Crucial to variety improvement programs is the reliable and accurate prediction of genotype’s performance across environments. However, due to the impactful presence of genotype by environment (G×E) interaction that dictates how changes in expression and function of genes influence target traits in different environments, prediction performance of genomic selection (GS) using single-environment models often falls short. Furthermore, despite the successes of genome-wide association studies (GWAS), the genetic insights derived from genome-to-phenome mapping have not yet been incorporated in predictive analytics, making GS models that use Gaussian kernel primarily an estimator of genomic similarity, instead of the underlying genetics characteristics of the populations. Here, we developed a GS framework that, in addition to capturing the overall genomic relationship, can capitalize on the signal of genetic associations of the phenotypic variation as well as the genetic characteristics of the populations. The capacity of predicting the performance of populations across environments was demonstrated by an overall gain in predictability up to 31% for the winter wheat DH population. Compared to Gaussian kernels, we showed that our multi-environment weighted kernels could better leverage the significance of genetic associations and yielded a marked improvement of 4–33% in prediction accuracy for half-sib families. Furthermore, the flexibility incorporated in our Bayesian implementation provides the generalizable capacity required for predicting multiple highly genetic heterogeneous populations across environments, allowing reliable GS for genetic improvement programs that have no access to genetically uniform material. Variety improvement programs are tasked with capturing heritable genomic response to selection across multiple growing environments and field seasons. While climatic uncertainty is outpacing variety development, the condition of global food, fuel, and fiber insecurity has become more vulnerable  models becomes unreliable in the presence of genotype-by-environment (G × E) interaction  and the USDA-ARS, a total of 242 DH lines derived from the intercross of Duster and Billings winter wheat varieties were used in the study. Traits analyzed include grain yield (GY) in kilograms per hectare (kg/ha), sodium dodecyl sulfate sedimentation value (Lorenzo and Kronstad Genotypes were derived using genotype-by-sequencing (GBS) technology, and 16,265 SNP markers were selected after filtering markers with >50% missing ratio. Missing genotypes of markers were imputed by the marker mean  and wood density in kg/m3 using X-ray densitometry (WDX-ray). The genotypic information regarding GBS SNP can also be found in Gamal El-Dien et al. , Aleza Lake, and Quesnel. Each site has 25 families with various sample sizes  model we proposed in the next section and the SE model is expressed as follows:yj is the response vector with length nj, nj is the total number of phenotypic observations in the jth environment, j = 1, …, m, m is the number of environments; 1nj is a vector of ones with length nj, μj is the overall phenotypic mean of individuals in the jth environment; gj is the random genetic effect of individuals in the jth environment, and we assume jth environment, Kj (size nj × nj) is the kernel matrix used to describe genetic similarity between individuals in the jth environment; bj is the random background genetic effect of the jth environment that is not explained by genetic markers in the gj, and we assume jth environment, Bj (size nj × nj) is a matrix representing the background genetic relationship of two individuals in the jth environment; ej is the random error term of the jth environment, and we assume jth environment and Inj is the identity matrix with size nj; gj, bj and ej are assumed to be independent.The kernel matrix in GS models is normally used to represent the genetic correlation between individuals that can be derived from either pedigree information or molecular marker data. To account for the relatedness in genetic background, the SE model implemented here was an extension of model 1 in Cuevas et al. , by addiy = T; g = T and g ~ N; b = T and b ~ N; e = T and e ~ N; g, b, and e are assumed to be independent; ym, μm, gm, bm and em are defined the same as in SE model.To fully capture G × E interaction, we proposed a generalization of model 3 in Cuevas et al. . The genKm are defined the same as in SE model; σg1m is the genetic covariance of individuals in the 1st environment and mth environment; Km1 (size n1 × nm) is the kernel matrix representing genetic relationship between individuals explained by genetic markers from the 1st and mth environment.In general, the genetic covariance matrix isBm are defined the same as in SE model; mth environment; Bm1 (size n1 × nm) is a matrix constructed to present the background relationship between two individuals that is not explained by genetic markers in the 1st and mth environment. With this model, background genetic relationship can be appropriately incorporated into both SE and ME models. For instance, when two individuals from the same family in the Interior spruce population, a half-sib relatedness of 0.25 was assigned to indicate their shared genetic background. While when the informative background relationship is unavailable, an identity matrix can be used for both background genetic variance and covariance matrices  is a positive definite function evaluated by marker genotypes; xi, xk are vectors of marker genotypes for the ith and kth individuals respectively, I, k = 1, …, nj, xi = T and xk = T, l = 1, …, p, p is the total number of markers; the allelic states of xil are coded as 0, 1, 2 for AA, Aa, and aa respectively; h is a positive bandwidth parameter that controls the rate of decay of the genetic correlation between two individuals. To determine the optimal value of the parameter, either a grid search method from cross-validation procedure or an empirical Bayesian approach  used in de Los Campos et al.  and our s* is the sample maximum of wl assigned to the lth marker is based on its minor allele frequency (MAF) and p-values from GWAS model with G×E interaction. The detailed formula of wl is the followingc1 is a constant; MAFl is the minor allele frequency of the lth marker; α and β are the parameters of Beta distribution density function; pvalue1l and pvalue2l are p-values of main genotypic effect and G × E interaction effect respectively from GWAS for the lth marker, these p-values are adjusted by false discovery rate at 0.05 to account for the multiple hypothesis testing problem T, pvalue2 = T, and MAF = T.To account for the potential effects of low-frequency variants while incorporating the test statistics from GWAS, we proposed the following formula (6) to determine the value of α and β in Eqs. ,,α and β  in Eqs.  and Yan  in Eqs.  suggesteMAF and WKPvalue respectively. As comparison, we denoted the WK contributed by both MAF and P value as WKMAF_Pvalue, and its weight wl is from Eq.  and the remaining 30% as TST (n30 × 1). For ME models, we followed cross-validation 2 (CV2) procedure in López-Cruz et al. (70 × m) and the rest 30% as TST (n30 × m). n70 and n30 stand for 70% and 30% of data, respectively. The random partition was repeated 50 times for SE and ME models respectively to generate an average prediction performance of each model. For WK, we selected the value that produced the highest prediction accuracy in TRN. The calculations of MAF and p values were based on each TRN-TST partition.Both Pearson’s correlation coefficient (PCOR) between observed and predicted phenotypes, and its mean squared error (MSE) were used to assess the model prediction accuracy for each environment. To assess the model prediction performance, we split the data into a training set (TRN) and a testing set (TST). We applied the estimation of model parameters from TRN to TST to get predicted phenotypes. For SE model, we randomly selected 70% of single-environment data as TRN  MAF distribution; 2) summary of phenotypes and the estimated heritability, and 3) prediction performance of the proposed models in the single- and multi-environment settings. PCORs were used to illustrate the prediction performance. Additionally, the results of MSE were found to be consistent with PCORs, i.e., a lower MSE tends to have a higher PCOR. The detailed evaluation of prediction performance can be found in Tables Beta(1: β) will converge to zero with large value of Beta random variables. Additionally, regarding to the context of MAF as the value of Beta random variable, 0.2 was considered as the large value.The distribution of common and rare SNP allele frequency for Duster × Billings DH population is shown in Fig. The distribution of MAF was found with a greater degree of rare alleles in all three sites of Interior spruce. There were about 86%, 88%, and 91% of SNPs with MAF < 0.2, for, PGTIS, Aleza Lake, and Quesnel, respectively Fig. .Boxplots of the four traits  across 3 years 2014–2016) for Oklahoma winter wheat are shown in Fig. 4–2016 fores and WDX-ray), Aleza Lake and Quesnel showed similarity in distribution and ranges , and the lowest was found in the correlation with DBH . The single-site heritability ranged from moderate to high (i.e., Growth phenotypes, HT and DBH, varied among the three Interior spruce sites, while traits related to wood density (e.g., WDges Fig. . Howeverges Fig. . Overallβ that produced the highest prediction accuracy of using WKMAF_Pvalue for both data, i.e., β = 12 for wheat (Fig. β = 200 for spruce (Fig. For the performance of WK, we present the results with eat Fig.  and β = uce Fig. .The average prediction accuracies of SE and ME models are shown in Fig. MAF model for GY and WHTPRO (Fig. MAF_Pvalue performed similarly to WKPvalue, and both significantly outperformed WKMAF for all studied traits. Compared with the ME_GK models, the increase of prediction accuracy from ME_WKMAF_Pvalue models ranged from 1 to 3%, 4 to 5%, and 6 to 7% for SDS, SKCSKW, and WHTPRO, respectively (Fig. MAF_Pvalue and ME_GK was found similar in 2014 and 2015, but ME_WKMAF_Pvalue produced significantly higher prediction accuracy for 2016 (i.e., 31% higher than ME_GK, Fig. Weighting with MAF and the association signal further improved the prediction performance by WK for ME models, with the exceptions of the reduced accuracy found in the ME_WKPRO Fig. . Among ares and 0.24 to 0.28 for WDX-ray. In Table Different from what was observed in the wheat dataset, the advantage of ME_GK over SE_GK was not as evident for Interior spruce, which might be a result of the large amount of variance that cannot be accounted for in the multi-environment models Table . The higMAF_Pvalue outperformed the other WK models almost in all traits, and the WKPvalue model showed slight advantage for WDres prediction in the PGTIS site (Fig. MAF_Pvalue. The greatest gain by using the WK models was, however, found in DBH in Aleza Lake; the benefit of using WK models for DBH was, however, diminished in PGTIS (Fig. X-ray. Due to the relatively indifferent prediction performance for WDX-ray across all models, the benefit of incorporating MAF and association signal was not observed. We suspect that the SNP predictors generated for Interior spruce are in weak