While gene expression networks are dominated by local cis-regulatory elements, we observe three genomic hotspots of unlinked trans-regulatory loci. These regulatory hubs are four times more drought responsive than the genome-wide average. Additionally, cis- and trans-regulatory networks are more likely to have opposing effects than expected under neutral evolution, supporting a strong influence of compensatory evolution and stabilizing selection. These results implicate trans-regulatory evolution as a driver of drought responses and demonstrate the potential for crop improvement in drought-prone regions through modification of gene regulatory networks.Environmental stress is a major driver of ecological community dynamics and agricultural productivity. This is especially true for soil water availability, because drought is the greatest abiotic inhibitor of worldwide crop yields. Here, we test the genetic basis of drought responses in the genetic model for C Panicum hallii.Drought is a major factor limiting crop productivity. Here, via eQTL analysis and comparative genomics, the authors show compensatory evolution between trans-regulatory loci and transcription factor binding sites that shape the drought response networks in the model C4 grass  Unlike annual plant species, which can escape environmental stress through flowering time evolution, perennial plants must persist through periods of drought. While constitutive drought tolerance can lead to slower growth and lower yields, there is considerable genetic variation in the physiological nature and efficacy of facultative responses to soil moisture variation among plants5. Leveraging such genotype-by-environment interactions (GxE), especially in response to drought, is key to crop improvement.Drought is the greatest abiotic determinant of agricultural yield6.Despite the central role that GxE plays in adaptation and plant productivity, the genetic basis of evolved differences in stress responses are poorly understood, except in a handful of laboratory model systems. However, it is clear that gene expression networks play particularly important roles in the evolution of physiological GxE as transcription factors and other regulatory elements are often environmentally induced7. Conversely, trans factors may cause correlated expression variation among many downstream genes, which should increase interference among loci and reduce the adaptive potential of global trans-regulatory evolution9. To this end, many global regulatory elements evolve much more slowly than their target sequences12. Combined, cis- and trans-regulatory elements shape the gene expression landscape and form the basis of environmental stress responses. Therefore, defining the regulatory elements that lead to evolved differences in stress responses will improve our understanding of stress adaptation and the genetic basis of GxE.Regulatory elements fall into two main categories: distant trans-acting modifiers (e.g. transcription factors) and local cis-regulatory elements (e.g. promoter or coding sequence variants). Selection works most efficiently on traits that act in isolation; therefore, cis-elements, which typically regulate a single gene, may be particularly important in adaptive evolutionPanicum hallii as a genomic model for Panicoid grasses13. The Panicoideae is a diverse subfamily of predominantly perennial warm-season grasses with efficient C4 photosynthesis14, which imparts drought-tolerance and some of the highest biomass production among plants15. Not surprisingly, the Panicoideae encompasses the most promising bioenergy feedstock crops, including switchgrass, Sorghum, big bluestem, Miscanthus, and sugar cane. The geographic distribution of P. hallii spans a massive moisture availability gradient: the lowland variety  inhabits riparian and coastal sites with >100 cm of annual precipitation while upland  populations are found across southwestern North America16 in both desert  and semi-arid habitats. The extensive physiological diversity13 of P. hallii and its close evolutionary relationship to key crops make it an ideal genetic model for biotechnology development in perennial biofuel feedstocks.To understand the genetic basis of drought stress tolerance in the context of perenniality, we have developed P. hallii drought responses, connecting DNA sequence variation to leaf-level physiology. We first assess the demographic history and population structure of the upland and lowland varieties of P. hallii. To understand the scale of genomic divergence between varieties, we compare complete de novo genome assemblies and annotations for a single genotype of each variety. We then explore the genetic basis of evolved drought-responsive gene expression in an F2 mapping population. Through eQTL mapping and comparative genomics, we demonstrate that trans-regulatory elements and transcription factor binding site evolution are key contributors to molecular drought responses in P. hallii. Combined, these results and genetic resources elevate P. hallii among the elite plant genomes, provide the genetic model for perennial feedstocks, and begin to decipher the complex drought-responsive genetic networks that have diverged between upland and lowland ecotypes.Here we present a set of experiments and analyses that dissect the genetic basis of filipes and hallii is likely due to both adaptation and historical demographic processes associated with paleo-climatic change in North America. To explore the recent evolutionary history of these varieties, we deeply re-sequenced (35x median sequence coverage) 15 filipes and 78 hallii natural accessions . This conclusion was confirmed by a molecular-clock based estimate of divergence of 1.08 M ybp. Furthermore, pairwise cross-coalescence, a measure of the degree of genetic divergence between populations17, between any two hallii and filipes subpopulations  of the largest two hallii subpopulations  and a representative var. filipes accession (FIL2)  Figs. b, 2a–d. ssembled –4. Critissembled . A totalHAL2 and FIL2 are derived or lost in each genome. Overall, the majority of high-confidence gene models  existed as either single copy (‘1:1’) orthogroups or orthogroups with two or more members in at least one genome  among orthologous clusters of genes. This analysis was performed via our GENESPACE pipeline  of present genes with the unannotated assembly sequence of syntenic orthologous regions in the other genome. The majority of PAV genes were private to either ps Table . Other sP < 1 × 10–16, Table P < 1 × 10−16), indicating that pseudogenized and deleted genes may represent biologically relevant presence-absence variation.To understand sequence variation underlying the remaining PAV genes, which also had at least one outgroup sequence in the network, we categorized the degree of sequence variation between CDS and un-annotated DNA sequence of the alternative genome into un-annotated (>90% sequence identity), pseudogenized (90–10% identity), and deleted ( < 10% identity) groups  gain and loss is not common despite the >1 My divergence time between HAL2 and FIL2. Such conserved gene content and synteny despite significant sequence divergence (mean π = 0.0195) makes P. hallii an ideal system to test hypotheses about sequence evolution, selection, and molecular adaptation.To confirm the quantitative genetic effects of the observed PAV, we counted expression of each unique allele across the two genomes in leaf tissue of an Fon Table . These rHAL2 and 34 FIL2 replicates and 243 FIL2xHAL2 F2 genotypes were subjected to a month-long natural drought. Half of the plants were watered 24 h prior to harvest (recovery treatment), while the remainder were harvested under existing drought conditions. At the physiological scale, midday leaf water potential (a measure of plant water status) was more responsive to re-watering among HAL2 than FIL2 plants  with one-to-one reciprocal best hit (RBH) orthologs between the two genomes. This test allowed us to count the total expression of 21,227 putative RBH orthologs  and similarly conserved TFBA  regions as genes without eQTL. Furthermore, since trans-regulated loci are targets of transcriptional regulatory elements, we expected transcription factor binding sites to be very conserved among genes with only trans-eQTL. Indeed, such genes had 1.45x greater transcription factor binding site sequence conservation (Fisher’s test P < 1 × 10−6) than genes with cis-eQTL, but less significantly conserved CDS regions  more GxE effects than all trans-eQTL outside this interval.Differential adaptation across habitats is an example of a genotype-by-environment interaction (GxE) for fitnessQTL Fig. , Table 326, from the entire F2 population at both pre-dawn and midday at the same time as RNA sampling. There were no significant QTL , which is the best available field-scale proxy for plant water status27. For example, expression of all but two genes regulated by trans-eQTL in the *3a primary hotspot were driven by plasticity of the FIL2, but not the HAL2 allele , is a well-documented drought-responsive WRKY transcription factor. Knockout alleles of ABO3 in A. thaliana induce extreme sensitivity to drought28. RT-qPCR revealed that the FIL2 ABO3 allele is 27.7x downregulated relative to the HAL2 allele across both well-watered and drought conditions  cis–trans regulatory networks.Elevated GxE among trans-eQTL, particularly within the hotspots, indicates possible selection on gene expression plasticity. To test the hypothesis of non-neutral regulatory network evolution, we examined the QTL effect distribution among the 684 genes with both cis- and trans-eQTL Table . Under aP = 0.015) and a very strong signal in the drought treatment, where allelic effects were greater than two times more likely to be antagonistic than under neutral expectations . However, the relative strength of reinforcing and antagonistic effects was highly dependent on the position of the trans-eQTL  population, derived from the F2 used in the eQTL study , RWC in the drought treatment , and significantly affected SPAD in both recovery  and drought treatments . Individually, each of these effects are not highly significant. Yet, when taken together we observe strong support for functional effects of allelic variation at the *3a hotspot with a Fisher’s combined test  and demonstrate the predictive potential and multi-environment effect of trans-acting transcriptional regulatory elements.Allelic variation at the *3b hotspot never significantly affected any treatment-trait combination, and the *7 hotspot had only one significant association  and Pacific Biosciences (SEQUEL) platforms at the Department of Energy Joint Genome Institute  and the HudsonAlpha Institute for Biotechnology .We sequenced the HAL2  and 119 (HAL2) joins were applied to the broken assemblies to form the final releases consisting of 9 chromosomes each. Short redundant sequence from contig ends were aligned to one another and collapsed when appropriate. A total of 18 (HAL2) and 450 (FIL2) repeated adjacent contig pairs were identified and collapsed. For the FIL2 release, a set of 30,315 (430.3 Mb) targeted clone sequences (Illumina), along with a set of 704,618  MOLECULO reads were used to patch 60 sequence gaps. Finally, Illumina reads were employed to correct any remaining MECAT consensus calling errors (e.g. homozygous SNPs and INDELs).We built a 325,613-marker map from shallow resequencing of the RIL population35 were used to produce 92,211 (HAL2) and 111,325 (FIL2) transcript assemblies from ~1100 M (HAL2) and ~1200 M (FIL2) 2 × 150 paired-end Illumina RNA-seq reads. Repetitive DNA elements were identified de novo with repeatModeler36. For mapping and genome comparisons, we soft-masked the genomes using repeatMasker37, with ancestral repeats from RepBase and the repeat annotations from repeatModeler output. Loci were determined by transcript assembly alignments and/or EXONERATE (https://github.com/nathanweeks/exonerate) alignments of proteins from Arabidopsis thaliana, soybean, Kitaake rice, sorghum, foxtail millet, Brachypodium distachyon, grape and Swiss-Prot proteomes. Gene models were predicted by homology-based methods, FGENESH + /_EST38 GenomeScan39, and AUGUSTUS via BRAKER140. The best-scoring predictions for each locus were selected using EST and protein support and penalized if overlapped with repeats. PASA was employed to add UTRs, splicing corrections, and alternative transcripts. High-confidence transcripts were called for loci with BLASTP Cscores >0.5, EST coverage, and <20% of CDS overlapping with repeats . Gene models with >30% TE domains (Pfam) were also culled. Finally, gene models with a short single exon (<300 BP CDS), without protein domain or with weak expression evidence were removed.PERTRAN  identify orthologous pairs