Traditional evaluation of crop biotic and abiotic stresses are time-consuming and labor-intensive limiting the ability to dissect the genetic basis of quantitative traits. A machine learning (ML)-enabled image-phenotyping pipeline for the genetic studies of abiotic stress iron deficiency chlorosis (IDC) of soybean is reported. IDC classification and severity for an association panel of 461 diverse plant-introduction accessions was evaluated using an end-to-end phenotyping workflow. The workflow consisted of a multi-stage procedure including: (1) optimized protocols for consistent image capture across plant canopies, (2) canopy identification and registration from cluttered backgrounds, (3) extraction of domain expert informed features from the processed images to accurately represent IDC expression, and (4) supervised ML-based classifiers that linked the automatically extracted features with expert-rating equivalent IDC scores. ML-generated phenotypic data were subsequently utilized for the genome-wide association study and genomic prediction. The results illustrate the reliability and advantage of ML-enabled image-phenotyping pipeline by identifying previously reported locus and a novel locus harboring a gene homolog involved in iron acquisition. This study demonstrates a promising path for integrating the phenotyping pipeline into genomic prediction, and provides a systematic framework enabling robust and quicker phenotyping through ground-based systems. Ferrous iron is soluble in soils but is readily oxidized by atmospheric oxygen3+. Generally, graminaceous species secrete phytosiderophores (PS) and transport Fe3+ into the roots in an Fe-PS complex, and non-graminaceous plants reduce Fe3+ through membrane-bound reductases before being transported by a Fe2+ transporterIron (Fe) is an essential nutrient for a plant’s survival and propagation. It is involved in many important biological processes in plants including photosynthesis and respiration. Iron exists in soil in ferrous Fe+ and ferferric Fe+ forms. Glycine max (L.) Merr.] grown in the upper Midwestern United States (US) where calcareous soil is prevalentIron deficiency chlorosis (IDC) is an important yield-limiting factor of soybeans . Hierarchical classification, which is a supervised learning approach, was used to map these quantitative visual measures to the visually rated IDC severity to construct an automated IDC classifier. FVR was the label used for classification, and the vector , representing the fraction of canopy area exhibiting necrosis and chlorosis, served as the input. The dataset  was randomly divided into two sets: the training dataset (75%) and the testing dataset (25%). We calculated three measures of classifier accuracy: (a) overall accuracy, (b) per-class accuracy, and (c) average per-class accuracy .Several classifiers including random forests, decision trees, support vector machines were tested. A hierarchical multilevel linear support vector machine (SVM) was the best classifier. In the first level, an SVM-based classifier separates the data into low, medium, and high susceptibility groups based on their yellow and brown percentages. In the second level, SVM is again deployed to further classify the susceptibility groups into score 1 or 2 (for the low susceptibility group), and score 4 or 5 (for the high susceptibility group). A flowchart of the hierarchical classification process is illustrated in Following this, a quantitative severity function is constructed that maps the vector  to a single number between 0 and 100. Here, 0 indicates no IDC symptoms, while 100 indicates substantial necrosis. A lower IDC score has correspondingly low values of the severity function while high IDC scores have high values of the severity function. Within an IDC rating class, specimens with higher necrosis (and chlorosis) have higher values of severity function. Severity mapping was formulated as a weighted linear combination of the components of the vector  because on error .http://soybase.org/). A total of 42,509 SNPs were identified. Among them, 60 unanchored SNPs were excluded from further analysis resulting in a dataset with a 0.5% missing rate. SNPs with a missing rate > 10% were ruled out. The remaining missing data were imputed using BEAGLE version 3.3.1 with default parameter settings34A total 465 of the 473 PIs was genotyped using the Illumina Infinium SoySNP50K BeadChip in a previous studyThe V5-V6 growth stage and the time point 3 (two weeks post V5-V6) had similar variation of FVR (score 1–5) but larger than that of the V2-V3 stage (score 1–4). However, soil pH values and SPAD measurements were collected at V5-V6 but not time point 3. Consequently, the ML-score and ML-severity of V5-V6 growth stage were further applied to genome-wide studies. Due to phenotypic data missing, 461 of the 465 genotyped PIs were involved in further study. The best linear unbiased predictions (BLUPs) of the trait breeding value of each line over four replications were calculated using the R package, lme43638The mixed linear model (MLM) equation was:N × 1 vector of the IDC trait BLUPs, N is the number of lines, μ is the overall mean, X is the marker genotypic matrix relating the individuals to the fixed marker effects α, P is the incidence matrix relating the individuals to the fixed principal component effects β based on the entire SNP dataset. In the present study, however, the model fitness test using Bayesian information criteria suggested no PC to be involved into the association analysis. Z is the incidence matrix relating the individuals to the random group effects u. The random group effect, u, follows a multivariate normal distribution with a mean of 0 and a variance-covariance matrix of 2KVg, where K is the kinship matrix using the entire SNP dataset, and Vg is the genetic variance component. The random error term, e, follows a multivariate normal distribution with a mean of 0 and the variance-covariance matrix, IVe, where I is the identity matrix, and Ve is the error variance component. The significance threshold for SNP trait associations was determined by a false discovery rate (FDR) <0.05. The Bayesian Information Criteria model fitness test suggested that no principal component should be included in the MLM. To determine the trait-associated loci, all significant SNPs located in close physical proximity were clumped at pairwise linkage disequilibrium (LD) values of r2 > 0.20. Only the strongest trait-associated SNP (or peak SNP) within each LD block was kept.where y is an Genomic predictions for ML-score and ML-severity were conducted by modeling the GWA-identified loci and SPAD measurements as having fixed effects and the genome-wide markers as having random effects with the ridge regression best linear unbiased prediction (RR-BLUP) approach. The RR-BLUP was performed using the rrBLUP package in the R programing language as described by Endelman (2011)y is a vector of the IDC trait BLUPs, X is a design matrix for the fixed effects β, Z is the marker genotypic matrix for the random marker effects (Var[u] = K is the identity matrix in the present study), and e is the residual error with Var[e] = r) between the IDC trait BLUPs and the genomic-predicted values.where How to cite this article: Zhang, J. et al. Computer vision and machine learning for robust phenotyping in genome-wide studies. Sci. Rep.7, 44048; doi: 10.1038/srep44048 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Mendelian randomization studies are often performed in an instrumental variables framework, using germline genetic variants as instruments for modifiable disease risk factors or exposures.,,Summary data Mendelian randomization refers to methods which use summary-level instrument-exposure and instrument-outcome association results  to obtain causal effect estimates. Two-sample Mendelian randomization refers to the application of Mendelian randomization methods to summary association results estimated in non-overlapping sets of individuals. These data can be obtained from the published literature, typically from summary results provided by consortia of genome-wide association studies (GWAS), or estimated directly from individual-level participant data.,Whereas the first formal extended elucidation of Mendelian randomization contained what are in essence two-sample Mendelian randomization estimates ,Even though the most natural