LD with the underlying genes and QTLs.In general, modeling with MAF and specific-trait association improved predictability, even when predicting phenotypes for genetically heterogeneous material across environments. Among the WK implementations, WKite Fig. . HT was TIS Fig. . The benGS performance can be influenced by many interrelated factors, including trait genetic architecture, heritability, and the relatedness among individuals between training and testing populations (Crossa et al. mentclass2pt{minimX-ray whose accuracies were found indifferent with the SE model. Compared to our results, the prediction analysis using the same half-sib families in Gamel El-Dien et al. (X-ray being the only exception. In this study, the multi-site heritability estimates (Shown in Fig. n et al.  presenten et al. , with WDmentclass2pt{minimThe conventional GK using genetic markers is only able to capture the overall genetic similarity between individuals. Although the bandwidth parameter in GK can adjust the distribution of genetic similarity (Pérez-Elizalde et al. The bandwidth parameter tuning in conventional kernel models could potentially create a better mapping between the overall genetic distance among individuals to the phenotypic variation (Pérez-Elizalde et al. Despite the increases in GWAS statistical power afforded in large international consortia (Willer et al. p-values of GWAS and MAF, was evident. The MAF component in our WK models aided in preserving rare but favorable variants, which are usually underpowered in GWAS, and in some cases, not even included in the analysis (Pongpanich et al. Here, we presented a flexible GS framework capable of incorporating important genetic attributes to breeding populations and trait variability while addressing the shortcomings of conventional GS models. Shown in Figs. Supplementary Material for Weighted Kernels Improve Multi-Environment Genomic Predictions


Successfully predicting adaptive phenotypic responses to environmental changes, and predicting resulting population outcomes, requires that additive genetic (co)variances underlying microevolutionary and plastic responses of key traits are adequately estimated on appropriate quantitative scales. Such estimation in turn requires that focal traits, and their underlying quantitative genetic architectures, are appropriately conceptualized. Here, we highlight that directly analyzing observed phenotypes as continuously distributed quantitative traits can potentially generate biased and misleading estimates of additive genetic variances and individual‐by‐environment and gene‐by‐environment interactions, and hence of forms of plasticity and genetic constraints, if in fact the underlying biology is best conceptualized as an environmentally sensitive threshold trait. We illustrate this scenario with particular reference to the key phenological trait of seasonal breeding date, which has become a focus for quantifying joint microevolutionary, plastic, and population responses to environmental change, but has also become a focus for highlighting that predicted adaptive outcomes are not always observed. Specifically, we use simple simulations to illustrate how potentially misleading inferences on magnitudes of additive genetic variance, and forms of environmental interactions, can arise by directly analyzing observed breeding dates if the transition to breeding in fact represents a threshold trait with latent‐scale plasticity. We summarize how existing and new datasets could be (re)analyzed, potentially providing new insights into how critical microevolutionary and plastic phenological responses to environmental variation and change can arise and be constrained. Will wild populations persist or be driven to extinction given rapidly changing environmental conditions? We urgently need to answer this question, and identify mechanisms that facilitate population persistence.Wild populations could in principle survive environmental changes through adaptive genetic evolution, and/or because individuals can directly modulate key characteristics (termed “traits”) that allow them to maintain high survival and reproductive success (resulting in adaptive “phenotypic plasticity”). Successfully predicting population outcomes therefore requires that we can adequately quantify forms of plasticity and underlying heritable genetic variation in key environmentally sensitive traits in wild populations. This in turn requires that we conceptualize, measure, and analyze key traits in ways that reasonably represent true underlying biology; it should otherwise be no surprise if predicted outcomes do not materialize in nature.Here, we highlight how misleading conclusions on forms of available genetic variation and plasticity can potentially arise if traits are analyzed as directly inherited continuously distributed phenotypes when in fact the underlying biology is better represented as a plastic “threshold trait” where environmental changes can cause individuals to switch between discrete alternative states.We highlight this situation by considering seasonal breeding date, which has become a key focal trait for understanding microevolutionary, plastic, and population responses to environmental changes, but has also become a focus for highlighting that predicted responses are commonly not fully observed. We show that the common practice of directly analyzing observed breeding dates can yield misleading inferences on available genetic variation and plasticity if individuals experience environmentally induced switches to breeding where date per se has little or no direct causal effect.We outline how future analyses of timings of breeding and other life‐history events could be reconceptualized and reimplemented, thereby potentially providing new insights into constraints on phenological changes and unifying different observed reproductive outcomes into a single conceptual framework.The ultimate persistence of populations experiencing changing environments and resulting maladaptation is expected to depend on forms and magnitudes of phenotypic plasticity and microevolutionary change, including microevolution of plasticity, in key environmentally sensitive traits that affect fitness  sufficiently to maintain temporal synchrony between peak resource demand and supply, and hence maintain population growth , yielding an observable breeding date. Hence, the only source of variation in breeding date is the specified variance in liability‐scale reaction norm intercept α . The choice of a logistic function is arbitrary, but readily generates different shapes through flexible parameterizations. For example, we can consider two scenarios where the rate of increase, and hence the envisaged progression of spring, is relatively slow or fast  among years or locations could cause the variances in breeding dates among individuals or lineages to differ across those years or locations, even without any variation in reaction norm slope. For example, take the two illustrative logistic scenarios to represent two consecutive years, where focal individuals breed in both years. Observed breeding dates are highly correlated across simulated individuals across the 2 years , but overall phenotypic variances differ substantially Figure .If breeding date were conceptualized and analyzed as a continuously distributed trait that is directly expressed on the observed date scale, such patterns of environmentally induced variation in phenotypic variance would be interpreted as evidence of individual and/or genetic variation in reaction norm slope  apparent variance in breeding date in late  versus early  springs, which could be taken to imply systematic environment dependence in additive genetic variance and/or opportunity for selection, and hence environment‐dependent microevolutionary potential  in a relatively early versus late spring Figure . Here, tVery similar patterns of phenotypic variation in observed breeding date can be readily generated by repeating the above simulations with alternative parameterizations comprising nonzero variance in liability‐scale reaction norm slope β rather than in intercept α. Indeed, broad patterns are effectively indistinguishable when given nonzero variance in β but not α, as when given nonzero variance in α but not β Figure  vs. 4B. These simple simulations also indicate that substantial variance in observed breeding date can potentially arise even with small simulated variance in β, or even in α Figures , 4, 5. TOf course, there could be nonzero variance in both α and β and potentially also nonzero covariance, generating a nondiagonal G‐matrix for the liability‐scale reaction norm , which themselves vary nonlinearly with calendar date, could commonly apply. Indeed, reproductive outcomes are widely treated as longitudinal threshold traits in animal breeding populations of the same species variances in liability‐scale reaction norm intercept and slope parameters, given sufficient phenotypic observations of breeding state and environmental variables across occasions and relatives . “BreediAlthough there are well‐established formulae for transforming between phenotypic‐scale and liability‐scale heritabilities for threshold traits  across appropriate time periods. Indeed, while analyses that simply estimate additive genetic variance in observed breeding date can be accomplished without explicitly considering any form of plasticity or hence environmental covariates , or that start breeding then stop then potentially start again , or whose exact breeding dates were unobserved, can all be included . NonbreeThe suggestion that components of genetic and environmental variance underlying observed breeding dates  may be more appropriately estimated on latent liability scales than on observed date scales does not necessarily invalidate existing estimates of selection on breeding date. Indeed, one robust observation across diverse systems is that there is commonly directional selection for earlier breeding, where individuals that breed early within particular seasons on average produce more (surviving) offspring . Given appropriate data structures, parameters defining reaction norms for labile plasticity could potentially be estimated within years rather than solely across years, reducing the multiyear timeframe required to draw inference. Hence, the imperative now is for the interested research community to harness collective expertise to develop, implement, and evaluate new analyses across available datasets. Direct analyses of dates can still be appropriate to answer some questions. Yet, careful (re)analyses of transitions to breeding, and other phenological traits, as plastic threshold traits could provide new insights into plastic, microevolutionary, and population dynamic responses to our rapidly changing world.The authors declare no conflict of interest.JMR conceived the ideas, undertook the simulations, and wrote the manuscript, with conceptual and editing input from PA.There are no primary data associated with this concept manuscript. Simulation code is provided as Supporting Information.Appendix S1: Liability formulationsAppendix S2: Simple scale transformationAppendix S3: Additional illustrationAppendix S4: Analysing the transition to breeding as a plastic threshold traitClick here for additional data file.