of genes, (2) define the scale and causes of presence absence variation among gene annotations, and (3) understand the scale of synteny between the 41 program but limits the search within known colinear (syntenic) blocks, generated by the multiple-collinearity inference program MCScanX42. This allows for the inference of orthology in duplicated chromosomal regions, as these appear as multiple distinct blocks in the alignments. In addition to pairwise peptide–peptide searches for orthologous gene groups, GENESPACE also conducts alignments against un-annotated genomic sequences (via BLAT43 and EXONERATE) to discover the sequence identity of pseudogenized or otherwise un-annotated loci. The pipeline outputs alignments and some general sequence-divergence statistics for all orthogroup sequences among all genomes considered.The GENESPACE pipeline . Drought treatment plants were harvested on 5 July 2013, while recovery treatment plants received 4 L of water on 7 July 2013 and were harvested on 8 July 2013. For each plant, we measured midday leaf water potential  with a Scholander-type pressure bomb  between 11:00 and 13:00. All plants reached anthesis by 5 July 2013.Leaf tissue harvest was conducted on 5 and 8 July 2013 between 11:00 and 13:00, where the most recent fully emerged leaf was immediately flash frozen with liquid nitrogen. For total gene expression assays, RNA  was extracted from 50–200 mg of homogenized  and DNase 1-treated leaf tissue with RNeasy Plant Mini kits (Qiagen). Total RNA libraries were prepared on a PerkinElmer SciClone NGS robotic liquid handling system using Illumina’s TruSeq Stranded mRNA HT Sample Prep kit with 1 µg RNA per sample, and 10 cycles of library amplification PCR. Library quantification by KAPA Biosystem’s next-generation sequencing library qPCR was accomplished on a Roche LightCycler 480 real-time PCR instrument. Sequencing was performed on the Illumina HiSeq 2000 sequencer and a TruSeq SBS sequencing kit .HAL2 and FIL2 genomes. Uniquely mapping reads were counted with STAR45 – by definition these reads represent allele-specific expression (ASE). Shared  reads were those that mapped to both orthologs; these were counted with the subread46 featureCount function. Total counts, calculated as the sum of ASE and shared counts, were used for eQTL analyses. High-confidence gene models with reciprocal best hit one-to-one orthologs and average total counts ≥1 were retained for further analysis. Total counts were voom23 normalized for eQTL analysis.To quantify expression, we mapped reads to concatenated genome assemblies and annotations of the 47. It is common to perform eQTL via one-way single QTL scans for each gene expression trait. However, there are several multi-locus correlated regions in our genetic map, where markers on one chromosome are in linkage disequilibrium (LD) with markers on another chromosome  for each transcript abundance phenotype was multiple-test corrected using the Q-value approach48. The maximum significant (α = 0.05) empirical P-value was enforced as the trans-significance threshold. Only trans-eQTL LOD peaks that were more significant than this threshold were retained. Since cis-eQTL were not subject to genomic scans, we employed a standard Q-value transformed ANOVA χ2P-value threshold, retaining cis effects with FDR-corrected P-values ≤0.05. Both cis- and trans-GxE effects were determined by comparing the additive and full models via likelihood ratio tests. The resultant P-values were FDR corrected in an identical manner as the additive cis-eQTL test. Finally, we dropped any cis- or trans-eQTL with maximum LOD scores <2.Both additive and QTL-by-treatment (GxE eQTL) scans were accomplished using the Haley-Knott algorithm on Hidden Markov Model multipoint genotype probabilities. The lowest genome-wide error rate-controlled empirical HAL2/(HAL2 + FIL2) allele-specific expression (ASE) for 15,082 gene models with >5 ASE counts in each parent. For each chromosome and F2 genotype, we conducted a 20-gene overlapping sliding window calculation of the proportion of HAL2-ASE. We expected clear tri-modality of HAL2 allele frequency within each window, where the HAL2 homozygotes were ~100% HAL2 alleles, the heterozygotes were ~50%, and the FIL2 homozygotes were ~0%. Given the F2 population, the three peaks should be in approximately a 1:2:1 segregation ratio. Windows that did not conform to these expectations were dropped from the analysis.To construct a linkage map, we calculated the ratio of To make calls, we first needed to develop thresholds that distinguished the three genotypes. Since the relative bias of allele frequency towards either parent in the heterozygote varied based on the markers in the window, a static threshold was not appropriate. Instead, we applied a dynamic threshold that separated the trimodal distribution of alleles into three bins. This dynamic thresholding eliminated library-specific biases towards either parent. The most common call (majority vote) in each 20-gene window was used as the genotype call. Calls were concatenated across libraries and chromosomes to produce a single genotype matrix.47, we culled markers within 0.5 cM, retaining the marker with lower segregation distortion. Finally, we tested for potentially problematic markers by assessing the genetic map size before and after dropping each marker. Those markers that resulted in an expansion of the map >1 cM were culled. The final map contained 1519 markers.Sliding window majority vote markers were processed to produce a saturated and non-redundant genetic map. Markers were first clustered into groups with identical genotypes. The marker with the least missing data was retained for each cluster of identical markers, resulting in a matrix of 3555 unique markers. We then clustered pairs of markers with ≤0.005 recombination fractions, retaining the marker that minimized missing data and segregation distortion. The physical assembly position was used to order markers and form linkage groups. After estimating a genetic map with the Kosambi mapping function49. For all chromosomes, the −log likelihood of the genetic map was maximized at 1 × 10−6  imply non-neutral evolution50. We also tested the odds ratio against the overall prevalence of antagonistic and reinforcing effects across the genome. This comparison allowed for inference of outlier regions relative to the genome average of cis-trans allelic effects.To test for selection on the evolution of gene expression, we employed a sign test where the odds ratio of cis- and trans- up- and down-regulatory evolution was tested via a Fisher’s exact test. Directional effects of each QTL were calculated using the fitqtl function in R/qtl. Estimates of QTL effects were calculated as the HAL2(query):FIL2(target) and FIL2(query):HAL2(target) protein BLAT43 scores. The genes where both BLAT runs produced the same set of maximal gene pairings were the initial set of RBH orthologs. Given the known high degree of synteny, we then culled this set to include only pairings where both genes were on the same chromosomal region, allowing for 20% of the total chromosome length as buffer.Reciprocal best hit (RBH) orthologs are defined as those pairs of genes where each is the other best matching sequence when compared to the alternate genome. Here we tested for 1:1 RBH orthologs by finding the best FIL2 CDS sequences were aligned against corresponding HAL2 sequences using Minimap251. The resulting alignment file was subset to 26786 HAL2-FIL2 orthologs. A pileup-formatted file was generated using SAMtools52 mpileup utility. VarScan253 was used to call variants (SNPs and INDELs). Those variants were then annotated using SnpEFF54. SNP and INDEL variant annotations were described as synonymous, moderate effect (e.g. missense mutation), high effect (e.g. premature stop), or insertion/deletion. All genes were classified as either having or lacking significant CDS evolution. Significant genes had at least one moderate or larger effect SNP or INDEL, while non-significant genes were monomorphic, or had only low effect variants.To annotate coding DNA sequences (CDS), 55 as positional frequency matrices. Affinity of each motif was scored for each promoter sequence and differential binding affinity was tested using the R package PWMEnrich56. Binomial tests for equal affinity were performed for each gene and transcription factor. Significance was determined by controlling for global false discovery rate at α = 0.05 by transforming the binomial P-values using the Benjami-Hochberg method. All genes were classified as either having or lacking significant TFBA evolution. Significant genes had at least one transcription factor with a significant binomial test while all transcription factors in non-significant TFBA genes had FDR-corrected binomial P-values ≥0.05.We annotated transcription factor binding affinity (TFBA) of the promoter sequences  by extracting and comparing relative binding affinity of a set of 35 transcription factor families. Transcription factor binding sites (motifs) were downloaded from the JASPAR2016 plant databaseP-value.In many cases, we sought to compare the relative prevalence of genes with and without TFBA and CDS evolution. To accomplish this, we employed a Fisher’s exact test, reporting the odds ratio and exact P. hallii genotypes; 78 var. hallii, and 15 var. filipes. We selected more hallii samples than filipes as the geographic range of hallii is far larger than that of filipes. If identical sample sizes were used, we would be comparing geographically proximate filipes and geographically distant hallii. Since there is at least some isolation-by-distance in P. hallii16, we instead opted to choose sample sizes that generally reflect the relative range size of each variety.We re-sequenced 94 HAL2 genome reference via bwa-mem57, followed by samtools52 to sort the bam and create a multisample mileup52. Single nucleotide polymorphisms (SNP) and insertion-deletion (indel) polymorphisms were called via the Varscan 2.4.053 pipeline as above, with a minimum coverage of 8, and minimum reads of 4. A binomial test was used to confirm the allelic state (homozygous or heterozygous) at a P-value of 0.05. SNPs within 25 bp of a repeat were removed. A minimum presence of allele in 90% samples was required for further analysis.Illumina HiSeq2500 2 × 150 reads were mapped to the 58 and TESS59 with a subset of 50k markers, that were LD pruned (parameters: --indep-pairwise 50 50 0.5) in plink60. A single sample with a membership coefficient (qi) of <0.7 was considered admixed.Population structure was estimated using fastStructure17). Sites were filtered for unique 24mers to minimize spurious variant calls. These data were input into MSMC217 to estimate effective population size and divergence using the following parameters: 4 haplotypes for each subpopulation, skipping ambiguous sites and a time segment pattern = ‘10*2 + 20*5 + 10*2’ and an estimated rhoOverMu of 0.25. We estimated rhoOverMu as 0.25 as the mean value from 100 iterations without the fixed recombination parameter of five sets of four haplotypes in each subpopulation and averaged them. To estimate scaled times were converted to years assuming a generation time of 1 year and a mutation rate of 6.5*10–8. 