Integrating genome-wide association studies (GWAS) with transcriptomic data, human complex traits and diseases have been linked to relevant tissues and cell types using different methods. However, different results from these methods generated confusion while no gold standard is currently accepted, making it difficult to evaluate the discoveries. Here, applying three methods on the same data source, we estimated the sensitivity and specificity of these methods in the absence of a gold standard. We established a more specific tissue-trait association atlas by combining the information captured by different methods. Our triangulation strategy improves the performance of existing methods in establishing tissue-trait associations. The results provide better etiological and functional insights for the tissues underlying different human complex traits and diseases. Establishing associations between human complex traits and tissues or cell types is essential in current genetics and biology. It provides useful etiological and functional insights for understanding the regulatory mechanisms underlying complex traits and diseases and subsequently directs the clinical research and even treatment. However, one can hardly answer such a question systematically by traditional experimental designs.Genome-wide association studies (GWAS) produced a tremendous amount of summary association data describing the associations between millions of single-nucleotide polymorphisms (SNPs) and various phenotypes. On the other hand, RNA-sequencing (RNA-seq) technology has generated high-throughput gene expression data not only in different tissues  but alsoSeveral methods have been proposed in recent years, prioritizing trait-relevant tissues or cell types . Most ofp = 2 × 10–4), small intestine (p = 0.01), spleen (p = 0.04), and adrenal gland (p = 0.05), supported by, e.g., the nutrient absorption function of the small intestine and the link between spleen and lipid metabolism (p = 2.05 × 10–13), pancreas (p = 3.83 × 10–13), thyroid (p = 9.85 × 10–13), uterus (p = 1.23 × 10–8), and small intestine . Most tissues’ p-values were lower than 0.05, but the spleen was ranked 19/44 and the adrenal gland 21/44. Their results were quite different from those by Regardless of these available methods, this is a typical discovery problem where a yes/no inference needs to be made for each test. Normally with the same null hypothesis, applying different methods to the same data produces similar answers as the statistical power is similar. However, for the tissue-trait association problem, the different methods developed are sometimes distinct not only in their setup but also in producing distinct discoveries. For example, tabolism . While iconditionally independent . Thus, based on the estimated operating characteristics, one can combine information captured by different kinds of methods testing tissue-trait associations, since none of the methods could capture the full information of the underlying biology.In fact, for three or more distinct methods testing the same set of null hypotheses, the sensitivity and specificity of each method can be estimated without any gold standard , as longHere, we aim to integrate the results from different methods to better investigate the tissue-trait association problem. We approach this by: 1) applying three distinct methods on the same set of tissue-trait pairs; 2) conducting maximum likelihood estimation of the sensitivity and specificity of each method in the absence of a gold standard; 3) subsequently combining the results from these methods to generate a more credible tissue-trait association atlas.Ai represent the unobservable true association status for the i-th pair of tissue and trait, where Ai = 1 represents associated, and Ai = 0 unassociated. In our model, ρ = P (Ai = 1) is the same for any given i, so without losing generality, we use A to denote Ai. Given a particular set of significance thresholds for K binary tests of the status of A, we have K random variables Y1, … , YK, for each of i = 1, … , n pairs of tissues and traits. Writing the true- and false-positive rates of the K binary tests as ϕk = P(Yik = 1|A = 1) and ψk = P(Yik = 1|A = 0), respectively, the unknown parameters are the prevalence of tissue-trait association ρ = P (A = 1) and θ = , k = 1, … , K. With K⩾3 observed tests, ρ and θ can be estimated by maximizing the likelihood functionK − 1, is no less than the number of parameters, 2K + 1. Assuming conditional independence of the K binary tests, i.e., given A and the outcome of any test Yi, one cannot predict the outcomes of the other tests, we havep-value thresholds for different tissue-trait association test methods, we used quasi-Newton method for optimization to solve the above maximum likelihood problem. We bootstrapped the observed binary data to assess the variation of the estimates. In this article, we repeated the bootstrap procedure for 99 times. Our implementation is publicly available as an R package (see Code Availability), which can assess three or more methods simultaneously. For the scenario of three methods, the maximum likelihood estimates (MLE) of the parameters can be derived analytically /(ψk (1 − ρ) + ϕkρ). Then, corresponding to Si, the FDR for the i-th tissue-trait pair could be calculated to quantify the confidence of the association:i, the