QTL-by-environment Interactions Research Articles

Multi-omics analysis reveals novel loci and a candidate regulatory gene of unsaturated fatty acids in soybean (Glycine max (L.) Merr)

BackgroundSoybean is a major oil crop; the nutritional components of soybean oil are mainly controlled by unsaturated fatty acids (FA). Unsaturated FAs mainly include oleic acid (OA, 18:1), linoleic acid (LLA, 18:2), and linolenic acid (LNA, 18:3). The genetic architecture of unsaturated FAs in soybean seeds has not been fully elucidated, although many independent studies have been conducted. A 3 V multi-locus random single nucleotide polymorphism (SNP)-effect mixed linear model (3VmrMLM) was established to identify quantitative trait loci (QTLs) and QTL-by-environment interactions (QEIs) for complex traits.ResultsIn this study, 194 soybean accessions with 36,981 SNPs were calculated using the 3VmrMLM model. As a result, 94 quantitative trait nucleotides (QTNs) and 19 QEIs were detected using single-environment (QTN) and multi-environment (QEI) methods. Three significant QEIs, namely rs4633292, rs39216169, and rs14264702, overlapped with a significant single-environment QTN.ConclusionsFor QTNs and QEIs, further haplotype analysis of candidate genes revealed that the Glyma.03G040400 and Glyma.17G236700 genes were beneficial haplotypes that may be associated with unsaturated FAs. This result provides ideas for the identification of soybean lipid-related genes and provides insights for breeding high oil soybean varieties in the future.

Genetic Dissection of Panicle Morphology Traits in Super High-Yield Hybrid Rice Chaoyou 1000.

The morphological characteristics of the rice panicle play a pivotal role in influencing yield. In our research, we employed F2 and F2:3 populations derived from the high-yielding hybrid rice variety Chaoyou 1000. We screened 123 pairs of molecular markers, which were available, to construct the genetic linkage map. Subsequently, we assessed the panicle morphology traits of F2 populations in Lingshui County, Hainan Province, in 2017, and F2:3 populations in Hangzhou City, Zhejiang Province, in 2018. These two locations represent two types of ecology. Hangzhou's climate is characterized by high temperatures and humidity, while Lingshui's climate is characterized by a tropical monsoon climate. In total, 33 QTLs were identified, with eight of these being newly discovered, and two of them were consistently detected in two distinct environments. We identified fourteen QTL-by-environment interactions (QEs), which collectively explained 4.93% to 59.95% of the phenotypic variation. While most of the detected QTLs are consistent with the results of previous tests, the novel-detected QTLs will lay the foundation for rice yield increase and molecular breeding.

Diversity and genetic architecture of agro-morphological traits in a Core Collection of European traditional tomato.

European traditional tomato varieties have been selected by farmers given their consistent performance and adaptation to local growing conditions. Here we developed a multipurpose core collection, comprising 226 accessions representative of the genotypic, phenotypic and geographical diversity present in European traditional tomatoes, to investigate the basis of their phenotypic variation, G×E interactions and stability for 33 agro-morphological traits. Comparison of the traditional varieties with a modern reference panel revealed that some traditional varieties displayed excellent agronomic performance and high trait stability, as good as or better than that of their modern counterparts. We conducted genome-wide association and genome-wide environment interaction studies and detected 141 quantitative trait loci (QTLs). Out of those, 47 QTLs were associated with the phenotype mean (meanQTLs) and 41 with stability (stbQTLs) and 53 QTL-by-environment interactions (QTIs). Most QTLs displayed additive gene actions, with the exception of stbQTLs, which were mostly recessive and overdominant QTLs. Both common and specific loci controlled the phenotype mean and stability variation in traditional tomato; however, a larger proportion of specific QTLs was observed, indicating that the stability gene regulatory model is the predominant one. Developmental genes tended to map close to meanQTLs, while genes involved in stress response, hormone metabolism and signalling were found within regions affecting stability. A total of 137 marker trait associations for phenotypic means and stability were novel, and therefore our study enhances the understanding of the genetic basis of valuable agronomic traits and opens a new avenue for an exploitation of the allelic diversity available within European traditional tomato germplasm.

Identification of QTL, QTL-by-environment interactions, and their candidate genes for resistance HG Type 0 and HG Type 1.2.3.5.7 in soybean using 3VmrMLM.