application of summary data Mendelian randomization methods is in the two-sample setting , it is possible in principle to use summary data methods in the one-sample context – i.e. when instrument-exposure and instrument-outcome associations are estimated in the same sample. However, summary data Mendelian randomization analyses using instrument-exposure and instrument-outcome associations in the same sample or in partially overlapping samples may be prone to weak instrument bias towards the exposure-outcome estimate that would obtained using conventional methods . Therefore, using instrument-exposure and instrument-outcome associations estimated in non-overlapping samples is preferable.IJE, the general issue of data harmonization is discussed.In a paper recently published in the P < 5.0 × 10-8) – hereafter referred to as dataset 1 – are normally extracted from published papers or a web repository.Based on the research question, researchers will identify (often multiple) genetic variants associated with an adequate exposure phenotype. For example, if interest lies in studying the causal effects of adiposity measures on a given outcome, then one could use as instruments genetic variants identified in GWAS of anthropometric traits such as body mass indexCRP gene region to evaluate the causal effect of CRP on CHD risk using Mendelian randomization.CRP gene region).Although the focus of this paper is on genetic instruments selected based on a GWAS of the exposure phenotype, it is possible that instruments are selected using other criteria. For example, genetic instruments may be selected based on results of functional studies of gene expression regulation or limited to variants located within the gene of interest. For example, the C Reactive Protein (CRP) Coronary Heart Disease (CHD) Genetics Collaboration selected four genetic variants in the r² or D’) are not informative regarding the direction of the correlation between the effect alleles of the target and LD proxy variants. Measures of correlation that are informative of direction (and therefore of phasing), such as Pearson’s correlation, can be estimated for example using publicly available reference panels, such as data from the 1000 Genomes Project for the relevant ancestry group. Of course, a strong positive correlation that is less than 1  only implies that the effect alleles of the target and the LD proxy variants are typically in phase, but not always (due to recombination events).Extract – typically from a web repository – summary-level instrument-outcome associations (dataset 2). For example, if the outcome is educational attainment, then one could obtain instrument-outcome associations between each adiposity-associated variant and educational attainment from the educational attainment GWAS.Ensure that all variants in dataset 1 are associated with the exposure in the same direction, typically positive . Such standardization is important for two main reasons: (i) it is required when applying a recently-developed summary data Mendelian randomization method called MR-EggerEnsuring that datasets 1 and 2 are identically coded regarding effect (e.g. exposure increasing) and other alleles. For example, if a given instrument has A as the effect allele and C as the other allele in dataset 1, then one must ensure that this same instrument is coded as having A and C as the effect and other alleles, respectively, in dataset 2. Ensuring that both datasets are coded from the same strand is very important to reduce issues with palindromic variants  and an exposure GWAS is only being used to obtain precise estimates of the instrument-exposure association, it is possible that the genetic instruments are missing from the exposure GWAS, and it may be necessary to replace them with LD proxies. Another step, related to but not actually part of the data harmonization process per se, is to adjust the scale of the causal effect estimate. For example, Ference and colleagues wanted to evaluate the causal effect of a 10-mmHg reduction in systolic blood pressure (exposure) on CHD (outcome).The final step would be to undertake quality control checks. One useful check is to compare  datasets 1 and 2, before and after harmonization, regarding effect allele frequency. If case-control data were used to generate the dataset, it is preferable to use effect allele frequencies estimated in controls only. In There might be problems in each step of the data harmonization process. These include: lack of standardization of the direction of the instrument-exposure association; selection of poor LD proxies for missing variants; using negatively, rather than positively, correlated alleles as correspondent between the target SNP and the LD proxy ; lack of allele harmonization between datasets; different genetic variants  between datasets ; and typographical errors introduced along the process .Another potential problem in data harmonization is strand issues – i.e. when the effect and other alleles in dataset 1 were defined based on the forward (5’→3’) DNA strand, but on the reverse (3’→5’) strand in dataset 2, or vice versa . TherefoIt is increasingly common in GWAS to perform imputation  using genetic datasets . Since choosing the effect allele is often an arbitrary decision, it is possible that effect allele coding differs between instrument-exposure and instrument-outcome datasets. Let us assume that this happened to our genetic variant of interest, so that the instrument-exposure association was estimated with C as the effect allele, but A was the effect allele in the instrument-outcome association. Let ,P < 5.0 × 10-8) in a GWAS on more than 80 000 individuals,Two recently published two-sample Mendelian randomization studies that evaluated the causal effect of CRP levels (exposure) on schizophrenia risk (outcome)https://www.med.unc.edu/pgc/files/resultfiles/scz2.snp.results.txt.gz]. This dataset was reduced to only the 18 variants associated with CRP (P < 5.0 × 10-8) (dataset 2). Both datasets were sorted according to rs numbers. All variants were identified as having the same allele pairs between datasets. Finally, we checked whether the effect  alleles matched in datasets 1 and 2. They did not: 11 out of 18 variants had different effect alleles. We harmonized the effect alleles in the two datasets, (and the corresponding regression coefficients) using the CRP-increasing alleles as the reference. Applying the inverse variance weighting (IVW) methodTo investigate this, we extracted regression coefficients, standard errors and effect alleles of all 18 CRP-associated single nucleotide polymorphisms (SNPs) identified in the CRP GWAS from the paper (i.e. dataset 1).IJE online. However, as can be seen in these Tables, 13 of the SNPs are identical across all three analysis sets, and the two proxies that Prins et al. use are attempting to tag the same associations at the SNPs that they proxy for, both of which were included in Inoshita’s analysis. Thus, Inoshita and colleagues and Prins and colleagues are using highly overlapping sets of genetic instrumental variables for CRP. Indeed, our analysis limiting to the SNPs used in the Prins’ and Inoshita’s studies showed that such differences in variants had almost no influence on the results.To explore the reason for these differences, we compared our harmonized datasets with the datasets provided in Prins’ and Inoshita’s publications. In our analyses using the same two datasets as both Inoshita and colleagues and Prins and colleagues, we found that all 18 of the SNPs that were genome-wide associated with CRP (dataset 1) were available in the schizophrenia GWAS (dataset 2), with no need for proxies, so we used all 18 (see previous paragraph). Inoshita and colleagues removed three of these 18 SNPs from their analyses because, although they were genome-wide significant in the combined discovery and replication sample meta-analyses, they were not in the discovery-only meta-analysis, and the authors had a priori decided that they wanted genome-wide significant variants in both discovery and combined samples. Prins and colleagues reported that five of the 18 CRP genome-wide significant SNPs were not in the schizophrenia GWAS dataset ; they found proxies (in tight LD) with two of these but did not include the other three. This means that somewhat different SNPs are used in the three analyses  — see The instrument-CRP coefficients