Global increase in ambient temperatures constitute a significant challenge to wild and cultivated plant species. Forward genetic analyses of individual temperature-responsive traits have resulted in the identification of several signaling and response components. However, a comprehensive knowledge about temperature sensitivity of different developmental stages and the contribution of natural variation is still scarce and fragmented at best.Arabidopsis thaliana accessions grown under long day conditions in four different temperatures ranging from 16 to 28 °C. We used Q10, GxE, phenotypic divergence and correlation analyses to assess temperature sensitivity and genotype effects of more than 30 morphometric and developmental traits representing five phenotype classes. We found that genotype and temperature differentially affected plant growth and development with variing strengths. Furthermore, overall correlations among phenotypic temperature responses was relatively low which seems to be caused by differential capacities for temperature adaptations of individual accessions.Here, we systematically analyze thermomorphogenesis throughout a complete life cycle in ten natural Genotype-specific temperature responses may be attractive targets for future forward genetic approaches and accession-specific thermomorphogenesis maps may aid the assessment of functional relevance of known and novel regulatory components.The online version of this article (doi:10.1186/s12870-017-1068-5) contains supplementary material, which is available to authorized users. Recurrent changes in ambient temperature provide plants with essential information about time of day and seasons. Yet, even small changes in mean ambient temperatures can profoundly affect plant growth and development resulting in thermomorphogenic changes of plant architecture . In cropElevated ambient temperatures affect of course also wild species in their natural habitats. Long-term phenology studies of diverse plant populations have revealed an advance in first and peak flowering and alterations in the total length of flowering times , 7. FurtArabidopsis thaliana. Model thermomorphogenesis phenotypes such as hypocotyl elongation [Our present knowledge on molecular responses to ambient temperature changes has significantly progressed by studies in ongation , hyponasongation , and altongation ). In thiongation –16. Primongation ), CRY2 [ongation  or the rongation , 20) . Fongation –23, DE-Eongation –26 and Eongation , 13.The investigation of signaling pathways that translate temperature stimuli into qualitative and quantitative developmental responses has so far largely been limited to either seedling development or flowering time. However, it seems likely that temperature responses in different phases of development either require variations of a canonical signaling pathway or involve at least partially specific signaling components. To enable the dissection of thermomorphogenic signaling at different developmental stages, it is vital to gather a comprehensive understanding of the diversity of temperature reactions throughout plant development.According to basic principles of thermodynamics, temperature-induced changes in free energy will affect the rates of biochemical reactions. As these effects should occur generally, albeit to different magnitudes, non-selective phenotypic responses can be expected to occur robustly and rather independently of genetic variation. Such traits may therefore be indicative of passive, thermodynamic effects on a multitude of processes. Alternatively, robust temperature responses may be due to thermodynamic effects on highly conserved signaling elements. These may be attractive targets for classic mutagenesis screens to identify the relevant regulatory components. In contrast, natural variation in thermomorphogenesis traits is likely the consequence of variability in one or several specific signaling or response components. It may be addressed by quantitative genetic approaches to identify regulators that contribute to variable temperature responses. Such genes may represent attractive candidates for targeted breeding approaches.A. thaliana, (ii) identify traits that are robustly affected by temperature with little variation among different accessions, and ask (iii) which traits are affected differentially by different genotypes and thus show natural variation in temperature responses.In this study we aim to (i) provide a map of developmental phenotypes that are sensitive to ambient temperature effects throughout a life cycle in the model organism A. thaliana accessions which were grown at 16, 20, 24, and 28 °C in climate-controlled environments under long day photoperiods (16 h light/ 8 h dark). Knowing that even a small randomly selected set of A. thaliana accessions covers a wide spectrum of genetic diversity [To realize this, we performed a profiling of numerous developmental and morphological traits which can be sorted into five main categories: juvenile vegetative stage, adult vegetative stage, reproductive stage, morphometric parameters and yield-associated traits. Phenotypes were analyzed in a subset of ten iversity , we chosiversity , 28), aniversity .A. thaliana.In addition to a meta-analysis of the phenotypic data, we provide accession-specific developmental reference maps of temperature responses that can serve as resources for future experimental approaches in the analysis of ambient temperature responses in A. thaliana accessions that were obtained from the Nottingham Arabidopsis Stock Centre [A. thaliana solution (ATS) nutrient medium [−2·sec−1 of cool white fluorescent lamps. We refrained from including a vernalization step because the primary focus of this study was to record morphology and development in response to different constant ambient temperature conditions.Phenotypic parameters Fig.  were assk Centre . Morpholt medium . Seeds wGermination rates were assessed daily on seeds cultivated on horizontal plates. Hypocotyl, root length, and petiole angles were measured in 7 days old seedlings grown on vertically oriented plates using ImageJ  and Root−2·sec−1 and long day photoperiods (16 h light/8 h dark). After imbibition for 3 days at 4 °C, seeds were grown in individual 5 × 5 cm pots, which were randomized twice a week to minimize position effects. Randomization was performed in blocks of 60 pots alternating between 8 positions in the cultivation chamber. In addition, pots within the trays of 60 plants were randomized in groups of 10 twice a week on alternate days to the block randomization of trays. Relative humidity of growth cabinets was maintained at 70% and plants were watered by subirrigation. Plants (n > 15) were photographed daily for subsequent manual determination of phenotypic parameters  using Image J [Total leaf area” was determined in the sense of foliar surface coverage so that overlapping leaf areas were only counted once. Determination of developmental progression largely followed the stages defined in Boyes et al. [All other analyses were performed on soil-grown plants cultivated in growth cabinets  at a PAR of 140 (+/− 20) μmol·m Image J . “Total s et al. . The vegSpectrophotometric determination of chlorophyll content was performed as described in .boxplot function contained in the graphics package. Heat maps were generated using the heatmap.2 function contained in the gplots package.Visualization and statistical analyses of the data were performed using the software R . Box ploanova and TukeyHSD function, respectively, which are both contained in the R stats package.ANOVAs for a single factor (either accession or temperature) and Tukey’s ‘Honest Significant Difference’ test as post hoc test were performed using the G, accession) or environment , and a significant genotype by environment interaction (GxE). Reaction norms for each analysis are shown in Additional file Variation in phenotype expression was analyzed by 2-way ANOVA according to Nicotra  and Whit10 temperature coefficient was calculated according to Loveys [w and Pc are the trait values at the warmer and cooler temperatures, respectively. Tw and Tc represent the corresponding temperatures in °C. We computed the geometric mean of the six Q10 values of all pairwise temperature combinations for each phenotypic trait to avoid artifacts caused by differential reaction norms/response shapes.The Qo Loveys .\documenst [Calculation of the index of phenotypic divergence Pst , 40) as  as st [4st  as\documUsing the two factorial design, two types of indices of phenotypic variation of a trait/phenotype were considered separately. The index of phenotypic divergence for genotypes , and total leaf area) due to too many missing values. The remaining 28 traits contained at most eight missing values (randomly distributed).which were replaced per trait by the arithmetic mean of the respective trait values. PCA was perfomed using the Juvenile vegetative stage (2–5 rosette leaves) and Adult vegetative stage (6–14 rosette leaves), respectively. Similarly, Inflorescence emergence, Flowering time_days and Flower.time_1. flower open were combined to form the trait group Flowering time (days). Spearman correlation coefficients were computed using the R stats package. Additionally, p values for each Spearman correlation coefficient were computed using the cor.test function. P values were subsequently corrected for multiple testing using the Benjamini-Hochberg correction implemented in the multtest package.Trait values for rosette leave traits were summarized by arithmetic means to trait groups labeled A. thaliana plants were cultivated in parallel throughout an entire life cycle at four different temperatures  under otherwise similar growth conditions  values of individual traits were summarized by phenotype classes. Thus, high variation within a phenotype class indicates that temperature effects on individual traits within that class are highly variable. The strongest variation within individual accessions was observed for morphometric phenotypes as represented by a wide whisker range and large boxes for all analyzed accessions. This is indicative for a high degree of diversity in the temperature responses of different morphometric traits. In contrast, a high variation of log2(Q10) values between different accessions implicates differential responses of different genotypes which was most prominent in reproductive stage traits.Taken together, juvenile and adult vegetative development responded highly conserved, whereas the reproductive stage and yield-associated traits showed higher variation between accessions and within individual accession, as indicated by the ranges/dimensions of the box plots in Fig. 2Q10 values among the two vegetative and the other phenotype classes indicated that genotype and environment effects may contribute differentially to phenotypic plasticity of different traits. We first used a 2-factorial ANOVA to assess which phenotypes show significant changes that can be attributed to genotype , environment , and/or GxE interaction. Subsequently, we used the variance partitioning approach [The differential variances of logapproach , 42, 43 10 values  had significant effects on the trait. Reaction norm plots for