50 bootstrap datasets obtained using MSMC tools, and simulations using the same parameters above were performed for each of the estimate to get the confidence intervals for population size estimates.To infer demographic history, samples were phased 64 to estimate the divergence times. A calibration time of 52 Mya was used for Brachypodium and Sorghum split. We performed four independent runs, each with 10 million burn-ins and 50 million chain length, saving every 5000 chains. LogCombiner64 was used to combine trees that have an effective sample size of at least 200. The consensus trees were further estimated in TreeAnnotator64 using mean and median node heights.OrthoFinderPhABO3q-F (5′-CCGCATACTGGATCTCACAA-3′) and PhABO3q-R (5′-TCTGAATCCAGTGGCACATC-3′) for amplifying the transcript of PhABO3 and PhUBIq-F (5′-TCATTTCGATGCTCTCTAGTCC-3′) and PhUBIq-R (5′-TTCCTGAGATTTGCGAACAATG-3′) for ubiquitin-conjugating enzyme  as the internal control. We carried out quantitative RT-PCR in a total volume of 10 μl containing 2 μl of the reverse-transcribed product above, 0.25 μM gene-specific primers and 5 μl LightCycler 480 SYBR Green I Master (Roche) on a Roche LightCycler 480 II real-time PCR System according to the manufacturer’s instructions. The measurements were obtained using the relative quantification method65.For quantitative RT-PCR, we isolated total RNA from the leaves using an RNA extraction kit . About 1 μg total RNA was reverse-transcribed using SSII reverse transcriptase (Invitrogen) in a volume of 80 μl to obtain cDNA. We used primers 7 individuals of the HAL2xFIL2 recombinant inbred line (RIL) population34 were grown at Brackenridge Field Laboratory  in spring and summer of 2016. Seeds were germinated in the BFL greenhouse on 29-Feburary and 3-March 2016. For each RIL line, seed coats for 40 seed were removed by scarification, and seeds were germinated in wet aquarium sand on petri plates. Sand was rewetted as necessary with Miracle Gro liquid fertilizer mix. Plate locations were randomly cycled daily in the greenhouse to standardize growth conditions. Germination occurred between 3–5 March and on 7–10 March. The healthiest seedlings were transplanted from sand to 32-cell trays to generate at least eight healthy replicates per line. Transplants were thinned to the most robust individual per cell between 23–29 March, and 294 lines with eight healthy individuals were selected for inclusion in the field design. On 7 April, plants were randomized within trays into the field experiment layout. To standardize growing conditions, trays were also cycled once in the greenhouse between transplanting and randomization.294 FFIL2 individuals. Individuals were spaced by 0.5 m along the length of the bed, and by 1.25 m along the width of the bed and between beds. Four individuals from each RIL line were randomized into both the wet treatment and the dry treatment beds to make a randomized split-plot design. Transplanting survival was very high, but nine plants were replaced in mid-May due to transplanting death. The entire field was irrigated on 14, 15, and 20 April to reduce transplantation shock. Thereafter, the wet treatment beds were frequently irrigated between 17-June and 8-August in order to achieve >50% soil volumetric water content. The dry treatment beds were irrigated at roughly 1/5th the frequency, at a level sufficient to achieve 30% soil volumetric water content, as measured with a Campbell Scientific CWS655 soil moisture probe. We measured two phenotypes: leaf relative water content (RWC = (weightfresh−wtdry)/(wtturgid−wtdry)) and leaf chlorophyll content . Phenotypic tissue harvest and measurements took place from 11–15 July 2016 between 9AM and 1PM.RIL individuals were transplanted in the field on 14–15 April in 32 interspersed wet and dry treatment beds, three individuals wide and 26 individuals long. These blocks were surrounded by a border row of HAL2 coordinate system of the F2 genetic map to the FIL2 (v2.0) coordinate system of the RIL genetic map34. The multipoint genotype probability for the proximate RIL marker to each hotspot was inferred via a hidden Markov model, as implemented in R/qtl’s calc.genoprob function. Finally, we applied single marker tests for marker-phenotype associations between RWC and SPAD in the three conditions  as implemented in R/qtl’s fitqtl function.The best linear unbiased predictors were calculated for each genotype-by-treatment combination, where bed was treated as a random effect in the split plot design. The maximal position of each trans-eQTL hotspot was extracted and converted from the Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10Reporting SummarySource Data 1Source Data 2


To date, 60 genetic variants have been robustly associated with birthweight. It is unclear whether these associations represent the effect of an individual’s own genotype on their birthweight, their mother’s genotype, or both.We demonstrate how structural equation modelling (SEM) can be used to estimate both maternal and fetal effects when phenotype information is present for individuals in two generations and genotype information is available on the older individual. We conduct an extensive simulation study to assess the bias, power and type 1 error rates of the SEM and also apply the SEM to birthweight data in the UK Biobank study.Unlike simple regression models, our approach is unbiased when there is both a maternal and a fetal effect. The method can be used when either the individual’s own phenotype or the phenotype of their offspring is not available, and allows the inclusion of summary statistics from additional cohorts where raw data cannot be shared. We show that the type 1 error rate of the method is appropriate, and that there is substantial statistical power to detect a genetic variant that has a moderate effect on the phenotype and reasonable power to detect whether it is a fetal and/or a maternal effect. We also identify a subset of birthweight-associated single nucleotide polymorphisms (SNPs) that have opposing maternal and fetal effects in the UK Biobank.Our results show that SEM can be used to estimate parameters that would be difficult to quantify using simple statistical methods alone. We describe a structural equation model to estimate both maternal and fetal effects when phenotype information is present for individuals in two generations and genotype information is available on the older individual.Using simulation, we show that our approach is unbiased when there is both a maternal and fetal effect, unlike simple linear regression models. Additionally, we illustrate that the structural equation model is largely robust to random measurement error and missing data for either the individual’s own phenotype or the phenotype of their offspring.We describe how the flexibility of the structural equation modelling framework will allow the inclusion of summary statistics from studies that are unable to share raw data.Using the structural equation model to estimate the maternal and fetal effects of known birthweight-associated loci in the UK Biobank, we identify three loci that have primary effects through the maternal genome and six loci that have opposite effects in the maternal and fetal genomes.,Birthweight is a complex trait, and low birthweight is robustly associated with increased risk of a range of cardiometabolic diseases in later life.http://egg-consortium.org/) and the UK Biobank,GCK gene, which cause a defect in the sensing of glucose by the pancreas, have radically different associations with birthweight according to their parent of origin. If inherited paternally, birthweight is lower due to reduced glucose sensing and consequent reduced insulin secretion, which results in reduced growth. But if maternally inherited (i.e. present in both mother and fetus), birthweight is close to the population average because the maternal hyperglycaemia compensates for the fetal defect in glucose sensing. In the case that the mother has hyperglycaemia due to a GCK mutation, but the fetus does not inherit the mutation, the birthweight is higher due to normal glucose sensing and thus above-average insulin secretion. This example reflects contrasting effects mediated through the intrauterine environment  and direct effects of the offspring’s genotype.We and others have begun to investigate the specific regions of the genome that influence fetal growth, using genome-wide association studies (GWAS). In a recent GWAS meta-analysis combining data from the Early Growth Genetics consortium .We performed simulations to investigate the bias, power and type one error rate of the SEM for modelling both the individual’s own genetic effect  and maternal genetic effects on birthweight. The model we used for generating the data is illustrated in G), the individual’s own genotype (SNP) and offspring’s genotype (GO) were generated. The individual’s own birthweight variable (BW), for each family i, was generated using the following equation:MV denotes the variance in birthweight explained by the maternal genotype , GG is a latent variable indexing the genotype of the individual’s mother, OV is the variance in birthweight explained by the individual’s own genotype , SNP is the genotype of the individual, U is a standard normal random variable representing all residual genetic and environmental sources of similarity between mother and offspring, Uβ is the total effect of U on the individual’s own birthweight and ɛ is a random normal variable with mean zero and variance needed to ensure that BW has unit variance asymptotically.For each scenario, we generated 10 000 replicates of 30 000 maternal-offspring pairs. For each replicate we generated grandparental  and paternal genotypes at a single locus. Assuming autosomal Mendelian inheritance, additivity and unit variance, latent variables for the genotype of the individual’s mother , for each family i, was generated using the following equation:OG is a latent variable indexing the offspring genotype, UOβ is the total effect of U on offspring birthweight and Oɛ is a random normal variable with mean zero and variance needed to ensure that BWO has unit variance asymptotically.Similarly, offspring birthweight (BWUβ = UOβ = 0.5). We considered the effects of: allele frequency ; the strength of the fetal genetic effect on birthweight ; and the strength of the maternal genetic effect on birthweight . We simulated the fetal and maternal genetic effects to have both increasing and decreasing effects on birthweight.In all simulations, the regression of phenotype on residual shared genetic and environmental factors was set to 0.5 , which respectively estimate the fetal and maternal genetic effects on birthweight; this is equivalent to the model typically used in genetic studies of birthweightP-values were calculated using Wald tests;SEM estimating both maternal and fetal effects as illustrated in P-value was compared with the Wald test P-value for the fetal effect;SEM estimating only the fetal effect; this model was fit to conduct a likelihood ratio test for the maternal effect and the likelihood ratio test P-value was compared with the Wald test P-value for the maternal effect;SEM estimating only the maternal effect, to conduct a likelihood ratio test for the fetal effect; this likelihood ratio test P-value from this test is referred to as the two degrees of freedom (2DF) test P-value.SEM with neither fetal nor maternal paths (i.e. both fixed to zero); this model was fit to conduct a likelihood ratio test of the overall SNP effect, and the For each simulated dataset we fit a series of models:P < 0.05 under the alternative hypothesis, and type 1 error rate the proportion of tests that reached P < 0.05 under the null hypothesis.Bias was defined as the mean difference between the estimated SNP effect and the true parameter across the 10 000 simulations, and was calculated for both the maternal and fetal effects. A 95% confidence interval was calculated around the bias to give an indication of the uncertainty in the estimate. Power was defined as the proportion of tests that reached In the UK Biobank, female participants were asked to report the birthweight of their first offspring to the nearest pound. After appropriate data cleaning, this left six discrete birthweight values for the offspring (see below). We therefore conducted a second set of simulations to investigate the effect of this type of measurement error, using the same method as described above but rounding the birthweight of the offspring to the nearest unit.2 value for the regression of BW* on BW, using the following equation:Given that birthweights of both individuals and their offspring are self-reported in the UK Biobank, we also assessed the potential effect of measurement error on both variables. To do this, we added a normally distributed error component to both simulated birthweight measurements, which is referred to as discrimination or classical measurement error.R2 , where lower values of R2 represent increasing measurement error. We used a subset of maternal and fetal effect sizes to get an idea of whether the impact of measurement error is influenced by effect size; neither a maternal or fetal effect (OV = 0% = MV), large fetal effect and no maternal effect , no fetal effect and a large maternal effect , large fetal and maternal effect  and large fetal and maternal effect in opposite directions. All simulations were conducted with an allele frequency of p = 0.5.IJE online) illustrates the three components of the SEM used to incorporate individuals with missing data; the first component models individuals with complete data, the second component models genotyped individuals who report their own phenotype but not their offspring’s, and the third component models genotyped mothers who report their offspring phenotype data but not their own. These three components are fit to the three subsets of data and then the likelihoods from each model are combined. Modelling the data in this way avoids list-wise deletion of cases due to missing phenotype information and makes maximum use of the observed data. If data are missing at random then our full information maximum likelihood approach returns asymptotically unbiased parameter estimates, and the most precise estimates that have this property.