these data, which were used under ethics approval for the current study, and so are not openly available to the public. The computational pipeline for autoencoder training and validation is available at The imputation results are exported in variant calling format (VCF) containing the imputed genotypes and imputation quality scores in the form of class probabilities for each one of the three possible genotypes . The probabilities can be used for quality control of the imputation results.–6). Overall, when performance across genomic segments, test datasets, and test array marker sets was combined, the autoencoders exhibited an average r-squared per variant of 0.352±0.008 in reconstruction of WGS ground truth genotypes versus an average r-squared per variant of 0.374±0.007, 0.364±0.007, and 0.357±0.007 for HMM-based imputation methods   . This di–04). Similarly, we quantified genomic segment complexity by the proportion of variance explained by the first two principal components as well as the number of principal components needed to explain at least 90% of the variance of HRC genotypes from each genomic segment. Concordantly, superior autoencoder performance was associated with a low proportion explained by the first two components and positively correlated with the number of components required to explained 90% of variance . These observations, with predictive features determined in the HRC training dataset and performance determined in the ARIC validation dataset, informed our tuning strategy.In order to understand the relationship between genomic segment features, hyperparameter values, and imputation performance, we calculated predictive features  for each genomic segment and determined their Spearman correlation with the differences in r-squared observed for the autoencoder vs Minimac4 . We obseWe then used the genomic features significantly correlated with imputation performance in the ARIC validation dataset to predict the performance of and select the hyperparameter values to advance to fine-tuning. An ensemble model inference approach was able to predict the genomic segment-specific performance of hyperparameter combinations with high accuracy . Autoenc–11) (Minimac4: –4), and 0.358±0.007 for Impute5 (Wilcoxon rank sum test p=2.01*10–5) . Detailed comparisons to Beagle5 and Eagle5 are presented in After tuning, autoencoder performance surpassed HMM-based imputation performance across all imputation methods, independent test datasets, and genotyping array marker sets. At a minimum, autoencoders surpassed HMM-based imputation performance in >62% of chromosome 22 genomic segments (two proportion test p=1.02 × 1001*10–5) . This su–4, respectively). Summary statistics for these comparisons are available in Tuning improved performance of the autoencoders across all genomic segments, generally improving the superiority of autoencoders relative to HMM-based approaches in genomic segments with complex haplotype structures while equalizing performance relative to HMM-based approaches in genomic segments with more simple LD structures . The autoencoder’s mean r-squared per variant ranged from 0.363 for HGDP to 0.605 for the Wellderly vs 0.340–0.557 for Minimac4, 0.326–0.549 for Beagle5, and 0.314–0.547 for Eagle5, respectively. Detailed comparisons are presented in in After merging the results from all genomic segments, the whole chromosome accuracy of autoencoder-based imputation remained superior to all HMM-based imputation tools, across all independent test datasets, and all genotyping array marker sets . The autoencoders’ mean r-squared ranged from 0.357 for African ancestry to 0.614 for East Asian ancestry vs 0.328–0.593 for Minimac4, 0.330–0.544 for Beagle5, and 0.324–0.586 for Impute5, respectively. Note, East Asian ancestry exhibits a slightly higher overall imputation accuracy relative to European ancestry due to improved rare variant imputation. Autoencoder superiority replicates when HGDP is split into continental populations  seconds for Minimac4, Beagle5, and Impute5, respectively . In theectively . These uArtificial neural network-based data mining techniques are revolutionizing biomedical informatics and analytics . Here, wSuperior imputation accuracy is expected to improve GWAS power, enable more complete coverage in meta-analyses, and improve causal variant identification through fine-mapping. Moreover, superior imputation accuracy in low LD regions may enable the more accurate interrogation of specific classes of genes under a greater degree of selective pressure and involved in environmental sensing. For example, promoter regions of genes associated with inflammatory immune responses, response to pathogens, environmental sensing, and neurophysiological processes (including sensory perception genes) are often located in regions of low LD . These kHMM-based imputation tools depend on end-user access to large reference panels or datasets to impute a single genome whereas pre-trained autoencoder models eliminate that dependency. However, further development is required to actualize this approach in practice for broad adoption. Autoencoders must be pre-trained and validated across all segments of the human genome – a computationally expensive task. Here we performed training only for chromosome 22. Autoencoder training is computationally intensive, shifting the computational burden to model trainers, and driving performance gains for end-users. As a result, inference time scales only with the number of variants to be imputed, whereas HMM-based inference time depends on both reference panel and the number of variants to be imputed. This allows for autoencoder-based imputation to extend to millions of genomes but introduces some challenges in the continuous re-training and fine-tuning of the pre-trained models as larger reference panels are made available. In addition, our current encoding approach lacks phasing information and no pre-phasing was performed. Pre-phasing can lead to substantial improvements in imputation accuracy. Future models will need to address the need for phasing and continuous fine-tuning of models for application to modern, ever-growing, genomic datasets.After expanding this approach across the whole genome, our work will provide a more efficient genotype imputation platform on whole genome scale and thus benefit genomic research especially in contexts where the computational power required for modern HMM-based imputation is not accessible. In addition to the speed, cost, and accuracy benefits, our proposed approach can potentially improve automation for downstream analyses. The autoencoder naturally generates a hidden encoding with latent features representative of the original data. This latent representation of the original data acts as an automatic feature extraction and dimensionality