H2 = 0.5–0.9) was observed for grain yield, spike weight, number of grains per spike, peduncle length, and plant height. Days to heading and grain yield could be partitioned based on accession origins. GWAS identified 154 marker-trait associations (MTAs) for yield and quality-related traits, 82 under D and 72 under W, and identified potential candidate genes. We identified 24 accessions showing high and/or stable yields under D conditions that can be recommended for cultivation in regions under the threat of global climate change.The objectives of this study were to identify genetic loci in the bread wheat genome that would influence yield stability and quality under water stress, and to identify accessions that can be recommended for cultivation in dry and hot regions. We performed a genome-wide association study (GWAS) using a panel of 232 wheat accessions spanning diverse ecogeographic regions. Plants were evaluated in the Israeli Northern Negev, under two environments: water-limited  and well-watered  conditions; they were genotyped with ~71,500 SNPs derived from exome capture sequencing. Of the 14 phenotypic traits evaluated, 12 had significantly lower values under D compared to W conditions, while the values for two traits were higher under D. High heritability ( Hence, to meet the challenge of feeding the growing world population, wheat production must grow by almost a billion tons by 2050 (from the current production of 2.1 billion tons). Instead, the growth rate of wheat yields has stagnated since the 1990s, mostly due to the severity of negative environmental factors such as drought or high temperatures, which are expected to worsen with global climate change cyt) [2 tolerance in algae [SNP WTa_008782 found on Chr. 1A.7 resides in a gene encoding a protein from a superfamily with RmlC-like cupin domains which are important storage proteins associated with plant development . RmlC-li2+ . Stimulia2+]cyt) . The 89 a2+]cyt) . SNPs WTin algae .ZAT18 gene positively regulated drought tolerance in transgenic Arabidopsis lines varying in ZAT18 expression [MTAs were located on Chr. 1B, and 2A, two on Chr. 2B, and two on Chr. 6B. The QTL 6B.7 resides at the same location as the high grain protein gene Gpc-B1 that was previously cloned ,56. SNP pression .In this study, we used GWAS to dissect the genetic basis of GY, yield components, and GPC, under two water regimes in field conditions. The phenotypic results identified high variability among accessions for all traits, and statistical analyses indicated that 14 traits were significantly affected by water deficit. The thermal imaging of the field and the calculated stress index confirmed that plants in the D treatment were more stressed than in W. Most importantly, the variability between plots indicated that the collection included accessions with a variety of responses to drought. It is known that there are a general decrease under water stress conditions in GY and most yield components ,58,59. WPpd-A1 and Ppd-B resulted in reduced grain weight and GY [The wheat panel comprised of landrace and modern cultivars of hexaploid wheat accessions from Europe, Asia, the Mediterranean, Africa, America, and Oceania, representing the worldwide eco-geographical range of grown cereals. The accessions were selected to identify trends in the frequency and location of sequence-predicted functional variants over geographical and environmental space . Most oft and GY . PCA anat and GY . The locp < 0.05). In allotetraploid plants such as wheat, genome asymmetry implies that the homoeologous genes on the A-, B-, and D-genomes each make differential contributions to various traits. Genome asymmetry was previously found in the proportion of domestication-related QTLs in the B- and A-genomes [GWAS identified 154 highly significant MTAs for nine of 14 traits . MTAs were found on most of the wheat chromosomes, but they were not equally distributed among the A-, B-, and D-genomes or within the chromosomes in each genome. The low number of SNPs mapped on genome D probably led to the identification of a very low number of MTAs on this genome. The low nucleotide diversity within the D-genome was described earlier ,74,75. W-genomes ,77. For -genomes .Yr36 was also cloned from Chr. 6B [Nor-B2 and Gli-B2 genes that are important for homologous recombination and GPC, respectively [OsGW2 is associated with grain width [TaGW2 cloned from Chr. 6A had SNPs in its promoter region associated with seed width and TKW [TaGW2 on Chr. 6B has a stronger effect on TKW than TaGW2 on Chr. 6A, and Hap-6B-1 was the preferred grain width and weight-increasing haplotype that had undergone strong positive selection [TaGW2-6B occurred at the tetraploid level and was found in the promoter regions [TaGW2 homologous in wheat and to confirm its function as it was known in rice as a negative regulator for grain width [TaGW2 copies resulted in smaller wheat kernels, thus suggesting that TaGW2 is a positive regulator of grain size-related traits [TaGW2 by gene editing and TILLING, confirmed its negative regulation mechanism and showed that in TaGW2-6B mutant caused the highest single-genome increases in grain size in the cultivar [TaGW2-6B in our GWAS study shows that it is found downstream of QTL 6B.6 MTA for SW under W  as compared with its location in the Norin cultivar. Many candidate genes were found for MTAs on Chr. 6B were associated with stress response are described in In the current study, we identified that Chr. 6B is an important source for 20 MTAs, of which 13 MTAs clustered into nine QTLs were found under D. These 13 MTAs contributed 27% of all 48 MTAs found on the B-genome under D. Seven MTAs for yield were found in four adjacent QTLs (6B.10–6B.13) under D and/or W conditions. Under D, we found QTLs for GY at 6B.10 and SW at 6B.12. Under D, we also found QTLs for SW and the NSpP at 6B.12; QTLs for GY and DH at 6B.11; and DH at 6B.13. We suggest that this region can be regarded as a hotspot of genes influencing yield in response to low water availability. On Chr. 6B, we also found two MTAs for GPC, the first (6B.1) is novel, while the second MTA found at 6B.7 mapped to the same location as the previously cloned Gpc-B1, which is derived from wild emmer wheat . This QT Chr. 6B ,88. Sequectively . Rice Osin width , and its and TKW . Furtherelection . The str regions . Severalin width ,94. Overd traits . Generatcultivar . SearchiTriticum aestivum) accessions selected from a larger global wheat diversity panel comprising 487 accessions of hexaploid and tetraploid wheat, that was assembled by the European consortium  and described previously by [https://wheat-urgi.versailles.inra.fr/Projects/Whealbi (accessed on 1 January 2019)). We first confirmed that plants have spring-type phenology under the Israeli winter conditions by growing them in 2015–2016. For the current 2016–2017 experiment we used spring-type bread wheat accessions, including landraces, and modern cultivars from 54 countries of the five continents: Europe (10), Asia (93) (37 from the Mediterranean and 56 from East Asia countries), America (18), Africa (12) and Oceania (6). The passport data of 232 accessions and varieties used in the current study are presented in The current study consisted of 232 bread wheat  in Israel. The experiment was conducted in a homogenous field, at Urim farm at the Northern Negev region , under two treatments: water-limited (D) and well-watered (W). The set up included two main plots, one per treatment, each consisting of three replicates in a randomized block design. Each experimental plot (1.2 m × 2 m) consisted of six 2 m long and 0.2 m spaced rows, sown at a rate of 170 seeds per m, 450 mm . A 2 m w, 450 mm . Weed, d2). Grains extracted from the 15 spikes were also used to determine grain protein content . The field plots were inspected twice weekly to determine days-to-heading (DH). A plot was determined as heading when the spike emerged for ¼ of its length in 50% of the plants (Zadoks DGS 53). Flag leaf length , Flag leaf width , and Flag leaf area of two plants/plot  and specific leaf weight (SLW = weight/LA) were assessed. Upon maturity, two plants of each plot were measured in the field for (a) plant height , (b) peduncle (upper internode) length , and (c) spike length . Subsequently, 15 spikes were manually harvested from each plot and used to determine the average spike weight . Spikes were threshed and grain weight per spike was calculated , grains were counted to determine grain number per spike (GNpS) and thousand-grain weight , grain filling efficiency (GFE = GWpS/SW), and the number of spikes per plot (NSpP = grain yield/GWpS) were calculated. Osmotic potential  was determined to sample leaves for 1–2 weeks after heading. Finally, the entire plot was harvested mechanically  and grain was weighed to determine total grain yield . Then, the flour was tested for GPC by Perten Inframatic 9520 NIR Flour Analyzer . ® Systems, Inc., Bilerica, MA, USA) was mounted on a 6-engine drone . More details on the thermal camera, flight height and pre-processing can be found in [canopy − Twet)/(Tdry − Twet). Where Tcanopy is the temperature of the canopy in the thermal image, and Tdry and Twet are two reference temperatures. Tdry was set as air temperature + 50 °C [wet was calculated using the energy balance equation [An aerial thermal imaging campaign was conducted at midday on April 20th, 2017. A FLIR SC655 camera ). The statistical package  was used for descriptive statistics, and correlation for all statistical analyses unless specified otherwise. Sample homogeneity was determined by the deviation of the coefficient of variation (CV). Variables with a scatter threshold CV greater than 35% were excluded from the analysis. Analysis of variance (ANOVA) was used to assess the possible effects of accessions and environmental conditions. The results were considered significant at p < 0.05 or p < 0.01 and the mean comparisons were performed using Tukey’s honest significant difference (HSD) test. The variation of each trait under the two watering regimes was presented by employing the “ggplot2” package in R (https://cran.r-project.org/web/packages/ggplot2/index.html (accessed on 3 May 2022)). The squared cosine values were calculated from principal component analysis (PCA). Squared cosine values of traits and genotypes provide obvious estimates about them. If genotypes or traits having higher values (factor scores >70) in 1PC and lower values in 2PC are regarded as promising genotypes or traits irrespective of conditions. If a genotype has, a lower square cosine value in the 1PC and has a higher squared cosine value in 2PC regarded as a notorious genotype [p < 0.05 using the “Corrplot” package (https://github.com/kwstat/corrgram (accessed on 29 April 2021)). BLUP values were calculated using Henderson’s matrix notation as follows: Y = Xβ + Zu + e. Where Y is the vector of observed phenotypes; β is an unknown vector containing fixed effects, including the genetic marker, population structure (Q), and the intercept; u is an unknown vector of random additive genetic effects from multiple background QTL for individuals/lines; X and Z are the known design matrices, and e is the unobserved vector of residuals. The u and e vectors are assumed to be normally distributed with a null mean and variances. Broad sense heritability (H2) in the individual environment was estimated by H2 = σ2a/σ2a + σ2e. Where: H2—heritability; σ2a as the additive genetic variance, and σ2e is the residual variance in the “Heritability” package (https://cran.r-project.org/web/packages/heritability (accessed on 13 December 2019)) in R language package ).All phenotypic data were normalized using the Shapiro–Wilk test before