overall FDR across all the tissue-trait pairs could be assessed byn+ = ∑iI(Si > 0), so that methods with high/low FDR are down-/up-weighted. φ−1 (rank (⋅)) stands for standard inverse-Gaussian transformation. As operating characteristics were estimated, the false discovery rate (FDR) for each method can be subsequently calculated as ρ = P (A = 1) while A indicate the true association status between traits and tissues. For each method, we gave the number of tests n = 1,000, 10,000, 100,000 and assigned 0–1 values to Yi, i = 1, … , n representing the binary test results. We gave the true values of the true- and false-positive rates of the K = 3 binary tests, i.e., ϕk = P(Yik = 1|A = 1) and ψk = P(Yik = 1|A = 0), and calculated the theoretical probability of each binary results combination P, assuming conditional independence. We randomly produced the binary results Yik  of the K = 3 methods from the multinomial distribution with the calculated corresponding probabilities P. Then, based on the simulated binary data Yik, we estimated the operating characteristics of the K = 3 methods θ =  and the prevalence ρ using our maximum likelihood procedure above. We repeated the simulation for 100 times to assess the variation of our estimates.We set the true prevalence Based on the modelling logic, we classified the methods reviewed by Data Availability). We used tissue-specific transcriptome data from the GTEx project version 7. Samples were collected from 48 non-diseased tissue sites  curve.We applied RolyPoly  and straFor every GWAS summary-level data, we performed LDSC to test heritability enrichment on tissue-specifically expressed genes in order to infer the associations between tissues and complex traits. We analyzed the tissue-level GTEx v7 gene expression data.For GTEx data, we used the median TPM value across individuals to represent the gene expression in each tissue. In each gene expression data set, following the procedure by % of expressed genes with the highest expression specificity score as the specifically expressed gene set. Then we extracted the genome start and end positions of the genes in each specifically expressed gene set based on GRCh37 reference. In stratified LDSC analysis, SNPs within the specifically expressed genes were annotated as 1 otherwise 0.For every tissue or cell type, we selected the 10p-values (one-sided) were used to test associations between each tissue/cell type and a phenotype.LD scores for the annotated SNPs in each tissue and cell type were calculated based on a one centiMorgan (cM) window. Only HapMap3 SNPs were retained for the analysis. We included all the pre-built baseline annotations in the ldsc software as covariates in the stratified regression model. We used the -overlap-annot argument and frequency files 1000G_Phase3_frq.tgz to confine our analysis on SNPs with MAF RolyPoly tries to catch the relationship between the variance of GWAS-estimated SNP effects and gene expressions in a tissue or a cell type in order to prioritize trait-relevant tissues or cell types.R2 > 0.2.Following the RolyPoly package tutorial, first, each GWAS data file was formatted. The positions of SNPs match GRCh37 reference genome. Second, we labeled genes by ENSG IDs and filtered out non-protein-coding genes. For normalization, we transformed, across all genes, the expression values to their quantiles. Across all the tissues, we inverse-normal transformed the values to standard normal distribution quantiles. We took absolute values to ensure the expression values are positive as the tutorial recommends. Third, an annotation file of the genes is required, consisting of the chromosome, start and end of the block, and a block label. The block label corresponds to the gene IDs in the expression data set. Following the settings in the tutorial, we chose a 10 kb window as a block centered at each gene’s transcription starting site (TSS). We produced this annotation file from the Ensembl GRCh37 gtf file. Autosomal genes and SNPs were analyzed. For LD reference data, we used the files provided by the RolyPoly package, calculated via PLINK based on 1,000 Genomes phase 3 reference, filtered with p-value threshold, each method is a binary test on n pairs of tissues and traits. Yik represents the outcome of the i-th test using the k-th method, k = 1, 2, … , K. 2K + 1 parameters are unknown and to be estimated, including the sensitivity and specificity of each method (denoted jointly as θ) and the prevalence of true associations (denoted as ρ) in the n tissue-trait combinations. The likelihood function isK⩾3, the available degrees of freedom (2K − 1) becomes no less than the numbers of parameters (2K + 1) so that we can estimate θ and ρ. An uncheckable but usually justifiable assumption in practice is that the evaluated methods are conditionally independent, 15 meaning that for a single test, one cannot easily predict the result from one method based on the result from another. The assumption fits the scientific problem we face here. We implemented a maximum likelihood estimation procedure to estimate θ for any number of K (see Code Availability).Since the true biological relevance between a pair of tissue and trait is mostly unclear, it is challenging to evaluate the each method’s performance in detecting tissue-trait associations. To take advantage of different analysis