reduction technique for downstream tasks such as genetic risk prediction. Moreover, the autoencoder-based imputation approach only requires a reference panel during training – only the neural network needs to be distributed for implementation. Thus, the neural network is portable and avoids privacy issues associated with standard statistical imputation. This privacy-preserving feature will allow developers to deploy real-time data-driven algorithms on personal devices (edge computing). These new features will expand the clinical applications of genomic imputation, as well as its role in preventive healthcare. Another point related to data privacy is that the autoencoders segment the genome, making reconstruction of an individual genome impossible even if reference data were somehow recoverable from the neural networks. Nevertheless, while there are no official data sharing restrictions on deep learning model weights generated from genomic data, future privacy risks may be discovered, necessitating further research into privacy concerns and differential privacy techniques for autoencoder-based genotype imputation. The paper describes a novel neural-network-based strategy for imputing unmeasured genotypes, which is a standard part of most association testing pipelines. The method is computationally intensive to train, but once training is complete the imputation is fast and accurate and does not require further access to a reference panel. It has the potential to be a practically-appealing alternative to existing methods. although further work (eg training of models) is required before this new approach can be applied genome-wide. public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 4 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by Molly Przeworski as the Senior Editor. The reviewers have opted to remain anonymous.Thank you for submitting your article "Rapid, Reference-Free Human Genotype Imputation with Denoising Autoencoders" for consideration by The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.Essential revisions:1) More precise technical details need to be provided about the method. Code used to train the method should be made available.2) Accuracy assessments should be made on a new dataset not used at any point in the training.3) Comparison with HMM should use a more diverse reference panel and with standard quality controls in place, with separate comparisons for rare vs common variants.4) The reason for the surprisingly low average accuracy of all methods, compared withprevious studies, needs to be identified and, probably, corrected. .5) Software for applying the pre-trained network to impute genotypes needs to be publicly available.Reviewer #1 (Recommendations for the authors):Supplemental Figures 12 and 13 – I appreciate the authors using various metrics for comparing imputation accuracies, but I think these figures are a bit confusing because it shows that SNPs with smaller MAF somehow have better imputation accuracy.Reviewer #2 (Recommendations for the authors):Two particular concerns for the authors:1) The code is not yet available. Once it is made available I'll be able to more thoroughly evaluate what the authors have done.2) As mentioned above, there is a bit of work to do on cleaning up the run time performance evaluations.Reviewer #3 (Recommendations for the authors):Besides the points mentioned in the public review, I have the following comments/suggestions:– While I am somewhat familiar with autoencoders, I found it quite hard to follow the description of "denoising" autoencoders. Part of the problem was that I did not appreciate that these are different from a regular autoencoder until I did a bit more reading. I'm not quite sure how to make the description more accessible to the audience who are not familiar with denoising autoencoders, but I think it would have helped me to have an equation giving the training objective function that is being optimized to supplement Figure 1.– The description of the HMM methods on p3 is inaccurate. For example, the hidden states are not the "to-be-imputed" variants  and the genotyped variants are not the "observed states" . In any case it needs rewriting.– p4 the analogy with single-cell "dropout" is misleading because the zeros in single cell data are not "missing data" in the same sense as the missing genotypes in genotype imputation. (See https://www.nature.com/articles/s41588-021-00873-4 for example).– p6: although ultimately performance is what matters, the genotype encoding seems a bit weird to me: specifically the way that 0 is used for both missing data and absence of the allele (which are different things!) Is this standard in the denoising autoencoder literature? Also, can you clarify what you mean by "scaled outputs can also be regarded as probabilities" and "This representation maintains the interdepencies among classes". Indeed, I don't see why this last is true: for example, the "true" genotype can never be , so if one of the pair is 0 the other must be 1, and this interdependency does not seem to be captured by the encoding.Reviewer #4 (Recommendations for the authors):Specific comments are given below.1. The authors trained their models using HRC reference panel, which consists of predominantly European ancestry individuals. They didn't mention the reference panel used in HMM-based imputations, and I assume it was also HRC. As we know, performance of HMM-based imputation depends on the reference panels. There are larger and more diverse reference panels publicly available (e.g. TOPMed freeze 8 reference panel through the TOPMed imputation server). Does AE still have values (whatever training datasets they are using) over the TOPMed imputation server? Evaluations with diverse reference panel is particularly important for at least two reasons: (1) diverse panels are widely used (if not the most widely used); (2) AE relies more on pretrained model that no longer retains individual haplotype level information than HMM-based methods, which is conceptually susceptible to heterogeneity in reference panel. The authors may not have access to individual-level TOPMed data for training their AE models. In that case, they should at least evaluate the performance with the 1000 Genomes Project as reference.2. The authors didn't mention any post-imputation QC steps, thus it's not clear to me which variants are included in their evaluations/comparisons. As we know, not all markers attempted  can be well imputed. It is essential to have post-imputation QC to filter out poorly imputed markers. The manuscript does not touch this important topic at all, rendering the method practically not useful. Also rather puzzlingly, the R2 showed in all the figures are largely in the range 0.2-0.6, which is inconsistent from what's reported in the literature. For