analysis. The problem of asymmetric distributions was addressed using the Box–Cox transformation in the R package . The genotyping of this collection was conducted within the framework of the consortium. All the information on DNA extraction, exome design, exome sequencing, and variant calling are available in . As membhttp://taylor0.biology.ucla.edu/structureHarvester (accessed on 1 July 2014)) to get the appropriate K value. Information about relationships is conveyed through the kinship (K) matrix, which is used in a mixed linear model (MLM) as the variance-covariance matrix between the individuals. To improve the statistics and power of the analysis, a kinship matrix (K) based on genetic markers was used in conjunction with the population structure (Q+K).The population structure of the wheat panel was assessed using the Bayesian clustering method in STRUCTURE version 2.3.4 . Populathttp://www.maizegenetics.net/GAPIT (accessed on 4 May 2022)) [p-values using QQ plots [p-values with the expected ones with a minimum deviation from the trend made it possible to choose models that more fully describe the MTA [p-value of 0.05, except for MTAs where the threshold was set to 0.1 due to low and moderate 2H. A region of ~1 Mbp that contains a few adjacent MTAs (clusters of MTAs) was regarded as a QTL region. Manhattan plots and SNP-density plots were generated by rMVP package [T. aestivum cv. Chinese Spring (IWGSC RefSeq annotation v2.1) was used to retrieve high-confidence genes surrounding each MTA, in a window of ±250 Kb.For GWAS we used the R package Genome Association and Prediction Integrated Tool (GAPIT) (y 2022)) . Five GWy 2022)) . The besQQ plots . The cho the MTA . MTAs we package . Gene anThe present GWAS identified significant genetic polymorphism and high phenotypic diversity in the response to water stress. Most of the measured phenotypic traits were negatively affected by water stress. Our analysis identified accessions, which mainly originate from the Mediterranean and Africa, that show high GY under water-limited conditions or with stable yield in W and D conditions. These excellent wheat accessions can be recommended for cultivation in regions experiencing low precipitation and increased temperatures. GWAS identified 154 MTAs, partly residing in clusters in QTL regions, that have a significant effect on GY, or yield components, and GPC under water-limited and/or well-watered conditions; some of them can be used for breeding. A higher number of MTAs identified under D were found in genome B than in A or D genomes, with Chr. 6B as the main contributor. Based on the physical location of the MTAs, we identified promising candidate genes underlying yield-related traits.


Branched-chain amino acids  are essential amino acids that are associated with an increased risk of cardiometabolic diseases (CMD). However, there are still only limited insights into potential direct associations between BCAAs and a wide range of CMD parameters, especially those remaining after correcting for covariates and underlying causal relationships.To shed light on these relationships, we systematically characterized the associations between plasma BCAA concentrations and a large panel of 537 CMD parameters  in 1400 individuals from the Dutch population cohort LifeLines DEEP and 294 overweight individuals from the 300OB cohort. After correcting for age, sex, and BMI, we assessed associations between individual BCAAs and CMD parameters. We further assessed the underlying causality using Mendelian randomization.A total of 838 significant associations were detected for 409 CMD parameters. BCAAs showed both common and specific associations, with the most specific associations being detected for isoleucine. Further, we found that obesity status substantially affected the strength and direction of associations for valine, which cannot be corrected for using BMI as a covariate. Subsequent univariable Mendelian randomization (UVMR), after removing BMI-associated SNPs, identified seven significant causal relationships from four CMD traits to BCAA levels, mostly for diabetes-related parameters. However, no causal effects of BCAAs on CMD parameters were supported.Our cross-sectional association study reports a large number of associations between BCAAs and CMD parameters. Our results highlight some specific associations for isoleucine, as well as obesity-specific effects for valine. MR-based causality analysis suggests that altered BCAA levels can be a consequence of diabetes and alteration in lipid metabolism. We found no MR evidence to support a causal role for BCAAs in CMD. These findings provide evidence to (re)evaluate the clinical importance of individual BCAAs in CMD diagnosis, prevention, and treatment.The online version contains supplementary material available at 10.1186/s12916-022-02688-4. The worldwide obesity epidemic represents a major health burden, with obesity leading to a spectrum of comorbidities that are the basis for cardiometabolic diseases (CMD). CMD are multifactorial metabolic diseases that can include insulin resistance (IR), type 2 diabetes (T2D), and cardiovascular disease (CVD) , 2, withMechanistic studies using mouse models have shed light on the pathways potentially involved. One leading hypothesis suggests that BCAAs, or their breakdown products (branched-chain keto acids), have a direct influence on key factors involved in the pathogenesis of diabetes through their interaction with the mammalian target of rapamycin (mTOR) signaling pathway , 12 and Relationships between BCAAs and other CMD traits are also emerging, but it is still unclear whether they represent important indicators of CMD risk or even play a causal role. In this regard, some of the most extensively studied CMD traits are CVDs, a set of diseases including atherosclerosis and myocardial infarction, that affect the heart and the circulatory system. Several studies demonstrated that increased concentrations of various BCAAs were associated with increased CVD risk   is a sub-cohort of the LifeLines cohort that consists of 1539 individuals. From April to August 2013, all participants registered at the LifeLines research site in Groningen were invited to participate in the LifeLines DEEP study, a study with deep omics profiling in addition to the regular LifeLines program. Eventually, 1539 randomly selected individuals participated in LLD. For these participants, extra biomaterials  were collected for various omics profiling, such as genetics, methylation, transcriptomics, metabolomics, proteomics, and microbiome. A detailed cohort description can be found in Tigchelaar et al.  and Zher2 at screening . Exclusion criteria were a recent cardiovascular event , a history of bariatric surgery or bowel resection, inflammatory bowel disease, renal dysfunction, increased bleeding tendency, use of oral or subcutaneous anti-coagulant therapy, use of thrombocyte aggregation inhibitors other than acetylsalicylic acid and carbasalate calcium (antithrombotic), or a contra-indication for magnetic resonance imaging (MRI). Participants who used lipid-lowering therapy temporarily discontinued this medication 4 weeks prior to the measurements. All women were postmenopausal and did not use hormonal replacement therapy. For all participants, blood samples for nuclear magnetic resonance (NMR)-based lipidomics, cytokines and cell counts, TMAO measures, and OLINK panel III CVD measurements were collected in the morning following an overnight fast. In the present study, we included 294 participants for whom fasting plasma metabolites were available. Due to different missing values for each dataset, the number of individuals analyzed differs as shown in Additional file 300OB is an obese cohort of 302 individuals aged 54–81 years old, who were enrolled in the study at the Radboud University Medical Center, Nijmegen, the Netherlands. A detailed description is provided in our earlier paper . In brieFor both cohorts, multiple concentrations of omics data are available. In this study, we used the detailed phenotypic data routinely used in clinic to assess CVD risk, non-invasive measures of fat distribution and carotid intima-media thickness (IMT) as a non-invasive measure of atherosclerosis, metabolomics (mainly including lipoproteins), TMAO and related metabolites, circulating proteins, and cell counts and cytokines.In 300OB, fat distribution was assessed using MRI, including volumes of visceral adipose tissue and subcutaneous adipose tissue, divided into deep and superficial subcutaneous adipose tissue, respectively. Hepatic fat content was quantified using localized proton magnetic resonance spectroscopy. Non-invasive measures of atherosclerosis of the carotid arteries included measurement of carotid IMT, carotid plaque presence and maximum plaque thickness, and plaque presence and maximum thickness in the common carotid, internal carotid, external carotid artery, and carotid bulbus. The presence of plaque was defined as focal thickening of the wall of at least 1.5 × mean IMT or an IMT > 1.5 mm, according to the Mannheim IMT consensus . All meahttp://www.olink.com/products.Blood samples of participants from both cohorts were collected separately and frozen at − 80 °C prior to any measurement. For both cohorts, circulating proteins from EDTA plasma samples were measured using commercially available OLINK Proteomics , the AB Inflammation Panel for 300OB (162 CVD II panel and inflammation panel), and OLINK Proseek Multiplex CVD III panel for LLD (92 CVD proteins). OLINK provides a multiplex immunoassay for high-throughput detection of protein biomarkers in liquid samples. Proteins are recognized by antibody pairs coupled to cDNA strands that bind in close proximity and extend by a polymerase reaction. In 300OB, proteins were excluded from analysis when the detection level of 75% was not met. Quality control (QC) was performed by OLINK Proteomics, with two samples that did not pass QC subsequently excluded from the analysis. OLINK panel data was available for 1294 participants from LLD and 294 samples from 300OB. More detailed information can be found at the OLINK site: For both cohorts, we profiled a wide range of plasma metabolites using NMR and the Nightingale Biomarker Analysis Platform . This plWe used ultra-high-performance liquid chromatography in combination with isotope dilution tandem mass spectrometry to analyze TMAO, choline, L-carnitine, and betaine for both cohorts and γ-butyrobetaine in plasma specifically in the 300OB cohort, as described elsewhere .Blood cell counts were measured for both cohorts, and we used six cell types related to immunity for further analysis: basophils, eosinophils, granulocytes, lymphocytes, monocytes, and thrombocytes. The cytokines for the LLD cohorts included IL (interleukin)-1β, IL-6, IL-8, IL-10, IL-12p70, and tumor necrosis factor-α (TNF-α) measured by ProcartaPlex multiplex immunoassay . Other inflammation markers, including leptin, adiponectin, IL-18, IL-18BP, and resistin, were measured using commercially available sandwich ELISA kits . For the 300OB cohort, measured cytokines included IL-1β, IL-6, IL-18 (including IL-18BP), and inflammation markers included adiponectin, leptin, and resistin, all measured according to protocols described earlier .phenotype ~ BCAA + age + sex + BMI. The independent and continuous dependent variables were scaled using a z-scale transformation  to be able to compare the effect size of different categories and in both cohorts. Logistic regression was used for binary phenotypes. Each BCAA was analyzed separately without mutually adjusting for the others.First, we identified age, sex, and BMI as important covariates in assessing the association between BCAAs and CMD