and standard errors in our and Inoshita’s dataset 1 were perfectly positively correlated. This indicates that effect and other alleles (not explicitly provided in Inoshita’s publication) were the same. However, when we compared our dataset 2 after harmonization with Inoshita’s, the correlations between the ln(odds ratios) were -0.82, and the correlations between the standard errors were 0.59. We then compared Inoshita’s dataset 2 with the raw schizophrenia dataset from the PGC. In this comparison, the correlation between the ln(odds ratio) was 0.94, indicating that many variants in Inoshita’s dataset 2 were coded as in the raw PGC dataset. This was suggestive of lack of harmonization between Inoshita’s datasets 1 and 2, because (as discussed above) it was necessary to flip some of the variants in the PGC dataset so that the effect allele was the CRP-increasing allele. Moreover, the correlation between standard errors of 0.59, possibly suggests a typographical error in Inoshita’s dataset 2, since the correlation between standard errors should be 1 even if there are issues with allele harmonization. After graphical inspection, we found that the coefficients and standard errors between Inoshita’s and the raw PGC instrument-schizophrenia datasets were identical aside from the single variant rs4129267. This variant had odds ratio [ln(odds ratio) standard error] of 1.026 (0.012) and 0.990 (0.042) per CRP-decreasing allele in the raw PGC and in Inoshita’s datasets , respectively. We do not know why this difference exists; it might be due to a typographical error because even the standard errors were different. Since all other variants in Inoshita’s dataset 2 were coded as in the raw PGC dataset, we assigned to the rs4129267 variant the same effect and other alleles as in the raw PGC dataset.Therefore, there were two errors in Inoshita’s dataset 2: (i) lack of allele harmonization between datasets 1 and 2, which resulted in some of the effect alleles in dataset 2 not corresponding to CRP-increasing alleles; and (ii) possibly a typographical error regarding variant rs4129267. Applying the IVW method to Inoshita’s datasets, as provided in their publication, yielded an odds ratio of 1.08  per 1-unit increment in ln(CRP). After excluding the rs4129267 variant, the odds ratio was 1.09 . After proper harmonization , the odds ratio was 0.87 . We also re-did our analysis using pre-harmonization datasets, and the resulting odds ratio was 1.09 . These results indicate that the differences between our and Inoshita’s results were largely due to lack of allele harmonization between datasets 1 and 2 rather than to differences in methods to compute the causal effect estimate or the typographical error.None of the issues above were detected in Prins’ dataset 2. When applying the IVW to their pre-harmonization datasets, the odds ratio was 1.10 . When using post-harmonization datasets, the odds ratio was 0.87  . All results are shown in Effect allele mismatches can lead to bias in the causal effect estimate in the opposite direction. Although this would not be a problem when the true causal effect is zero, the estimates can be biased if the true causal effect is non-zero. The size of this bias will depend on the proportion of effect allele mismatches and their weight in the causal effect estimate. For example, the bias may just attenuate the causal effect estimate when only a few genetic instruments present effect allele mismatches. However, when most of the instruments or the strongest variants are mismatched, the bias may be strong enough to reverse the causal effect estimate .www.r-project.org] that can be used to harmonize summary-level datasets of genetic associations as IJE online) and on GitHub [https://github.com/FernandoHartwig/GenEpi_R_Scripts]. There are others scripts available that aid with harmonization and other steps of two-sample Mendelian randomization analyses, such as those in the TwoSampleMR package [https://github.com/MRCIEU/TwoSampleMR], which is used in the recently developed web database and analysis platform called MR-Base [http://www.mrbase.org/].Data harmonization has been only briefly discussed in Mendelian randomization guidelines published to date.Providing both the original and harmonized datasets and describing the harmonization process with enough information for reproducibility will likely minimize the chance that errors in data harmonization are distorting two-sample Mendelian randomization findings. The process of data harmonization should be included when publishing or sharing the analysis code. This practice would also assist reviewers (who should ask for and check harmonized datasets) in assessing whether or not the harmonization has been done correctly. Data harmonization is clearly essential for accurate two-sample Mendelian randomization analyses and should be carefully performed and clearly reported.Two-sample Mendelian randomization studies are analogous to literature-based meta-analyses, in that they can be performed using publicly available data and can be used to produce publishable papers – receiving consequent academic reward in the absence of any primary data collection or indeed expertise in the field under investigation. In the field of meta-analysis, the corruption of the scientific literature that can occur in this situation has been well documented.IJE online.The Medical Research Council (MRC) and the University of Bristol fund the MRC Integrative Epidemiology Unit . N.M.D. is supported by the Economics and Social Research Council (ESRC) via a Future Research Leaders Fellowship [ES/N000757/1].Supplementary DataClick here for additional data file.


In these analyses, we were able to identify and replicate a few broad impact eQTL although the overall number was small even when applying CONFETI. In light of these results, we discuss the broad impact eQTL that have been previously reported from the analysis of human data and suggest that considerable caution should be exercised when making biological inferences based on these reported eQTL.Genome-wide expression Quantitative Trait Loci (eQTL) studies in humans have provided numerous insights into the genetics of both gene expression and complex diseases. While the majority of eQTL identified in genome-wide analyses impact a single gene, eQTL that impact many genes are particularly valuable for network modeling and disease analysis. To enable the identification of such broad impact eQTL, we introduce CONFETI: Confounding Factor Estimation Through Independent component analysis. CONFETI is designed to address two conflicting issues when searching for broad impact eQTL: the need to account for non-genetic confounding factors that can lower the power of the analysis or produce broad impact eQTL false positives, and the tendency of methods that account for confounding factors to model broad impact eQTL as non-genetic variation. The key advance of the CONFETI framework is the use of Independent Component Analysis (ICA) to identify variation likely caused by broad impact eQTL when constructing the sample covariance matrix used for the random effect in a mixed model. We show that CONFETI has better performance than other mixed model confounding factor methods when considering broad impact eQTL recovery from synthetic data. We also used the CONFETI framework and these same confounding factor methods to identify eQTL that replicate between matched twin pair datasets in the Multiple Tissue Human Expression Resource (MuTHER), the Depression Genes Networks study (DGN), the Netherlands Study of Depression and Anxiety (NESDA), and multiple tissue types in the Genotype-Tissue Expression (GTEx) consortium. These analyses identified both  The discovery of expression Quantitative Trait Loci (eQTL) from the analysis of genome-wide genotype and gene expression data has played an important role in the study of cellular processes and complex disease. Here, we introduce CONFETI: Confounding Factor Estimation Through Independent component analysis, an analysis framework that has been designed to identify eQTL with broad impacts on the expression levels of many genes. The CONFETI framework takes advantage of Independent Component Analysis (ICA) to separate putative genetic and non-genetic factors in a confounding factor mixed model analysis, such that broad impact eQTL are not corrected out of the analysis as confounding