common variants, HMM-based imputation methods have been reported to attain R2 > 0.8 (if not even much higher); and for rare variants, the mode is close to zero. The expected bimodal distribution is not observed. Please clarify. For similar reason, quality assessment should be performed for common and rare variants separately.3. Have the authors evaluated the computationally identified hotspots? Are they largely consistent with the "true" recombination hotspots? Based on Figure 1E, these hotspots are calculated according to LD. What if the reference panel contains diverse populations? The LD calculated based on heterogeneous individuals would be meaningless.eLife. Your revised article has been evaluated by two of the original Reviewers, Molly Przeworski (Senior Editor) and a Reviewing Editor.Thank you for resubmitting your work entitled "Rapid, Reference-Free Human Genotype Imputation with Denoising Autoencoders" for further consideration by The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:1. You need to clearly report the (very considerable) training time required for the autoencoder. This relates to comments from both Reviewers which I repeat here:Reviewer 2: "I don't think the authors are dealing enough with performance issues and the need to share training times for tuning. First, in the revision the authors have edited/added Figure 6 which shows a runtime comparison, however, the methods section description (lines 308-315) does not mention how only prediction time was taken into account, as the authors seem to be explaining in the Response to Reviews document. More importantly, given that software release is mostly a proof of principle- pre-trained models are available for chr22 only -further, genome-wide inference a user would have to (as I understand it): download a reference set, train tiled auto-encoders for the genome on their own hardware, and then do inference on their data of interest. Surely then it's important to profile the performance of this bit of the pipeline for the user."Reviewer 4. That "the training process is going to take approximately one year to finish." would severely limit the application of the method. If the authors, as developers, do not release pre-trained models, we would be relying on extremely motivated and computationally savvy users to perform the pre-training. Along the line, reporting only the inference speed  becomes insufficient since the users would need to pre-train the models for all other chromosomes before they can apply the models to their target data.2. You need to address the original request to compare against HMMs from a diverse reference. This request was made in the original decision, but the response instead focussed on the diversity of the target samples, which is a different issue. This relates to the following comment from Reviewer 4:For major comment 1, I was not referring to a diverse target but referred to a diverse reference. I know that HRC includes the samples from the 1000 Genomes Project but the aggressive variant filtering and the predominant European ancestry individuals  make it a lousy example as a diverse reference. Essential revisions:1) More precise technical details need to be provided about the method. Code used to train the method should be made available.We have made the source code and detailed instructions for use available publicly at Github.The computational pipeline for autoencoder training and validation is available at:https://github.com/TorkamaniLab/Imputation_Autoencoder/tree/master/autoencoder_tuning_pipeline.The python script for calculating imputation accuracy is available at: https://github.com/TorkamaniLab/imputation_accuracy_calculator.2) Accuracy assessments should be made on a new dataset not used at any point in the training.The MESA, Wellderly, and HGDP datasets are all independent datasets, never used for training, nor model selection. Only HRC was used as reference panel or for training, and ARIC was used for model tuning. We included a statement in the methods clarifying this point.3) Comparison with HMM should use a more diverse reference panel and with standard quality controls in place, with separate comparisons for rare vs common variants.Two of our independent testing datasets , are from highly diversified multi-ethnic cohorts. HGDP includes 828 samples from 54 different populations representing all continental populations and including remote populations like Siberia, Oceania, etc. This reference panel is described in more detail in the reference below and likely represents the most diverse human genome dataset available.Bergström A, et al., Insights into human genetic variation and population history from 929 diverse genomes. Science. 2020 Mar 20;367(6484):eaay5012.4) The reason for the surprisingly low average accuracy of all methods, compared withprevious studies, needs to be identified and, probably, corrected. .We show average accuracy of 0.2-0.6 in Table 4, but that is the average aggregate R2 per variant across all variants . The reviewer points that the accuracy should be R2>0.8, but this R2>0.8 expectation applies only to common variants . Our results reflect this level of accuracy (R2>0.8) for common variants as plotted in Figure 4. The aggregate accuracy we report in Table 4 is substantially lower because the vast majority of genetic variants are rare, falling below the 1% allele frequency threshold and pulling down the overall average. The parent HRC reference publication below, as well as other supporting references we provide, demonstrate this is expected and conforms with our results.References:Rubinacci S, Delaneau O, Marchini J. Genotype imputation using the positional burrows wheeler transform. PLoS genetics. 2020 Nov 16;16(11):e1009049.Our curves in Figure 4 replicate this graded accuracy across allele frequencies with higher accruacy above 1% allele frequency. Other examples:McCarthy S, Das S, Kretzschmar W, Delaneau O, Wood AR, Teumer A, Kang HM, Fuchsberger C, Danecek P, Sharp K, Luo Y. A reference panel of 64,976 haplotypes for genotype imputation. Nature genetics. 2016 Oct;48(10):1279.Vergara C, Parker MM, Franco L, Cho MH, Valencia-Duarte AV, Beaty TH, Duggal P. Genotype imputation performance of three reference panels using African ancestry individuals. Human genetics. 