parameters. Next, we explored whether other lifestyle and dietary factors can be potential confounders. If a factor is an important confounder, we expected to see a significant association between this factor and the exposure, i.e., BCAAs. We therefore made use of the LLD cohort to assess the associations between BCAAs and all potential lifestyle and dietary covariates using a univariable regression model. The lifestyle and dietary factors assessed included current smoking status, intake of alcohol, meat, fruit, vegetables, and coffee and total energy intake in kcal and macronutrients   and model errors are assumed to be independent (2), to have a constant variance (3), and to be normally distributed (4). In addition, the predictors are assumed to be measured without error (5), and there are assumed to be no unmeasured confounders that affect both the response and predictor variables (6). To ensure that major assumptions 1–4 were fulfilled, we manually inspected diagnostic plots of the models for each BCAA–phenotype combination. To conform with the normality assumption, we log-transformed 27 phenotypes  < 0.05. These are reported as the FDR-value in both the tables and in the Results section where appropriate. All analyses were performed using R version 3.61.We note that we included BMI as a covariate because its causal role in BCAAs and cardiometabolic traits has been widely studied. In this study, we wanted to correct for the confounding effects of BMI so we could investigate the associations of BCAAs with various CMD-related parameters, including fat distribution, independent from overall obesity as represented by BMI. NMR measurements in the 300OB cohort were also adjusted for batch number. Where applicable, we included additional covariates, including protein and meat intake and HOMA-IR for NMR analysis in LLD, as mentioned in the “r2 < 0.001 in 1000G EUR samples. Proxies were added automatically by the TwoSampleMR R package. To estimate the causal effect of BCAAs on CMD parameters, we used SNPs associated with the sum of all three BCAAs  to overcome the potential confounding effect of the other two BCAAs when using separate BCAAs as the exposure.To determine causality between BCAAs and associated factors, two-sample bi-directional MR was performed using the R package TwoSampleMR v.0.5.6 with default settings . The genp value < 0.05 using IVW and nominally significant results  using two other MR approaches  and the MR PRESSO [p value < 0.05) that estimates the pleiotropy and tries to correct for it by removing outliers; (4) MR results were not driven by single SNPs, as tested using leave-one-out analyses ; or (5) genetic instruments were strong as estimated using F-statistics (F > 10). We also estimated heterogeneity using Cochran’s Q-test but did not filter out the results based on this measure.To calculate univariable MR (UVMR) estimates, we used Wald ratios meta-analyzed by the inverse variance weighted (IVW) method . InstrumSSO test , 57);  and heterogeneity using Cochran's Q-test.BMI has previously been shown to affect both BCAA levels and CMD parameters. Moreover, BMI, BCAAs and CMD parameters have shared associated genetic variants. To overcome the potential violation of the 3rd MR assumption in the UVMR analyses, we removed BMI-associated SNPs published by the GIANT consortium  from theWe performed the analyses in both directions and corrected for multiple testing using the Benjamini–Hochberg method separately for each group of phenotypes  and for each direction.n = 1400) and 300OB (n = 294) cohorts and their respective fasting plasma BCAA concentrations are summarized in Additional file p = 5.68 × 10−8), while the average concentrations of leucine and valine were 3.1 μM (p = 5.16 × 10−5) and 7 μM (p = 0.0017) lower, respectively, compared to the LLD cohort , followed by leucine (mean betaLLD = 0.09) and valine (mean betaLLD = 0.07) (one-way ANOVA P = 1.71 × 10−16). This observation implies that different BCAAs may have a divergent impact on CMD. While zooming in on different categories of CMD parameters, we found shared associations of BCAAs for all five glycemic traits, including fasting plasma levels of glucose, insulin, HbA1c, HOMA-IR index, and diabetes status. However, BCAA-specific associations were found for lipidomic traits and proteomics , while the estimated effect size was 0.10 (p = 8.16 × 10−4) for leucine and -0.07 (p = 7.94 × 10−3) for valine , while the association was much weaker for leucine (βleu = 0.20) and not significant for valine   in the 300OB cohort , followed by leucine 263) and valine (202)   (Additional file Out of 756 pair-wise associations for 252 CMD parameters that were tested in both the LLD and 300OB cohorts, 202 associations showed significant heterogeneity between the two cohorts (Although we identified numerous associations between BCAAs and cardiometabolic traits, and specifically with plasma lipids, using both clinical measures and detailed NMR plasma lipid levels measurements, the associations alone are insufficient to provide insights into the underlying causality. To investigate the causality of the identified associations, we performed bi-directional two-sample MR analysis using genetic variants as IVs (Fig. Q-test. This implies complexity in causality and suggests some caution in data interpretation.Obesity has previously been reported to causally contribute to both CMD parameters and BCAAs , 4, 41. Valine, leucine, and isoleucine—the BCAAs—are essential amino acids that are used for protein synthesis but also play important roles in signaling pathways. Increased plasma BCAA concentrations have been found to increase the risk of IR and diabetes and some causal pathways have been proposed , 14–16, We created an inventory of 827 significant BCAA associations with CMD-related parameters. We not only replicated previous findings of associations with glycemic-related factors and all three BCAAs , 41, we BCAAs appear to have both common and specific associations. A large set of available CMD parameters allowed us to accurately compare the association effects between isoleucine, leucine, and valine. Under the presumption that these three BCAAs have similar functions, many studies have missed the specific effects of each BCAA and broaden their conclusions based on the study of single amino acids and/or of their individual effects to all BCAAs. It is becoming increasingly clear that the associations of specific BCAAs with CVD may differ substantially , 65. TheAnother important finding is the relationship of BCAAs, obesity, and lipid metabolism. As noted above, BCAAs appear to have particularly strong associations with lipid profile. We found that these associations depend on age and BMI. First, effect sizes were higher in the 300OB cohort of overweight/obese individuals, who were also considerably older. Second, valine showed a large number of associations with opposing directions across the two cohorts, a conflict that was resolved after matching for age and BMI of individuals from the two cohorts.While BCAAs clearly play a role in IR and diabetes, previous studies reported conflicting results on the direction of causal relationship in these associations: Lotta et al. reported that changes in BCAA levels contribute to IR and the incidence of type 2 diabetes , whereasWe acknowledge several limitations. This cohort-based, epidemiological study primarily provided population-level association evidence, as well as future directions for investigating the role of BCAAs in CMD. However, the cross-sectional association design of the current study led to several limitations. First, the identified associations may not directly reflect the observations from animal-based, mechanistic biology studies, as experimental settings vary greatly. Second, our association approach assumes linear relationships between BCAAs and CMD parameters, which might not always be the case. Larger studies using non-linear models are needed to capture these complex relationships. Third, the identified associations do not imply causality. While we did employ MR to estimate directions of causality for these associations, only a few causal relationships were supported, and these were predominantly in the direction from CMD parameters to BCAA levels. However, the causal effects of BCAAs on CMD parameters were more difficult to estimate due to the lower number of BCAA-associated SNPs available for the analyses. Lastly, violation of assumptions for the MR analyses may occur even when performing a rigorous sensitivity analysis, potentially leading to false conclusions. Further studies are needed to elucidate the potential underlying mechanisms of the identified associations and causal links.We performed a cohort-based association study of BCAAs with cardiometabolic parameters. Our findings can serve as an extensive catalog to propagate future BCAA and CMD research. Interestingly, BCAAs appear to be a heterogeneous group of amino acids with potentially diverse CMD-associated effects, which suggests they should be targeted separately in biomedical, clinical and experimental research.Additional file 1:Tables S1-S10.Table S1 - Phenotype description. Table S2 - Association of BCAAs with potential covariates. Table S3 - The results of association analysis between BCAAs and CMD parameters adjusted for age, sex and BMI. Table S4 - The results of association analysis between BCAAs and CMD parameters adjusted for age, sex, BMI and eGFR. Table S5 - Meta analysis of association results in LLD and 300OB cohorts. Table S6 - The results of association analysis between BCAAs and NMR lipoproteins performed in the 300OB cohort adjusted for age, sex and BMI after removing individuals with DM. Table S7 - The results of association analysis between BCAAs and NMR lipoproteins in LLD cohort adjusted for age, sex, BMI and HOMA-IR. Table S8 - The results of association analysis between BCAAs and NMR lipoproteins in a subset of the LLD cohort, that was matched by age and BMI with the 300OB cohort. Table S9 - The list of CMD parameters used in MR analyses and their accession ids. Table S10 - The results of multivariable MR analyses. Table S11 - The results of univariable MR analysesAdditional file 2:Figures S1-S5.Figure S1 - Effect size comparison with and without adjustment for eGFR. Figure S2 -Effect size comparisons of BCAAs association with fat distribution in the 300OB cohort. Figure S3 - Effect size comparisons of BCAA associations with cytokines and cell counts in both the LLD and 300OB cohorts. Figure S4 - Effect size comparisons of BCAA associations with TMAO and its precursors in both the LLD and 300OB cohorts. Figure S5 - Effect size comparison with and without correcting for diabetes and insulin resistanceAdditional file 3. STROBE-MR checklist. STROBE-MR checklist - A checklist of recommended items to address in reports of Mendelian randomization studies