strategies, we start by estimating each method’s operating characteristics in the absence of a gold standard. Under a particular n is the number of tests by each method in one simulation. We repeated the simulation 100 times for each simulation setting to obtain the empirical distribution of the estimates. The receiver operating characteristic (ROC) results showed that our estimates were consistent. The estimates converged to the true values as the sample size increased. We also tested our procedure under different levels of true prevalence . Based on these same GWAS summary statistics and the same gene expression data of 48 tissues from the GTEx project, we obtained tissue-by-trait p-value matrices for RolyPoly and LDSC, respectively. We extracted p-values of the eQTL method for the same GWASed traits from the original publication by the GTEx consortium  to 1 (highest strength). Conditioned on the positive discoveries, we incorporated the false discovery rate (FDR) of each method to calculate the FDRs for the combined association scores .p-value threshold and evaluated the corresponding FDR , height, and birth weight. It reflected the biological complexity of those phenotypes. In particular, blood lipids showed strong signals in the liver and also associations with the adrenal gland, visceral adipose tissue (VAT), small intestine, and whole blood. Conversion of blood cholesterol into cortisol hormone in the adrenal  and adipEducational attainment and most psychiatric disorders showed robust brain-specific associations. The link between spleen and Alzheimer’s disease (AD) indicates that AD is immune-related and is not significantly related to the brain tissues. This finding agrees with the theory that immunity and inflammation play an essential role in AD .Fasting phenotypes showed associations with fewer tissues. Fasting glucose level was significantly linked to the pancreas, the same as T2D. However, the pancreas association was not significant for fasting insulin and proinsulin levels, possibly due to the limited statistical power of these GWAS and low heritability of these two traits.Among the obesity-related anthropometric traits, only the waist-hip ratio (WHR) was strongly associated with subcutaneous adipose tissue. Such an association cannot be detected in body mass index (BMI) and waist circumference, regardless of the large sample size of BMI GWAS meta-analysis. Such results suggest WHR as a more robust quantity that captures adipose-induced obesity. BMI and waist circumference may be more easily influenced by the postnatal environment or regulated by nerves or hormones while showing more associations with the brain. We noted that obesity measurements did not share a similar profile with blood lipids.Uterus showed strong associations with traits like Educational attainment, birth weight, and breast cancer. Ovary also showed no or weaker associations with these traits. However, other genital organs, such as the testis and vagina, had no similar signals. These findings likely implied the maternal genetic effects on these traits, potentially relevant to pregnancy .Based on the three methods’ estimated operating characteristics, analog to standard ROC, we examined each method’s FDR as a function of its number of claimed positives . Though In the absence of a gold standard, we assessed the operating characteristics of three methods that prioritize tissues associated with complex traits and diseases. Then, we evaluated the estimation procedure in simulation and obtained a ensemble-analyzed score to construct tissue-trait associations by integrating results from different methods. We proved that our results had better FDR level than results from other existing methods. With practice, we established a more credible association atlas across 44 human tissues and 27 complex traits and diseases.Our analysis is different from conventional meta-analysis. Normally, meta-analysis refers to researchers combining results obtained from different samples/studies using the same method (or very similar methods), in order to reach larger sample size thus higher statistical power. However, we combined different results from distinct methods based on the same/similar data source. This is similar to the “ensemble” idea in the field of machine learning. Thus, we are not performing any meta-analysis for power (to improve sensitivity) but rather gathering more information to reduce FDR (to improve specificity).conditionally independent. This means that the methods considered in our likelihood inference need to be as distinct as possible, preferably based on distinct assumptions and modelling logic. Therefore, simultaneously including similar methods based on similar modeling ideas would obviously violate the conditional independence assumption. The three methods we chose differ in the underlying statistical models, and they indeed produce sufficiently distinct results to justify conditional independence. Our assessment of the operating characteristics found the limited performance of the RolyPoly and eQTL-based methods. LDSC, focusing on the enrichment of heritability or genetic association signals on tissue-specific gene expressions, showed slightly better performance. Such an observation indicates that methods that properly account for LD structure across the genome tend to have less noise in the inferential