each phenotype are shown in Additional file ues Fig. .st, [To assess genotype and temperature contributions in a more quantitative manner, we next used a variance partitioning approach , 42, 43.st, ) at each10 values . This is particularly obvious for yield-related traits such as total number of seeds per plant and silique as well as silique length. Here, temperature effects on phenotype variation were low for Col-0, C24 and Bay-0, whereas considerably higher As each phenotypic trait has been assigned a value for genotype and temperature effects, they can easily be compared to assess which of the two has a stronger influence on the phenotypic plasticity. To allow a direct comparison of effects, we compared mean values for ons Fig. .Temperature effects on vegetative development showed a high, largely robust impact with little variance in cts Fig. . A scattors Fig. . While vSeveral yield-associated phenotypes such as total number of seeds, seed size, and seed weight showed varying degrees of temperature sensitivity, likely caused by the partially distinct temperature effects on individual accessions Fig. .The fundamental impact of temperature on the phenotypic responses is also reflected in the results of the principle component analysis (PCA). The PCA was performed on mean-centered and scaled data in order to allow integration of data with different scaling. PC1 which covered 50% of the observed variation, allowed a clear separation of samples via temperature Fig. . Here, tP < 0.05) were retained in the analysis . We used the rank-based Spearman correlation coefficients for pairwise comparisons of averaged trait (group) values among all accessions to account for potential non-linear relationships and minimize outlier effects. As to be expected from the varying degrees of genotype and temperature effects on different traits, phenotypic correlations also varied considerably. To filter for robust correlations, only significant correlations , and among traits within the reproductive phase (e.g. flowering traits and the onset of silique production). In addition, temperature-induced reduction in total leaf area correlated strongly with the decrease in developmental time in vegetative and reproductive phases. Similarly, the reduction in developmental times and total leaf area were moderately correlated to the effect on several seed-associated traits Fig. .Model temperature phenotypes such as petiole and hypocotyl length showed a positive correlation and were in turn correlated or inversely correlated with several other phenotypes or trait groups. However, temperature responses in primary root length under these experimental conditions showed an even more robust connection to many other traits. Mostly, these were inverse correlations with the exception of other seedling traits which were positively correlated with primary root lengths Fig. .P-value threshold was set to 0.1 in the analysis which retained only the strongest (inverse) correlations. Inspection of the correlation patterns reveals remarkable differences among accessions  for plant development was demonstrated for germination rates and plant respiration [Developmental timing of juvenile and adult vegetative growth was significantly affected by genotype and temperature Additional file 2:A. thaliana accessions. (PDF 12069 kb)Sample sizes, identity and geographic origin of analyzed Additional file 3:Reaction norm plots of each phenotype for each of the analyzed genotypes. (PDF 12067 kb)Additional file 4:Summary of Col-0 thermomorphogenesis. (PDF 12069 kb)Additional file 5:Summary of Bay-0 thermomorphogenesis. (PDF 12069 kb)Additional file 6:Summary of C24 thermomorphogenesis. (PDF 12069 kb)Additional file 7:Summary of Cvi-0 thermomorphogenesis. (PDF 12069 kb)Additional file 8:Summary of Got-7 thermomorphogenesis. (PDF 12069 kb)Additional file 9:Summary of Ler-1 thermomorphogenesis. (PDF 12069 kb)Additional file 10:Summary of No-0 thermomorphogenesis. (PDF 12069 kb)Additional file 11:Summary of Rrs-7 thermomorphogenesis. (PDF 12069 kb)Additional file 12:Summary of Sha thermomorphogenesis. (PDF 12069 kb)Additional file 13:Summary of Ws-2 thermomorphogenesis. (PDF 12069 kb)Additional file 14:Natural variation in developmental timing. (leaves vs. days). (PDF 12069 kb)Additional file 15:GxE interaction analysis results. (PDF 12069 kb)Additional file 16:Detailed information on genotype and temperature effects on phenotypic variation. (PDF 12069 kb)Additional file 17:Temperature effect on yield. (PDF 12069 kb)Additional file 18:Correlations among temperature responses in individual accessions. (PDF 12069 kb)


Triticum aestivum L., using 557 lines in five environments. Secondary traits on training and test sets, and grain yield on the training set were modeled as multivariate, and compared to univariate models with grain yield on the training set only. Cross validation accuracies were estimated within and across-environment, with and without replication, and with and without correcting for days to heading. We observed that, within environment, with unreplicated secondary trait data, and without correcting for days to heading, secondary traits increased accuracies for grain yield by 56% in pedigree, and 70% in genomic prediction models, on average. Secondary traits increased accuracy slightly more when replicated, and considerably less when models corrected for days to heading. In across-environment prediction, trends were similar but less consistent. These results show that secondary traits measured in high-throughput could be used in pedigree and genomic prediction to improve accuracy. This approach could improve selection in wheat during early stages if validated in early-generation breeding plots.Genomic selection can be applied prior to phenotyping, enabling shorter breeding cycles and greater rates of genetic gain relative to phenotypic selection. Traits measured using high-throughput phenotyping based on proximal or remote sensing could be useful for improving pedigree and genomic prediction model accuracies for traits not yet possible to phenotype directly. We tested if using aerial measurements of canopy temperature, and green and red normalized difference vegetation index as secondary traits in pedigree and genomic best linear unbiased prediction models could increase accuracy for grain yield in wheat,  Triticum aestivum L., breeding programs. GS is the use of markers covering the whole genome for selection. With GS, reviewed by Genomic selection (GS) and high-throughput phenotyping (HTP) have great potential to increase the efficiency of wheat, In wheat, canopy temperature (CT) and normalized difference vegetation index (NDVI) are associated with components of grain yield (GY) and can be routinely measured using HTP platforms . Canopy In plant and animal breeding, indirect selection for traits that are expensive or difficult to measure using correlated secondary traits is common. Examples from wheat breeding include selection for reduced plant height to improve harvest index and lodging resistance, and selection for higher protein to improve quality. Selection on secondary traits is advantageous when the secondary trait is highly heritable, highly genetically correlated with the target trait, and it is inexpensive to measure relative to the target trait. One of the challenges of using secondary traits for indirect selection is that the relative utility of secondary traits is situation dependent. Incorporating secondary traits in multivariate pedigree or genomic prediction models partially overcomes this problem because genetic covariances between traits are estimated using a model training set that is representative of the selection candidates and evaluated in the target environment(s). When used in multivariate pedigree or genomic prediction models, secondary traits have been found to improve prediction accuracy and reduce bias compared to univariate models, especially when secondary traits are measured on both the model training population and the selection candidates  was recorded as the number of days from germination until 50% of spike emergence in each plot, and was recorded in the first replicate of each trial. Lodging, which was observed only in the optimal environment, was recorded visually on a zero to five scale. GY was the total plot GY measured after maturity.High-throughput phenotypic data were collected with a thermal  and hyperspectral camera  mounted to a manned aircraft. Data were collected around solar noon time on each date, aligning the aircraft to the solar azimuth for data acquisition. Images of the experimental fields were obtained, and formatted to tabular data by calculating the mean value of the pixels inside the center of each individual trial plot represented as a polygon area on a map.images were used to compose a unique mosaic that were then manually georeferenced. The original image data were stored in Kelvin units × 100, and pixel values were converted to Celsius degrees according to the formula /100 – 273.15.The 38 cm per pixel CT data were corrected with a linear calibration using parameters calculated based on previous field and camera measurements. For each flight, the individual The 30 cm per pixel hyperspectral data were calibrated radiometrically with coefficients provided by the Laboratory for Research Methods in Quantitative Remote Sensing of the Consejo Superior de Investigaciones Científicas  derived with a calibrated uniform light source. Dark frame subtraction was also performed to reduce the noise of the sensor. Correction to decrease the effects of the atmospheric conditions in the images was performed by modeling irradiance based on sun-photometer field measurements . The images were orthorectified and coarsely georeferenced based on the built-in Inertial Navigation System (INS). For data extraction, images were aligned manually whenever images did not overlay the plot polygons due to INS inaccuracy.Data from CT, RNDVI, and GNDVI were grouped into VEG and GF stages  as in Panrep is the number of replicates of the breeding lines in the trial (nrep = 3). The variance components were estimated by fitting the model:ijy is the phenotype, µ is the mean, ig is the random effect of genotype assuming identical and independently distributed (iid) jr is the random effect of replicate with iid ijε is the residual with iid p-value < 0.001) were identified using Studentized residuals. If outliers were found, they were removed and repeatability was recalculated.Within each trial within environment, we calculated repeatability for CT, GNDVI, and RNDVI measured on individual dates, and GY. This within-date repeatability, based on the phenotypic data, was calculated as ndate is the number of phenotype dates for the trait, which ranged from two to five . Variance components were estimated by fitting a mixed model similar to (1) but adding the random effects of the dates and the interactions date × environment as:ijky is the phenotype, µ is the mean, ig is the random effect of genotype with iid jd is the random effect of date with iid k(j)r is the random effect of replicate nested within date with iid i,jgd is the random effect of genotype-by-date interaction with iid ijkε is the residual with iid 2r < 