The cooperative strategy of phenotypic traits during the growth of plants reflects how plants allocate photosynthesis products, which is the most favorable decision for them to optimize growth, survival, and reproduction response to changing environment. Up to now, we still know little about why plants make such decision from the perspective of biological genetic mechanisms.In this study, we construct an analytical mapping framework to explore the genetic mechanism regulating the interaction of two complex traits. The framework describes the dynamic growth of two traits and their interaction as Differential Interaction Regulatory Equations (DIRE), then DIRE is embedded into QTL mapping model to identify the key quantitative trait loci (QTLs) that regulate this interaction and clarify the genetic effect, genetic contribution and genetic network structure of these key QTLs. Computer simulation experiment proves the reliability and practicability of our framework.Populus euphratica, namely, aboveground stem length - underground taproot length, underground root number - underground root length, which represent relationships of phenotypic traits in two spatial dimensions of plant architecture. The analytical result shows that our model is well applicable to datasets of two dimensions.In order to verify that our framework is universal and flexible, we applied it to two sets of data from Our model helps to better illustrate the cooperation-competition patterns between phenotypic traits, and understand the decisions that plants make in a specific environment that are most conducive to their growth from the genetic perspective. The comQuantitative trait locus (QTL) mapping can locate QTLs or genes related to complex quantitative traits on chromosome, which is always the interest of biogenetics and has been successfully applied to many breeding projects . HoweverIn this paper, we establish a general and universal model framework, which takes into account the dynamic characteristics of plant growth and the interaction between two traits, screens out key QTLs regulating this pattern, and figures out the genetic structure Figure 122.1Populus euphratica , the phenotypic value of seedling i isQTL mapping based on DIRE identifies QTLs that mediate the dynamic growth and interaction between traits . We desiwhere where the length of )) model .Based on the following hypotheses, we can detect whether a QTL regulates the interaction growth:where n samples for the null hypotheses isHypotheses test is realized by maximum likelihood estimation (MLE). The likelihood function of where J is the number of genotypes of target QTL, jLR) is calculated aswhere LR follows the law of chi-square distribution according to its construction principle, and its degree of freedom is the difference between the number of parameters of p value is compared with the critical threshold after FDR  correction to reduce false positives.In the process of hypotheses test solution, parameter estimation is realized by Expectation Maximization (EM) algorithm . Accordilgorithm .2.4The significant QTLs obtained from hypotheses test play key roles in regulating the growth of phenotypic traits. By constructing the genetic network of these QTLs, we can better understand the genetic mechanism of phenotypic variation. We introduce the replication factor equation , which rk  for trait 1 and trait 2, respectively. We only retain QTLs that have a greater impact on QTL k through variable selection in the LASSO regression model:k, where l. LASSO  selects k; k, where the overall genetic effect On the other hand, the number of nodes in the network may be more than that of time points. To ensure the accuracy, Legendre orthogonal polynomial (LOP) is firstly applied to fit the genetic effect curve of this QTL and obtain more time point information by interpolation on the curve.2.5CV) is a normalized measure to evaluate the dispersion of probability distribution. It can be used to compare the dispersion of data among different phenotypic traits on the basis of eliminating influence of dimension. We use it to quantitatively describe the change of dispersion of each phenotypic trait over time. The calculation formula is as follows:Coefficient of Variation (where 2.6We define the proportion of phenotypic variation caused by genetic factors (or heritability explained by chosen QTLs) as phenotypic variation explained (PVE), and it is calculated by means of variance analysis. First of all, take the target trait phenotype as the dependent variable and genotypes as the independent variables to conduct generalized linear regression, and then perform variance analysis on the regression result to obtain the PVE value .33.1Populus euphratica at a series of time points. Phenotypic values of them both display bigger dispersion with time. The width of the violin gradually narrows, while the vertical height constantly increases, indicating that the differences among progenies increase over time. Taking taproot length as an example for detailed analysis, the height range of the violin at 3 days is 0-20mm, that is, taproot length of all samples does not exceed 20mm at this time. The widest width of the violin shows the concentrated distribution of taproot length in F1 population, and the taproot length of most seedlings is between 1 and 5mm. By the 18th day, the height of the violin has a significant increase, meaning that some samples grow very fast during this period, while some grow slowly. At the moment, the range of the violin is about 1-10mm, i.e., taproot length of most samples is relatively close, about 1-10mm. By the 62nd day, the distribution range of the taproot length has expanded to 0-150mm, and the shape of the violin is very close to a line, indicating that the differences among samples further enlarge, some of the taproots are 150mm long, while others are only about 10mm long. The growth of underground roots also shows similar characteristics, the difference among samples increases with time , the coefficient of determination  encodes pentapeptide repeat containing protein At4g14850, which is a homologous protein of LOI1  of 93 and 94 significant QTLs by quantifying the dynamic genetic contribution of markers to growth Figure 4The growth of phenotypic traits is largely influenced by key QTLs. Although these identified QTLs jointly regulate the overall growth of target trait, there are great differences in their roles and importance in the genetic network. These QTLs do not exist independently, they are subject to epistatic effects from other QTLs besides direct genetic effects produced by themselves. We renumbered these QTLs and constructed their genetic effect network to clarify their interactions and how these QTLs directly or indirectly affect the growth of target traits. These genetic networks, including stem length network, taproot length network, root number network and root length network, share similarities in structure Figure 53.4Populus euphratica under different sample size (n) and heritability  can be found below: Populus euphratica, interpretation of data and guidance for data analysis. QF provides guidance for data analysis and simulation. All authors contributed to the article and approved the submitted version.KL performed data analysis and wrote the manuscript. X-YZ and RW conceived of the idea, designed the model and contributed to the revision of the manuscript. XW participated in the design of the data analysis. HG and DY participated in data analysis and gene annotation. MY provided data of


A central aim of genome-wide association studies (GWASs) is to estimate direct genetic effects: the causal effects on an individual’s phenotype of the alleles that they carry. However, estimates of direct effects can be subject to genetic and environmental confounding, and can also absorb the ‘indirect’ genetic effects of relatives’ genotypes. Recently, an important development in controlling for these confounds has been the use of within-family GWASs, which, because of the randomness of Mendelian segregation within pedigrees, are often interpreted as producing unbiased estimates of direct effects. Here, we present a general theoretical analysis of the influence of confounding in standard population-based and within-family GWASs. We show that, contrary to common interpretation, family-based estimates of direct effects can be biased by genetic confounding. In humans, such biases will often be small per-locus, but can be compounded when effect size estimates are used in polygenic scores. We illustrate the influence of genetic confounding on population- and family-based estimates of direct effects using models of assortative mating, population stratification, and stabilizing selection on GWAS traits. We further show how family-based estimates of indirect genetic effects, based on comparisons of parentally transmitted and untransmitted alleles, can suffer substantial genetic confounding. In addition to known biases that can arise in family-based GWASs when interactions between family members are ignored, we show that biases can also arise from gene-by-environment (G×E) interactions when parental genotypes are not distributed identically across interacting environmental and genetic backgrounds. We conclude that, while family-based studies have placed GWAS estimation on a more rigorous footing, they carry subtle issues of interpretation that arise from confounding and interactions. In the standard ‘population-based’ approach, the GWAS is conducted on a set of ‘unrelated’ individuals. The associations that are detected can arise when a variant causally affects the trait or when it is in tight physical linkage with causal variants nearby.Central to the aims of GWASs is the estimation of variants’ effect sizes on traits of interest. These effect size estimates are important for identifying and prioritizing variants and implicated genes for functional followup, and may be used to form statistical predictors of trait values or to understand the causal or mechanistic role of genetic variation in traits. Understanding sources of error and bias in GWAS effect size estimates is therefore crucial.The interpretation of GWAS effect size estimates is complicated by four broad factors . First, Since our primary interest here will be genetic confounding, we briefly describe some potential sources of the long-range allelic associations that drive it: population structure, assortative mating, and selection on the GWAS trait.Population structure leads to genetic correlations across the genome when allele frequencies differ across populations or geographic regions: sampled individuals from particular populations are likely to carry, across their genomes, alleles that are common in those populations, which induces correlations among these alleles, potentially across large genomic distances. Such genetic correlations persist even after the populations mix, as alleles that were more common in a particular source population retain their association until uncoupled by recombination.Assortative mating brings alleles with the same directional effect on a trait  together in mates, and therefore bundles these alleles in offspring and subsequent generations. This bundling manifests as positive genetic correlations among alleles with the same directional effect , which cFinally, natural selection on a GWAS trait can result in genetic correlations by favoring certain combinations of trait-increasing and trait-decreasing alleles. A form of selection that is expected to be common for many traits of interest is stabilizing selection, which penalizes deviations from an optimal trait value. By favoring compensating combinations of trait-increasing and trait-decreasing alleles, stabilizing selection generates negative correlations among alleles with the same directional effect , 1974, aThe potential for dynastic, environmental, and genetic confounds to bias GWAS effect size estimates has long been recognized , and so One promising way forward is to estimate allelic effects within families, either by comparing the separate associations of parentally transmitted and untransmitted alleles with trait values in the offspring , or by aConsistent with both the presence of substantial confounds in some population-based GWASs and the mitigation of these confounds in within-family GWASs, family-based estimates of direct effect sizes and aggregate quantities based on these estimates  are substantially smaller than population GWAS estimates for a number of traits, most notably social and behavioural traits . LikewisOur aim