process. The eQTL method appeared to have inflated sensitivity as it does not consider genome-wide architecture.conditionally independent. Under this assumption, if two methods report similar results, then we have more confidence on such results, as we have evidence from two conditionally independent sources. Nevertheless, it is still possible that a good method might be down-weighted by two bad/biased methods, especially when the two bad methods are too much underpowered, i.e., simultaneously reporting a large number of negatives. So, in practice, we need to consider methods that have reasonable statistical power, so that our combined inference results can gain more information and produce more specific discoveries with smaller FDR.When we assess three imperfect testing methods, while no gold standard exists, the assumption of our likelihood inference is that the methods are ρ might also be of interest, referring to the global proportion of true associations. The interpretation of ρ would be more straightforward if we could estimate a trait-specific proportion of truly associated tissues; However, this would only be ideal if the number of tissues assessed is large. In the current analysis, having only an overall prevalence parameter would maximize our power for estimating the key sensitivity and specificity parameters. The estimated prevalence only slightly varies as long as the thresholds for the three testing methods are not too extreme . However, some trait pairs with high genetic correlation didn’t quite share a similar tissue-association pattern, such as waist circumference and waist-hip ratio , and BMI and waist-hip ratio . Though we usually consider these three traits as similar predictors of health, it seems that waist-hip ratio might be affected by some particular pathways in the subcutaneous adipose tissue rather than in brain tissues or neurons. The trait pairs with high genetic correlations but not so similar tissue-association profiles may suggest new insights on tissue biology and underlying pathways.The methods for establishing tissue-trait associations generally link genome-wide association signals to tissue-specific gene expression information. If we look into the genetic correlations  Supplem, it is nCompared to previous studies that applied single methods, we obtained more specific trait-relevant tissues. Nevertheless, we still lack clear biological explanations for many tissue-trait associations. For example, there is a link between human height and artery: Does it reflect the negative genetic correlation between heart disease and height , or doeshttps://github.com/xiashen/triangulation. The software LDSC we used in this paper is available at https://github.com/bulik/ldsc. The R package RolyPoly for inferring relevant cell types and tissues for complex traits is available at https://github.com/dcalderon/rolypoly.The code we used in our analysis is available as an R package triangulation at:


We found that 8 of the 54 SNPs showed significant GxE. Candidate genes underlying variation in root pulling force included those involved in nutrient transport. Although they are often treated separately, variation in the ability of plant roots to sense and respond to variation in environmental resources including water and nutrients may be linked by the genes and pathways underlying this variation. While functional validation of the identified genes is needed, our results expand the current knowledge of root phenotypic plasticity at the whole plant and gene levels, and further elucidate the complex genetic architecture of maize root systems.High-throughput, field-based characterization of root systems for hundreds of genotypes in thousands of plots is necessary for breeding and identifying loci underlying variation in root traits and their plasticity. We designed a large-scale sampling of root pulling force, the vertical force required to extract the root system from the soil, in a maize diversity panel under differing irrigation levels for two growing seasons. We then characterized the root system architecture of the extracted root crowns. We found consistent patterns of phenotypic plasticity for root pulling force for a subset of genotypes under differential irrigation, suggesting that root plasticity is predictable. Using genome-wide association analysis, we identified 54 SNPs as statistically significant for six independent root pulling force measurements across two irrigation levels and four developmental timepoints. For every significant GWAS SNP for any trait in any treatment and timepoint we conducted  Originating approximately 400 million years ago, roots evolved at least twice in early plant lineages and provided anchorage . FollowiIn addition to their fundamental biological importance and intrinsic structural complexity, roots and root systems vary among species, genotypes, and environments. Within a given species, RSA is highly plastic, responding to variation in nutrient status and soil composition . RSA traPhenotypic plasticity in the form of altered rates of growth and timing of development of organs and traits are common adaptive responses for both RSA and above ground traits in plants . While pPhenotypic plasticity for agriculturally important traits, has been proposed as a breeding target for optimizing response to environmental stress . ImplemeArabidopsis