0.01. Individual low-repeatability dates were then removed if doing so improved File S1) contained 616 lines.Similarly, whenever there were multiple measurements across dates we calculated overall repeatability across time and space within each trial for CT-VEG, CT-GF, GNDVI-VEG, GNDVI-GF, RNDVI-VEG, and RNDVI-GF. Overall repeatability for each trait within trial within environment was calculated as  to five , nrep isijklmy is the phenotype, µ is the mean, ig is the fixed effect of genotype (BLUE), jt is the random effect of trial with iid kd is the random effect of trait measurement date with iid l(jk)r is the random effect of replicate within trial and date with iid m(jkl)b is the random effect of incomplete block within trial, date, and replicate with iid ijklmε is the residual with iid e.g., GY), the random effect of date was excluded from model (3). For DTHD, which was measured only once, and on one replicate, the date, replicate, and block effects were excluded from model (3). To enable us to simulate a scenario where the individuals in the test set are not grown in a replicated incomplete block design, as is the case in wheat breeding prior to the yield testing phase, we removed the effects of replicate and incomplete block from model (3), and used this model to estimate BLUEs on a per replicate basis.To estimate genetic values for traits measured across multiple dates for subsequent use in prediction modeling, for each environment, we estimated best linear unbiased estimates (BLUEs) of the breeding lines by fitting the mixed model:y.To enable across-environment prediction model training, BLUEs were also estimated for each trait across all environments except one which was designated as the validation (testing) environment. To estimate these BLUEs, a random effect for environment was included in model (3), all effects except for the genotype effect were nested within environment, and data from all environments except the validation environment were included in ijkly is the phenotype, µ is the mean, ig is the random effect of genotype with iid jt is the random effect of trial with iid k(j)r is the random effect of replicate within trial with iid l(jk)b is the random effect of incomplete block within trial and replicate with iid ith genotype in the jth trial, kth replicate and lth block, and ijklε is the residual with iid ith genotype in the jth trial in model (4).For prediction model validation, best linear unbiased predictors (BLUPs) of the breeding lines were calculated for GY within each environment by fitting the mixed model:Genotyping-by-sequencing (GBS) .SNP calls for the set of 1092 breeding lines were extracted, and then markers were filtered so that percent missing data and percent heterozygosity per marker did not exceed 80% and 20%, respectively. Next, lines with > 80% missing marker data were removed, and markers were recoded as –1, 0, and 1, corresponding to homozygous for the minor allele, heterozygous, and homozygous for the major allele respectively. Lines that did not overlap with the set of 616 lines with quality phenotypic data for all traits in all environments were removed. Next, markers with a minor allele frequency < 0.01, and > 80% missing data were removed, and missing data were imputed with the marker mean. A total of 12,083 SNPs scored on 557 individuals was used for subsequent analysis.File S2) was estimated according to equation 15 in File S3) was estimated as 2× the coefficient of parentage.For the set of 557 lines with quality phenotypic and genotypic data, the genomic relationship matrix . A random effect of genotype-by-date interaction effect was added to model (3) for variance component estimation. Square roots of heritabilities were also estimated for all traits corrected for DTHD by adding a fixed effect covariate for DTHD to the model. For traits that were measured at one point in time (such as GY), For traits measured across multiple time points, square root of broad sense heritability (phenotypic selection accuracy) on a single plot basis, n is the number of traits, y1 is a vector of BLUEs for trait one, yn is a vector of BLUEs for trait n, where BLUEs were estimated using model (3), X is the fixed effects design matrix, which is the same for each trait, u1 is a vector of fixed effects for trait one, un is a vector of fixed effects for trait n, Z is the random effects design matrix, which is the same for each trait, a1 is a vector of fixed effects for trait one, an is a vector of fixed effects for trait n, ε1 is a vector of residuals of trait one, and nε is a vector of residuals for trait n. Variance components were estimated assuming A is the pedigree relationship matrix, G is the genomic relationship matrix, and H is the variance-covariance matrix for the breeding values of the traits. In both models, I is an identity matrix, and R is residual variance-covariance matrix between the traits. The covariance matrices H and R were assumed unstructured. For each relationship matrix, A and G, correlations were estimated twice, once including a fixed effect covariate for lodging in the optimal environment, and once including a fixed effect covariate for DTHD in all environments and lodging in the optimal environment. To estimate the genetic correlations between DTHD and GY in each environment, and with each relationship matrix, we used bivariate models (model (5), with n = 2 traits).Genetic correlations between traits including CT-VEG, CT-GF, GNDVI-VEG, GNDVI-GF, RNDVI-VEG, RNDVI-GF, and GY were calculated based on estimates of variances and covariances from a multivariate Gaussian mixed model:iy are the BLUEs of the breeding lines from model (3), µ is the mean, ig is a random effect of genotype with iε is the residual error with iid After quality control, complete data on 557 breeding lines remained, and was used for prediction modeling. Accuracies from a multivariate mixed model incorporating GY on the training set only, and secondary traits on both the training and test sets  were comR.The multivariate prediction models were as described in model (5), and assumed either Accuracies were estimated using fivefold cross validation with the same fold assignment for all analyses. For each fold, the predictive ability was calculated as the Pearson’s correlation between predictions for GY and the BLUPs for GY from model (4). Prediction accuracy, Multivariate prediction model accuracies were estimated once where BLUEs of secondary traits on the test set included data from all three replicates, and once where BLUEs of secondary traits on the test set were estimated using data from the first replicate only. Accuracies were also estimated including a covariate for DTHD in the prediction models.1y and yn equal to the vectors of BLUEs of the individuals for traits 1 and n, respectively, estimated on a per-replicate basis. To correct for the replicate effect, a random effect of replicate nested within trait was included in the multivariate prediction model, and individuals were assumed unrelated with I is an identity matrix. The predictions resulting from this model were of total genetic values, whereas the predictions from pedigree and genomic selection models were of breeding values.To estimate the prediction accuracy for the case where pedigree or genomic relationship information is not available, but phenotypic data for GY is available on the training set and phenotypic data for secondary traits is available on all individuals, we fit the same set of within-environment multivariate prediction models as before, except with , on either a line mean or single plot basis, depending upon whether secondary traits were replicated or not replicated in the prediction model. To estimate the effects and significance of these factors, we fit the linear regression modeliy is the multivariate accuracy minus the univariate accuracy for the corresponding univariate model, µ is the mean, ir is the effect of relationship matrix used in the prediction model, ijm is the effect of environment, All genomic and pedigree prediction model accuracies estimated from cross validation within environment were analyzed to assess four factors affecting the accuracy gained from using secondary traits in pedigree and genomic prediction: i. the relationship matrix used in prediction modeling, ii. the environment, iii. the mean magnitude of the genetic correlation,For high-throughput phenotyping, the software ArcMap  was used to convert images to tabular data, and for manual georeferencing. ImapQ  was used to correct the CT data with a linear calibration. Autopano Giga  was used to construct mosaics of multiple images. ENVI software  was used to convert pixel values to Celsius degrees. HyproQ  was used to process the hyperspectral data.http://www.r-project.org). The package ‘ASReml-R’ (http://cran.r-project.org/package=EMMREML) was used to fit univaraite genomic prediction models. The regression model assessing factors affecting accuracy was fit using the R package ‘lm’.The coefficient of parentage was estimated using the ‘browse’ application in the International Crop Information System software package. All other analyses were done in the R programming language and software environment  are an average across estimates using A and G. Correlations ≥|0.09| are significant at the 0.05 level of significance. Genetic correlations between GY and secondary traits . Drought and severe drought showed a similar pattern of genetic correlations, which was different from that of optimal, late heat, and early heat.In general, genetic correlations estimated with y traits  ranged iMultivariate pedigree and genomic prediction models that incorporated secondary trait data on training and test sets were consistently, and often substantially, more accurate than their corresponding univariate prediction models for GY within environment , demonstOn average, without correcting for DTHD, secondary traits measured on all three replicates in the test set led to a 67% improvement in pedigree prediction accuracy, and an 85% improvement in genomic prediction accuracy. When we used only one replicate of secondary trait data on the test set, secondary traits lead to a 56% increase in pedigree prediction accuracy, and a 70% increase in genomic prediction accuracy.When correcting for DTHD, on average, secondary traits improved pedigree prediction accuracy 37%, and genomic prediction accuracy 48%, when secondary trait data on the test set was replicated. When only one replicate of secondary trait data were used on the test set, secondary traits increased pedigree prediction accuracy 17%, and genomic prediction accuracy 24%.Overall, we observed consistent trends in accuracy. Multivariate prediction models with replicated secondary trait data on the test set were most accurate, followed by multivariate prediction models with unreplicated secondary trait data on the test set, and univariate prediction models. Also, secondary traits had a slightly larger impact on accuracy in the genomic prediction models compared to the pedigree prediction models, and correcting for DTHD consistently reduced accuracies and led to smaller differences in accuracy between the multivariate and univariate models. The largest impact of correcting