variation. We show that CONFETI has better performance for identifying broad impact eQTL compared to the most widely applied confounding factor correction methods when applied to simulated data. We also applied CONFETI and these same methods to identify eQTL that replicate between twin pairs from the MuTHER consortium, the Depression Genes Networks study (DGN), the Netherlands Study of Depression and Anxiety (NESDA), and common tissue type pairs in the Genotype-Tissue Expression (GTEx) consortium. Surprisingly, while CONFETI had comparable replication performance compared to other methods, we were able to identify and replicate a very small number of broad impact eQTL overall. We discuss reports of broad impact eQTL in humans and suggest that they should be interpreted with caution. Suchans-eQTL , 17, 18,ans-eQTL , 20. Genans-eQTL , which ians-eQTL –26. Discans-eQTL –30. As aans-eQTL –51.trans-regulators [trans-eQTL networks [For studies that leverage eQTL as a foundation for network modeling or for identifying candidate disease risk loci, eQTL that are associated with multiple genes can be particularly valuable. For directed network modeling, the value of such broad impact eQTL is clear, since the network inference depends on tracking the impact of eQTL through multiple genes –56. Whengulators , and tranetworks  could renetworks , 62 or fnetworks . Broad inetworks –65 and mnetworks , but havnetworks .trans-genes, statistical power has been suggested as a possible reason for the relatively lower reporting of broad impact eQTL in humans, since trans-eQTL tend to have relatively weak associations in humans compared to model organisms [9 to 1010 for array based studies [11 to 1012 for data collected by next-generation sequencing technologies [trans-pairs [trans-associations at all [trans- compared to cis-eQTL genome-wide, making the identification of broad impact eQTL with multiple trans-gene effects almost impossible.Since broad impact eQTL are expected to primarily affect rganisms . Further studies  and 1011ns-pairs , 67, 68 s at all . A consecis- and trans-eQTL by increasing detection power [A promising analysis strategy that could partially alleviate the statistical difficulties in identifying broad impact eQTL is the use of confounding factor analysis . Confounon power , 77, a kon power , 79. Preon power , and usion power . HoweverIn this study, we describe a new framework that is designed to improve on the performance of confounding factor methods to identify broad impact eQTL. The CONFETI  framework makes use of the machine learning method Independent Component Analysis (ICA) to separate genetic components from non-genetic components learned from multivariate gene expression variation. ICA is a widely used blind source separation method applied to problems such as voice and image separation, and more recently to high dimensional gene expression data to estimate non-Gaussian generative sources from an observed mixture –84. CONFTo show the potential of CONFETI for the discovery of broad impact eQTL, we evaluated performance using simulated genome-wide data. For these simulated datasets, we show that the CONFETI framework successfully corrects for the effects of the confounding factors without explaining away broad impact eQTL. We also show that CONFETI has considerably increased performance compared to the most commonly applied confounding factor analysis methods.cis- and trans-eQTL. While we found that CONFETI had better or comparable performance to other methods in the replication of both cis- and trans-eQTL with individual gene impacts, after careful modeling and consideration of population structure, confounding factors, annotation inconsistencies, read alignment artifacts, and visual inspection of false positive indicators, we were able to identify only a few replicating broad impact eQTL at a genome-wide significance threshold in the MuTHER lymphoblastoid cell line (LCL) dataset. Taken together, these results suggest that robustly identifiable broad impact eQTL in humans have considerably smaller effects per gene than the bulk of eQTL. We discuss the implications of these results when considering factors such as sample size that can impact broad impact eQTL discovery, as well as for the use of previously reported broad impact eQTL as a foundation for making biological inferences.We then assessed the ability of the CONFETI framework and these other methods to identify and replicate eQTL between matched twin pair datasets in the Multiple Tissue Human Expression Resource (MuTHER) , betweenThe CONFETI framework is constructed to systematically avoid the tendency of other confounding factor analysis methods to model broad impact eQTL as confounding variation. This is accomplished by leveraging Independent Component Analysis (ICA) to identify generative sources of multivariate gene expression variation and then screening candidates based on component correlations with genotypes, which are then omitted from the confounding factor correction . ICA is g-dimensional vector of gene expression values for a single sample, and independent components g-dimensional vectors of gene weights that are shared among all samples and the scalar component coefficients aij represent the contribution of each independent component i  or any other factor analysis method , ICA is The complete CONFETI framework involves running ICA on multivariate gene expression data, an automated detection step to identify candidate broad impact eQTL by assessing associations with genotypes, and omission of these factors for the construction of the random effect sample covariance matrix used in a mixed model confounding factor analysis . While ttrans-eQTL by jointly estimating the covariance matrix with genotype effects to avoid including those effects in the correction [We note that our framework differs from ICA methods for eQTL detection that treat the identified ICs as meta-genes, where these methods cannot reliably distinguish the specific gene effects of individual eQTL , 93. Therrection . Howeverrrection , which thttps://github.com/jinhyunju/confeti). The independent component estimation features are using functions adopted from the fastICA R package [To apply ICA to gene expression data and generate a sample covariance matrix, we developed a custom R package  and all genotypes. As in fixed effect eQTL models, we fit a linear regression model with the IC coefficient as the dependent variable and the genotype values as independent variables. After calculating p-values for each IC coefficient and genotype pair, we identified candidate broad impact eQTL using a global Bonferroni corrected p-value threshold of 0.05. Components with at least one significant association are marked as candidate genetic components. After filtering out r (0 ≤ r < k) components with significant genotype association, we reconstruct expression matrix Y* originating from non-genetic factors using the remaining k − r components:Y* is an n × g matrix, A* is a n × (k − r) matrix and S* is a (k − r) × g matrix.After decomposing the observed data Given that the overall CONFETI method makes use of the phenotype and genotype data both in the filtering out of candidate genetic effects and in the identification of significant genotype-gene expression associations, using the full dataset could lead to model over-fitting impacts in the selection and removal of ICs. To assess this issue, we compared the approach of using CONFETI on the full dataset to a strategy where we split the genotype data into two random subsets. For the splitting strategy, we used one of the genotype subsets for filtering candidate genetic effects and the remaining genotypes for the eQTL analysis, we then repeated the analysis flipping the subsets that are used for filtering and eQTL analysis, and the combined the results. With this splitting strategy, genotypes used for the removal of candidate genetic effects do not overlap with the genotypes that are being tested for eQTL, such that each genotype is only accessed once in each subset.From the analysis of multiple datasets, we found that the results obtained by using the full dataset and the splitting strategy largely overlapped with only minor differences . A possiK for the random effect part of the mixed model. Our first approach was to use a simple location-scale normalization of each gene of Y*:We used two