thaliana  which is an alternative and a higher throughput technique compared to shovelomics based excavation for removing root systems from a field. RPF is quantified through the process of attaching the base of the shoot with a rope to a digital force gauge and applying manual, vertical force until the root system is extracted from the soil. The force required to pull the root system out of the ground is measured by the force gauge and recorded as RPF. This method provides a simple, instantaneous and quantitative measurement of the roots system during extraction. We have successfully used the RPF technique to identify QTL for root system size in ca napus , and QTLca napus . While Rca napus . Due to Here we used RPF, along with subsequent imaging of pulled root systems, to examine means and plasticity of RSA traits in the SAM diversity maize panel. We phenotyped this population at multiple developmental stages across two field seasons and differential irrigation treatments to investigate GxE in RSA traits. We then performed GWAS on these measurements, which identified a number of candidate genes potentially underlying the variation in root traits. Important questions addressed in this work are: (1) What proportion of trait variance in RPF and RSA in maize is explained by genetics, the environment and GxE? (2) What is the genetic architecture of RPF and RSA in maize across development and irrigation treatments? (3) Is there evidence for GxE at the individual gene level?2O5 in 2018 and 190 lb/ac N, 60 lb/ac P2O5, and 4 lb/ac Zn in 2019. Each plot consisted of two 12-foot rows with 30-inch spacing between rows and 9-inch spacing between plants within rows. The irrigated treatments received approximately 1 inch of water per week, while the drought treatments were irrigated until well-established (~5 weeks after planting) and then received only natural precipitation, except at the root harvesting when it also received irrigation to homogenize the root harvesting process  was used to pull the root crown vertically from the soil. Root crowns were cleaned with water and imaged to obtain additional RSA measurements using the DIRT image analysis software  before b1Spearman’s rank correlation coefficients were calculated using the ‘‘chart.Correlation’’ function in the ‘‘Performance Analytics’’ package in R.We estimated broad-sense heritability of traits using a random effect one-way ANOVA model. We split phenotypic data by trait, timepoint, and treatment and used the lmer function in the R package “lme4” v1.1-21 , treatinvia GWAS, the best linear unbiased predictors (BLUPs) were calculated from genotype simple means by treating genotype as a random effect using the R package “lme4” v1.1-21 . This plasticity in RPF is positively associated with plasticity in shoot mass, even on a percent of wet treatment basis .Across treatments and growing seasons, variance component analysis indicated that GxE accounted for a range of 1.2–9.8% of the phenotypic variation in RPF . OverallThe FarmCPU GWAS model controls for false discoveries by accounting for kinship and population structure while still providing high statistical power for candidate gene identification . Additiopost hoc ANOVA on each of the 54 significant GWAS SNPs for RPF that we identified. We tested effects of SNP, treatment, and SNP-by-treatment interaction. To account for potentially confounding effects of population structure, we included PCA scores generated from SNP data in the ANOVA model. Through this analysis, we found that eight of the significant GWAS SNPs for RPF showed a significant QTLxTreatment effect  RPF at all developmental stages sampled  on root system width. This is consistent with the role of PHO1;2A in phosphorus transport, given phosphorus signaling’s role in regulating shallow root angles . The consistent lack of co-located candidate genes across all the RSA traits suggests that despite being correlated, independent phenotypic variation was present which allowed our analyses to identify candidate genes uniquely associated with these trait’s measurable variation. We note however that GWAS models such as FarmCPU are not optimal for explicitly testing whether the same loci are affecting traits across developmental stages, environments or growing seasons and thus may be one reason our GWA efforts did not identify overlap in RSA candidate genes. post hoc tests for GxE for all significant GWAS SNPs and identified 12 SNPs that showed significant GxE: 8 for RPF, 2 for shoot mass, and 1 each for root mass and area. Although we identified 48 candidate genes for flowering time, none showed significant GxE which is reflective of this trait’s overall lower phenotypic plasticity . Our finding of nitrogen signaling genes exhibiting GxE in response to drought is supportive of previous reports showing differential expression of homologous nitrogen signaling genes in response to water stress in other plant species  roles in nutrient signaling from roots to shoots and (2) greater expression in root tissue such as eb191650 . This iseriments . Additiothaliana , and AMTot-based . Future AMT5, SLAH2, and PHO1;2A were not identified as candidate genes for RSA traits other than RPF via GWA, our post hoc analyses with the alternate SNP alleles at these genes identified significant differences in other traits such as root area, depth, and width