for DTHD was observed in drought. In drought, without correcting for DTHD, secondary traits lead to the largest percent increase in accuracy compared to all other environments. In contrast, when correcting for DTHD in drought, secondary traits led to no improvement or a decrease in accuracy. The smallest impact of correcting for DTHD was observed in late heat, where the multivariate and univariate prediction accuracies were largely unaffected.Without correcting for DTHD, across-environment multivariate pedigree and genomic prediction models incorporating secondary trait data on training and test sets were consistently, and substantially, more accurate than their corresponding univariate prediction models . On averWhen correcting for DTHD, across-environment multivariate pedigree and genomic prediction models were frequently about as accurate as, or less accurate than, their corresponding univariate prediction models . On avervs. not replicated in the test set, and correcting for DTHD increased the univariate prediction accuracies and reduced the gain in accuracy from using secondary traits.The overall trends for across-environment prediction were that multivariate models were more accurate than univariate models only without correcting for DTHD, secondary traits lead to greater accuracies when secondary trait data were replicated Table S1). When secondary trait data were replicated on both training and tests sets, and prediction models did not correct for DTHD, multivariate prediction models that assumed lines were unrelated were actually slightly more accurate on average compared to the multivariate pedigree and genomic prediction models. This indicates that, without estimates of relationship, secondary trait data can be useful for predicting total genetic values of GY.We found that, on average, when predictor trait data were not replicated on the test set, and when correcting for DTHD, multivariate prediction models that assumed lines were unrelated were either equally accurate or slightly less accurate than genomic and pedigree predictions incorporating secondary traits (P << 0.01) with an adjusted 2r = 0.78. Based on this model, we found that the gain in accuracy from using secondary traits was significantly associated with a) P < 0.05), and b) P << 0.01) (P << 0.01).The regression model that we fit to examine factors affecting the accuracy gained from using secondary traits in pedigree and genomic prediction was significant (<< 0.01) . We alsoper se, and GY data from selection candidates’ relatives. Second, by using a model training set evaluated for all traits in the target set of environments, secondary traits are appropriately weighted, depending in part upon the magnitude and the direction of their genetic correlations with GY. Because a quality control procedure was used prior to prediction modeling, an important assumption of this study is that there are no major technical errors in the HTP data collection that would give rise to near zero repeatability for trait measurements. We expect this assumption to hold true as HTP data collection and imaging processing pipelines continue to improve, minimizing technical errors.This study found that, in wheat, GNDVI, RNDVI, and CT measured across the crop growth cycle using an aerial HTP platform can substantially improve genomic and pedigree prediction model accuracies for GY when observed on training and test sets and used as secondary traits in multivariate models. Our prediction-model-based approach is an improvement upon conventional indirect selection based on secondary traits for two reasons. First, by using a prediction model, we take advantage of secondary trait data on the selection candidates There was no improvement in accuracy when secondary traits were observed on the training set only, which is consistent with a similar study that evaluated secondary traits for feed intake in cattle . Thus, ivs. within-environment prediction may be misleading. Based on percent increase in accuracy, without correcting for DTHD, secondary traits appeared to be much more beneficial for prediction across environment than for prediction within environment, when in fact the numerical increases in accuracy due to secondary traits in across-environment prediction were lower than those of within-environment prediction.Due to genotype-by-environment interaction, within-environment prediction accuracies were always higher than across-environment prediction accuracies. Thus, comparing the percent increases in accuracy due to secondary traits in across- Correcting for DTHD improved univariate prediction accuracies across-environment, which suggests that the genotype-by-environment variance for GY corrected for DTHD is lower than that of uncorrected GY. For both within- and across-environment prediction, correcting for DTHD reduced the genetic correlations between GY and the secondary traits, which in turn reduced the accuracy gained from including secondary trait data on the test set. In plant breeding, GY is sometimes corrected for DTHD or another phenological trait in order to avoid indirect response to selection for that trait. To take full advantage of secondary trait data while avoiding indirect selection on a phenological trait, a better approach may be to include data on the phenological trait in a multivariate prediction model along with any available secondary traits, and then use the multivariate BLUPs to calculate a selection index with GY and the phenological trait weighted appropriately.per se. However, to ensure the best estimates of breeding values, utilizing pedigree or genomic relationship information is recommended.If pedigree or genomic relationship information are not available, total genetic value for GY can be predicted using secondary trait data, assuming there is a population of lines phenotyped for both GY and secondary traits across multiple replicates that can be used to train a multivariate prediction model. Prediction accuracies for GY genetic value estimated in this way were frequently very similar to prediction accuracies for GY breeding values estimated using multivariate genomic and pedigree prediction models. If we assume that all the genetic variance is additive, this suggests that multivariate pedigree and genomic prediction accuracies were often driven primarily by secondary trait information on the individuals The accuracy gained from using secondary traits was associated with We have shown that, in wheat, GY secondary traits measured using an aerial HTP platform can be used to increase pedigree and genomic prediction model accuracies for GY when observed on both the model training and test sets. These prediction models could be useful for making selections in generations where GY cannot be measured accurately but secondary traits can. In crop breeding, there are instances where selection candidates can be phenotyped for some traits, but, due to insufficient seed, high cost of phenotyping, severe weather events, and/or long juvenile phase duration, not all traits of economic importance can be phenotyped. In these cases, traits correlated with the economically important traits could be used in pedigree and genomic prediction models to improve selection accuracy without delaying selection. This approach appears promising in wheat and should be investigated in other crops especially as HTP become more accessible.Additional research is needed before secondary traits from HTP can be used routinely in wheat breeding to increase pedigree and genomic selection accuracy for GY when GY cannot be measured directly on the selection candidates. First, in this study, we used a simple repeatability model for GNDVI, RNDVI, and CT measurements within a growth stage; however, time series models for measurements of these traits taken across time need to be compared to identify the best model for each trait. This could improve the phenotypic selection accuracy of GNDVI, RNDVI, and CT, potentially leading to better prediction accuracies when these traits are used in pedigree and genomic selection. To help address this need, we are currently working on evaluating repeatability, multivariate, and random regression models for GNDVI, RNDVI, and CT. Second, this study used secondary trait data from large plot sizes suitable for measuring GY, but, for selection, it will be useful to use secondary traits from plots that are of small size due to limited seed availability. Thus, the utility of secondary traits measured using HTP in pedigree and genomic prediction models need to be assessed for the case where the test set individuals are sown in a small plots. Lastly, HTP data analysis pipelines that lead to better data quality and faster speed of processing should continue to be developed.


Oryza sativa L.). The study was performed using 59 rice genotypes with 525 SNPs derived from DArTseq platform. Population structure analysis revealed only two distinct genetic clusters where genotypes were grouped based on environmental adaptation and pedigree information. Analysis of molecular variance indicated a low degree of differentiation among populations suggesting the need for broadening the genetic base of the current germplasm collection. GWAS revealed 22 significant associations between DArTseq-derived SNP markers and rice grain quality traits in the test genotypes. In general, 2 of the 22 significant associations were in chromosomal regions where the QTLs associated with the given traits had previously been reported, the other 20 significant SNP marker loci were indicative of the likelihood discovery of novel alleles associated with rice grain quality traits. DArTseq-derived SNP markers that include SNP12_100006178, SNP13_3052560 and SNP14_3057360 individually co-localised with two functional gene groups that were associated with QTLs for grain width and grain length to width ratio on chromosome 3, indicating trait dependency or pleiotropic-effect loci. This study demonstrated that DArTseq markers were useful genomic resources for genome-wide association studies of rice grain quality traits to accelerate varietal development and release.Microarray-based markers such as Diversity Arrays Technology (DArT) have become the genetic markers of choice for construction of high-density maps, quantitative trait loci (QTL) mapping and genetic diversity analysis based on their efficiency and low cost. More recently, the DArT technology was further developed in combination with high-throughput next-generation sequencing (NGS) technologies to generate the DArTseq platform representing a new sequencing tool of complexity-reduced representations. In this study, we used DArTseq markers to investigate genetic diversity and genome-wide association studies (GWAS) of grain quality traits in rice ( Oryza sativa L.) is increasingly becoming a major food crop in sub-Saharan Africa (SSA). Globally, rice is one of the most widely cultivated cereal crops distributed across diverse geographical, ecological and climatic conditions [indica, japonica and javanica, have been conserved in global gene banks [Rice  for important agronomic traits. Furthermore, the magnitude of genetic variability and the extent to which the desirable characters are heritable largely