ρ in We also assessed the impact of when individuals did not have both their own and their offspring birthweight available. UK Biobank phenotype data were available on 502 643 individuals, of whom 279 959 reported their own birthweight at either the baseline or follow-up visits. There were 7693 individuals who were part of multiple births and were excluded from the analyses. Of the 9034 individuals who reported their own birthweight at both baseline and follow-up, 401  were excluded because the two values differed by more than 0.5 kg. For those individuals who reported different values between baseline and follow-up (<0.5 kg) we took the baseline measure for the analyses. Finally, we excluded individuals who reported their own birthweight to be <2.5 kg or >4.5 kg [24 138 (9%) individuals with birthweight <2.5 kg and 14 065 (5%) individuals with birthweight >4.5 kg], as these are implausible for live term births before 1970. In total, 233 662 individuals had data on their own birthweight matching our inclusion criteria.Women in the UK Biobank were also asked to report the birthweight of their first child to the nearest pound. We used the same inclusion criteria as for their own birthweight, leaving 210 405 individuals with birthweight of their first child , 109 205 of whom had also reported their own birthweight.K-means (K = 4) clustering approach based on the first four genetically determined principal components. A subset of 89 296 unrelated individuals with genotype data, a valid birthweight for themselves or their first child and genetically of ‘White European’ ancestry were included in the analysis. Of these, 24 962 were men who only reported their own birthweight. Among the women, 8723 reported only their own birthweight, 24 645 reported only that of their first child and 30 966 reported both. We adjusted both the individual’s own birthweight and the birthweight of their first child for the principal components that were associated with birthweight, adjusted the individual’s own birthweight for sex (sex was not reported for the offspring) and then created z-scores. A subset of 58 autosomal SNPs out of the 60 birthweight-associated SNPset al.et al.Genotype data from the May 2015 release were available on a subset of 152 248 individuals. In addition to the quality control metrics performed centrally by the UK Biobank, we excluded individuals who were related. We defined a subset of ‘White European’ ancestry samples using a IJE online).IJE online). However, there was a decrease in the precision of the estimate (i.e. increase in the standard error) as the measurement error increased (IJE online); this bias differed across allele frequency and true effect size for both the maternal and fetal effects, and no clear pattern was observed. The bias was less than 4% of the true value in all scenarios and substantially lower than the bias introduced in the linear models.When there was measurement error in either the individual’s own birthweight or the birthweight of their offspring, the estimates of maternal and fetal effects were unbiased , the computational time is approximately 100 times faster using the covariance matrices than the raw data. There is not a substantial difference in computational time between datasets with different amounts of missing data for the phenotype of the individual or their offspring when fitting the model using the raw data, but there is a difference for variants with lower minor allele frequencies which take longer to run than common variants. When using covariance matrices, however, it takes slightly longer to fit the model when data are missing for either the individual or their offspring, because the model fits two or three sub-models simultaneously . The estimates from the model fit with the raw data are the same as those using with covariance matrices. In comparison with a linear model, the SEM using covariance matrices takes about three times as long to compute with a sample size of 30 000 individuals  and eight SNPs have evidence for both. Perhaps the most interesting SNPs are those where the birthweight-increasing allele identified in Horikoshi et al.HHEX-IDE, CDKAL1, ADCY5 and ANK1-NXK6-3).IJE online) present the full results from the two linear models  and the SEM. These results show that for SNPs where the maternal and fetal effects go in opposite directions , the fetal effect estimated in the GWASet al.N = 12 909 individuals). IJE online) displays forest plots for the maternal and fetal effects for each of the 58 birthweight-associated SNPs, using both the SEM in the UK Biobank and conditional linear regression in the EGG cohorts. The confidence intervals surrounding the estimates from the conditional linear regression analyses are larger than those from the SEM, due to the smaller sample size in the former study . Estimates obtained using both procedures were similar for most SNPs. Formally, after Bonferroni correction for the 58 tests, no significant heterogeneity was detected between estimates from the SEM and estimates from the conditional linear regression for either the maternal or the fetal effects (heterogeneity P > 0.05/58 = 9 x 1 0−4). The largest heterogeneity between the SEM and the conditional regression for the maternal effect was at the ACTL9 locus , where the conditional linear regression resulted in a (non-significant) negative estimate of the effect of the maternal T allele on offspring birthweight, whereas the SEM resulted in a positive estimate of the effect of the same allele on offspring birthweight. However, the result from the maternal GWAS analysis presented in Horikoshi et al.To confirm our results, we compared estimates of maternal and fetal effects obtained from the SEM with those from the conditional linear regression model implemented in Horikoshi In this article, we have presented a method for estimating and testing maternal and fetal effects. The approach uses data from mother-offspring pairs for whom genotype data are available for the mothers only and phenotype data are available on both individuals. Our method is  unbiased when both maternal and fetal effects exist, which improves on the traditional linear model which estimates each effect separately while assuming the other to be absent. The approach is flexible and can be used when either the individual’s own phenotype or the phenotype of their offspring is not available. The ability to incorporate studies with only an individual’s own or their offspring’s phenotype, in combination with mother/offspring pairs with complete data, will transform many aspects of perinatal research, as it provides a large increase in statistical power to disentangle maternal and fetal effects which have been difficult to resolve until now.G) . For example, these offspring males contribute directly to the estimation of the maternal effect on birthweight  is correlated with his mother’s observed genotype at the same locus (SNP) , but not their offspring’s phenotype, are modelled in the top half of ,To illustrate the method, we used birthweight because there is clear evidence that both maternal and fetal effects exist.The most common study design used when trying to estimate fetal and maternal effects is to have maternal/offspring pairs, with phenotype information on the offspring and genotype information on both the mother and the offspring. These studies are then analysed using a standard linear regression model adjusting for both the maternal and the offspring genotype, which is often referred to as ‘conditional analysis’. One of the benefits of the SEM we describe here is that the coefficients for the maternal and fetal effects are on the same scale as the coefficients from a conditional analysis, and therefore a meta-analysis could be conducted across multiple cohorts with different study designs. Alternatively, because the model can be fit with observed covariance matrices, if the phenotypes of the mother and offspring are both standardized and the effect allele frequency is known, then the summary statistics  from an unconditional analysis for either the fetal effect or the maternal effect can be incorporated into this SEM. This makes it a potentially very powerful approach, as cohorts with phenotype data and genotypes from mother, child or both, can all be incorporated. It also avoids the need to share raw data, which can be problematic for some cohorts, but still allows for all cohorts to be included in the analysis and therefore the sample size maximized.One of the biggest advantages of this SEM is that it is robust to missing data, either for the individual’s own phenotype or the phenotype of their offspring. This is an advantage over conditional analysis, which uses only those mother/offspring pairs that have genotype data from both persons. It can even be used when no individuals have phenotypes measured on both themselves and their offspring; however, the power to detect a maternal or fetal effect is reduced and a small bias is introduced to the maternal effect estimate. There are unlikely to be many studies with this study design, as the majority would have a combination of individuals with complete data with individuals missing data for their own phenotype or the phenotype of their offspring. Additionally, it is robust to measurement error involving either the individual’s own phenotype or the phenotype of their offspring. However, increasing measurement error in both phenotypes will increase the standard errors and therefore decrease statistical power, similar to the effect of measurement error on ordinary least squares regression.There are four potential limitations to this SEM. First, although we have shown that the model fits well under a range of minor allele frequencies, in some situations it has difficulty optimizing with low frequency variants . This can often be resolved using the mxTryHard function in OpenMx, which makes several attempts to optimize the model and returns results from the most optimal fit. Second, the SEM assumes multivariate normality between the observed variables and linearity between the genotypes and phenotypes. We have simulated our phenotypes to be normally distributed and ensured that birthweight data in the UK Biobank were approximately normally distributed. In the case of non-normality, an appropriate data transformation can help ensure that the assumption of multivariate normality is satisfied. Third, we assumed additive genetic effects for both the fetal and maternal contributions. An additive model is used in the vast majority of genome-wide association studies in the literature, and theory and data show that the overwhelming majority of genetic loci act in an additive fashion.The SEM using observed covariance matrices takes approximately three times longer to compute than an unconditional linear model. Therefore, there is potential for this method to be used in large genomic studies, such as genome-wide studies. A new method for fitting SEMs in genome-wide association studies in a computationally feasible fashion has recently been developed,et al.MTNR1B, and near ACTL9 and EBF1). This result is consistent with the conditional analysis of 12 909 mother-offspring pairs in Horikoshi et al.MTNR1B and EBF1. The initial finding of a fetal effect appears to be due to the bias in the linear model, and therefore the fetal effect size was approximately half of the maternal effect size estimated using the SEM. We also identified six SNPs where the maternal and fetal effects were in opposite directions . Interestingly, four of these SNPs that exhibited maternal and fetal effects in opposing directions , consistent with what is known regarding the underlying biology at these loci.A recent study by Horikoshi In summary, we describe a new method for estimating unbiased maternal and fetal effects using studies where genotype data are available for only the individual and not their offspring. We have shown that the type 1 error rate of the method is appropriate, there is substantial statistical power to detect a genetic variant that has a moderate effect on the phenotype and reasonable power to detect whether it is a fetal and/or maternal effect. We have also illustrated that this method could be useful for accurate estimation of fetal and maternal effects in large genetic studies, such as genome-wide association studies, as the computational time is not substantially larger than the standard linear model.N.M.W. is supported by a National Health and Medical Research Council Early Career Fellowship (grant number APP1104818). D.M.E. is funded by an Australian Research Council Future Fellowship (grant number FT130101709) and a Medical Research Council programme grant (grant number MC_UU_12013/4). Access to the UKBB study data was funded by University of Queensland Early Career Researcher Grant (2014002959).Supplementary DataClick here for additional data file.