2018 Apr;137(4):281-92.5) Software for applying the pre-trained network to impute genotypes needs to be publicly available.We now share the pre-trained autoencoders (including model weights and inference source code), as well as instructions on how to use them for imputation.. We have added this information to the Data Availability subsection of the Methods.These resources are publicly available at https://github.com/TorkamaniLab/imputator_inferenceReviewer #1 (Recommendations for the authors):Supplemental Figures 12 and 13 – I appreciate the authors using various metrics for comparing imputation accuracies, but I think these figures are a bit confusing because it shows that SNPs with smaller MAF somehow have better imputation accuracy.Yes, this is a bit of an accuracy paradox: since most of the genotypes in rare variants are homozygous reference, concordances and F-scores are inflated due to the overwhelming abundance of the negative class. In order to address this source of confusion, we have added a note to the captions of these figures explaining this phenomenon and pointing the reader to Figure S14  for a more accurate picture of balanced accuracy.Reviewer #2 (Recommendations for the authors):Two particular concerns for the authors:1) The code is not yet available. Once it is made available I'll be able to more thoroughly evaluate what the authors have done.We made both pre-trained models and the source code available now.2) As mentioned above, there is a bit of work to do on cleaning up the run time performance evaluations.We have clarified the major concerns on the performance comparisons, including further clarification that all the testing results shown are from independent datasets not used for training, nor tuning; and that the runtime comparisons extracted from HMM refer to the prediction step only, excluding the time for I/O and HMM iterations.Reviewer #3 (Recommendations for the authors):Besides the points mentioned in the public review, I have the following comments/suggestions:– While I am somewhat familiar with autoencoders, I found it quite hard to follow the description of "denoising" autoencoders. Part of the problem was that I did not appreciate that these are different from a regular autoencoder until I did a bit more reading. I'm not quite sure how to make the description more accessible to the audience who are not familiar with denoising autoencoders, but I think it would have helped me to have an equation giving the training objective function that is being optimized to supplement Figure 1.We edited/included a couple of sentences in the introduction and methods, defining what is the most basic difference between typical autoencoders and the denoising autoencoder. We hope this helps to further clarify this issue.– The description of the HMM methods on p3 is inaccurate. For example, the hidden states are not the "to-be-imputed" variants  and the genotyped variants are not the "observed states" . In any case it needs rewriting.Thanks for catching this. We corrected the HMM definition in the introduction.– p4 the analogy with single-cell "dropout" is misleading because the zeros in single cell data are not "missing data" in the same sense as the missing genotypes in genotype imputation. (See https://www.nature.com/articles/s41588-021-00873-4 for example).While there is some subtlety to this point, single-cell “dropout” includes both molecules that actually do not exist in the cell at the time of sampling as well as molecules that do exist but are not captured by the single-cell assay. Our own experience with scRNAseq data confirms this, taking the same library and sequencing it more deeply (or applying other molecular techniques to deplete abundant species) leads to the discovery of a larger number of genes per cell.These are true missing data.Despite this, we agree the scRNAseq example is complex and perhaps confusing – a simpler example more true to the nature of missing data in genotype data would be more appropriate. Therefore we’ve replaced those examples with the more classic image applications.– p6: although ultimately performance is what matters, the genotype encoding seems a bit weird to me: specifically the way that 0 is used for both missing data and absence of the allele (which are different things!) Is this standard in the denoising autoencoder literature? Also, can you clarify what you mean by "scaled outputs can also be regarded as probabilities" and "This representation maintains the interdepencies among classes". Indeed, I don't see why this last is true: for example, the "true" genotype can never be , so if one of the pair is 0 the other must be 1, and this interdependency does not seem to be captured by the encoding.We rescale the outputs by the following formula:AE output example : x′ = x′ref ∗  = 0.55 ∗ 0.10 = 0.055x′ = (1 − x′ref) ∗ x′alt = 0.45 ∗ 0.90 = 0.405x′ = x′ref ∗ x′alt = 0.55 ∗ 0.90 = 0.495where x’ is the reconstructed outputs from the autoencoders for reference (ref) and alternate  alleles.Next, we convert the rescaled outputs into probabilities  by using a softmax function:We have removed the statement about interdependencies to avoid confusion. However, as a point of interest for the reviewer – while we have yet to test this point – 0,0 genotypes may actually be possible – when the position containing the SNP locus is deleted in the genome. This gets a bit complex and we’re not absolutely sure whether we would be able to capture this sort of event with our encoding, so we’ve simply removed the statement.Reviewer #4 (Recommendations for the authors):Specific comments are given below.1. The authors trained their models using HRC reference panel, which consists of predominantly European ancestry individuals. They didn't mention the reference panel used in HMM-based imputations, and I assume it was also HRC. As we know, performance of HMM-based imputation depends on the reference panels. There are larger and more diverse reference panels publicly available (e.g. TOPMed freeze 8 reference panel through the TOPMed imputation server). Does AE still have values (whatever training datasets they are using) over the TOPMed imputation server?We included further clarification in the methods section:“We utilized HRC as reference panel for the HMM-based imputation tools, which is the same dataset used for training the autoencoders, and we applied the same quality control standards for both HMM-based and autoencoder-based imputation.”Until recently, HRC has been the standard for imputation (and is still often used). Both the HMM-method and our autoencoders would improve with the use of an expanded reference. The fairest comparison is to use the same reference for both approaches.Evaluations with diverse reference panel is particularly important for at least two reasons: (1) diverse panels are widely used (if not the most widely used); (2) AE relies more on pretrained model that no longer retains individual haplotype level information than HMM-based methods, which is conceptually susceptible to heterogeneity in reference panel. The authors may not have access to individual-level TOPMed data for training their AE models. In that case, they should at least evaluate the performance with the 1000 Genomes Project as reference.We have evaluated our models on data that is significantly more diverse than the 1000 Genomes . Two of our independent testing datasets , are from highly diversified multi-ethnic cohorts. HGDP includes 828 samples from 54 different populations representing all continental populations and including remote populations like Siberia, Oceania, etc. This reference panel is described in more detail in the reference below and likely represents the most diverse human genome dataset available – more diverse  than TopMed.Bergström A, et al., Insights into human genetic variation and population history from 929 diverse genomes. Science. 