determines the success of any plant breeding program . ConsequMore recently with the advances in next generation sequencing (NGS) technologies, genotyping by sequencing (GBS) has emerged as a promising genomic approach for simultaneous exploration of plant genetic diversity and molecular marker discovery ,25,26. TOryza sativa L.) genotypes.With advances in microarray-based marker technology, Diversity Arrays Technology (DArT) markers have become the genetic markers of choice for construction of high-density maps, mapping quantitative trait loci (QTL) and genetic diversity analysis based on their efficiency and low cost . AdditioInternational Center for Tropical Agriculture (CIAT), Madagascar (MDG), Tanzania (TZ) and Institut d’Economie Rurale. This research study was approved and conducted at the Biosciences eastern and central Africa-International Livestock Research Institute (BecA-ILRI) Hub, Nairobi, Kenya. Test materials were assessed for determinants of grain quality  using dehusked grains. Grain shape was classified on the basis of grain length (GL), grain width (GW) and length to width ratio (L/W), where measurements were read using a vernier calliper as described by Cruz and Khush [The present study used a collection of 59 rice genotypes, which included 2 popular landraces, 36 upland and 21 lowland rice collections . The aboAmylose and amylopectin content of the starch was determined by the method of Gibson et al.  using a  Juliano  with sliGelatinization temperature (GT) was assessed indirectly as the alkali spreading value of hulled kernels as per modified procedure of Little et al. . Twelve Quick-DNA™ Plant/Seed 96 Kit, where a single individual plant was considered for each genotype. Subsequently, 40 μl of a 50 ng/μl DNA of each sample were sent to Diversity Arrays Technology (DArT) Pty Ltd, Australia (http://www.diversityarrays.com/dart-map-sequences) for whole genome scan using Diversity Arrays Technology (DArT) markers. Whole-genome genotyping for the 59 rice genotypes was carried out using Genotyping-By-Sequencing (GBS) technology as described by Elshire et al. [Total genomic DNA was isolated from leaves of three-week old plants using the ZYMO research e et al.  using 18DArTseq SNP derived markers were filtered to remove bad SNPs and genotypes using PLINK 1.9 software in MS window and R statistical software, where genotypes with > 30% missing data, SNP loci with >20% missing data  and rareWe investigated the genetic structure and relationship among 59 rice genotypes using 525 DArTseq-derived SNP markers distributed across the rice genome as described by Pritchard et al. . BayesiaR2), and only P-values ≤0.01 for each pair of loci were considered significant.Linkage disequilibrium analysis was performed using TASSEL V5.3.1 software  with selDeterminants of grain quality including grain length (GL), grain width (GW), grain length/width ratio (L/W), amylose content (AC) and gelatinization temperature (GT) were considered for association mapping. Association mapping analysis was performed with TASSEL V5.3.1 software  using boThe number of accessions, number of alleles, genetic diversity, heterozygosity, polymorphism information content (PIC) and major allele frequency of the eight populations is shown in K ranging from 1 to 10, and by inferring on Delta K of Evanno et al. [st) estimate value of 0.134 generated by PLINK 1.9 software, genotypes were grouped into two major clusters  and based on 525 DArTseq SNPs, two major clusters were clearly distinguished among all rice populations  consisteThe genetic distance among the different populations was estimated with 525 DArTseq-derived SNP markers . The greAnalysis of molecular variance (AMOVA) among the 59 rice genotypes indicated that 11.24% of the variance was due to genetic differentiation among the populations, 67.30% of the variance was accounted by genetic differentiation among individuals within populations, while the remaining 21.46% of the variance was due to the differences within individuals .Grain shape (measured as the grain length-to-width ratio) and starch related qualities such as amylose content and gelatinization temperature ), are the main properties considered for selecting breeding lines with improved quality . In thisP-values were used to determine the association of QTLs with markers while percent variance explained (PVE) predicted the magnitude of QTL effects. Manhattan plots for grain quality traits were generated in GWAS indicating the most significant associations >3)) (P < 0.001) association signals were detected for grain quality traits , grain width (GW), grain length/width ratio (L/W), amylose content (AC) and gelatinization temperature (GT) were considered for genome-wide association studies (GWAS) using 525 DArTseq SNP derived markers. Association mapping analysis was performed with TASSEL V5.3.1 software  using bolue)>3)) . A quantlue)>3)) . A totaly traits . For AC,y traits . The AC ene.org/ ); the otGenome level profiling of rice germplasm collections is a critical initial step in identification of divergent parents for effective utilization in rice breeding programs. The present study is the first major effort to perform genetic diversity studies and population structure analysis on a panel of 59 rice germplasm collections in South Sudan for effective breeding.Our study highlights the potential of highly informative and selective DArTseq-derived SNP markers for genetic diversity analysis and genome wide association studies in rice. Results of the diversity analysis based on geographical origin  indicatest) estimate value of 0.134 and a small percentage variation (11.2%) among populations as revealed by analysis of molecular variance . The other 20 significant SNP loci suggested the likelihood discovery of novel alleles associated with rice grain quality traits. Furthermore, SNP12_100006178, SNP13_3052560 and SNP14_3057360 individually co-localised with two functional gene groups that were associated with QTLs for grain width and grain length to width ratio on chromosome 3, indicating trait dependency or pleiotropic-effect loci. Hu et al. [We identified twenty-two significant associations with PVE of between 19–48% for rice grain quality traits in the entire set of genotypes, including 1 association with AC, 10 associations with ASV, 6 associations with GW and 5 associations with L/W . In the u et al.  identifiu et al.  also ideThe present study demonstrates the potential of highly informative and selective DArTseq-derived SNP markers for genetic diversity analysis and genome wide association studies in the tested rice genotypes. This study also provides a direction for breeding efforts in the selection of parents from the current collection with potential for novel genes or QTLs for important agronomic traits. A low degree of differentiation among sampled populations suggested the need for widening on the genetic base through the introduction of distant or wild relatives. However, the study also indicated that wide variability exists in the current rice germplasm collections for grain quality traits probably due to intercrossing between populations. Genome-wide association studies successfully identified and tagged 22 DArTseq-derived SNP loci significantly associated with rice grain quality traits. Among these, two SNP loci were found in regions where the QTL associated with the given traits had previously been reported, while the other 20 significant associations were indicative of the likelihood discovery of novel alleles associated with rice grain quality traits. Significant QTL associations for AC allele (C/T) was traced back to parent K5; ASV alleles  were located in parents ART2-4L3P1-2-1, BG400-1, JARIBU and SUPA TZ; while the co-localised QTLs for GW and L/W came from JARIBU, BR4 and ART3-8L6P3-2-2-B. These parents are potential sources of major effect QTLs for grain quality traits that can be exploited for rice crop improvement. In addition, the results of this study suggested that genetic progress can be attained by intercrossing genotypes from TZ with MDG and CIAT which appeared to be distantly related. Furthermore, from this study, we identified useful targets for QTL validation, fine mapping and cloning that will help rice breeders in contributing to enhancement of rice grain quality traits through marker assisted breeding.S1 File(XLS)Click here for additional data file.


Saccharomyces cerevisiae POLs across many environments, achieving near complete trait heritability and precisely estimating additive (73%), dominance (10%), second (7%) and third (1.7%) order epistasis components. We map quantitative trait loci (QTLs) and find nonadditive QTLs to outnumber (3:1) additive loci, dominant contributions to heterosis to outnumber overdominant, and extensive pleiotropy. The POL framework offers the most complete decomposition of diploid traits to date and can be adapted to most model organisms.Explaining trait differences between individuals is a core and challenging aim of life sciences. Here, we introduce a powerful framework for complete decomposition of trait variation into its underlying genetic causes in diploid model organisms. We sequence and systematically pair the recombinant gametes of two intercrossed natural genomes into an array of diploid hybrids with fully assembled and phased genomes, termed Phased Outbred Lines (POLs). We demonstrate the capacity of this approach by partitioning fitness traits of 6,642  Dissecting the architecture of complex trait is challenging. Here, Hallin, Märtens et al. devises Phased Outbred Lines (POLs) in order to accurately decompose growth trait variation in diploid yeast across different environments. Decomposing the trait variation within natural populations into its genetic components is a fundamental goal of biology that has proven to be challenging161011131416MATa and 86 MATα haploid Saccharomyces cerevisiae strains. These haploids were randomly drawn from a twelfth generation two-parent intercross pool, constructed using highly diverged (0.53% nucleotide difference) wild strains, here termed North American (NA) and West African (WA). Only two alleles segregate at each polymorphic site, with on average equal representation in the poolTo accurately decompose diploid trait variation, we first isolated and sequenced the full genomes of 86 MAT and LYS2 loci (With only a modest number of 172 haploid genomes sequencedYS2 loci . Hybrid n≥4) manner, using a high resolution growth phenomics platform designed to minimize noise and biasGAL3 (WA premature stop codon) and DAL  genes respectively21r; r: 0.27; median r: 0.21). This agrees with the hypothesis that distinct genetic factors control population expansion in different growth phases21r=−0.02) and often of moderate or large magnitude , their F12 haploid parents, the diploid NA and WA founders and their hybrid in a well replicated , dominance  and pairwise and third order epistatic effects (interlocus interactions) (Based on the actions) . We firsactions) . The simactions) . When adactions) . Due to H2=80–99% depending on the trait, median 91%, DAL genesThe large sample size, known large variation in relatedness and absence of environmental variation allowed us to estimate nonadditive variance