Coffea arabica, the most economically important species of the genus Coffea. Therefore, this study aimed (i) to evaluate the applicability and accuracy of GS in the prediction of the genomic estimated breeding value (GEBV); (ii) to estimate the genetic parameters; and (iii) to evaluate the time reduction of the selection cycle by GS in Arabica coffee breeding. A total of 195 Arabica coffee individuals, belonging to 13 families in generation of F2, susceptible backcross and resistant backcross, were phenotyped for 18 agronomic traits, and genotyped with 21,211 SNP molecular markers. Phenotypic data, measured in 2014, 2015, and 2016, were analyzed by mixed models. GS analyses were performed by the G-BLUP method, using the RKHS (Reproducing Kernel Hilbert Spaces) procedure, with a Bayesian algorithm. Heritabilities and selective accuracies were estimated, revealing moderate to high magnitude for most of the traits evaluated. Results of GS analyses showed the possibility of reducing the cycle time by 50%, maximizing selection gains per unit time. The effect of marker density on GS analyses was evaluated. Genomic selection proved to be promising for C. arabica breeding. The agronomic traits presented high complexity for they are controlled by several QTL and showed low genomic heritabilities, evidencing the need to incorporate genomic selection methodologies to the breeding programs of this species.Genomic Selection (GS) has allowed the maximization of genetic gains per unit time in several annual and perennial plant species. However, no GS studies have addressed  Genetic plant breeding started with the phenotypic selection of individuals that positively stood out in the segregating populations. In the 1980s, molecular markers were developed and used as an auxiliary tool to phenotypic information  was developed by Meuwissen et al. , being cWith the development of NGS (Next Generation Sequencing) platforms, GS has become a reality for several economically important species, including annual and perennial plants. The use of the NGS platforms has made SNP markers (Single Nucleotide Polymorphisms) economically feasible   to evaluate the applicability and accuracy of GS in the prediction of the GEBV; (ii) to estimate the genetic parameters; and (iii) to evaluate the time reduction of the selective cycle by GS in an Arabica coffee breeding.In the experimental area, soil liming and planting fertilization were performed according to the crop requirement. The genotypes were planted on February 11, 2011. Plants were arranged at spacing of 3.0 m between rows and 0.7 m between plants. No phytosanitary control method was used against rust, cercosporiosis, and leaf miner. The experiment was evaluated in the experimental area of the Department of Plant Pathology of the Universidade Federal de Viçosa, Brazil , in 2014, 2015, and 2016.C. arabica breeding program of Epamig/UFV/Embrapa , which contrast in relation to resistance to coffee rust, 13 progenies were obtained from the C. arabica genotypes listed in Table The phenotypic evaluations of 18 agronomic traits  were performed Table  in the 1The continuous traits were measured as described in Table yy) and phenotypic heritabilities , totaling 195 genotypes were evaluated. Phenotypic data were corrected for years, plots, and years × plots interactions, from which the selective accuracies ;p is the permanent effects between plants (random effect);r is the effects between population types (random effect);b is the effects between plot (random effect);i is the effects of progenies x years interaction (random effect);e is the residue vector (random effect).The uppercase letters represent the incidence matrices for these effects.Young and fully expanded leaves of the 195 genotypes were collected, and the genomic DNA was extracted using the methodology described by Diniz et al. . The DNAThe DNA concentration of the samples was standardized and sent to RAPiD GENOMICS, Florida/USA, for probes construction, sequencing, and identification of SNP molecular markers  of the GS model obtained by the result of the mean correlation between the GEBV and the observed phenotypic values was estimated.Cross-validation is a method used to evaluate the generalization capacity of a predictive model from a dataset. When applying this method, the dataset is partitioned into mutually exclusive subsets. The population, composed of 195 coffee trees, was divided into 13 folds−180 individuals were used for training or estimation of the predictive models and 15 individuals were used for validation. The process was repeated 13 times so that each part was used once as a validation set. In the end, the predictive capacity (rGenomic selection (GS) analyses were performed using the G-BLUP method via the RKHS (Reproducing Kernel Hilbert Spaces) procedure, with the Bayesian algorithm Gianola, . The BGLThe general mixed linear model Resende, , 2008 wai is equal to 0, 1, or 2 for the genotypes mm, Mm, and MM, respectively, for the biallelic and codominant marker i (SNP); and Wij is the element i of row j of matrix W, regarding individual j.The genomic estimated breeding value (GEBV) of individual j is given by rgy) is estimated by correlating the predicted genomic values with the corrected phenotypic values, being equivalent to the predictive capacity of the GS to estimate phenotypes  controlling each trait was estimated by the expression rggis the accuracy of the GS; nQTL is the number of QTL controlling each trait; and h2 is the individual heritability  that must be evaluated to obtain the desired accuracy was estimated by the expression The effect of the number of markers on the selective accuracy was evaluated. Predictive accuracy, with a set of markers composed of different SNP densities, was estimated by the G-BLUP method, using the RKHS (Reproducing Kernel Hilbert Spaces) procedure with a Bayesian algorithm Gianola, . The BGLgg is the selective accuracy of GS; Lf is the mean time required for the selection cycle based on phenotypes; ryy is the accuracy of the phenotypic selection; LGS is the mean time required for the selection cycle based on GS , compared with selection based on phenotypes alone, was estimated by the expression 2phen) and selective accuracies (ryy) were estimated using the mixed model methodology (REML/BLUP) (Table 2phen (0.01); conversely, plant height (PH) and canopy diameter (CD) showed the highest values for this parameter (0.90). Most of the evaluated traits presented high magnitude of ryy, with the exception of SD.Eighteen traits of agronomic importance were analyzed in 195 coffee trees. The individuals make up 13 families, which were obtained from crosses between parents of the Catuaí group and Híbrido de Timor (HdT). From the phenotypic data, heritabilities  Table . For allgy) of the 18 traits ranged from −0.01 to 0.40, for number of reproductive nodes (NRN) and canopy diameter (CD), respectively  ranged from 0.25 to 1.92 for number of reproductive nodes (NRN) and number of vegetative nodes (NVN), respectively. Most of the traits evaluated showed a b estimate close to the unit. The standard error of these estimates ranged from 0.77 to 3.25.Estimates of the predictive capacity (rly Table . The stagg) are presented in Table gg was not estimated for number of reproductive nodes (NRN) since its predictive capacity estimate was negative. The estimated rgg values of the other traits ranged from 0.06, for maturation uniformity (MU) and leaf width (LW), to 0.61, for canopy diameter (CD). A high correlation was observed between the estimates of rgg and gg and rgy (99%).Selective accuracy estimates obtained with the GS (rgg) and number of QTL.The number of QTL that controlled the trait (nQTL) ranged from 149 to 17,758 for canopy diameter (CD) and leaf width (LW), respectively Table . The agrNi) required to obtain a desired selective accuracy (rggd) is presented in Table ggd estimates are intended. Based on the data, 322–53.701 of individuals should be evaluated for canopy diameter (CD) and leaf width (LW), respectively, to obtain a selective accuracy estimate of 0.7, considered as of high magnitude  when using a larger number of SNPs  of 18 coffee trees agronomic traits were estimated from phenotypic data. The magnitude of the yy of high magnitude. Accuracy depends mainly on the ratio between the mean residual variation and the genotype variation. In its turn, the mean residual variation depends on the number of replications and the control when conducting the experiments  or Maturation uniformity (1–4), the technique called Generalized Linear Model should be used. This was done and the results did not differ so much from those got by using the standard procedure of Linear Mixed Model. This is in line with theory, which preconizes that the higher the number of score scale classes, the smaller the benefit from using the Generalized Linear Model technique. For small class numbers, the expected theoretical benefits are