approaches to construct the sample covariance matrix analysis  by estimC is an n × Q matrix initialized by projecting the observed data onto the first Q principal components explaining 95% of the variance and is further optimized in the process, and θ is the set of hyperparameters consisting of qth column of C, Cq⋅ in constructing the sample covariance matrix:K.For our second approach, we couple CONFETI with PANAMA (Probabilistic ANAlysis of genoMic dAta)  that est package  for the p in n individuals are:n is the number of samples, g the number of genes, s the number of SNPs, and v the number of covariates. Each gene expression vector n × 1 and is mean centered. The n × (1 + v) genotype and covariate matrix X contains a single genotype as the number of minor alleles coded as 0,1,2 and any additional v number of covariates. v) × 1 dimensional coefficient vector representing the fixed effect of the SNPs and covariates on gene p. The confounding effect is included in the model as a n × 1 random effect K is the n × n sample covariance matrix constructed the corresponding confounding correction method, K in the random effect, and n × 1 vector representing the independent error for gene p with scalar weight We model the genetic effects from SNPs and covariates as fixed effects and confounding factor effects as random effects, such that the expression levels for gene K), which is kept constant when testing individual genotypes against phenotypes, to avoid the computational burden of recalculating K for every phenotype.We compared CONFETI-I and CONFETI-P to a simple linear regression with no confounding factor correction (LINEAR), including PCA projections as fixed effects (PCA), probabilistic estimation of expression residuals (PEER) , and mixlrgprApply function from the R package lrgpr [glmApply function from lrgpr and used a Wald test for significance testing.For each comparison of methods on simulated or real data, we ran each method to be as equivalent as possible, including the same covariates and using the same linear mixed model fitting function. For CONFETI-I, CONFETI-P, PANAMA, and ICE we used ge lrgpr  to fit tge lrgpr , the numcis- and trans-eQTL relationships. To simulate eQTL, a matrix with a dimension of number of genotypes × number of expression phenotypes was first created that marks genotype and phenotype pairs cis- if the starting position of the gene and the genotype were within 100,000 base pairs distance and trans- if the distance was greater. From this matrix we sampled 2500 genotype and phenotype pairs which consisted of 80% cis- and 20% trans-genotypes. In total, for each simulated dataset, we included 2000 cis-eQTL, 500 trans-eQTL, and 10 broad impact eQTL. We simulated each broad impact eQTL to affect 10% of the expression phenotypes. Effect sizes for cis-eQTL were sampled from trans-eQTL and broad impact eQTL were sampled from trans-effects) to reflect observed effect sizes in real data. After the eQTL effects were simulated, we added normally distributed random noise sampled from To mirror real cases where a reasonable number of broad impact eQTL have been repeatedly identified, we used yeast as a model –65. To ccis-, trans- or broad impact and the recovery rate for each category at different FDR thresholds was calculated by dividing the number of true genotype phenotype pairs that were called significant by the total number of true genotype phenotype pairs in each category. To provide an upper bound metric on how well methods could recover each of these eQTL types, we also simulated the same scenarios without any confounding factors and reported the ROC curves after running LINEAR. We labeled these results ‘TMR’ for ‘Theoretical Maximum Recovery’ since these represent the maximum recovery expected in theory if confounding factors were perfectly modeled by the confounding factor methods.We ran each of the methods CONFETI-I, CONFETI-P, PANAMA, ICE, PEER, PCA, and LINEAR on each of the 100 datasets using the method settings and parameters as described above. To evaluate performance for each method, we ranked the eQTL for each method according to their p-values and then calculated the True Positive Rate (TPR) and False Positive Rate (FPR) and generated Receiver Operating Characteristic (ROC) curves for each method, where we also calculated the area under the curve for each method across the simulation scenarios. True eQTL were further labeled as We analyzed data from the Multiple Tissue Human Expression Resource (MuTHER)  project,We ran eQTL analysis on the adipose, lymphoblastoid cell line (LCL), and skin datasets obtained through the MuTHER project . Based oWe also analyzed data from the DGN  and NESDr2 > 0.99 and removed SNPs which were deprecated in dbSNP .For the analysis of the GTEx datasets, we selected 4 pairs of tissues  from GTEx release v6 (dbGaP Accession phs000424.v6.p1) with over 150 samples that have both RNA-seq gene expression and SNP array genotypes . For genmp asp values for every gene to calculate λpdiff, = 1 − λp.We fit CONFETI-I, CONFETI-P, PANAMA, ICE, PEER, PCA, and LINEAR for every phenotype and genotype pair in each of the datasets using the method settings and parameters as described above. To control for population structure, we included principal components derived from the genotypes, using the first five , three , and two  principal components as covariates in each analysis. While a permutation approach is often applied to avoid any systematic inflation or deflation of the p-values, this was computationally infeasible for this study given the number of datasets analyzed and number of methods applied to each dataset. We therefore calculated the genomic inflation factor λ for each expression phenotype, a statistic which has been shown to provide a good metric for assessing model fit and appropriate p-value distributions , 72. Thecis- if the SNP and gene were located on the same chromosome within 1 Mb, and trans- otherwise.After calculating p-values for all phenotype and genotype pairs, we adjusted the p-values using Benjamini-Hochberg multiple hypothesis correction. The corrected p-values represent upper bounds on False Discovery Rate (FDR) . We usedtrans-eQTL using two methods. First, we used annotated gene relationships available from NCBI (ftp://ftp.ncbi.nih.gov/gene/DATA/gene_group.gz) to identify trans-eQTL where the SNP was within 1Mb of a gene related to the eQTL gene . Because not all gene relationships were captured in the NCBI annotation, we searched for additional, potentially unannotated pseudogenes using the BLAT tool [trans” screening revealed that a number of the replicating trans-eQTL were artifacts arising due to incorrect/ambiguous mapping of RNA-seq reads that are in fact caused by cis-regulation of a gene, which shares sequence similarity with the eQTL gene. We also visually inspected eQTL for artifact or false positive indicators .To avoid potential artifacts caused by ambiguous RNA-seq alignment we screened LAT tool  to aligncis- and trans- SNP per cytoband per gene. Using this criteria, we measured the replication of eQTL between and across different tissues counting the overlapping cytoband and gene pairs that were called significant in each dataset. We marked broad impact eQTL by searching for genotypes that showed more than a single trans-eQTL associations on different chromosomes that replicated between at least one twin or tissue pair.In order to avoid double-counting eQTL associated with multiple linked SNPs, we selected at most one significant cis-, trans- and broad impact, in the presence of confounding factors. We also included the theoretical maximum recovery (TMR) as an upper limit of eQTL detection for each eQTL category, where the phenotype data has only normally distributed random noise added without any confounding factor effects. For both sparse and dense confounding factor effects, all methods showed significant improvements over LINEAR (linear regression without confounding factor correction), and CONFETI-I correctly identified the most eQTL at every FDR threshold . The enrichment of regulatory signals in the LCL dataset on the region of chromosome 6 which rs3817963 is located is proximal to the major histocompatibility complex (MHC) region, which is critical in immune cell function. A cluster of replicating eQTL on the same region of chromosome 6 was also found in the Adipose and Skin twin