components with unprecedented accuracy. Thus, additivity, dominance and pairwise epistasis accounted for almost all trait variation ; this epistasis variance contribution equalled one third of the largest dominance variance estimate . We estimated that third order interactions accounted for 1.7% of the trait variation on average . This is25GAL3 stop codon variant, as well as the DAL1 and DAL4 non-synonymous and stop codon mutations, known to account for most of the variation in galactose and allantoin growth respectively  of the QTLs contributed significantly to both additive and nonadditive phenotype components, but the majority were private to one of them . The non% of the r=0.27, P<0.0001) QTLs were subtelomeric; almost all (84%) of these were pleiotropic. This agrees with previous haploid studies, and adds credibility to the suggestion that hypervariable subtelomere structures and ORF compositions account for much of the remarkably large trait variation in yeast27Only 32 of 145 (22%) additive and nonadditive QTLs called were mapped in a single environment, reflecting that extensive pleiotropy is the rule rather than the exception . Almost The degree to which offspring phenotypes deviate from the mean of the parent phenotypes, heterosis, and which genetic factors that account for this difference are central questions in breeding. Capitalizing on the scale of our screen , we established the phenotype discordance of the POLs from those inferred for their diploid parents (Methods) with previously unattainable completeness. Hybrid offspring where the inferred parents differed significantly from each other were retained for discordance analysis . The majority of such offspring  that could be unambiguously called deviated significantly from the midparent and were thus midparent heterotic (Methods). Depending on the threshold 23–41% of these cases corresponded to the offspring being either superior (best parent heterosis) or inferior (worst parent heterosis) to both parents, with equal prevalence of best parent and worst parent heterosis . This is29χ2 test, P<0.01; Overdominance (heterozygotes at a locus being superior to both homozygotes), dominance (heterozygotes at a locus differing from the mean of the homozygotes) and epistasis can all contribute to best parent heterosis. However, calling such contributions is challenging because multiple effects often act in parallel. In particular, overdominance may be modified by epistasis such that it only manifests in a minority of genetic backgroundst-test, P<0.01). This suggests that dominance-by-dominance or dominance-by-additive interactions potentiate the best parent heterosis by shifting dominant or additive loci to overdominant, creating best parent heterosis, in a minority of backgrounds. For the chr. IX QTL with a near universal fitness trade-off, NA/WA heterozygotes were consistently enriched among offspring with superior growth rate, implying overdominance  and introduction of sex-specific auxotrophic markers, POLs impose no requirements on the yeast genotypes used; the design is lineage agnostic. However, removal of the yeast sex-switch renders the cross directional and prevents the construction of a full diallel cross, something that is otherwise possible in for example monoecious plants where individuals express both sexes. The diploid hybrids have identical marker composition, avoiding growth effects derived from artificial auxotrophies that confound many haploid crossing designs38Traits have been exhaustively mapped and decomposed in haploid models1011123235The framework allowed partitioning diploid trait variation into its major components with little room for confounding effects, due to nearly all trait variation being accounted for. Additive effects explained the vast majority of phenotypic variation, with approximately equal variance contributions from dominance and pairwise interactions at around 10% and 7%, respectively. The large explanatory power of additive genetics is well in line with findings in haploid screens101240A stable haploid phase, indefinite storage as frozen stocks and easy mating will remain distinct advantages of yeast. Nevertheless, POLs can be employed in most higher model organisms, with only slight modifications to the approach. Panels of extensively recombined offspring can be generated using two or more founder parents in mouse, plants, flies and worms434546MATa, ura3::KanMX, ho::HygMX and MATα; ura3::KanMX; ho::HygMX; lys2::URA3. Haploids of different mating types were robotically mated on rich medium  in all pairwise combinations combining their complementary LYS and URA auxotrophies using a RoToR HDA robot . Haploid cells of the same mating type do not mate and this feature prevents the construction of a full diallel cross . Diploid hybrids were selected twice on Synthetic Minimal (SM) medium  glucose and pH buffered to 5.8 with 1% (w/v) succinic acid, 2% agar). The theoretical maximum amount of POLs from our experimental design was 7,396 (86 × 86); however, one F12 haploid strain  was contaminated prior to mating and all 86 hybrids spawning from this cross were therefore discarded . Furthermore, 8 F12 haploids were identified as having chr. IX aneuploidy (see ‘Genotype construction' below), the hybrids spawning from these haploids were included in the phenotyping in order to investigate the aneuploidy's effect on the phenotype. They were, however, excluded in all downstream analysis since they could interfere with the QTL mapping and they have a large fraction of missing genotypes on chr. IX. We do find a possible effect of the chr. IX aneuploidy mainly on the mean growth phenotype (see F12 outbred lines were derived from a multigeneration two way intercross between ancestors of the North American (YPS128) and West African (DBVPG6044) populations, as describedet al.MATα 41, 53, 67 and MATa 206, 222, 223, 253, 258. Contaminated diploid hybrids and hybrids with chr. IX aneuploidies were excluded. Phased genomes of the 6,642 diploid hybrid offspring (81 MATa x 82 MATα) retained for the genetic analysis was constructed in silico using custom R code.The haploid F12 parents were previously sequenced by short read sequencing, and mapped to the S288C reference genome in order to call segregating sites, infer genotypes and characterize the recombination landscapen=4 replicates for each experimental plate, with replicates initiated from two different pre-cultures and run in different instruments and plate positions to minimize bias. Their 172 haploid F12 parents  and their diploid NA and WA ancestral lineages  were phenotyped separately. Every 4th position was reserved for internal controls . These 384 controls were interleaved with experiments on pre-culture plates, ensuring equal treatment of controls and experiments. High resolution population size growth curves were obtained using Epson Perfection V700 PHOTO scanners  and the Scan-o-matic frameworkHigh resolution growth phenotyping on solid agar medium was performed using a 1536-colony plate layout. Each plate  was cast with exactly 50 ml of Syntetic Complete medium at 50C ). Casting was performed on an absolutely leveled surface with drying for ∼1 day. The base medium was supplemented with additional stressors or alternative carbon or nitrogen sources as indicated . The 7,3et al.We estimated additive relatedness from genotypes. We derived formulae for efficient computation of the covariance due to dominance, pairwise and third order interaction effects . We fittet al.X is a centred and standardized genotype matrix, and the normalizing constant c is the average diagonal value of XXT. This is in contrast to the mapping in R/qtl where we instead modified the phenotype used, as stated at the beginning of this section. QQ-plots , the distribution of the rest of P values follows the expected uniform distribution under the null.QTL calling was performed using the ‘scanone' function with the ‘marker regression' method in R/qtl ref.  with estQQ-plots  confirm t-test to detect POLs significantly deviating (α<0.01) from the mean parent phenotype, either overperforming (positive mid parent heterosis) or underperforming (negative mid parent heterosis). The parent phenotypes used were estimated from all POLs descending from the given parent as described under ‘QTL mapping' in Methods, the variance of the mean parent phenotype was set to equal that of the most variable parent. POLs deviating from the mean parent were then tested using a Student's t-test (α<0.01) for positive deviations from the strongest parent  and for negative deviations from the weakest parent . Hybrids deviating significantly from the two parents, but not from the estimated mid-parent, was called as not deviating from the mid parent expectation. Hybrids not falling into any of the stated categories were set as ambiguous and not considered, this might manifest as for example a hybrid not being significantly different from either parent.We used a Student's χ2 test, 115 QTLs were used, corresponding to all unique QTLs between the additive and nonadditive QTL scan. Entries to the χ2 test were: observed number of heterozygotes and observed number of homozygotes (summed) among BPH POLs and the corresponding expected numbers, given distributions among all POLs. A range of cut-offs for significance was tested and the stability of results across cut-offs ascertained. We cannot completely exclude that pseudo-overdominance, that is, tightly linked loci with dominance of opposite parental alleles, confuse some assignments of overdominance. However, given the small linkage regions, we expect pseudo-overdominance to be rare and the associated overestimation of overdominance to be small. We tested for dominance similarly, but pooling the weaker homozygote state with the heterozygote state and calling significant enrichment of the better homozygote among BPH POLs. If the better homozygote was enriched, and the weaker was not, cases where the fraction of heterozygous was unchanged or enriched were called as dominance. Underdominance contributions to worst parent heterosis were called as for overdominance, but as enrichments of the heterozygous genotype among worst parent heterotic POLs. Finally, dominance contributions to worst parent heterosis were called as for dominance in best parent heterosis, but as enrichment of the weaker homozygote.To test for overdominance contributions to best parent heterosis we compared the expected and observed number of heterozygous genotypes among best parent heterotic POLs (defined as above). Calling overdominance as overrepresentation of the heterozygous state with no overrepresentation of either homozygous state. This was performed for each QTL separately using a https://github.com/j-hallin/y10k, and is available upon request.All data associated with this study is available in 5354555657How to cite this article: Hallin, J. et al. Powerful decomposition of complex traits in a diploid model. Nat. Commun.7, 13311 doi: 10.1038/ncomms13311 (2016).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figures 1-8, Supplementary Table 1, Supplementary note 1 and Supplementary References.Genotypes.Phenotypes.Variance decomposition simulations.Variance decomposition.QTL summary.