in this paper is to study a general model of confounding in GWASs, to generate clear intuition for its influence on estimates of effect sizes in both population- and family-based designs. A number of the issues that we analyze have previously been raised, particularly in the context of population-based GWASs e.g., ; here, wOur first focus is on confounding—and genetic confounding in particular—in the absence of G×E and G×G interactions. To better understand the differences between population and within-family GWASs, we first study a general model of genetic confounding in the absence of G×E and G×G interactions. We derive expressions for estimators of direct effects in both population and within-family GWASs, as functions of the true direct and indirect effects at a locus and the genetic confounds induced by other loci. In doing so, we find that family-based estimates of direct effects are in fact susceptible to genetic confounding, contrary to standard interpretation. Reassuringly, in many of the models we consider, the resulting biases are likely to be small in humans. We also address a related case: family-based GWAS designs that consider transmitted and untransmitted parental alleles and in which the indirect (or ‘dynastic’) effect of an allele is estimated from its association with the offspring’s phenotype when carried by the parent but not transmitted to the offspring. We show that this estimator of indirect effects can be substantially biased by genetic and environmental confounds, in a similar way to population estimates of direct effects. Next, we consider various sources of genetic confounding—assortative mating, population structure, and stabilizing selection on GWAS traits— and how they influence estimates of direct effects in both population and within-family GWASs.We then turn to sibling indirect effects, which are known to bias estimates of direct effects in sibling-based GWASs , 2022. WFinally, we consider G×E and G×G interactions, showing how their presence can bias population and family-based estimates of direct genetic effects in contrasting ways, complicating the interpretation of family-based estimates.2A and B are in positive cis-LD if, when an individual inherits A from a given parent, the individual is disproportionately likely to inherit B from that parent  and trans-linkage disequilibrium (trans-LD). Genetic variants t parent . A and Br parent . These cr parent . To quanL, each of which segregates for two alleles. For ease of interpretation, and without loss of generality, we designate the ‘focal’ allele at locus l ∈ L to be the allele that directly increases the trait value, and we denote by pl the frequency of this allele. Allelic effects are assumed to be additive within and across loci, such that the trait value of an individual can be writtenConsider a trait Y influenced by genetic variants at a set of polymorphic loci 2.1The variants at a genotyped locus will usually not themselves have causal effects on the trait, but will instead be in cis-LD with—and thus ‘tag’—causal variants at nearby loci. Thus, we typically think of the association at a focal genotyped locus as reflecting the direct contributions of a relatively small number of tightly linked loci, al locus . Under tEffect size estimation in a population GWAS is complicated by the presence of environmental and genetic stratification. Under the model in  parents . Vλ is tThe environmental confound is onfounds ,D; and aThe direct genetic confounds arise because an allele carried by an offspring at 1Thus, as is now well appreciated, population-based GWASs potentially suffer from many types of confounds . In prac2.2The two within-family association study designs that we consider are parent-offspring GWASs and sibling GWASs. Other designs have been proposed to control for genetic and environmental confounding in the estimation of aggregate quantities such as heritability e.g., , but ourParent-offspring studies can be used to estimate trait associations separately for parentally transmitted and untransmitted variants at a locus  and gλU . The aimIn Similarly, an estimate of the direct effect can be obtained from pairs of siblings by regressing the differences in their phenotypes on the differences in their genotypes at the focal locus  locus λ . An assuIn differences between trans- and cis-LD, and moreover, that the biases in within-family studies are driven only by LD between the focal locus and causal loci on the same chromosome The derivations above further show that, while population association studies are biased by sums of trans- and cis-LD between the focal locus and all causal loci Because the difference between two siblings in their maternally inherited genotypes is independent of the difference in their paternally inherited genotypes, we may consider maternal and paternal transmissions separately in studying how a locus For effect size estimation at ds exist ,F: couplWe first consider the case where the recombination rate between  λ and l . Therefohe trait . If the not both . In thishe trait . When λ In contrast, if tes at λ ,F. Put dTherefore, only linked loci In a species with many chromosomes, such as humans, for a given locus, there will be many more unlinked loci than linked loci. Therefore, the set of loci that can confound a family-based association study at a given locus will be much smaller than the set of loci that can confound a population association study at the locus. It will often be the case, therefore, that biases in the estimation of direct genetic effects will be smaller in family-based studies than in population studies, a point that we explore below when we consider sources of genetic confounding.We now return to the regression of the trait on the untransmitted genotype in parent-offspring GWASs,  effects  and 7, fTherefore, estimating the indirect effect by regressing the trait value on the untransmitted genotype is highly susceptible to environmental confounding as well as both direct and indirect genetic confounding, in a similar way to estimating the direct effect via a population-based association study . Adjustm2.3A current drawback to family-based GWASs is that sample sizes are often small, limiting power to estimate direct genetic effects. Because of this limitation, instead of estimating per-locus effect sizes in family designs, investigators often measure the within-family phenotypic association of a combined linear predictor, a polygenic score (PGS), constructed using effect size estimates across many loci from a population GWAS. In the sibling-based version of this study design, the difference in siblings’ population-based PGSs is regressed on their difference in phenotypes e.g., . In pareWhen such PGS regressions are used within families for the same phenotype as the population GWAS, a non-zero slope of the PGS is usually interpreted as reflecting the fact that the PGS—despite having been calculated from a population GWAS and therefore subject to many potential confounds—nevertheless does capture the direct genetic effects of alleles. When the PGS for one phenotype is regressed within families on the value of another phenotype, non-zero slopes are often interpreted as evidence that direct genetic effects on the two phenotypes are causally related, for example through pleiotropic effects of the alleles involved.Suppose that we have performed a population GWAS for trait 1, generating effect size estimates pβlsee . Note thThe intuition for In the absence of confounding and under some simplifying assumptions, the sibling PGS covariance measures the contribution of each locus included in the PGS to the additive genic covariance between traits 1 and 2 that is tagged by the genotyped variants included in the PGS see . Under tInterpretation of the sibling PGS slopes is more complicated in the presence of genetic confounding see , which iIn summary, in the presence of confounding, non-zero sibling PGS slopes cannot be viewed as de facto evidence for causal relationships between traits.3As we have seen, genetic confounding of association studies depends, in ways that vary across study designs, on levels of non-local cis- and trans-LD between the study locus and loci that influence the study trait. Below, we consider various processes that give rise to non-local cis- and trans-LD, and their likely impact on the different association study designs. We focus our attention on the potential for these sources of LD to confound measurement of several key metrics. First, the average deviation of the estimated effect size from its true value, tability . It is agithub.com/cveller/confoundedGWAS.In what follows, for simplicity, we ignore indirect effects and assume that there is no environmental confounding  or distinct traits (cross-trait assortative mating). For example, humans are known to exhibit same-trait assortative mating for height and cross-trait assortative mating for educational attainment and height ; this bias too will then gradually shrink to zero as recombination erodes the remaining cis-LD . ConcomiAn important practical question is how genetic confounding affects the GWAS loci we prioritize for functional follow-up and for use in the construction of polygenic scores. SNPs are usually prioritized on the basis of their GWAS p-value, which is proportional to the estimated variance explained by a SNP, However, analysis of human GWASs suggests that quantitative traits can have widely different genetic architectures, with, in particular, substantial differences in the effective numbers of causal loci involved and in the distribution of minor allele frequencies  and independent of the direction and size of effects at individual loci. Therefore, the LD induced by these allele frequency differences will, on average, not bias effect size estimates in a population GWAS:However, the LD induced by population structure will inflate the average squared effect size estimate, and by extension the variance of effect size estimates . In Appesee also .In contrast, because effect size estimates from within-family GWASs are not confounded in this model of isolated populations, the average squared effect size estimate will not differ substantially from its expectation in an unstructured population .While we have focused on a simple model of two isolated populations, the result that within-family association studies are not confounded holds for other kinds of population structure as well. Specifically, we may be concerned that a population GWAS suffers from genetic confounding along some given axis of population stratification. However, the family-based estimates will be unbiased by confounding along such an axis if the maternal and paternal genotypes at each locus are exchangeable with respect to each other along this axis . This reSelection and phenotype-biased migration can also generate allele frequency differences among populations  is not a major determinant of genome-wide relatedness at non-causal loci . Nor wilAgain, these issues largely vanish in family-based studies, although phenotype-biased migration can cause transient differences in cis- and trans-LD that lead to biases in family-based estimates of direct effects  and 7.3.3When populations that have previously been separated come into contact, alleles from the same ancestral population remain associated with each other in the admixed population until they are dissociated by recombination. If allele frequencies had diverged between the ancestral populations, this ‘ancestry disequilibrium’ can translate to cis-LD between loci affecting a trait , potentiFor concreteness, we again consider a simple model where two populations have been separated for some time, allowing allele frequencies to diverge between them. The