pair, however, we only found replicating eQTL associated with genes on different chromosomes in the LCL dataset  to avoid over-correcting genetic effects in eQTL mixed model confounding factor analysis. CONFETI provides an easy to implement solution for a known problem with eQTL confounding factor methods: the tendency of these methods to model the effects of eQTL with broad impacts on many genes as confounding variation. In sum, the CONFETI approach provides a method for finding broad impact eQTL while leveraging the advantages of confounding factor analysis for eQTL discovery, a capability that has not been systematically implemented in currently available confounding factor analysis software.in vivo for MuTHER adipose and skin datasets, and the even great heterogeneity across distinct studies of DGN and NESDA, it seems likely that different levels of sampling heterogeneity are also influencing broad impact eQTL discovery.In our real data evaluation of CONFETI and other methods, we found that confounding factor correction methods, especially linear mixed model based methods, increased the findings of replicating eQTL. This was also the case for identifying broad impact eQTL that replicated at a genome-wide significance level between datasets. While we did not find any replicating broad impact eQTL for the GTEx tissue pairs, we did find a number of broad impact eQTL when analyzing the MuTHER LCL dataset. Given that broad impact eQTL appear to have relatively small per gene impacts and the larger sample size of MuTHER compared to the GTEx datasets we analyzed, this supports power, and therefore sample size, as being a critical issue when detecting broad impact eQTL. However, this is clearly not the only critical factor, since only one broad impact eQTL was identified by PEER in the MuTHER Adipose dataset, only one was identified by ICE in the Skin dataset, and no broad impact eQTL were identified when comparing results for the considerably larger DGN and NESDA studies. Given LCL are likely to allow a more controlled and homogeneous measurement of gene expression variation compared to the mixed cell populations sampled trans-eQTL compared to the FDR of less than 1% threshold used in our study. Small et al. narrowed down the targets to investigate by testing a single genotype rs4731702, which significantly lowered the multiple testing burden [−8 which corresponded to an FDR threshold of less than 10% in Grundberg et al. [trans associations are the most prone to statistical false positives, it seems reasonable to view these previous reports of broad impact eQTL with caution.We were not able to replicate a small number of broad impact eQTLs reported by previous studies in the MuTHER Adipose dataset , 61. Onetrans-eQTL seem less dispersed [In contrast to humans, broad impact eQTL have been easier to detect in model organisms and ispersed . Given tS1 FigThe components that had the strongest association with gender labels estimated by ICA (left) and PCA (right) for the Skin-Leg GTEx dataset . Gene we(PNG)Click here for additional data file.S2 Fig(A) The overlap of eQTL identified for the full dataset and splitting strategy. (B) Comparison of -log10 p-values for significant eQTL identified with the full dataset (x-axis) and splitting strategy (y-axis).This figure shows a typical result obtained when comparing CONFETI-I using the full dataset analysis to the splitting strategy. The MuTHER Adipose subset1 was analyzed using CONFETI-I with both strategies. A total of 2,633 hits were identified by both approaches and only 99 and 79 unique hits were identified for the splitting and full dataset analyses respectively. (PNG)Click here for additional data file.S3 Fig(A) The recovery rate of simulated cis- (left), trans- (middle) and broad impact eQTL (right) for a range of FDR significance thresholds for each method averaging over the 50 simulated datasets with a mix of dense and sparse confounding factors. The theoretical maximum recovery (TMR) shows the recovery when no confounding factors are included. (B) The Area Under the Curve (AUC) for the receiver operator characteristic (ROC) curves. (C) Box-plots of genomic inflation factors calculated for each method for each method across the 50 simulated datasets with a mix of sparse and dense factors.(PNG)Click here for additional data file.S4 Fig(A) MuTHER and (B) GTEx.Boxplots of the range of median λ genomic inflation factors calculated for each expression phenotype for each method in every dataset of (PNG)Click here for additional data file.S5 Figcis- and trans-eQTL versus FDR for each of the methods applied to every dataset.Plots showing the counts of (PNG)Click here for additional data file.S6 Figcis-eQTL and (Bottom) trans-eQTL in the DGN dataset and one of the two twin subsets of the NESDA study is shown for a range of FDR for all confounding factor correction methods.The number of identified (Top) (PNG)Click here for additional data file.S7 Figcis- and trans-eQTL versus FDR for each of the methods applied to every (A) MuTHER and (B) GTEx dataset.Plots showing the counts of replicating (PNG)Click here for additional data file.S8 Figcis-eQTL and trans-eQTL between the DGN dataset and two twin subsets of the NESDA study is shown for a range of FDR for all confounding factor correction methods.The number of replicating (PNG)Click here for additional data file.S9 Figcis- and trans-eQTL found by each method in the respective tissue types are ordered on the x-axis by the amount of overlap between methods. Colored bars corresponding to their method indicate that the particular eQTL replicated. The total numbers of replicating eQTL for each method is shown on at the end of each bar. Results are shown for (A) Adipose, (B) LCL, and (C) Skin twin pairs.Replicating (PNG)Click here for additional data file.S10 Figcis- and trans-eQTL found by each method in the respective tissue types are ordered on the x-axis by the amount of overlap between methods. Colored bars corresponding to their method indicate that the particular eQTL replicated. The total numbers of replicating eQTL for each method is shown on at the end of each bar. Results are shown for A. Adipose, B. Artery, C. Heart, and D. Skin tissue pairs.Replicating (PNG)Click here for additional data file.S11 Figcis-eQTL shown in gray bands within the next layer, and replicating trans-eQTL as blue bands in the innermost layer where red lines connect each trans-eQTL to the associated gene with gene annotations labeled in blue outside the circle. Replication shown for (A) Adipose, (B) LCL, (C) Skin twin pairs.Chromosomes are plotted in the outermost circles with replicating (PNG)Click here for additional data file.S12 Figcis-eQTL shown in gray bands within the next layer, and replicating trans-eQTL as blue bands in the innermost layer where red lines connect each trans-eQTL to the associated gene with gene annotations labeled in blue outside the circle. Replication after removal of pseudogenes are shown for (A) Adipose, (B) Artery, (C) Heart, and (D) Skin tissue pairs.Chromosomes are plotted in the outermost circles with replicating (PNG)Click here for additional data file.S1 Tablecis and trans-eQTL count and genes are shown for replicating broad impact eQTL.Detailed information about the dataset, significant SNP, method, (TXT)Click here for additional data file.S1 Text(PDF)Click here for additional data file.