Pedigree-based management of genetic diversity in populations, e.g., using optimal contributions, involves computation of the Z is a matrix relating animals to genotypes. For the relationship matrix For genomic relationships, an efficient indirect computation with quadratic instead of cubic cost is We present efficient methods to compute elements and statistics of the genomic relationships  Optimal contribution –3 is a mputation . Here wecument}K , and we Genomic evaluation considers several tens of thousands of single nucleotide polymorphisms (SNPs) that are distributed across the whole genome, and in the most frequent implementation (genomic best linear unbiased prediction (GBLUP), or single-step GBLUP) it uses a so-called genomic relationship matrix. Following this approach, the accuracy in the evaluation of breeding values is improved compared to that of pedigree-based evaluation by exploiting existing linkage disequilibrium with neighboring quantitative trait loci (QTL) . ConsequHowever, because of linkage between these high-density SNPs, indirect hitch-hiking also affects gene transmission at loci other than SNPs and QTL . This farealized instead of expected relationships, and take into account Mendelian segregation and linkage due to the finite size of the genome [Sonesson et al.  illustrae genome . Thus, ge genome  tried toWhen monitoring evolution of genetic variability over time, or even optimizing management of genetic diversity at a given time, some individuals of interest may be ungenotyped  and  relationships by combining pedigree and genomic information should be estimated. A natural approach is to use the matrix usually called g status . Althougmentclasspt{minimaThe objective of our study was to develop an indirect method for computing genomic relationship coefficients and vector functions  context .The new approach was evaluated using data from dairy goat and dairy sheep breeding programs. We also discuss the issues that raise from using Consider the genomic relationship matrix }G=ZZ′/k , where \r et al.  presenteEither of the matrix–vector products in rom BLAS . Note thVectors ollowing  based onranspose , 17. TheMatrix mentclasspt{minimaThe inverse of An additional problem arises from the fact that the two terms forming a et al.  and Chria et al.  suggesteument}β) . If the ment}A22 , 19, 20.However, considering the genomic base as the reference is preferable, i.e. modifying approach , which pmic base . This pamic data , and repo et al.  showed tst index  and theyt groups , a case The following algorithms to compute cument}A  and theyument}AΓ .Matrix Let The computation method is indirect for two reasons. First, because it uses the difference mentclasspt{minimament}H-1 :\documenTo obtain Then, we obtain From Eq. , we obtaentclass1pt{minimaFinally, Compute Ax using ,Compute Compute Compute Compute To summarize, in order to compute Product ncestors , 27. If When programming, it can be handled as follows. For any working vector chniques , 28, 29. and Eq.  becomes The indirect method can be used for monitoring and optimization diversity in large livestock populations: its implementation areas are briefly described in the “x′Hx+w′x . If all The fast indirect method is only used to compute (and possibly store) matrix mentclass2pt{minimare used  or variaare used , 31. In In this section, we present elements to yield statistics in a scale that can be used by breeders. Genomic relationship coefficients derive from a statistical construction that has been basically developed for genomic evaluation purposes  althoughA pragmatic compromise consists in optimization based on genomic relationships, possibly with metafounders, while the results (e.g. average inbreeding) are converted into more conventional scales before editing in output files. Conversion into conventional (pedigree-based) coefficients is carried out via a shift factor erations . These fMoreover, n et al. , who shostimated , i.e. ifx for producing young bucks in 2016 was 1135 (129 genotyped and 1006 ungenotyped): 44 genotyped male candidates, 769 ungenotyped female candidates . After applying filtering criteria , 38,997 For both breeds, these datasets were not affected by genomic selection, which is planned only for the near future. The genotypic values in t}m SNPs , 21, 22.In both cases, using the indirect method and optimized computations of Parameter mic base .The terms of mentclass2pt{minim-matrix genomic relationships involving ungenotyped individuals are estimated by regression and consequently, are intermediate between conventional relationships and true genomic relationships. The standard deviation of the difference between pedigree-based and genomic coefficients substantially decreased from 2 to 1.1  are not genotyped in the future as in our operational list, the efficiency of the selection optimization will be affected in comparison with full genotyping. If the objective is to maximize genetic gain while constraining for genomic inbreeding rate [Deciles of entclass1pt{minimasee Fig. . Basicalentclass1pt{minima1.1 Fig.  for the entclass1pt{minimaFrom the 2069 genotyped individuals, 129 were in the operational list. The remaining 1940 genotyped individuals were reduced to 1500 or 1000 or 500 in order to check the effect of reducing the genomic information. These individuals were selected by considering the highest relationship with the 1006 ungenotyped individuals from the operational list to reduce the loss of genomic information. Three different values were obtained for the operational section of Conversion of genomic relationships into pedigree-based coefficients for animals of the operational list provided the following results: shift factor Parameter Figure mentclass2pt{minimThe mean value of the difference of relationships based on The analytic expressions of the relationship matrix lgorithm , is possIn spite of the above-mentioned methodological improvements, computing estimated genomic relationship coefficients when needed is quite demanding in terms of memory requirements and computation time. Although this does not pose a problem for national genetic evaluations, this might be a hurdle for some breeding companies that use local personal computers. First, all the genotyped individuals should be accounted for, even if they are little related or unrelated with the ungenotyped individuals under consideration (a fact confirmed by the study on the Alpine breed). This unfavorable finding can be puzzling at first sight but is quite natural because pedigree founders  exhibit substantial genomic relationships (the Converting genomic coefficients into pedigree-based coefficients, ideally through formulas that are established before starting genomic selection, was proposed and tested on the Alpine data. This might help breeders to really implement genomic management in parallel with genomic selection, a mind attitude imperiously needed . In partWe presented efficient computation methods of products


Julia. Software and detailed documentation are freely available at https://github.com/JingZhai63/VCselection.High-throughput sequencing technology has enabled population-based studies of the role of the human microbiome in disease etiology and exposure response. Microbiome data are summarized as counts or composition of the bacterial taxa at different taxonomic levels. An important problem is to identify the bacterial taxa that are associated with a response. One method is to test the association of specific taxon with phenotypes in a linear mixed effect model, which incorporates phylogenetic information among bacterial communities. Another type of approaches consider all taxa in a joint model and achieves selection via penalization method, which ignores phylogenetic information. In this paper, we consider regression analysis by treating bacterial taxa at different level as multiple random effects. For each taxon, a kernel matrix is calculated based on distance measures in the phylogenetic tree and acts as one variance component in the joint model. Then taxonomic selection is achieved by the lasso (least absolute shrinkage and selection operator) penalty on variance components. Our method integrates biological information into the variable selection problem and greatly improves selection accuracies. Simulation studies demonstrate the superiority of our methods versus existing methods, for example, group-lasso. Finally, we apply our method to a longitudinal microbiome study of Human Immunodeficiency Virus (HIV) infected patients. We implement our method using the high performance computing language  The advent of high-throughput sequencing technologies has produced extensive microbial community data, which reveals the impact of human microbes on health and various diseases Mardis, . Microbi1 regularization. Another possible strategy to overcome the sparsity of microbial data is to cluster multiple OTUs into their higher phylogenetic levels, e.g., genus, order, and phylum. Shi et al. : groups of sequences that correspond to taxonomic clusters or monophyletic groups  is the subject-specific random effects. L is the total number of microbiome taxonomic clusters, N is the total number of individuals and hl is the random effects generated by microbiome taxa l with covariance Kl is a positive-definite kernel matrix derived from a distance matrix that is calculated based on the OTU abundances of taxa in the phylogenetic tree. Two common distance matrices are UniFrac Distance . We incorporate the phylogenetic tree information by using kernel matrices. We reduce the dimensionality of large and very sparse OTU abundances within a cluster by translating them into a random effect. Furthermore, our method can be applied to a longitudinal design, where an unpenalized variance component that captures the correlation of repeated measurements is included. Our Majorization-Minimization (MM) algorithm for variance component selection guarantees estimation and selection computational efficiency  with model parameters whereβ and σ2 by minimizing the lasso penalized log-likelihood functionFor the selection of non-zero variance components among a large number of variance components, we estimate the regression parameter i ≥ 0. The first part −L of the penalized function (Equation 4) is the negative log-likelihood defined in Equation (3). The second part is the lasso penalty to enforce shrinkage of high-dimensional components. We do not penalize fixed effects β. λ is the tuning parameter controlling model complexity; ci ∈ {0, 1} allows differential shrinkage of specific variance components. For example, when modeling longitudinal phenotypes with random intercept model, the corresponding variance component is unpenalized and always stays in the model. ci can be chosen using different weighting schemes based on prior knowledge such as functional annotations.subject to nonnegativity constraint σβ and variance components σ2. We follow the same strategy to solve the lasso penalized likelihood estimation problem (Algorithm 1).Minimizing the penalized negative log-likelihood is challenging due to non-convexity. Based on the Majorization-Minimization (MM) algorithm 2−( represents the tth-step update of V−1. Given βt), where θ = , the majorization step operates by creating a surrogate function g(θ|θt) that satisfies two conditionswhere θt+1)(. Then we haveThe second M of the MM principle minimizes the surrogate function to produce the next iterate f(θ) is driven downhill. We combine two following majorizations to construct