that were consistent with their differences in RPF  root phenotypic plasticity is predictable for some maize genotypes, (2) RSA in maize is a highly complex trait controlled by many functionally diverse genes, and (3) RPF is an efficient phenotype capable of identifying candidate genes associated with variation in additional root architectural traits. Future studies using functional genetic techniques such as mutant screens and QTL mapping in RIL populations are needed to validate the candidate genes identified in this study and accurately quantify effect sizes of alleles across developmental stages and environments. Additionally, there is a need to develop field and analysis designs that improve our ability directly test for QTLxE in statistically robust genome-wide analysis. Overall, the results discussed here extend our knowledge of root phenotypic plasticity in maize at the whole-plant, and gene levels and further elucidate the highly complex genetic architecture controlling variation in maize RSA.The datasets presented in this study can be found in online repositories. The names of the repository/repositories and accession number(s) can be found in the article/PW helped acquire phenotype data, performed the GWAS, and wrote the manuscript. KL helped acquire phenotype data, performed the GxE analyses, and wrote the manuscript. KH helped acquire phenotype data and assisted with manuscript writing. JLM helped with experimental design, acquiring phenotype data, analyses, and manuscript writing. JKM designed and supervised the experiment, provided guidance for phenotypic analyses, and assisted with manuscript writing. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Functional traits are phenotypic traits that affect an organism’s performance and shape ecosystem-level processes. The main challenge when using functional traits to quantify biodiversity is to choose which ones to measure since effort and money are limited. As one way of dealing with this, Hodgson et al.  introduced the idea of two types of traits, with soft traits that are easy and quick to quantify, and hard traits that are directly linked to ecosystem functioning but difficult to measure. If a link exists between the two types of traits, then one could use soft traits as a proxy for hard traits for a quick but meaningful assessment of biodiversity. However, this framework is based on two assumptions: (1) hard and soft traits must be tightly connected to allow reliable prediction of one using the other; (2) the relationship between traits must be monotonic and linear to be detected by the most common statistical techniques .Tetrahymena thermophila, which vary both in their measurement difficulty and functional meaningfulness. They were classified as: easy traits , intermediate traits (movement traits) and hard traits (oxygen consumption and population growth rate). We detected a high number (> 60%) of non-linear relations between the traits, which can explain the low number of significant relations found using linear models and PCA analysis. Overall, these analyses did not detect any relationship strong enough to predict one trait using another, but that does not imply there are none.Here we addressed those two assumptions by focusing on six functional traits of the protist species Our results highlighted the need to critically assess the relations among the functional traits used as proxies and those functional traits which they aim to reflect. A thorough assessment of whether such relations exist across species and communities is a necessary next step to evaluate whether it is possible to take a shortcut in quantifying functional diversity by collecting the data on easily measurable traits.The online version contains supplementary material available at 10.1186/s12862-022-02102-w. Biodiversity is declining at an alarming rate –5, requiThe main challenge when measuring functional diversity within a species relates to the choice of which functional traits to measure. There are too many traits to measure them all, and efforts are limited, thus usually only a subset of possible traits are chosen , 18, oftTetrahymena thermophila, a unicellular ciliate that has widely been studied as a model system in cellular and molecular biology for more than 80 years and in ecology and evolutionary biology for over a decade ),T. thermophila strains and replicates, our study failed to reveal any relations between traits that would allow predicting one trait from another. However, this does not imply there is no relation between these traits in reality. It is possible that relations only appear or change in specific environmental conditions [Despite a set of informed predictions about expected relations between soft and hard life-history traits and a high statistical power resulting from a large number of nditions , 74 due nditions ; for an nditions . For exanditions , 66, tigOur findings corroborate the idea that relying on soft traits that are simple and easy to measure as indirect proxies –77, may T. thermophila shows a high degree of plasticity when the environmental conditions change [All strains were maintained, before and during the experiment, under standardized culture conditions that allow only clonal reproduction , 79. This change , 33, 34.The experimental design involved measuring the six traits of interest for the 40 strains