Soybean cyst nematode (SCN, Heterodera glycines Ichinohe) is an important disease affecting soybean yield in the world. Potential SCN-related QTLs and QTL-by-environment interactions (QEIs) have been used in SCN-resistant breeding. In this study, a compressed variance component mixed model, 3VmrMLM, in genome-wide association studies was used to detect QTLs and QEIs for resistance to SCN HG Type 0 and HG Type 1.2.3.5.7 in 156 different soybean cultivars materials. The results showed that 53 QTLs were detected in single environment analysis; 36 QTLs and 9 QEIs were detected in multi-environment analysis. Based on the statistical screening of the obtained QTLs, we obtained 10 novel QTLs and one QEI which were different from the previous studies. Based on previous studies, we identified 101 known genes around the significant/suggested QTLs and QEIs. Furthermore, used the transcriptome data of SCN-resistant (Dongnong L-10) and SCN-susceptible (Suinong 14) cultivars, 10 candidate genes related to SCN resistance were identified and verified by Quantitative real time polymerase chain reaction (qRT-PCR) analysis. Haplotype difference analysis showed that Glyma.03G005600 was associated with SCN HG Type 0 and HG Type 1.2.3.5.7 resistance and had a haplotype beneficial to multi-SCN-race resistance. These results provide a new idea for accelerating SCN disease resistance breeding.

Genome-wide association studies reveal novel QTLs, QTL-by-environment interactions and their candidate genes for tocopherol content in soybean seed.

Genome-wide association studies (GWAS) is an efficient method to detect quantitative trait locus (QTL), and has dissected many complex traits in soybean [Glycine max (L.) Merr.]. Although these results have undoubtedly played a far-reaching role in the study of soybean biology, environmental interactions for complex traits in traditional GWAS models are frequently overlooked. Recently, a new GWAS model, 3VmrMLM, was established to identify QTLs and QTL-by-environment interactions (QEIs) for complex traits. In this study, the GLM, MLM, CMLM, FarmCPU, BLINK, and 3VmrMLM models were used to identify QTLs and QEIs for tocopherol (Toc) content in soybean seed, including δ-Tocotrienol (δ-Toc) content, γ-Tocotrienol (γ-Toc) content, α-Tocopherol (α-Toc) content, and total Tocopherol (T-Toc) content. As a result, 101 QTLs were detected by the above methods in single-environment analysis, and 57 QTLs and 13 QEIs were detected by 3VmrMLM in multi-environment analysis. Among these QTLs, some QTLs (Group I) were repeatedly detected three times or by at least two models, and some QTLs (Group II) were repeatedly detected only by 3VmrMLM. In the two Groups, 3VmrMLM was able to correctly detect all known QTLs in group I, while good results were achieved in Group II, for example, 8 novel QTLs were detected in Group II. In addition, comparative genomic analysis revealed that the proportion of Glyma_max specific genes near QEIs was higher, in other words, these QEIs nearby genes are more susceptible to environmental influences. Finally, around the 8 novel QTLs, 11 important candidate genes were identified using haplotype, andvalidated byRNA-Seq data and qRT-PCR analysis. In summary, we used phenotypic data of Toc content in soybean, and tested the accuracy and reliability of 3VmrMLM, and then revealed novel QTLs, QEIs and candidate genes for these traits. Hence, the 3VmrMLM model has broad prospects and potential for analyzing the genetic structure of complex quantitative traits in soybean.

Analysis of a Multi-Environment Trial for Black Raspberry (Rubus occidentalis L.) Quality Traits.

U.S. black raspberry (BR) production is currently limited by narrowly adapted, elite germplasm. An improved understanding of genetic control and the stability of pomological traits will inform the development of improved BR germplasm and cultivars. To this end, the analysis of a multiple-environment trial of a BR mapping population derived from a cross that combines wild ancestors introgressed with commercial cultivars on both sides of its pedigree has provided insights into genetic variation, genotype-by-environment interactions, quantitative trait loci (QTL), and QTL-by-environment interactions (QEI) of fruit quality traits among diverse field environments. The genetic components and stability of four fruit size traits and six fruit biochemistry traits were characterized in this mapping population following their evaluation over three years at four distinct locations representative of current U.S. BR production. This revealed relatively stable genetic control of the four fruit size traits across the tested production environments and less stable genetic control of the fruit biochemistry traits. Of the fifteen total QTL, eleven exhibited significant QEI. Closely overlapping QTL revealed the linkage of several fruit size traits: fruit mass, drupelet count, and seed fraction. These and related findings are expected to guide further genetic characterization of BR fruit quality, management of breeding germplasm, and development of improved BR cultivars for U.S. production.