2020 Mar 20;367(6484):eaay5012.2. The authors didn't mention any post-imputation QC steps, thus it's not clear to me which variants are included in their evaluations/comparisons. As we know, not all markers attempted  can be well imputed. It is essential to have post-imputation QC to filter out poorly imputed markers. The manuscript does not touch this important topic at all, rendering the method practically not useful. Also rather puzzlingly, the R2 showed in all the figures are largely in the range 0.2-0.6, which is inconsistent from what's reported in the literature. For common variants, HMM-based imputation methods have been reported to attain R2 > 0.8 (if not even much higher); and for rare variants, the mode is close to zero. The expected bimodal distribution is not observed. Please clarify. For similar reason, quality assessment should be performed for common and rare variants separately.We included further clarification in the methods explaining that no post-imputation QC was applied. However, we bin performance by allele frequency which relates to imputability. And the output of our model includes genotype probabilities which can be used as a measure of post-imputation QC for end-users. This point is now explained in the Genotype Encoding section of Methods, and in the documentation of the imputation software repository available at:https://github.com/TorkamaniLab/imputator_inferenceAs for overall accuracy, we show average accuracy of 0.2-0.6 in Table 4, but that is the average aggregate R2 per variant across all variants (no MAF filter or binning applied). The reviewer points that the accuracy should be R2>0.8, but this R2>0.8 expectation applies only to common variants . Our results reflect this level of accuracy (r2>0.8) for common variants as plotted in Figure 4. The aggregate accuracy we report in Table 4 is substantially lower because the vast majority of genetic variants are rare, falling below the 1% allele frequency threshold and pulling down the average. The parent HRC reference, as well as other supporting references we provide, demonstrate this is expected and conforms with our results.References:Rubinacci S, Delaneau O, Marchini J. Genotype imputation using the positional burrows wheeler transform. PLoS genetics. 2020 Nov 16;16(11):e1009049.McCarthy S, Das S, Kretzschmar W, Delaneau O, Wood AR, Teumer A, Kang HM, Fuchsberger C, Danecek P, Sharp K, Luo Y. A reference panel of 64,976 haplotypes for genotype imputation. Nature genetics. 2016 Oct;48(10):1279.Vergara C, Parker MM, Franco L, Cho MH, Valencia-Duarte AV, Beaty TH, Duggal P. Genotype imputation performance of three reference panels using African ancestry individuals. Human genetics. 2018 Apr;137(4):281-92.3. Have the authors evaluated the computationally identified hotspots? Are they largely consistent with the "true" recombination hotspots? Based on Figure 1E, these hotspots are calculated according to LD. What if the reference panel contains diverse populations? The LD calculated based on heterogeneous individuals would be meaningless.Although we have not manually verified this across the whole genome, we have done several comparisons across regions of known recombination hotspots versus our LD based tiling method. One of the examples is shown in Similarly, we have compared our LD-based tiling boundaries of HRC versus 1000G. The plot  shows anHowever, we had to further split certain segments that were too large due to GPU memory limitations (see Methods).As expected, the sub-segments resulting from this further split did not match to known recombination sites.The manuscript has been improved but there are some remaining issues that need to be addressed, as outlined below:1. You need to clearly report the (very considerable) training time required for the autoencoder. This relates to comments from both Reviewers which I repeat here:Reviewer 2: "I don't think the authors are dealing enough with performance issues and the need to share training times for tuning. First, in the revision the authors have edited/added Figure 6 which shows a runtime comparison, however, the methods section description (lines 308-315) does not mention how only prediction time was taken into account, as the authors seem to be explaining in the Response to Reviews document. More importantly, given that software release is mostly a proof of principle- pre-trained models are available for chr22 only -further, genome-wide inference a user would have to (as I understand it): download a reference set, train tiled auto-encoders for the genome on their own hardware, and then do inference on their data of interest. Surely then it's important to profile the performance of this bit of the pipeline for the user."Reviewer 4. That "the training process is going to take approximately one year to finish." would severely limit the application of the method. If the authors, as developers, do not release pre-trained models, we would be relying on extremely motivated and computationally savvy users to perform the pre-training. Along the line, reporting only the inference speed  becomes insufficient since the users would need to pre-train the models for all other chromosomes before they can apply the models to their target data.We have now expanded the description of the implications of the inference time at the end of the Results section with a discussion of the considerable training time required to generate pre-trained models that achieve our reported inference time. We contrast this with HMM-based imputation tools, statin that they are more easily adaptable to the de-novo application of novel reference panels (lines 541 – 551).2. You need to address the original request to compare against HMMs from a diverse reference. This request was made in the original decision, but the response instead focussed on the diversity of the target samples, which is a different issue. This relates to the following comment from Reviewer 4:For major comment 1, I was not referring to a diverse target but referred to a diverse reference. I know that HRC includes the samples from the 1000 Genomes Project but the aggressive variant filtering and the predominant European ancestry individuals  make it a lousy example as a diverse reference.We have acquired the TOPMed reference cohort and performed HMM-based imputation using this reference panel. A description of this reference panel is provided in methods (lines 147 – 160). Imputation accuracy comparisons are provided at the cohort level  and broken down by ancestry . The autoencoder retains superior performance even when the HMM has access to a more diverse cohort except in the case of MESA – which is a component of TOPMed and contains a significant rate of familial relationship to the rest of the TOPMed cohort. Additional minor edits to support the addition of this analysis are made throughout the manuscript.