Juglans cinerea L.), black walnut (J. nigra L.), and Japanese walnut (J. ailantifolia Carr. var. cordiformis) using vegetative characters and then with functional adaptive traits associated with seedling performance. When projected onto the progenitor trait space, naturally occurring hybrids (J. × bixbyi Rehd.) between butternut and Japanese walnut showed introgression toward Japanese walnut at vegetative characters but exhibited a hybrid swarm at functional traits. Both results indicate that hybrids have morphological and ecological phenotypes that distinguish them from butternut, demonstrating a lack of ecological equivalency that should not be carried into restoration breeding efforts. Despite these discrepancies, some hybrids were projected into the space occupied by butternut seedlings’ 95% confidence ellipse, signifying that some hybrids were similar at the measured traits. Determining how to consistently identify these individuals is imperative for future breeding and species restoration efforts involving hybrids. Discriminant analysis provides a useful technique to visualize past selection mechanisms and current variation in hybrid populations, especially when key ecological traits that distinguish progenitors are unknown. Furthermore, discriminant analysis affords a tool to assess ecological equivalency of hybrid populations and breeding program efforts to select for certain traits and monitor the amount of variability of those traits, relative to progenitors.Hybridization has been implicated as a driver of speciation, extinction, and invasiveness, but can also provide resistant breeding stock following epidemics. However, evaluating the appropriateness of hybrids for use in restoration programs is difficult. Past the F1 generation, the proportion of a progenitor’s genome can vary widely, as can the combinations of parental genomes. Detailed genetic analysis can reveal this information, but cannot expose phenotypic alterations due to heterosis, transgressive traits, or changes in metabolism or development. In addition, because evolution is often driven by extreme individuals, decisions based on phenotypic averages of hybrid classes may have unintended results. We demonstrate a strategy to evaluate hybrids for use in restoration by visualizing hybrid phenotypes across selected groups of traits relative to both progenitor species. Specifically, we used discriminant analysis to differentiate among butternut ( Naturally occurring hybridization between native and exotic species can dilute native gene pools and result in extinction, especially of rare species . HybridiGiven that hybrids exist, their functionality influences the degree to which they threaten native populations and is the major factor in determining their effects on ecosystem integrity. Depending on the interplay between the fitness contributions of genetic material from both progenitors relative to the selection environment, hybrids may (1) introgress toward one of the progenitor species or (2) persist as an intermediate group, as is the case with most natural hybrid zones . AlternaIdentifying which trajectory a hybrid population is currently on would provide important information to evaluate how serious a threat hybridization poses to rare species  and overHelianthus and Iris . The ability to simultaneously evaluate hybrids at multiple, often correlated traits is especially important, as fitness is not defined by a single character or by appearance per se, but rather by the interplay among traits that allow continued growth, survival, and most importantly, contributions to future generations.We present an application of multivariate discriminant analysis  to identFigure 1). Directional selection toward one progenitor would result in distinct clustering of hybrids from an intermediate point between progenitors to the progenitor with greater fitness . If both progenitors contribute equally to fitness (or if hybrids have greater fitness in an intermediate environment) the hybrid cluster will be maintained intermediate to progenitor clusters . If hybrid speciation has occurred, the cluster will also be distinct, but may occupy a separate area of the parameter space . Finally, if limited or no selection has occurred, or if F1 hybrid fitness facilitates the establishment of future hybrid generations . They may also occupy novel trait spaces. In each instance, the size and shape of the hybrid cluster will depend upon the strength of the fitness component and the strength and direction of selection. The demography of progenitor populations, the number of hybrid generations in coexistence and their fecundity can mask selection effects .In the context of hybridization between progenitors with distinct phenotypes, and assuming that genetic contributions are equal and that the environment is constant, the overall hybrid population would be expected to express some derivation of four basic trajectories , between butternut (J. cinerea L.) and heartnut (J. ailantifolia Carr. var. cordiformis) is examined using suites of qualitative vegetative descriptors and quantitative functional adaptive traits drawn from the literature. Black walnut (J. nigra) was included as an outgroup to expand the trait combination space and ensure a two-dimensional ordination. Results from both trait suites are discussed in the context of the potential ecological equivalence of J. × bixbyi to butternut for conservation.To illustrate this approach to hybrid assessment, the trajectory of naturally occurring hybrids . The majority of the vegetative characters were taken from the Descriptors for Walnut (Juglans spp.) , and rachis texture (viscid or not viscid) were also assessed based on their potential to serve as vegetative descriptors or because they appeared to vary among seedlings of the taxa grown in the greenhouse.All four taxa were characterized at 33 vegetative morphological characters and functional adaptive traits (p.) IJD: : leaf coTable 1). Photosynthetic rate and transpiration were obtained on 23 and 24 August 2012 using a LI-6400 portable photosynthesis system fitted with a 6400-02B LED light source. The LI-6400 was operated under default settings with CO2, PAR, and temperature set to 400 ppm CO2, 1300 μmol m-2 s-1 PAR, and 25.0°C. CO2 and PAR were set high to exceed differential capabilities by species. Relative humidity in the reference chamber was maintained at 44.4–55.5%. Measurements were taken from 1100 to 1700 h as previous measurements on a subset of seedlings found no variation in photosynthetic rate from sun-up to sun-down (data not shown). Measures were logged after A had plateaued for at least 30 s.The majority of functional adaptive traits were associated with seedling survival or quality assessment : height,n = 2) that maximize the among group variance are generated, with the constraints that each eigenvector must be a linear combination of the sample traits, and that all eigenvectors must be orthogonal to each other. The first step functions similarly to a multivariate analysis of variance and the second is similar to principle correspondence analysis  is assigned to a predefined group, in this case a progenitor species or an outgroup. Variables are then analyzed for differences among pre-defined groups and eigenvectors  using the vegetative or adaptive trait suite. Data from these individuals were then plotted on the discriminant axes and each species cluster was enclosed within a 95% confidence ellipse  were excluded from analysis. Five J. × bixbyi individuals included in the adaptive trait projection were excluded from the vegetative projection. Due to transgressive rachis pubescence in hybrids, this trait was encoded as a quantitative variable in the vegetative character analysis. As traits in both analyses were carefully chosen a priori, variables were not assessed for differences among pure species using separate analysis of variance tests prior to running the discriminant function . Variables were then standardized to function .J. cinerea, J. nigra, and J. × bixbyi were collected in fall, 2011 from provenances archived at research plantations and from naturally occurring trees throughout Indiana, USA (Table 2). J. ailantifolia var. cordiformis seed from six of the most common cultivars (Table 2) was obtained from Grimo Nut Nursery . After collection, seeds were hulled, washed, and allowed to air dry. On December 19, 2012  and December 20, 2012 (J. ailantifolia) seeds were rinsed in cold water, packed into bags filled with moistened, sifted peat moss by family, and cold stored at 5°C at the Purdue University Wright Forestry Center . For measurement of seed characteristics (data not shown), on April 18, 2012 all seeds were unpacked, rinsed in cold water to remove excess peat, and returned to cold storage.Seeds from J. cinerea and J. nigra  and 125 (J. ailantifolia) days. To further minimize emergence time variation and avoid potting unviable seed, all material was pre-germinated following the methods of ® with Coir (MM 560) growing media and placed in the greenhouse set to maintain 26.7/18.3°C (day/night) on April 23, 2012. Seeds were removed and re-sown, every 3 days to visualize emergence. Seeds with radicle emergence less than 5 mm were wrapped in wet burlap to prevent desiccation and returned to the cooler at 5°C.To account for both interfamilial and species variation in seedling emergence time