below 10%.C. arabica, C. canephora, and C. racemosa, 7,538 SNPs were identified, and 180 were selected for validation in C. arabica and C. canephora accessions from Puerto Rico   of From the information of the GS predictive equations, genomic heritability (gy) and the regression coefficient or prediction bias (b), associated with observed phenotypic values and predicted genetic values, are practical measures of the ability of the methods to make accurate and unbiased predictions, respectively  were of low to moderate magnitude  refers to the correlation between the true genotypic value of the genetic treatment and that estimated or predicted from the phenotypic information . This fact can be justified by the increase in the predictive complexity in function of the larger number of genes controlling the trait. When several genes affect a trait, their effects are usually small, and, consequently, the accurate estimation is challenging . An inversely proportional relation was observed between nQTL and selective accuracy  with the increase in the number of SNPs. The increase in the markers density guarantees the conservation of marker-QTL associations and allows obtaining high selective accuracies  than in A . This increase in the amount of information by using the genomic matrix G can, sometimes, lead to better and more precise estimations, and predictions. This fact can explain the differences between the results from genomic and phenotypic approaches observed in our paper. Another aspect is referring to the ability of SNPs to capture causal variants associated to the traits. Some markers are more informative for some traits than for others. This can explain the different behaviors presented by the different traits.With globalization and a significant increase in the world's population, the demand for techniques to assist breeders in the development of new cultivars has intensified. In this sense, the elucidation and use of genomic information, including GS studies, allows the access to genetic information, which is potentially useful for coffee breeding programs. The increased knowledge of the genetic variation in breeding populations will reduce the time and resources intended to development a new cultivar. Moreover, it will enable the selection of breeding lines/cultivars of superior quality, which are more adapted and productive.C. arabica breeding for reducing the selection cycle time. Agronomic traits are highly complex; they are controlled by several QTL, and present low genomic heritabilities, evidencing the need to incorporate genomic selection methodologies in the breeding programs of this species.Genome-wide selection proved to be promising for TS conceived the work, analyzed the data, discussed the different aspects of Genomic Selection, and wrote the first draft of the paper. EC conceived the work, supervised the data analysis, discussed the different aspects of Genomic Selection, and wrote the paper. EA provided technical assistance with DNA extraction, marker analysis, and wrote the paper. AO, AP, NS, and LZ provided phenotypic data from the breeding program and supervised the work. MR analyzed the data and discussed the different aspects of Genomic Selection, while the final manuscript was written in collaboration.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.


The Vrs1 gene, controlling the number of rows in the spike, was found to be associated with spikelet number of main spike, spikelet number per plant, grain number per plant, grain number per spike, and 1,000 grain weight in multiple environments and by multi-locus GWAS methods. Therefore, the above results evidenced the feasibility and reliability of genome-wide association studies in doubled haploid population, and the QTNs and their candidate genes detected in this study are useful for marker-assisted selection breeding, gene cloning, and functional identification in barley.The agronomic traits, including morphological and yield component traits, are important in barley breeding programs. In order to reveal the genetic foundation of agronomic traits of interest, in this study 122 doubled haploid lines from a cross between cultivars “Huaai 11” (six-rowed and dwarf) and “Huadamai 6” (two-rowed) were genotyped by 9680 SNPs and phenotyped 14 agronomic traits in 3 years, and the two datasets were used to conduct multi-locus genome-wide association studies. As a result, 913 quantitative trait nucleotides (QTNs) were identified by five multi-locus GWAS methods to be associated with the above 14 traits and their best linear unbiased predictions. Among these QTNs and their adjacent genes, 39 QTNs (or QTN clusters) were repeatedly detected in various environments and methods, and 10 candidate genes were identified from gene annotation. Nineteen QTNs and two genes ( Hordeum vulgare L, 2n = 2x = 14), one of the first domesticated grains in the Fertile Crescent  in barley, so it is difficult to obtain their genetic foundation and molecular mechanism. Plant height and its component traits serve as major plant morphological traits affecting barley seed yield. An appropriate plant height is a prerequisite for obtaining the desired yield in barley-breeding programs. To date, more than 30 types of dwarfing or semi-dwarfing genes have been detected, while only a few have been successfully used in barley breeding program, such as Traditionally, QTL mapping has been widely applied in the genetic dissection of quantitative traits in barley , Gao et al.  and multi-parent advanced generation intercross (MAGIC) populations, and proved to be powerful tool for uncovering the basis of key agronomic traits in maize and barley  use GWAS to further dissect the genetic foundations for main agronomic traits in our previous studies of Ren et al. , 2014 anOne hundred and twenty-two DH lines, derived from a cross between barley cultivar “Huaai 11” (six-rowed and dwarfing) and barley cultivar “Huadamai 6” (two-rowed), was used in this study. The details of the materials and field experiments were described in the previous studies of Ren et al. , 2014 anFourteen agronomic traits for the above DH population were measured in 2008–2009, 2009–2010, and 2011–2012, and all the three datasets had been reported by Ren et al. , 2014 any = lmer (Trait ~ (1|Genetype) + (1|Year)). The three single-year phenotypic values  for each trait of 3 years were calculated using the R package Lme4 . The Vrs1 locus controlling row number of barley was integrated with SNP markers for GWAS. All the above information has been described in Ren et al. . All parameters in GWAS were set at default values. The critical thresholds of significant association for the five methods were set as LOD = 3  were named as “qtn (qtnc)” + trait name abbreviation + chromosome + detected QTL order on chromosome.t-test was used to test the phenotypic difference between the two genotypes.For each QTN, all the DH lines were firstly divided into two groups based on their QTN genotypes, then http://plants.ensembl.org/Hordeum_vulgare/Info/Index and https://www.uniprot.org/uniprot), some genes around reliable QTNs (or clusters) were selected for each trait. By combining gene annotation information, protein domain function in database and previous reports, and expressional information (http://barlex.barleysequence.org), then, candidate genes for each trait were mined.According to the recent genome sequence release of barley Ibsc,  and the Using five multi-locus GWAS methods in the R package mrMLM v3.1, GWAS for 14 agronomic traits were performed. A total of 913 significant QTNs were found to be associated with the 14 agronomic traits in 3 years and their BLUP values Table . The numThe significant QTNs repeatedly detected by multiple methods were list in Table qtnPH-1H-1 , qtnPH-2H-1 , qtnPH-3H-2 , qtnPH-7H-1 , qtnPH-7H-2 , and qtnPH-7H-3 , located on chromosome 1H, 2H, 3H, 7H, 7H, and 7H, explained 0.63–4.07, 2.82–4.64, 3.13–9.03, 1.07–2.39, 2.31–6.07, and 0.69–2.68% of total phenotypic variation, respectively. Two reliable QTN clusters for PH, qtncPH-2H-2  and qtncPH-3H-1 , were identified in at least 2 years and methods, explained 2.12–3.79 and 2.15–7.23% of total phenotypic variation, respectively  for PH, was located on 7H  accounting for a highest phenotypic variation (3.53–22.62%) among the four QTNs and QTN clusters  for PH, accounting for 4.88–21.70% of the phenotypic variation. qtncIL3-6H-1 located on the chromosome 6H , explained phenotypic variation of 1.89–3.68%. For IL4, qtncIL4-3H-4 , co-located in the same region of qtncIL3-3H-3 for IL3 and qtncPH-3H-1 for PH mentioned above, explained 5.73–15.97% of phenotypic variation. Therefore, the region on chromosome 3H: 631,342,028–636,535,362 bp is a more credible QTN cluster for PH and the components traits, regulating the PH through controlling IL3 and IL4  explained less (1.79–6.02%) phenotypic variation, while QTN qtnIL4-7H-7 (7H: 360793216 bp) showed a high explanation (6.10–19.57%) for