populations then come into contact and admix in the proportions clλ per generation, so that, Suppose that, just before admixture, the frequencies of the focal allele at a given locus How do these patterns of LD affect a population GWAS? If allele frequency differences between populations arose from neutral drift, they will be independent of effect sizes at causal loci and across loci, and therefore will not contribute, on average, a systematic directional bias to effect size estimates. However, they will inflate the average squared effect size estimate, by a smaller amount than for a population GWAS performed when the populations were still separated (because of the elimination of trans-LD under random mating in the admixed population). Moreover, this amount will decline in the generations after admixture as the remaining cis-LD is eroded by recombination ; Fig. 5.Although within-family GWASs were not genetically confounded when the populations were separate , they become genetically confounded in the admixed population, as all trans-LD is eliminated by random mating in the admixed population, leaving an excess of cis-LD relative to trans-LD that biases effect size estimates  and 7. AIn comparing the average squared effect size estimate in a population and a family-based GWAS, we observe that the value in the population GWAS rapidly declines to approximately the same level as the value in the within-family GWAS, despite the former having started at a much higher level in the initial admixed population . The expIn addition to drift, and as discussed above, selection and phenotype-biased migration can generate systematic, signed (effect-size correlated) LD, which would lead to systematic cis-LD in the descendent admixed population. These would lead to larger inflations of genetic variance and genetic correlations than would be expected had allele frequency divergence between the ancestral populations been due to drift alone, and would complicate interpretations of genetic correlations as being due to pleiotropy. Moreoever, if the admixed population is more than a few generations old such that LD between unlinked loci but not linked loci has largely been broken down, then population- and family-based estimates of these quantities might be similar.Factors other than selection and phenotype-biased migration can also generate non-pleiotropic genetic correlation signals in family-based studies of admixed populations. In fact, the use of confounded population GWAS effect sizes can be sufficient. As an example of the confounding of genetic correlations in admixed populations due to a confounded GWAS for one trait, consider the GIANT-GWAS height polygenic score. Owing to confounding within Europe , the hei3.4Stabilizing selection—selection against deviations from an optimal phenotypic value—is thought to be common , and hasTo quantify these biases, we consider the model of he trait .Under these same assumptions, we calculate in Thus, the bias in effect size estimation can be calculated given estimates of the phenotypic variance and heritability of the trait, the harmonic mean recombination rate, and the strength of stabilizing selection . In the Attenuation of effect size estimates is larger if stabilizing selection is stronger or if the trait is more heritable. Taking height as an example, heritability is ~0.8, es of LD . More geS/VP≈170 .Given the estimate  average .The quantitative importance of these biases will vary by application. In situations where the goal is gene discovery, for example, 5% reductions in effect size estimates are unlikely to flip the statistical significance of variants with large effects on a trait. However, the attenuations in effect size estimates caused by stabilizing selection are systematic across loci, and therefore could substantially affect aggregate quantities based on these estimates. For example, the range of average reductions in population effect size estimates calculated above for human traits would translate to reductions in naive estimates of SNP-based heritabilities of between 0.5% and 10% (~6% in the case of height). If effect sizes are estimated by within-family GWAS, on the other hand, the reductions in these SNP-based heritability estimates would be much smaller.As a further example, by generating negative LD between alleles with the same directional effect on the trait, the impact of stabilizing selection opposes, and therefore masks, the genetic impact of assortative mating . A practAs in our analysis of assortative mating above, if stabilizing selection ceases in some generation, the negative LD that built up during the period of stabilizing selection will decay over subsequent generations, rapidly for pairs of loci on different chromosomes and more slowly for linked pairs of loci. Patterns of selection on human traits have changed over time—for example, the strength of stabilizing selection on birth weight has relaxed . In gene3.5Indirect effects of siblings’ genotypes on each other’s phenotypes are known to be a potential source of bias in sibling-based GWASs , and cani’s phenotype can be writtenHow would a population GWAS be affected by the same sibling indirect effects? Sibling The other channel by which sibling indirect effects can influence a population GWAS is driven by the genotypic correlation among siblings, and is easiest to understand if we assume that sibling indirect effects are weak 3.6Up to this point, we have assumed that alleles’ direct effects do not vary across environments or genetic backgrounds. To generate intuition for the influence of If we perform a sibling GWAS by taking pairs of full siblings al locus . The intWe can compare this estimate from a sibling GWAS to one from a population GWAS, again under the assumption of no genetic confounding or indirect effects from siblings:he locus . The appLike the family-based estimate, the population-based effect size estimate is distorted when heterozygotes are not randomly distributed over family backgrounds As noted above, because of current sample size constraints in family-based studies, a common strategy is to calculate the association of population-based PGSs and phenotypic differences among family members. In the absence of confounding, it is clear from  studies , but theAn allele’s effect could also systematically differ across families Up to this point, we have also ignored parent-offspring interactions as a possible source of bias in family-based studies. Following the the same logic above, interactions between parents’ and offsprings’ alleles will result in family GWAS estimates that are the average effect of the focal allele in an offspring conditional on the genetic background of a heterozygous parent. Thus, again, a non-random distribution of genetic backgrounds in heterozygous parents is a potential source of bias.One way that heterozygous parents might exhibit a non-random distribution of genetic backgrounds is via trait-based assortative mating, which could therefore modify the way that epistasis and parent-offspring interactions influence effect size estimation in a family-based GWAS relative to a population GWAS and relative to the true average population effect.A final, overarching complication is that the individuals participating in a population GWAS are not a random subset of the population(s) from which they are drawn , and fam4It has long been recognized that population GWASs in humans can be biased by environmental and genetic confounding . CurrentEffect size estimates from within-family GWASs are less affected by these various confounds. In the absence of Genetic confounding is caused by long-range LD between loci that affect the trait or traits under study. To illustrate the potential for genetic confounds to bias GWAS effect size estimates, we have considered several sources of long-range LD. Some of these—assortative mating, selection on GWAS traits, and phenotype-biased migration—can cause systematic directional biases in GWAS effect size estimates. Others, such as neutral population structure, cause random biases that influence the variance of effect size estimates and related quantities. Assortative mating and neutral population structure have received considerable theoretical attention in the GWAS literature e.g., ,b. Here,We wish to emphasize stabilizing selection in particular as a potential source of systematic confounding in GWASs. Stabilizing selection has been well studied in the quantitative genetics literature but less so in the context of GWASs, despite its expected ubiquity. By selecting for compensating combinations of trait-increasing and trait-decreasing alleles, stabilizing selection generates negative LD between alleles with the same directional effect on the trait , 1974, aLlocal in For a given genotyped locus in a GWAS, there is no bright line between local ‘tagged’ LD and long-range confounding LD, and one reasonable objection to the approach taken here is that that we have used an arbitrary definition of the causal loci that are locally tagged by a genotyped locus  causally affect a child’s phenotype  and study the effects of PGSs within families . For one, SNPs are usually chosen for inclusion in the PGS on the basis of their statistical significance in a population GWAS. This approach prioritizes SNPs whose effect size estimates are amplified (or even wholly generated) by confounding  link between A and B. These effects can be exacerbated if the two traits have different genetic architectures . InsteadAlso complicating the interpretation of family-based effect size estimates are various types of interactions. Indirect effects between siblings can bias family estimates of direct genetic effects  in ways As we have further shown here, om GWASs . The intom GWASs , reinforIn summary, family-based studies are a clear step forward towards quantifying genetic effects, with large-scale family studies carrying the potential to resolve long-standing issues in human genetics. However, these designs come with their own sets of caveats, which will be important to understand and acknowledge as family-based genetic studies become a key tool in the exploration of causal effects across disparate fields of study.github.com/cveller/confoundedGWAS.All simulations were carried out in SLiM 4.0 . Code isFor the purpose of carrying out sibling association studies in our simulations, we assumed a simple, monogamous mating structure: each generation, each female and each male is involved in a single mating pair, and each mating pair produces exactly two offspring (who are therefore full siblings). To maintain the precisely even sex ratio required by this scheme, we assumed that a quarter of mating pairs produce two daughters, a quarter produce two sons, and half produce a son and a daughter. Population sizes were chosen to ensure that these numbers of mating pairs were whole numbers, and mating pairs were permuted randomly each generation before assigning brood sex ratios .Each generation, per-locus effect size estimates were calculated for both population-wide and sibling GWASs. The former were calculated as the regression of trait values on per-locus genotypes, while the latter were calculated as the regression of sibling differences in trait values on sibling differences in per-locus genotypes.N = 40,000.In all simulations, the total population size was For our general cross-trait assortative mating setup, traits 1 and 2 are influenced by variation at sets of bi-allelic loci Our aim is to simulate a scenario where assortative mating is based on females’ values for trait 1 and males’ values for trait 2, such that, across mating pairs, the correlation of the mother’s PGS for trait 1, First, we choose initial ‘perturbation sizes’ Supplement 1