with a number of replicates that allowed reaching adequate statistical power for the analyses. The number of replicates was therefore a priori set to take into account the intrinsic error with which each trait can be measured in our microcosm setup, different for each trait, and slightly boosted to compensate for the limited but existing risk of losing some replicates due to bacterial contamination of the culture or potential other technical problems: 18 for growth measurements (measured over 5 days); 10 for measuring both the morphology, movement (snapshot measures) and oxygen consumption (measured over 2 h). For each strain, replicates each originated from different mother cultures, created from the stock culture three days before the experiment. This way of proceeding ensured that the replicates reflected the natural variability within each strain. To detect bacterial and fungal contamination, which can put cells under stress and alter their traits, we ran contamination tests after each trait measurement. These contamination tests were done by inoculating a Petri Dish containing a nutrient medium  with a few drops of the experimental cultures; contamination was detected by the presence of some fungal or bacterial development after three days at 27 °C. Contaminated samples were discarded from the analyses. We first created mother cultures for each strain and replicate by putting 500 µL of the corresponding culture stock and 6 mL of fresh axenic medium in a 30 mL cell culture container . Then, each mother culture was placed horizontally to favor oxygen ingress into the medium, and thus population growth. After a 3-day growth period, the measure of the six traits was performed on each replicate according to the protocols detailed below.2) and shape  were quantified [Morphology and movement traits were measured from digital images and videos recorded under a dark field microscope , 80 by pantified . NGDR isOxygen consumption was measured by quantifying the decay in dissolved oxygen concentration in a sealed high-density culture. Cell abundance was quantified in each mother culture (i.e. one replicate of a given strain) using a two-step process. In a first step, by measuring optical density at 550 nm , we were able to estimate the absorbance of the culture. In a second step, we combined that absorbance along with other factors (e.g. cell size) obtained from the pictures taken previously to estimate the cell abundance in the culture , 80. Thigcfit function  in its stationary phase by a factor of five, to allow exponential growth; experimental cultures were placed in 24-multiwell plates . Cell density was estimated every two hours over five days using optical density at 550 nm . The growth rate µ of each experimental culture was estimated as the slope of the optical density increase over time in its linear phase using the  package ).To explore relations between the six traits, we averaged all replicates at the strain level because we were interested in functional traits exhibited by the strains, considered as the biological unit of replication, without integrating the within-strain variation between the replicates. This also compensated for the unequal number of replicates for the six traits. We were left with 51 discarded out of 721 replicates for growth and 18 discarded out of 400 replicates for morphology/movement/oxygen consumption, with a minimum replicate per strain of 12 for the growth and 8 for the other traits. All statistical analyses were performed on this set of 40 means at the strain level for each of the six traits. Morphology and movement traits, measured at the cell level, were in addition first averaged for every replicate to give the same weight to each replicate estimate irrespective of the number of cells identified on pictures and videos. Then, we performed two complementary analyses on our results.glm function, Gaussian distribution and identity link [gam function in mgcv R package, smoother estimation method: REML [In a first analysis, we explored the existence and linearity of pairwise relations between functional traits, by comparing a linear model (ity link ) with a od: REML ). GAM arod: REML . They arFactoMineR [factoextra [In a second analysis, to examine the global dimensionality and test if the predictions of the models could be improved by combining several traits together, we conducted a principal component analysis (PCA) on standardized data  byeach model. When outlined, the non-linear GAM is significantly better than the linear model (e.d.f. > 1), otherwisethe non-linearity does not improve the model’s fit and the GAM is behaving exactly as the linear model, hence thesame D.exp.Additional file 2. Supplementary Figure 2. PCA analysis performed on the six functional traits (averaged at the strain level) for39 T. thermophila strains, without the D14 which was suspected to be an outlier. The left panel represent thedistribution of the strains along dimensions 1 and 2 (A) and along dimensions 1 and 3 (C). The numbers stand forthe labels of the strains. The right panel represent the associated correlation circles along the first and seconddimensions (B) and the first and third dimensions (D). The functional traits are colored based on their measurementdifficulty.Additional file 3. Supplementary Table 1. Output of the Generalized Additive Models (G.A.M.) performed