and the subsequent effects on growth , stratifJ. nigra  to 126  remained moist; watering then occurred every 2–3 days to maintain field capacity. On July 6, 2012, chlorophyll mutants were also discarded. Seedlings were moved from benches to a cinderblock grid on the floor from July 28 to 29, 2012. Defoliation occurred from 15 to 21 September 2012, after which watering ceased. Plants were destructively harvested for biomass measurements and root volume on November 2, 2012. From May 22 to September 21, 2012, average temperature and relative humidity were (mean ± SD): 25.7 ± 6.1°C and 30.1 ± 7.1%.On May 22, 2012, seeds were planted as a completely randomized design into the top 7 cm of 9.63-L pots , pre-filled with 3783.9 ± 184.1 g of MM 560 mixed with 48.2 g of Osmocote PlusJ. ailantifolia, J. cinerea, and J. nigra were effectively differentiated by the eigenvectors generated from both the vegetative and adaptive discriminant analyses . The two eigenvectors for each analysis described essentially all of the variation in their respective datasets (proportion of trace: Table 3). Trait loadings were relatively high for two vegetative traits: initial shoot color and leaf texture (Table 3). No adaptive traits were exceptional at discriminating species, with total biomass describing the most variation across both linear discriminant analyses .Seedlings of J. ailantifolia, J. cinerea, and J. nigra clustered tightly in the vegetative trait LDA . There was no overlap among 95% confidence ellipses, and J. ailantifolia–J. cinerea were separated the least by the canonical discriminant functions, perhaps reflecting taxonomic proximity. The J. cinerea ellipse  had the greatest dispersion overall, potentially reflecting larger genetic variation among sampled individuals relative to the other species. When hybrids were applied onto the parameter space, most individuals fell on a gradient between J. ailantifolia and J. cinerea ellipses . Roughly 50% of the hybrids fell within the J. ailantifolia ellipse, with 21% in the J. cinerea ellipse, and 23.5% intermediate in a space not occupied by either progenitor species’ ellipse (Table 4).Seedlings of J. ailantifolia, J. cinerea, and J. nigra based on functional adaptive traits were fairly distinct and reasonably well separated . There was some overlap between J. cinerea and J. nigra ellipses, with both equivalent distances from the J. ailantifolia ellipse. Hybrids projected onto the parameter space were widely and relatively evenly dispersed . The largest proportion (36.6%) of hybrids fell within the J. nigra ellipse including the overlap with the J. cinerea ellipse. If the combined proportion of individuals occupying the overlap between the J. cinerea and J. nigra ellipses were excluded, most 23.3% of the total hybrids occupied the J. ailantifolia parameter space (Table 4). Only 16.4%  of hybrids fell within the J. cinerea ellipse. Furthermore, 17.8% of hybrids represented novel combinations of progenitor traits and fell outside the parameter space occupied by J. ailantifolia, J. cinerea, and J. nigra ellipses.Clusters for J. ailantifolia space and 4 (5.5%) fell within J. cinerea space in both analyses. Half-sib progenies were fairly consistent in agreement across the two analyses, but the proportion of assignments within each family was highly variable (Table 5). Projections of only hybrids exhibiting initial stem color (red), the trait with the highest loading and corresponding to J. cinerea phenotype, did not all fall within J. cinerea parameter space in the functional adaptive trait analysis. Of these 13 individuals four fell within J. cinerea adaptive trait parameter space; four were outside J. ailantifolia, J. cinerea, and J. nigra parameter space; and the remaining five within J. nigra (2), J. ailantifolia (2), and intermediate J. ailantifolia/J. cinerea space (1).Hybrid projections in the vegetative and adaptive trait LDAs were not synonymous. Of the 73 hybrids remaining after exclusion of individuals with missing data points in the adaptive analysis, only 11 (15.1%) fell within Juglans demonstrates how discriminant analysis can be used to visualize the current hybrid trajectory based upon individual hybrid responses relative to the progenitor species’ responses. Without an assessment of current demography and selection pressures, however, it is not possible to parse out factors associated with hybridization, notably genetic, and demographic swamping . As few individuals fell onto parameter space not occupied by J. cinerea, J. ailantifolia, or intermediate to the two, simple removal of Japanese walnut and J. ailantifolia-like hybrids ; they were more consistent with Trajectory 4 than Trajectory 1. Many individuals fell outside the progenitors’ or the intermediate parameter space, indicating that they represented novel phenotypes (Table 4). Interestingly, the hybrid cluster expanded more in the direction of black walnut  than it did to the southeast. This possibly reflects better representation of hybrid phenotype combinations in this region of the parameter space and could indicate that additional outgroups, like Persian walnut (J. regia L.) would reveal even greater variation in hybrids. Trajectory 1 and 4 indicate that the use of hybrids in butternut restoration should be carefully weighed, as the phenotypes of hybrids are widely variable and probably unpredictable, even in uniformly mesic conditions. Assuming that the chosen functional traits adequately describe the autecological differences between butternut and heartnut, the data shows that only 28.7% of hybrids might match the physiology of J. cinerea. On the other hand, 23.3% of hybrids would match the physiology of J. ailantifolia on those sites, leading to survival in scenarios where butternut might not survive, e.g., flood , or become invasive , the observation that even hybrids from the same half-sibling progeny varied widely for both trait suites (Table 5) and presented constellations of traits unlike either progenitor indicates that general broadcasting of hybrid trees for use in lieu of butternut should be avoided  × shortleaf (P. echinata Mill.) F1 hybrids at several functional traits. They suggested that the hybrid’s reduced basal crooking, a trait associated with sprouting following fire and highly expressed in shortleaf pine, maintained the genetic integrity of shortleaf pine under a fire regime. Now that fire is essentially absent from the ecosystem, other traits govern hybrid fitness relative to progenitors. The selection of traits for analysis depends on knowledge of progenitors’ ecological function. When a particular trait is known to be essential for functionality, multivariate techniques are not essential for assessing hybrid ecological similarity. This is commonly the case for natural hybrid zones, where discrepancies in adaptive trait variation are suspected due to existing environmental gradients . DiscrimDiscriminant analysis is most useful when there is little information on progenitor ecological function. It can demonstrate how hybrids relate to progenitors across a wide suite of traits and potentially, what traits distinguish the two progenitors under a particular selection regime. This is especially important for analysis of hybrids between native and exotic congeners, which may have considerable overlap in their ecological function. As demonstrated here, combinations of many factors, not a single trait, defined differences between butternut and Japanese walnut.Ultimately, fitness is governed by survival and contributions to future generations. Trees in this study were grown under low stress conditions and only chloroplast mutants, which would be less fit in any environment, were removed. As such, no selection occurred, an issue with most hybrid studies . The groThis approach to trajectory assessment is most useful for analysis of naturally occurring hybrids or later generation artificial hybrids. It bypasses the need to separate individuals into classes, which are highly variable , throughPC designed and installed the experiment, collected and analyzed the data, and co-wrote the paper. NL contributed to data analysis and interpretation, and co-wrote the paper. KW assisted with data interpretation and co-wrote the paper. DJ supervised the research, helped to design the experiment, and co-wrote the paper.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.