The inbred line TZEI 135 displayed relatively larger positive GCA effects for GY when mated either as male or female and was identified as the best tester. TZEI 135 × TZEI 182 was identified as the best single-cross tester across environments. Results of the assessment of the relative importance of GCA and SCA effects revealed the predominance of additive gene action over the non-additive. Six HGs of inbreds were identified using the HGCAMT and three, based on the DArTseq marker genetic distance method, were the most efficient. The best hybrids in this study significantly out-yielded the best checks by 21, 46, and 70% under CHDS, HS, and TDS, respectively. These hybrids should be extensively tested in on-farm trials for possible commercialization in sub-Saharan Africa.Information on combining ability and heterotic patterns of multiple stress-tolerant inbred lines are fundamental prerequisites for devising appropriate breeding strategies for the development of climate-resilient maize hybrids. In the present study, we evaluated 150 single cross hybrids derived from the North Carolina Design II (NCD II) along with six commercial checks under terminal drought stress (TDS), heat stress (HS), and combined drought and heat stress (CHDS)conditions. The objectives of the study were to: (i) determine the combining ability of the inbred lines and identify the best testers across the stresses; (ii) classify the inbred lines into heterotic groups (HGs) based on the general combining ability of multiple traits (HGCAMT) and sequencing-based diversity array technology (DArTseq) and (iii) assess the performance and stability of the lines in hybrid combinations. The inbred lines showed significantly ( Zea mays L.) is an important cereal crop cultivated globally for multiple purposes, such as staple food, livestock feed, edible oil, biofuel, and raw material for the synthesis of various industrial products [Maize  and specific combining ability (SCA) of a breeding population is critical for the adoption of the most appropriate breeding strategy to improve the traits of interest . While Ginations . An ultiinations  showed tinations . Akinwalinations  defined inations , a good The North Carolina Design II is one of the prominent mating designs in plant breeding for classifying inbred lines into appropriate HGs and identifying desirable testers for use in hybridization . ConventBreeders at the International Institute of Tropical Agriculture (IITA) in collaboration with the National Agricultural Research Institutes (NARS) of WCA have, over the years, developed several DS-tolerant inbred lines. Efforts at determining the mode of gene action controlling the inheritance of GY and other traits in these inbred lines have yielded conflicting reports. For example, previous studies ,19 have Assess the importance of general combing ability (GCA) and specific combining ability (SCA) for grain yield and other key agronomic traits in a set of newly developed inbred lines under independent and combined drought and heat stress conditions;Identify inbred and hybrid testers across test environments;Assign the inbred lines into heterotic groups based on the GCA of multiple traits (HGCAMT) method and DArTseq markers, and assessed the performance and stability of the hybrids under the test environments.Striga resistant inbred lines as well as hybridization between a drought-susceptible population and drought-tolerant inbred lines. In addition, some of the lines were derived from two IITA bi-parental populations. Detailed information on the methodology and strategies adopted for the development of the inbred lines as well as the genetic backgrounds of the broad-based source populations, Striga resistant, drought-tolerant, and susceptible inbred lines, and the IITA-biparental populations have been extensively described in a previous study [1 progenies (single cross hybrids) were generated and six commercial hybrids with good levels of tolerance to DS and CHDS conditions were included as checks for field evaluations. The pedigree information of the parental lines, their reactions to the stresses as well as the sets into which they were placed, and a description of the checks have been presented in Thirty DS- and CHDS-tolerant early maturing inbred lines were selected for this study based on preliminary evaluation (data not presented) under DS and CHDS. These included 15 of each white and yellow endosperm maize inbred lines derived from diverse sources. First, some of the inbred lines were extracted from broad-based populations derived from exotic and local germplasm with broad adaptation to dry and hot climates identified based on many years of extensive testing in the savannas of WCA. The second set of inbred lines was developed through crosses involving a broad-based drought-tolerant population and elite us study . The 30 2O5, and K2O ha−1 (15:15:15) at planting. Three weeks later, 60 kg ha−1 of urea was applied as a top dressing. The HS and CHDS blocks were supplied with irrigation water using a drip irrigation system at Manga and a furrow irrigation system at Kadawa. At both locations, irrigation was suspended on the CHDS block at 34 days after planting to induce DS at elevated temperatures prior to and during flowering and grain filling periods. Irrigation was resumed 10 days after completion of grain filling but was conducted if and when the plant showed signs of severe leaf rolling and wilting during the early mornings. The HS block received irrigation water from planting to physiological maturity. At both Manga and Kadawa, the flowering and grain filling periods generally occurred in April when day and night temperatures were relatively high in both years  under terminal drought stress (TDS), HS, and CHDS conditions during the growing and dry seasons of 2018 and 2019, respectively. The hybrids were also evaluated under CHDS at the IITA experimental site at Kadawa, Nigeria  between February and June in 2018 and 2019. A 12 × 13 alpha lattice design with 2 replications was used in all the experiments. At all locations, three seeds were planted in single-row plots, each 3 m long. Inter and intra row spacings were 0.75 m and 0.4 m, respectively. Two seedlings were maintained per hill