A compressed variance component mixed model framework for detecting small and linked QTL-by-environment interactions.

Detecting small and linked quantitative trait loci (QTLs) and QTL-by-environment interactions (QEIs) for complex traits is a difficult issue in immortalized F2 and F2:3 design, especially in the era of global climate change and environmental plasticity research. Here we proposed a compressed variance component mixed model. In this model, a parametric vector of QTL genotype and environment combination effects replaced QTL effects, environmental effects and their interaction effects, whereas the combination effect polygenic background replaced the QTL and QEI polygenic backgrounds. Thus, the number of variance components in the mixed model was greatly reduced. The model was incorporated into our genome-wide composite interval mapping (GCIM) to propose GCIM-QEI-random and GCIM-QEI-fixed, respectively, under random and fixed models of genetic effects. First, potentially associated QTLs and QEIs were selected from genome-wide scanning. Then, significant QTLs and QEIs were identified using empirical Bayes and likelihood ratio test. Finally, known and candidate genes around these significant loci were mined. The new methods were validated by a series of simulation studies and real data analyses. Compared with ICIM, GCIM-QEI-random had 29.77 ± 18.20% and 24.33 ± 10.15% higher average power, respectively, in 0.5-3.0% QTL and QEI detection, 43.44 ± 9.53% and 51.47 ± 15.70% higher average power, respectively, in linked QTL and QEI detection, and identified 30 more known genes for four rice yield traits, because GCIM-QEI-random identified more small genes/loci, being 2.69 ± 2.37% for additional genes. GCIM-QEI-random was slightly better than GCIM-QEI-fixed. In addition, the new methods may be extended into backcross and genome-wide association studies. This study provides effective methods for detecting small-effect and linked QTLs and QEIs.

Identification of QTLs for resistance to maize rough dwarf disease using two connected RIL populations in maize.

Maize rough dwarf disease (MRDD) is a significant viral disease caused by rice black-streaked dwarf virus (RBSDV) in China, which results in 30% yield losses in affected summer maize-growing areas. In this study, two connected recombinant inbred line (RIL) populations were constructed to elucidate the genetic basis of resistance during two crop seasons. Ten quantitative trait loci (QTLs) for resistance to MRDD were detected in the two RILs. Individual QTLs accounted for 4.97–23.37% of the phenotypic variance explained (PVE). The resistance QTL (qZD-MRDD8-1) with the largest effect was located in chromosome bin 8.03, representing 16.27–23.37% of the PVE across two environments. Interestingly, one pair of common significant QTLs was located in the similar region on chromosome 4 in both populations, accounting for 7.11–9.01% of the PVE in Zheng58×D863F (RIL-ZD) and 9.43–13.06% in Zheng58×ZS301 (RIL-ZZ). A total of five QTLs for MRDD resistance trait showed significant QTL-by-Environment interactions (QEI). Two candidate genes associated with resistance (GDSL-lipase and RPP13-like gene) which were higher expressed in resistant inbred line D863F than in susceptible inbred line Zheng58, were located in the physical intervals of the major QTLs on chromosomes 4 and 8, respectively. The identified QTLs will be studied further for application in marker-assisted breeding in maize genetic improvement of MRDD resistance.

QTL-By-Environment Interaction in the Response of Maize Root and Shoot Traits to Different Water Regimes.