IL4  were found to be associated with plant height component traits IL1, IL2, IL3, and IL4, respectively. For IL1, qtnMSL-2H-7 located on chromosome 2H: 727,985,438 bp, was repeatedly detected not only in three environments and BLUP values but also by multiple methods to be significantly associated with MSL, and explained phenotypic variation about 2.09–18.16% : Three reliable QTNs and one QTN cluster were detected for MSL. Among which, qtnSMS-2H-9 referred to Vrs1 , located at 2H , was identified in all the situations and methods to be significantly associated with SMS  with minor effect was associated with SMS (Table Spikelet number of main spike (SMS): S Tables , accountqtnSLP-2H-10  and one reliable QTN clusters qtncSLP-2H-11  close to Vrs1  were identified in multiple environments and by multiple methods to be significantly associated with SLP, explaining high proportions of total phenotypic variation, 14.87–55.05 and 8.97–80.30%, respectively. The reliable QTN cluster qtncSLP-4H-1 with a minor effect (2.82–4.14%), mapped on the region 15,498,372–16,168,735 bp of chromosome 4H, was detected in 2 years and the BLUP (Tables Spikelet number per plant (SLP): One reliable QTN qtncSP-2H-12, located on 2H: 648,821,931–652,030,802 bp overlapping with Vrs1, was detected in three environments and BLUP value and by multiple methods to be associated with SP, accounting for 7.61–52.32% of the phenotypic variation. qtncSP-2H-13, located on chromosome 2H , was detected in two environments and by multiple methods to be associated with SP, explaining 6.49–11.95% of the phenotypic variation (Tables Spike number per plant (SP): Two reliable QTN clusters for SLP were detected. qtncGP-2H-14 with a high proportion of total phenotypic variation (19.56–37.44%), located at 2H: 649,558,019–650,438,830 bp, was detected in 2010 and BLUP value to be associated with GP. The qtncGP-2H-15 with a high explanation (3.41–34.59%), close to Vrs1 , was detected in three environments and by multiple methods to be associated with GP , close to Vrs1, showed a high proportion of phenotypic variation (9.77–71.5%) for GS. The qtnGS-2H-17 referred to Vrs1  was significantly associated with GS, explaining a high percentage (49.99–72.25%) of the phenotypic variation. The reliable QTN qtnGS-2H-18, located at chromosome 2H , was significantly associated with GS in 2009 and 2010 and multiple methods, accounting for 1.06–10.05% of the phenotypic variation (Tables Grain number per plant (GP) and grain number per spike (GS): The QTN cluster qtnGWS-2H-19, derived from the same associated SNP 2_625783669  as GS, was detected for GWS in 2009 and 2010 and by multiple GWAS methods with 0.74–6.25% proportion of phenotypic variation (Tables Grain weight per plant (GWP) and grain weight per spike (GWS): One QTN on 4H  was found to be associated with GP, GWP and GWS with 3.97–9.17% proportions for the phenotypic variation. The QTN qtnTGW-2H-20, located at Vrs1 , was significantly associated with TGW in multiple environments and GWAS methods, explaining high percentage (32.77–56.66%) of the phenotypic variation. The qtnTGW-3H-5  and qtnTGW-7H-8  were significantly associated with TGW, explaining 2.19–4.39 and 4.39–11.22% of the phenotypic variation, respectively : three reliable QTNs were detected for TGW. The t-test. Here, six reliable QTNs were used to underlying the phenotypes difference as an example. The details were showed in Figure According to the QTN genotypes, all the DH lines were divided into two different groups to test whether the significant difference of corresponding phenotypes of the QTN genotypes exist using qtnSMS-2H-9 for SMS, qtnGS-2H-17 for GS, and qtnTGW-2H-20 for TGW) had the significant differences of phenotypic averages between their two genotypes in all four environments  had the significant differences in all four environments  for the main agronomic traits and the reliable QTLs in previous studies , qtncIL3-3H-3 , and qtncIL4-3H-4 , located on the hotspot of 3H , Qitw3-13 for IL2, Qith3-13 for IL3, and Qifo3-14 for IL4 were detected close to the region of SSR markers Bmag13  and Bmag877  on 3H, respectively  between Bmag13  and e06m30.8.3 in Sameri et al.  for PH related traits, QTN clusters i et al. . CompareqtnPH-7H-1 , qtnPH-7H-2 , and qtncIL1-7H-4  were detected in same region of chromosome 7HS to be significantly associated with PH and IL1, respectively. These three QTNs are likely the same to the two QTLs qIN3-7Hs and qIN4-7Hs identified between markers HVCMA  and ABG701  in Sameri et al.  for SMS, qtnGS-2H-17  for GS, qtnTGW-2H-20  for TGW, qtnSLP-2H-10  and qtncSLP-2H-11  for SLP, and qtncGP-2H-14  and qtncGP-2H-15  for GP were detected at Vrs1  and the nearby region of 2H with highly phenotypic variation  for SMS, Qgs2-4  for GS, Qtgw2-1  and Qtgw2-2  for TGW, Qslp2-6  for SLP, and Qgp2-2  for GP , qtnSMS-2H-8 , qtncSLP-4H-1 , and qtnTGW-7H-8  were consistent with the QTLs Qmsl2-7 , Qsms2-1 , Qslp4-2 , and Qtgw7-4  of Wang et al. (Among 11 previously reported QTNs (or clusters) for spike and yield related traits, it is worth noting that most were located close to the region of on Table , includig et al.  (Table 1qtnIL2-7H-6 was a novel QTN associated with IL2 accounting for a higher proportion of phenotypic variation (22.85–55.77%). And the candidate gene HORVU7Hr1G058360 , close to qtnIL2-7H-6 , may involve in regulating IL2. For other minor effect QTNs (QTN clusters), three reliable candidate genes  were identified to be close to the region of qtncSP-2H-13, qtnGS-2H-18 (or qtnGWS-2H-19), and qtn(GP-GWP-GWS)-4H-2, respectively (Table For 20 novel reliable QTNs (QTN clusters) detected by multi-locus GWAS, most had minor effects Table . It is wThe comparison between QTLs in previous studies  was identified on the region  of three QTN clusters for plant height related traits  was detected to be associated with SMS (qtnSMS-2H-9), GS (qtnGS-2H-17), and TGW (qtnTGW-2H-20) with high proportion of phenotypic variation in multiple environments and by multi-locus GWAS methods in current study , including qtnSLP-2H-10  and qtncSLP-2H-11  for SLP, qtncGP-2H-14 , and qtncGP-2H-15  for GP, and qtncSP-2H-12  for SP, were detected in multiple situations and by multi-locus GWAS methods with high proportion of phenotypic variation , encoded a S-adenosylmethionine (SAM)-dependent-MTases, which was identified on the region  of three QTN clusters for plant height related traits  gene, and soybean transgenic lines over-expressed GmATG8c showed higher plant height than the wild type  for IL2, encoding a S-acyltransferase with DHHC-cysteine-rich domain  encoding homeobox-like protein with SANT/MYB domain, was close to the QTN qtnPH-3H-2  for PH  for MSL , HORVU2Hr1G094080 , encoding a protein with BTB/POZ domain , was detected about 40 Kb from the QTN cluster qtncSP-2H-13  protein containing BTB/POZ domain, which shares high similarity with Arabidopsis BOP1 and BOP2 , HORVU2Hr1G094080.1 showed highest level of expression in developing inflorescences. Therefore, candidate gene HORVU2Hr1G094080 performed the similar function as HvCul4, BOP1, and BOP2 to control the spike number per plant (SP).For spike number per plant (SP), 2_625783669  was detected significantly associated with these 2 traits. HORVU2Hr1G126690 , encoding a protein with N-acetyltransferase domain, was detected about 83 Kb from the marker 2_625783669 . Thus, the candidate gene HORVU2Hr1G126690 may affect the GS and GWS through the similar function of OsSNAT1.For grain number per spike (GS) and grain weight per spike (GWS), marker 4_497278091  was significant associated with GP, GWP, and GWS. HORVU4Hr1G075070 , encoding Patatin, was detected at 4_497278091  leads to missing many significant QTNs, particularly small-effect QTNs  and proved to be powerful tool for uncovering the basis of key agronomic traits in maize and barley  were previously reported, and eight candidate genes need to be further validated. The results validated the feasibility and reliability of GWAS in DH population and the good complementary to traditional QTL analysis. All the results will facilitate elucidating genetic basis of agronomic traits and improving marker-assisted selection breeding in barley.Available online at: In this study, five multi-locus GWAS methods were performed for 14 main agronomic traits in 122 doubled haploid (DH) lines. Thirty-nine reliable QTNs and/or QTN clusters were repeatedly detected in multiple environments and methods 10 candidate genes for the interest traits were detected, 19 QTNs and two genes (DS and XR conceived and designed the experiments. XH, XR, JW, and LL conducted the experiments and phenotyping measurements. XH and JZ performed the analysis. XH and JZ wrote the paper. GS, XR, and DS modified the manuscript. CL produced the Huaai 11 and Huadamai 6 DH population. All the authors read and approved the final version of this manuscript.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.