to achieve a density of 66,667 plants/ha. At Manga, experiments under TDS were planted in the middle of September each year to induce natural DS at the reproductive stages in November. Trials under HS and CHDS were planted on opposite blocks separated by 10 m to prevent spillover of irrigation water. The trials were planted on the same day in the second week of February to ensure that the flowering and grain filling stages coincided with the peak temperature in April  . Similarth years . Pre- anDays to anthesis (AD) and silking (SD) were recorded for each plot when 50% of the plants had their pollen shed and silks extruded, respectively. The anthesis-silking interval was computed by subtracting AD from SD. Plant and ear heights (PLHT and EARHT) were recorded on representative plants of each plot at physiological maturity. PLHT was measured from the base of the plant to the tip of the tassel while EARHT was measured from the base of the plant to the node bearing the uppermost ear. Plants with tassel blasting (TB) and leaf firing (LF) symptoms were counted for the HS and CHDS plots. Ear rot (EAROT) was counted on each harvested plot and converted to percentages. Plant aspect (PLASP) was rated based on the assessment of the general architecture of plants in a plot as they appeared by sight using a scale of 1–9 where 1 = excellent overall-physical-appearance, 2 = very good overall-physical-appearance, 3 = good overall-physical-appearance, 4 = relatively good overall-physical-appearance, 5 = acceptable physical appearance, 6 = relatively poor overall-physical-appearance, 7 = poor overall-physical-appearance, 8 = very poor overall-physical-appearance, and 9 = extremely poor overall-physical-appearance [https://ordering.diversityarrry.com/files/DArTDNAisolation.pdf accessed on 20 June 2018). The DNA quality was determined through 0.8% gel electrophoresis, with the DNA concentration quantified by a Nano-drop spectrophotometer . Subsequently, the genotyping was performed at BeCA-ILRI, Nairobi, Kenya using the Integrated Genomic Services and Support (IGSS) platform. Ninety-six samples were multiplexed per sequencing lane and the SNPs calling was performed with DArT’s proprietary software, DArTSoft as previously described [The GBS protocol developed by Elshire et al.  was adopescribed . Reads aescribed . In totaescribed . The minEach location by year combination was regarded as a test environment. Analysis of variance (ANOVA) was performed for each research condition  to determine the effects of genotype (G), environment (E), and the interaction (GEI). Subsequently, a combined analysis of variance was conducted across the three test conditions. The ANOVA was performed using the general linear model (PROC GLM) of the Statistical Analysis System (SAS) via a random statement with a test option . In the sGY is the grain yield under stress, EPP is ear per plant, ASI is anthesis silking interval, PLASP is plant aspect, and LDC is stay-green/leaf death characteristic. A positive BI value indicated tolerance to the applied stress while a negative BI value indicated susceptibility [A base index (BI) that incorporated superior grain yield, ASI, PLASP, EPP, EASP, and LDC was used to select the best and worst-performing hybrids under each stress condition . The tratibility .2 = 40%). The statistical model adopted for the HGCAMT method is given below:Y is the genetic value depicting relatedness among inbred lines based on the GCA of multiple traits (HGCAMT), i to n; G is the individual GCA effects of inbred lines for trait i; g is the mean of GCA effects across inbred lines for trait i; s is the standard deviation of the GCA effects of trait i; ξij is the residual of the model associated with the combination of inbred i and trait j.The heterotic grouping method based on the GCA of multiple traits (HGCAMT) postulated by Badu-Apraku et al.  was usedSimilarly, the DArTseq SNP data was converted to the Euclidean distance matrix, from which a dendrogram was constructed to depict HGs at 40% dissimilarity.For each research condition  the DArTseq based GD and the HGCAMT methods of heterotic grouping were evaluated to determine the most effective method. This was achieved by assembling all the 150 hybrids from the highest to the lowest based on GY under each and across research conditions and dividing the total number of hybrids for each method into two major groups, that is the inter-group and intra-group crosses. Then, the hybrids were ranked based on GY and divided into three groups. Group one (high-yielding hybrids) comprised the top 50 hybrids, group two (intermediate hybrids) consisted of hybrids ranked between 51 and 100, and group three (low-yielding hybrids) was composed of hybrids ranked between 101 and 150. The better classification method was chosen using the method of Fan et al. . AdditioInbred and single cross testers were identified by using the criteria of Pswarayi and Vivek .ijŶ is the average yield of genotype i in environment j; jY is the average yield-across genotypes in environment j; 1λ and 2λ are the singular values for PC1 and PC2 respectively; i1ξ and i2ξ are the PC1 and PC2 scores, for genotype-i; j1η and j2η are the PC1-and -PC2 scores, for environment j; ijε is the error associated with the genotype-i in the environment.The least significant (LS) means for GY obtained from data combined across the research conditions was subjected to genotype main effects plus genotype by environment interaction effects (GGE) biplot analysis and the result was displayed as graphs showing (1) a “which-won-where” pattern to identify mega-environments, and (2) ranking of hybrids based on yield and stability . The GGEp ≤ 0.001) for GY and other traits , and set by E interactions were highly significant (r traits . Partitir traits . Furtherr traits . The setr traits .p < 0.01 and 0.05) negative and positive GCA effects for GY and key secondary traits under the applied stresses  based on the pedigree, endosperm color, and reaction to the stresses . The firBreeding efficiency based on HGCAMT and DArTseq GD methods ranged from 32% to 41.6% and 32% to 43.2%, respectively . The DArPswarayi and Vivek,  demonstrResults of the top 20 and worse 10 hybrids based on index selection under the research conditions are presented in From the GGE-biplot analysis, the first two axes (Axis 1 and Axis 2) together explained 75.66% of the variation in GY of the hybrids A. The poTwo environments, ) fell within the sector that had TZEI 135 × TZEI 501 and TZEI 240 × TZEI 1517  as the vThe best hybrid should always demonstrate high mean yield performance as well as stability across test environments. In this study, the “mean performance vs. stability” GGE-biplot view was used to identify the highest yielding and most stable single cross hybrid across the test environments . The thiThe combining ability of the 30 early maturing inbred lines was investigated in the present study under TDS, HS, and CHDS to obtain information on target agronomic traits for devising breeding strategies to improve the traits. An important requirement for the classification of germplasm into distinct HGs is the availability of adequate genetic variability. In the present study, the NCD II-derived single cross hybrids and their parental inbred lines displayed a wide range of variation for the traits measured under the test environments. In particular, the genotypic variations due to hybrids were highly significant for GY and some other traits, indicating the presence of adequate genetic differences among the parental lines and their derived hybrids. This implied that superior hybrids and promising lines could be identified for improvement through selection under the stresses. These results are consistent with the findings of previous studies which reported significant genetic variation among maize germplasm evaluated under similar stress conditions ,8. The e1 family selection, full-sib family, and half-sib family methods should be adopted to accelerate progress in the development of superior hybrids for DS and HS prone environments. The inbred lines with significant and positive GCA effects for EPP and GY are expected to contribute favorable alleles to EPP and GY while those with significant and negative GCA effects would contribute favorable alleles for ASI, PLASP, and EASP. Four inbred lines  had positive GCA-female and GCA-male effects for GY under CHDS, HS, and across test environments making them suitable for use as either female or male parents in the development of hybrids tolerant to the stresses. Similarly, under HS, the significant and positive GCA-female effects recorded for GY in TZEI 1013 and TZEI 7 suggested that these inbred lines could be important donors of beneficial alleles for enhanced GY potential when used as female parents. The same explanation holds for inbred lines TZEI 17, TZEI 18, and TZEI 240, which showed significant and positive GCA-male effects for GY under HS. Interestingly, inbred line TZEI 135 consistently displayed significant and positive GCA effects for GY and EPP and negative and significant GCA effects for PLASP and EASP, as both male and females, making it the best combiner for the four important traits in the favorable direction (increased EPP and GY and desirable PLASP and EASP). It is striking to note that our study identified nine inbred lines as good combiners  for plant height in environments where shorter hybrids were typically preferred to minimize lodging. The larger GCA-female effects over the GCA-male for traits such as LDC, LF, and TB under HS and LDC under DS revealed that maternal effects played a major role in the inheritance. Thus, to take advantage of possible cytoplasmic inheritance, the inbred lines with significant and negative GCA-female effects for these traits should be used as female parents in their respective crosses. Additionally, TZEI 17 and TZEI 1517 with significant and negative GCA-female and GCA-male effects for LDC under HS, and TZEI 242 showing negative GCA–female and male effects for TB and LF under CHDS when used as either female or male parents, could contribute favorable alleles for delayed senescence leading to increased photosynthesis and ultimately, higher GY.The two complementary methods used to assess the importance of GCA and SCA variances both showed that GCA variances were larger than the SCA variances for all measured traits , Table 3Striga infested environments. The DArTseq marker-based HG method grouped the 30 inbreds into three groups, consistent with their pedigrees and endosperm colors. Interestingly, all inbred lines in HG II were tolerant to both DS and CHDS. Thus, these inbred lines could be crossed to others in the opposing HGs to generate high-yielding hybrids for DS and CHDS-prone environments [The 30 inbred lines analyzed in this study were also classified into HGs using two different grouping methods, namely the HGCAMT method postulated by Badu-Apraku et al.  and the ronments ,46,47,48Pswarayi and Vivek  recommenIn the present study, the average GY recorded for NCD II generated hybrids under HS (3715 kg/ha) was higher than that reported by Nelimor et al.  when a sGenotypic adaptation and stability in grain yield are two important attributes constrained by the interaction between genotype and environment (GEI), which is a major factor responsible for the variation in the performance of genotypes in contrasting environments. Among the objectives of this study was to identify hybrids that combined good yield and stable performance across a range of production environments for further testing for possible release and commercialization in the sub-region. The presence of significant GEI effects for GY and the majority of the measured traits under each and across the test environments indicated that the hybrids differed in their GY performance in the contrasting test environments. Consequently, the “which-won-where” and the “mean performance vs. stability” GGE biplot view were used to identify hybrids with location-specific and broad adaptation, respectively for GY. The first and second axis (Axis 1 and Axis 2) from the “which-won-where” view of the GGE biplot explained 75.66% of the variation in GY suggesting that Axis 1 and Axis 2 adequately estimated the environment-centered data. Entries 101 (TZEI 135 × TZEI 501) and 4 (TZEI 240 × TZEI 1517) showed specific adaptation to environments HSME  and HSMF  for high GY. Based on the “mean performance vs. stability” GGE biplot analysis, hybrids 101 (TZEI 135 × TZEI 501) and 45 (TZEI 501 × TZEI 528) were identified as the most stable hybrids across the test environments with entry 101 (TZEI 135 × TZEI 501) as the best hybrid because of its high GY across the test environments. This hybrid should therefore be extensively tested in on-farm trials to confirm the consistency of the performance and stability for commercialization in SSA.The results of the present study showed that additive gene action was predominant over the non-additive for GY and most measured traits, suggesting that the GCA component largely accounted for the differences among the inbred lines. The DArTseq genetic distance-based method was more efficient in grouping the inbred lines and was used to identify TZEI 135 as the best tester under each and across test environments. The single cross hybrid TZEI 10 × TZEI 17 was identified as the best tester under HS while TZEI 135 × TZEI 182 was the best across environments. The most stable and high yielding hybrid across environments was TZEI 135 × TZEI 501 and should be tested in on-farm trials to confirm its consistency in performance for possible commercialization in SSA.