Drought is a major abiotic stress factor limiting maize production, and elucidating the genetic control of root system architecture and plasticity to water-deficit stress is a crucial problem to improve drought adaptability. In this study, 13 root and shoot traits and genetic plasticity were evaluated in a recombinant inbred line (RIL) population under well-watered (WW) and water stress (WS) conditions. Significant phenotypic variation was observed for all observed traits both under WW and WS conditions. Most of the measured traits showed significant genotype–environment interaction (GEI) in both environments. Strong correlations were observed among traits in the same class. Multi-environment (ME) and multi-trait (MT) QTL analyses were conducted for all observed traits. A total of 48 QTLs were identified by ME, including 15 QTLs associated with 9 traits showing significant QTL-by-Environment interactions (QEI). QTLs associated with crown root angle (CRA2) and crown root length (CRL1) were identified as having antagonistic pleiotropic effects, while 13 other QTLs showed signs of conditional neutrality (CN), including 9 and 4 QTLs detected under WW and WS conditions, respectively. MT analysis identified 14 pleiotropic QTLs for 13 traits, SNP20 (1@79.2 cM) was associated with the length of crown root (CR), primary root (PR), and seminal root (SR) and might contribute to increases in root length under WS condition. Taken together, these findings contribute to our understanding of the phenotypic and genotypic patterns of root plasticity in response to water deficiency, which will be useful to improve drought tolerance in maize.

Novel and major QTL for branch angle detected by using DH population from an exotic introgression in rapeseed (Brassica napus L.).

A high-density SNP map was constructed and several novel QTL for branch angle across six environments in Brassica napus were identified. Branch angle is a major determinant for the ideotype of a plant, while the mechanisms underlying this trait in Brassica napus remain elusive. Herein, we developed one doubled haploid population from a cross involving one Capsella bursa-pastoris derived B. napus intertribal introgression line with the compressed branches and wooden stems, and constructed a high-density SNP map covering the genetic distance of 2242.14cM, with an average marker interval of 0.73cM. After phenotypic measurements across six environments, the inclusive composite interval mapping algorithm was conducted to analyze the QTL associated with branch angle. In single-environment analysis, a total of 17 QTL were detected and mainly distributed on chromosomes A01, A03, A09 and C03. Of these, three major QTL, qBA.A03-2, qBA.C03-3 and qBA.C03-4 were steadily expressed, each explaining more than 10% of the phenotypic variation in at least two environments. Compared with other results on rapeseed branch angle, these major QTL were newly detected. In QTL by environment interactions (QEI) mapping, 10 QTL were identified, and the QTL average effect and QEI effect were estimated. Of these, 7 QTL were detected in both single-environment analysis and QEI mapping. Based on the physical positions of SNPs and the functional annotation of the Arabidopsis thaliana genome, 27 genes within the QTL regions were selected as candidate genes, including early auxin-responsive genes, small auxin-up RNA, auxin/indoleacetic acid and gretchenhagen-3. These results may pave the way for deciphering the genetic control of branch angle in B. napus.

Development of a QTL-environment-based predictive model for node addition rate in common bean.

This work reports the effects of the genetic makeup, the environment and the genotype by environment interactions for node addition rate in an RIL population of common bean. This information was used to build a predictive model for node addition rate. To select a plant genotype that will thrive in targeted environments it is critical to understand the genotype by environment interaction (GEI). In this study, multi-environment QTL analysis was used to characterize node addition rate (NAR, node day- 1) on the main stem of the common bean (Phaseolus vulgaris L). This analysis was carried out with field data of 171 recombinant inbred lines that were grown at five sites (Florida, Puerto Rico, 2 sites in Colombia, and North Dakota). Four QTLs (Nar1, Nar2, Nar3 and Nar4) were identified, one of which had significant QTL by environment interactions (QEI), that is, Nar2 with temperature. Temperature was identified as the main environmental factor affecting NAR while day length and solar radiation played a minor role. Integration of sites as covariates into a QTL mixed site-effect model, and further replacing the site component with explanatory environmental covariates (i.e., temperature, day length and solar radiation) yielded a model that explained 73% of the phenotypic variation for NAR with root mean square error of 16.25% of the mean. The QTL consistency and stability was examined through a tenfold cross validation with different sets of genotypes and these four QTLs were always detected with 50-90% probability. The final model was evaluated using leave-one-site-out method to assess the influence of site on node addition rate. These analyses provided a quantitative measure of the effects on NAR of common beans exerted by the genetic makeup, the environment and their interactions.