Hybrid breeding is the main strategy for improving productivity in many crops, especially in rice and maize. Genomic hybrid breeding is a technology that uses whole‐genome markers to predict future hybrids. Predicted superior hybrids are then field evaluated and released as new hybrid cultivars after their superior performances are confirmed. This will increase the opportunity of selecting true superior hybrids with minimum costs. Here, we used genomic best linear unbiased prediction to perform hybrid performance prediction using an existing rice population of 1495 hybrids. Replicated 10‐fold cross‐validations showed that the prediction abilities on ten agronomic traits ranged from 0.35 to 0.92. Using the 1495 rice hybrids as a training sample, we predicted six agronomic traits of 100 hybrids derived from half diallel crosses involving 21 parents that are different from the parents of the hybrids in the training sample. The prediction abilities were relatively high, varying from 0.54 (yield) to 0.92 (grain length). We concluded that the current population of 1495 hybrids can be used to predict hybrids from seemingly unrelated parents. Eventually, we used this training population to predict all potential hybrids of cytoplasm male sterile lines from 3000 rice varieties from the 3K Rice Genome Project. Using a breeding index combining 10 traits, we identified the top and bottom 200 predicted hybrids. SNP genotypes of the training population and parameters estimated from this training population are available for general uses and further validation in genomic hybrid prediction of all potential hybrids generated from all varieties of rice. Superior performances may be indicated by improved function of any biological process in the hybrid offspring , the least absolute shrinkage selection operator (LASSO), Bayes B and empirical Bayes  and the population means (β^) for all ten traits of the current hybrid population are given in Table K11 is given in Data K21, users need to use their own SNP data that match the 102 795 SNPs of the current hybrid population.The average prediction abilities drawn from replicated 10‐fold CV for ten agronomic traits are depicted in the bar‐plots of Figure Equation  and alsoGeng (japonica) rice and 11 Xian (indica) rice, were not included in the parents of the 1495 hybrids; yet the prediction abilities were reasonably high for most of the traits. We concluded that the 1495 hybrid population may be used for prediction of hybrids derived from other inbred lines.We predicted 100 hybrids grown in Wuhan from a half diallel cross experiment using the pooled phenotype of 1495 hybrids of the training population for six traits. The prediction abilities for the six traits are 0.542, 0.616, 0.544, 0.580, 0.916 and 0.866, respectively, for YD, GN, KGW, PH, GL and GW. Plots of the predicted trait values against the observed trait values are shown in Figure For 3000 germplasms, there are 3000 (3000 − 1)/2 = 4 498 500 potential hybrids. However, we only predicted 44 636 hybrids that are possibly grown in the field for commercial release because one parent of each hybrid of this kind is a maintainer line . The predicted phenotypes of these hybrids were given in Data jI is the selection index score for individual j, kw is the economic weight for the kth trait for k = 1,2,…,10 (there are ten traits included in the index) and y^∗jk is the standardized predicted value for trait k from the jth individual hybrid. To avoid duplicated usage of correlated traits, we divided nine traits (excluding yield) into three groups: the first group contained four yield components ; the second group contained PL, GL and GW; and the last group contained HD and PH. Among the nine traits, the correlation coefficient between PL and PH is greater than 0.5  model. We also extended the basic additive model to incorporate genotype by environment interaction (G × E) to form a G × E model. The A‐D and G × E models are described in Notes et al. /2 = 4 498 500. Selection of a few hybrids from this large pool means an extremely high selection intensity. Even though we only have a pool of 44 636 hybrids that are realistically selectable, they still represent a large base for GS. Therefore, genomic hybrid breeding is a very promising tool to improve grain yield in hybrid breeding of rice as well as other crops. Compared to GS using random populations where parameters have to be retrained in every few generations of selection to capture the changes of genetic parameters due to selection, genomic hybrid breeding is a one‐time event once a hybrid is identified, genomic hybrid breeding is done. Therefore, hybrid breeding is expected to benefit significantly from GS.In the quantitative genetics theory, selection response is determined by heritability and selection intensity, as expressed in the breeders’ equation, Rf1 on chromosome 10. Thus, to make use of the top 200 predicted hybrids in a three‐line hybrid breeding program, one must make sure all the 61 inbreds except for Minghui63 have restorer genes. In this respect, it is known that the Rf1 complex consists of two genes named as Rf1a and Rf1b, while Rf1b is due to an amino acid alternation of Ser‐to‐Asn caused by a G‐to‐A variation responsible for fertility restoration  is a training population that includes 1495 hybrids evaluated by Huang et al. . Among tet al. . The twoGeng rice and 11 Xian rice varieties . Each plot consisted of four rows with 10 plants per row, where the F1 hybrids were planted in the middle two rows and the two parents of the F1 hybrid were planted in the two peripheral rows. Seedlings of 30 days old were transplanted to the field, with a layout of 16.7 cm between plants within a row and 33.3 cm between rows. The field management followed the normal agricultural practice. Only eight plants in the middle of each row were used for phenotyping, and the plot mean was calculated and eventually used as the observed phenotypic value for the hybrid. Six traits were measured from the two replicated experiments. This population was used to test the prediction abilities for the training population of 1495 hybrids (the very first population). The six traits are YD, GN, KGW, PH, GL and GW. The average trait values of the two replicates (sites) were used as the phenotypic values for comparison with the predicted values. The prediction ability from this test population was defined as the correlation between the observed and the predicted phenotypic values for the trait of interest. The number of SNPs identified in the 21 parents was two million based on the version 7 map of Geng Nipponbare.The second test population (Pop 2) is a hybrid population including 210 hybrids which was derived from a half diallel cross experiment involving ten et al., Xian and Geng, a small group of intermediate varieties, and two small varietal groups aus/boro and aromatic basmati/sadri. Among the 3000 accessions, 27 varieties are maintainer lines. Of the remaining 3000 − 27 = 2973 lines, 58.2% are Xian, 27.9% are Geng, 9.4% are aromatic basmati/sadri and the last 4.5% are the intermediate type  is the one released by the 3K Rice Genome Project  = 2559 potential hybrids from intermediate type× (Xian + Geng), resulting in a total of 39 560 + 2517 + 2559 = 44 636 potential hybrids to be predicted.Rice is a self‐pollinated crop, and there are no hybrids occurring in nature. To commercially develop hybrid rice, breeders rely on a three‐line mating system or a two‐line mating system. These systems depend on male sterile lines who can only accept pollens from other lines. There are no male sterile lines in the 3000 rice accessions. Since the nuclear genomes of the sterile lines and the maintainer lines are the same, we choose maintainer lines from the 3000 rice accessions as pseudomale sterile lines to infer the genotype of potential hybrids. Genotypes of the potential hybrids of the maintainer lines and conventional lines were deduced from the parental genotypes and then used to predict the phenotypic values. Of the 3000 accessions, 27 varieties are maintainer lines . The downloaded paired‐end reads of all the hybrid rice accessions were aligned against the reference genome using the BWA software with the BWA‐MEM algorithm /2 = −0.5. Similarly, when the mating type was A2A2 × A1A2, their hybrid was then coded as (0+1)/2 = 0.5. When the mating type was A1A2 × A1A2, their hybrid was coded as (−1+0+0+1)/4 = 0. In summary, the genotype of a potential hybrid can take the following numerical values: −1, −0.5, 0, 0.5 and 1, depending on the mating types of the parents.The 102 795 common SNPs shared by both the training population and the predicted population were used to develop the prediction model and to predict phenotypes of potential hybrids in 3K rice genome programme. The genotypes of SNPs were coded by −1 for one homozygote, 0 for the heterozygote and 1 for the other homozygote. For example, if m markers isy is an n × 1 vector of the phenotypic values of a quantitative trait measured from n individuals, X is a design matrix with rank q for all covariates, β is a vector of effects for the covariates (non‐genetic effects), Zk=Zjk is an n × 1 vector of genotype codes for marker k for individual j, kγ is the additive effect of marker k and ε is an n × 1 vector of residual errors with an assumed N distribution. The numerical code for individual j at locus k is defined as jkZ = −1 for A1A1, jkZ = 0 for A1A2, and jkZ = 1 for A2A2. Assume that all marker effects follow a normal distribution with zero mean and a common variance, γk&x007E;N, for all k = 1,2,…,m, where ϕ2 is an unknown polygenic variance. ξ is n × 1 vector of polygenic effect. When there is no other covariate except the intercept, X is an n × 1 vector of unity and β is simply a scalar of intercept. The expectation of y is E(y) = X β and the variance of y is var(y) = V, whereλ=ϕ2/σ2 is the variance ratio. The restricted log likelihood function for parameter λ isThe BLUP method was used to perform prediction. The linear mixed model that includes all β and σ2, the restricted log likelihood is only a function of λ. The Newton method of iteration was used to find the restricted maximum likelihood estimate of λ. To improve the computational speed, we also adopted the eigenvalue decomposition algorithm  model . Eventually, all parts are predicted using samples that exclude the parts to be predicted. We often choose K = 10 and thus call the method a 10‐fold cross‐validation  with the two locations treated as two blocks. The linear model for the CRBD design isjky is the phenotypic value of the trait of interest of the jth hybrid measured from the kth location for j = 1,2,…,n, k = 1,2 and n = 1495, µ is the grand mean, jα is the genetic effect of the jth hybrid, kβ is the effect of the kth block and jkε is the residual error (may contain a G × E interaction effect) with an assumed N distribution. This is a mixed model with kβtreated as a fixed effect and jα as a random effect following a N distribution for all j = 1,2,…,n. The broad‐sense heritability is defined asBroad‐sense heritability, The two variance components were estimated from variance component analysis presented in Table The authors declare no conflict of interest.Y. Cui and S. Xu designed the project and developed the statistical models for prediction. R. Li performed the SNP calling of 1495 hybrids. G. Li and Q. Zhang conducted the field trail and phenotyping. F. Zhang and T. Zhu participated in the development of statistical models. J. Ali and Z. Li provided the information of selection index. Y. Cui prepared the first draft and Z. Li and S. Xu revised the manuscript. All the authors approved the final version of the manuscript.Data S1 The kinship matrix of K11.Click here for additional data file.Data S2 Predicted values of the 100 hybrids from the half diallel crosses.Click here for additional data file.Data S3 Predicted values of potential hybrids from the 3000 germplasms for 10 agronomic traits .Click here for additional data file.Data S4 Predicted values of potential hybrids from the 3000 germplasms for 10 agronomic traits .Click here for additional data file.Data S5 Predicted values of potential hybrids from the 3000 germplasms for 10 agronomic traits .Click here for additional data file.Data S6 Relevant information of 3,000 rice varieties of the 3K rice genome project.Click here for additional data file.Note S1 Additive & dominant (A‐D) model.Note S2 G×E interaction model.Table S1 Estimated parameters for 10 traits of the 1495 hybrids.Table S2 Prediction abilities of the test population (Pop 2) using phenotypes collected from different locations of the training population (Pop 1).Table S3 Correlation matrix between 10 agronomic traits.Table S4 Estimated parameters for 10 traits of the 1495 hybrids from the additive‐dominant (A‐D) model.Table S5 Information of 21 inbred lines of the half diallel cross experiment (Pop 2).Table S6 Information of 27 maintainer lines of the 3K rice genome project (Pop 3).Table S7 Distribution of SNPs on the 12 chromosomes of rice.Table S8 ANOVA table for estimating variance components that are required for estimating the broad sense heritability.Figure S1 Predicted phenotypes plotted against observed phenotypes of the 1495 hybrid rice for 10 traits .Figure S2 Prediction abilities using phenotypes collected from Hangzhou and Sanya separately and prediction abilities using mean phenotype of the two sites (pooled).Figure S3 Three‐line mating system. The three‐line mating system involves three lines.Figure S4 Distribution of the 3,000 rice accessions from five distinct groups of the 3K Rice Genome Project.Figure S5 Sketch of a K‐fold cross validation where K = 10.Click here for additional data file.