the surrogate function. First, with all Vi being positive semidefinite, Zhou et al. 2 of pl is obtained by combining Equations (6) and (7)which separates st)( is an irrelevant constant term.where g(σ2|σt)2 to zero. The update We minimize the surrogate function (Equation 8) by setting the derivative of or 0, whichever yields the largest objective value. The alternating updates repeat untiltol is the pre-specified tolerance. The default tolerance is 10−4.where g-Measure is an indicator of the model selection accuracy. g-Measure = 1 indicates the best accuracy and g-Measure = 0 the worst  and specificity (true negative rate) alone  of the 31 clusters are computed and converted to kernel matrices asGiven simulated microbiome count data and taxonomic information, we classify 2,353 of 2,964 OTUs to 30 genera (taxa clusters) and the remaining 611 of 2,964 OTUs are grouped into the 31st cluster named K are scaled to have unit Frobenius norm.followed by a positive definiteness correction  with different numbers of non-zero variance components. In Supplementary Material section The sample size is fixed at prevolleta and veillonella.2 non-zero variance components: l = 1, 2, …, 5 and Anaerococcus, Atopobium, Actinomyces, Campylobacter, and Capnocytophaga.5 non-zero variance components: l = 1, 2, …, 15 and Actinomyces, Anaerococcus, …, and Neisseria are listed in Table 15 non-zero variance components: n = 50 with 5 non-zero variance components. We compare the selection performance using kernels defined by 5 different distance measures: variance adjusted weighted UniFrac distance (KVAW) Chang et al., K0, K0.5)    in all 4 scenarios for cross-sectional design because the gglasso package cannot handle longitudinal data.We applied VC-lasso to scenarios 1-3 using both longitudinal and cross-sectional designs. Scenario 4 is performed using a cross-sectional design only. We compare our approach with group-lasso  and testing (20%). Five-fold cross-validation is performed in training set to estimate the optimal λ*. Selection performance is evaluated and reported by applying λ* to the testing set.We set the within-individual variance The simulation results are summarized in Figures g-Measure versus tuning parameter λ from cross-validation is presented in Figure g-Measures remain stable or slightly decrease as λ getting larger under moderate effect size when The trajectories of g-Measure) and prediction . In Figure g-Measure of VC-lasso under different sample sizes using a longitudinal design. For both cross-sectional and longitudinal designs, g-Measure of VC-lasso boosts with increased sample size and effect sizes. Except for the third quartile of g-Measure over 1,000 replicates for sample size, n = 20, VC-lasso always outperforms group-lasso in this scenario.Figures n = 50 has similar AUROC with n = 100, which indicates the optimal prediction we can receive under this simulation setting. The AUROC of group-lasso (red bar) is similar under different sample sizes and shows no advantages compared to the VC-lasso.Area under receiver operating characteristic (AUROC) is used to evaluate the prediction performance Figure  when effg-Measure for both VC-lasso and group-lasso in a cross-sectional design, while Figure g-Measure for VC-lasso in a longitudinal design.Figures g-Measure , both methods do not perform well  fluid were collected for microbiome profiling. The inclusion criterion for this cohort were: (1) HIV infection and (2) CD4 count less than 500 * by AIC and BIC.Twigg III et al.  comparedp-values from exact tests, i.e., score test (eScore), likelihood ratio test (eLRT), and restricted likelihood ratio test (eRLRT) , Prevotella (p = 0.01), and Porphyromonas (p < 0.01). Using baseline data, we identify five genera associated with FEV1, among which Corynebacterium and TM7 genera incertae sedis are also selected by using longitudinal data. Several selected genera received insufficient attention in HIV-infected populations previously, for example, Anaerococcus and Megasphaera. Studies have shown that Anaerococcus became more abundant in children with asthma after azithromycin treatment , four of them show significant association with FEF , i.e., Prevotella, Rothia, Campylobacter and TM7_genera_incertae_sedis. Twigg III et al.  and uBiome (https://ubiome.com/). Selection for higher-order interactions with random effect, such as microbiome and treatment regime interactions (Gopalakrishnan et al., The VC-lasso is not limited to random intercept model for longitudinal studies. More complex random effect models, such as random intercept and random slope model, can also be used. More generally, the extension of our method to multivariate responses is expected to have better prediction performances. In the precision medicine era, with the rapid development of sequencing techniques and decreasing costs, the personal microbiome sequencing is already available to the consumer, e.g., American Gut (1 and ℓ2 regularizations (Jacob et al., In practice, knowledge is needed about which taxonomy level should be aimed at to develop strategies for intervention. Considering multiple level taxonomic data, one can extend VC-lasso to include tree topologies (Wang and Zhao, JZ implemented method and carried out data analysis. JZ wrote the manuscript with support from JK, HZ, and JJZ. HZ helped supervise the project. HT and KK provided pulmonary microbiome data. JJZ supervised the project.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.


BS00022896_51-2ATT, BobWhite_c10539_201-2DAA, Excalibur_c73633_120-3BGG, and Kukri_c35508_426-7DTT were significantly associated with KNPS in all environments. Our findings demonstrate the effective integration of association mapping and linkage analysis for KNPS, and underpin KNPS as a target trait for marker-assisted selection and genetic fine mapping.Kernel number per spike (KNPS) in wheat is a key factor that limits yield improvement. In this study, we genotyped a set of 264 cultivars, and a RIL population derived from the cross Yangmai 13/C615 using the 90 K wheat iSelect SNP array. We detected 62 significantly associated signals for KNPS at 47 single nucleotide polymorphism (SNP) loci through genome-wide association analysis of data obtained from multiple environments. These loci were on 19 chromosomes, and the phenotypic variation attributable to each one ranged from 1.53 to 39.52%. Twelve (25.53%) of the loci were also significantly associated with KNPS in the RIL population grown in multiple environments. For example,  Yield improvement is an on-going endeavor in wheat breeding. Wheat yield is determined by spike number per unit area, kernel number per spike (KNPS) and thousand kernel weight. Increased yield mainly depends on increased KNPS when the other two parameters are unchanged  were detected simultaneously in multiple environments. Through genome-wide association analyses, Zanke et al.  markers have been extensively adopted due to their high density, representativeness, stable inheritance, and capability of automatic detection ] introduced from the International Maize and Wheat Improvement Center (CIMMYT), Mexico. The average KNPS for Yangmai 13 exceeds that of C615 . The mean KNPS was computed by a best linear unbiased predictor (BLUP) method . SNP loci at frequencies lower than 0.05 were not considered, the threshold P of association signals was set as the 1/SNP marker number , or namely P < 4.99 × 10−5, −Log P > 4.30. The genetic effects of favorable alleles at associated loci in the cultivar set, and in the RIL population were tested via ANOVA on SPSS 21.0.Genetic diversity of SNP markers was analyzed on PowerMarker 3.25  for cultivars, compared to 0.513 and 0.833 (P < 0.001) for the RIL population  and best linear unbiased predictions (BLUP) indicated coefficients of variation of KNPS data in the range 9.58–14.84%. Between-environment correlation coefficients for KNPS varied between 0.521 and 0.874  varied from 0.500 to 0.998 (mean 0.785), polymorphism information content (PIC) varied between 0.004 and 0.375 (mean 0.238), and gene diversity varied between 0.004 and 0.500  and between-individual relationship coefficient  of the cultivar population were determined. The population divided into two subpopulations Figure , and ΔK P < 4.99 × 10−5). The associated loci were distributed across all chromosomes except 1D and 4D, and the explained phenotypic variation (R2) ranging from 1.53–39.52% , BobWhite_c10539_201 (2D), Excalibur_c73633_120 (3B), BS00063906_51 (6B), and GENE-4456_153 (7B) were significantly associated with KNPS in two or more environments  and was detected in all environments . In particular, four favorable alleles, BS00022896_51-2ATT, BobWhite_c10539_201-2DAA, Excalibur_c73633_120-3BGG, and Kukri_c35508_426-7DTT were significantly associated with KNPS in all environments. BS00022896_51-2ATT had a large genetic effect on KNPS  were polymorphic between Yangmai 13 and C615. Furthermore, the genetic effects of the favorable alleles in the cultivar population were analyzed by ANOVA in the RIL population. Twelve loci  were significantly correlated with KNPS in multiple environments  were significantly associated (P < 0.05) with KNPS in the RIL population grown in a different set of environments. In particular, BS00022896_51-2ATT, BobWhite_c10539_201-2DAA, Excalibur_c73633_120-3BGG, and Kukri_c35508_426-7DTT were significantly associated with KNPS in all conditions  were not validated in the RIL population. The main reason for this was the restricted bi-allelic polymorphism in a single segregating population. New strategies for combining linkage mapping and association analysis have been reported. For example, nested association mapping (NAM) is considered the most effective method to explain the genetic basis of quantitative traits for low-level LD species. NAM more effectively and economically scans at the genome-wide level, and helps to integrate molecular variation at the molecular level with that of complex phenotypic traits , QChl-A.caas-2AL.2 , and QChl-A.caas-2DS (BS00081578_51-tplb0021c10_951) affecting SPAD value of chlorophyll content at anthesis, respectively  coincided with spike length, QMd.ubo-7A.3 (IWB319-IWB23989) with days to maturity and QPh.ubo-7B (IWB10498-IWA7330) with plant height, respectively , 2B (2), 2D, 3B, 4A, 7A, and 7B, respectively. The SNPs 8 RIL population developed from Zhou 8425B/Chinese Spring and detected 11 KNPS QTLs distributed in chromosomes 1B, 2A, 2B, 2D, 3A, 3B, 4A, 4B, 6B, and 7B. Three loci, QKNS.caas-4AL (Kukri_rep_c106490_583-RAC875_c29282_566), QKNS.caas-3AL (RAC875_c61934_186-wsnp_Ex_c45877_51547406), and QKNS.caas-3B (RAC875_c10909_1180-BobWhite_c22016_155) were detected in multiple environments. In the present study five associated loci BS00022896_51 (2A), BobWhite_c10539_201 (2D), Excalibur_c73633_120 (3B), BS00063906_51 (6B), and GENE-4456_153 (7B) were significantly associated with KNPS in two or more environments (Table BS00022896_51-2ATT, BobWhite_c10539_201-2DAA, Excalibur_c73633_120-3BGG, BS00063906_51-6BGG, and GENE-4456_153-7BTT in the analyzed population were 64.82, 70.45, 92.82, 50.00, and 41.29%, respectively (Table Breeding is a process of combining favorable alleles (Ge et al., Conceived and designed the experiments: JG, PG, and SC. Performed the experiments: WS, YZ, and JC. Analyzed the data: JG and WS. Contributed reagents/materials/analysis tools: XY, JL, ZZ, XC, YX, DS, and XZ. Wrote the manuscript: JG, WS, and CH.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.