Epistatic Association Mapping for Alkaline and Salinity Tolerance Traits in the Soybean Germination Stage

Soil salinity and alkalinity are important abiotic components that frequently have critical effects on crop growth, productivity and quality. Developing soybean cultivars with high salt tolerance is recognized as an efficient way to maintain sustainable soybean production in a salt stress environment. However, the genetic mechanism of the tolerance must first be elucidated. In this study, 257 soybean cultivars with 135 SSR markers were used to perform epistatic association mapping for salt tolerance. Tolerance was evaluated by assessing the main root length (RL), the fresh and dry weights of roots (FWR and DWR), the biomass of seedlings (BS) and the length of hypocotyls (LH) of healthy seedlings after treatments with control, 100 mM NaCl or 10 mM Na2CO3 solutions for approximately one week under greenhouse conditions. A total of 83 QTL-by-environment (QE) interactions for salt tolerance index were detected: 24 for LR, 12 for FWR, 11 for DWR, 15 for LH and 21 for BS, as well as one epistatic QTL for FWR. Furthermore, 86 QE interactions for alkaline tolerance index were found: 17 for LR, 16 for FWR, 17 for DWR, 18 for LH and 18 for BS. A total of 77 QE interactions for the original trait indicator were detected: 17 for LR, 14 for FWR, 4 for DWR, 21 for LH and 21 for BS, as well as 3 epistatic QTL for BS. Small-effect QTL were frequently observed. Several soybean genes with homology to Arabidopsis thaliana and soybean salt tolerance genes were found in close proximity to the above QTL. Using the novel alleles of the QTL detected above, some elite parental combinations were designed, although these QTL need to be further confirmed. The above results provide a valuable foundation for fine mapping, cloning and molecular breeding by design for soybean alkaline and salt tolerance.

Genetic Basics of Seed Traits in Soybean with Bayes Hierarchical Generalized Linear Model Method

Seed size and shape traits in soybean play a crucial role in yield and appearance quality. In this study, an experiment was performed to detect main-effect quantitative trait loci (MQTL), QTL-by-environment (QE), QTL-by-cytoplasm (QC), and QTL-by-QTL (QQ) interactions for the soybean seed traits (length, width, thickness, length-to-width, length-to-thickness, width-to-thickness, and 100-seed weight) using Bayes hiearchical generalized linear model approach. Evaluation of these traits for the 504 F 2:3 –F 2:7 families from the direct and reciprocal crosses of Lishuizhongzihuangdou × Nannong 493-1 was carried out in 2007–2011, respectively, and the 504 F 2 plants were scanned by 152 SSR markers. As a result, a total of 89 MQTL, 35 QQ interactions, 33 QE interactions and 20 QC interactions were detected. As for the above seven traits, there were 7, 10, 10, 19, 19, 17, and 7 MQTL; 1, 10, 6, 0, 6, 9, and 3 QQ interactions; 5, 7, 6, 3, 6, 2, and 4 QE interactions; and 2, 1, 3, 8, 4, 2, and 0 QC interac tions respectively. The total proportion of phenotypic variance explained by the above four types of QTL for each trait is 12.42–61.79%, 0–23.21%, 0.35–1.51%, and 0–14.16%, respectively, indicating that the most important genetic component is MQTL, the second one is epistasis, and the last one is QE interaction. Pleiotropic effects were observed in all kinds of QTL, while various types of QTL shared with one same locus were found to be response for a seed trait as well. These results revealed genetic basis of seed size and shape traits in soybean, and provide reference information for marker assisted breeding.

10.1007/s11177-008-3013-z

The objective of this study was to dissect the genetic control of days to flowering (DTF) and photoperiod sensitivity (PS) into the various components including the main-effect quantitative trait loci (QTLs), epistatic QTLs and QTL-by-environment interactions (QEs). Doubled haploid (DH) lines were produced from an F1 between two spring Brassica napus cultivars Hyola 401 and Q2. DTF of the DH lines and parents were investigated in two locations, one location with a short and the other with a long photoperiod regime over two years. PS was calculated by the delay in DTF under long day as compared to that under short day. A genetic linkage map was constructed that comprised 248 marker loci including SSR, SRAP, and AFLP markers. Further QTL analysis resolved the genetic components of flowering time and PS into the main-effect QTLs, epistatic QTLs, and QEs. A total of 7 main-effect QTLs and 11 digenic interactions involving 21 loci located on 13 out of the 19 linkage groups were detected for the two traits. Three main-effect QTLs and four pairs of epistatic QTLs were involved in QEs conferring DTF. One QTL on linkage group (LG) 18 was revealed to simultaneously affect DTF and PS and explain for the highest percentage of the phenotypic variation. The implications of the results for B. napus breeding have been discussed.

The genetic basis of flowering time and photoperiod sensitivity in rapeseed Brassica napus L.

The objective of this study was to dissect the genetic control of days to flowering (DTF) and photoperiod sensitivity (PS) into the various components including the main-effect quantitative trait loci (QTLs), epistatic QTLs and QTL-by-environment interactions (QEs). Doubled haploid (DH) fines were produced from an F1 between two spring Brassica napus cultivars Hyola 401 and Q2. DTF of the DH lines and parents were investigated in two locations, one location with a short and the other with a long photoperiod regime over two years. PS was calculated by the delay in DTF under long day as compared to that under short day. A genetic linkage map was constructed that comprised 248 marker loci including SSR, SRAP and AFLP markers. Further QTL analysis resolved the genetic components of flowering time and PS into the main-effect QTLs, epistatic QTLs and QEs. A total of 7 main-effect QTLs and 11 digenic interactions involving 21 loci located on 13 out of the 19 linkage groups were detected for the two traits. 3 main-effect QTLs and 4 pairs of epistatic QTLs were involved in QEs conferring DTF. One QTL on linkage group (LG) 18 was revealed to simultaneously affect DTF and PS and explain for the highest percentage of the phenotypic variation. The implications of the results for B. napus breeding have been discussed.

A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize.

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F(5) maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.

The main effects, epistatic effects and environmental interactions of QTLs on the cooking and eating quality of rice in a doubled-haploid line population

Amylose content (AC), gel consistency (GC) and gelatinazation temperature (GT) are three important traits that influence the cooking and eating quality of rice. The objective of this study was to characterize the genetic components, including main-effect quantitative trait loci (QTLs), epistatic QTLs and QTL-by-environment interactions (QEs), that are involved in the control of these three traits. A population of doubled haploid (DH) lines derived from a cross between two indica varieties Zhenshan 97 and H94 was used, and data were collected from a field experiment conducted in two different environments. A genetic linkage map consisting of 218 simple sequence repeat (SSR) loci was constructed, and QTL analysis performed using QTLMAPPER 1.6: resolved the genetic components into main-effect QTLs, epistatic QTLs and QEs. The analysis detected a total of 12 main-effect QTLs for the three traits, with a QTL corresponding to the Wx locus showing a major effect on AC and GC, and a QTL corresponding to the Alk locus having a major effect on GT. Ten digenic interactions involving 19 loci were detected for the three traits, and six main-effect QTLs and two pairs of epistatic QTLs were involved in QEs. While the main-effect QTLs, especially the ones corresponding to known major loci, apparently played predominant roles in the genetic basis of the traits, under certain conditions epistatic effects and QEs also played important roles in controlling the traits. The implications of the findings for rice quality improvement are discussed.

A biplot approach for investigating QTL-by-environment patterns

Due to the universal presence of genotype by environment interactions, understanding the pattern of quantitative trait loci (QTL)-by-environment interactions is a prerequisite for effective marker-assisted selection. In this report, we describe a biplot approach for investigating QTL-by-environment patterns. This approach involves two steps. It starts with a two-way table containing effects of individual QTLs in individual environments for the trait under investigation. This table is decomposed into principal components via singular value decomposition, and the first two principal components are plotted for both QTLs and environments to form a biplot. The resulting ‘QQE biplot’ contains information on QTL main effects (Q) and QTL-by-environment interactions (QE). A QQE biplot displays the QTL-by-environment patterns and allows visualization of: (1) the magnitude of the effect of a QTL, (2) the average effect of a QTL and its stability across environments, (3) the effects of a QTL in individual environments, (4) the similarity/dissimilarity among QTLs in effect and response to the environments, (5) the similarity/dissimilarity among environments in modulating QTL effects, (6) any differentiation of mega-environments, and (7) the combination of QTL alleles for maximum/minimum expression of the trait for each environment or mega-environment. A case study is provided using the QTL-by-environment two-way table for barley yield.