on relationshipsbetween the different traits of T.thermophila. The below diagonal part of the figure with white boxes correspondsto GAMs performed on the values of all 40 strains, while the above diagonal part with grey boxes corresponds toGAMs performed on only 39 strains, thus considering the strain D14 as an outlier.Additional file 4. Supplementary Table 2. The square cosine of the different traits on the first three dimensions of the PCA. Thesquare cosine indicates how well a variable is represented on a considered dimension, and goes from 0  to 1 (the variable is completely represented on that dimension).Additional file 5. Supplementary Figure 3. On the bottom left panel are displayed pairwise relationships among the six functionaltraits measured for the 40 T. thermophila strains. Each dot represents the log of the average value of all replicatesat the strain level, on which we fitted a linear regression, its predictions are shown in blue. Above every graph is displayed the deviance explained (D.exp) of the GLM on the logtransformeddata (in blue) and the GAM on the data before log transformation (in red) for comparison. The inseton the top right displays a boxplot of the deviance explained by those two methods, across all fitted pairwiserelationships, for comparison. On average, the GAM performed better.


Empirically assessing the impact of preselection on genetic evaluation of preselected animals requires comparing scenarios that take different approaches into account, including scenarios without preselection. However, preselection is almost always performed in animal breeding programs, so it is difficult to have a dataset without preselection. Hence, most studies on preselection have used simulated datasets, and have concluded that genomic estimated breeding values (GEBV) from subsequent single-step genomic best linear unbiased prediction (ssGBLUP) evaluations are unbiased. The aim of this study was to investigate the impact of genomic preselection (GPS) on accuracy and bias in subsequent ssGBLUP evaluations, using data from a commercial pig breeding program.We used data on average daily gain during performance testing, average daily gain throughout life, backfat thickness, and loin depth from one sire line and one dam line of pigs. As these traits have different weights in the breeding goals of the two lines, we analyzed the lines separately. For each line, we implemented a reference GPS scenario that kept all available data, against which the next two scenarios were compared. We then implemented two other scenarios with additional layers of GPS by removing all animals without progeny either (i) only in the validation generation, or (ii) in all generations. We conducted subsequent ssGBLUP evaluations for each GPS scenario, using all the data remaining after implementing the GPS scenario. Accuracy and bias were computed by comparing GEBV against progeny yield deviations of validation animals.Results for all traits and in both lines showed a marginal loss in accuracy due to the additional layers of GPS. Average accuracies across all GPS scenarios in the two lines were 0.39, 0.47, 0.56, and 0.60, for average daily gain during performance testing and throughout life, backfat thickness, and loin depth, respectively. Biases were largely absent, and when present, did not differ greatly between the GPS scenarios.We conclude that the impact of preselection on accuracy and bias in subsequent ssGBLUP evaluations of selection candidates in pigs is generally minimal. We expect this conclusion to apply for other animal breeding programs as well, since preselection of any type or intensity generally has the same effect in animal breeding programs.The online version contains supplementary material available at 10.1186/s12711-022-00727-5. In animal breeding, parents of the next generation are often selected in multiple stages, with the initial stages of selection referred to as preselection –3. SelecIn our previous studies , 4, whicThus, the aim of this study was to investigate the impact of GPS on accuracy and bias in subsequent ssGBLUP evaluations, using data from a commercial pig breeding program in which preselection was performed. To achieve this aim, we used the full dataset as control and retrospectively implemented additional layers of GPS. The additional layers of GPS were implemented by discarding animals that did not have progeny in the data. Since GEBV were used to select parents of next generations in this breeding program, discarding animals without progeny in the dataset can be considered as additional GPS. Then, we compared results from subsequent ssGBLUP evaluations after these additional layers of GPS against results from ssGBLUP evaluation using the full available data. Our subsequent genetic evaluations only involved reevaluation of preselected animals, either with or without preculled animals in the subsequent evaluations.We obtained data on pig production traits (average daily gain during performance testing (ADGT), average daily gain throughout the pig’s lifetime (ADGL), backfat thickness, and loin depth) that were collected between 1970 and 2020 for one sire line and one dam line from Topigs Norsvin. These traits are part of the breeding goals of each line. However, there was more emphasis on reproduction traits than on production traits in the dam line. Details on the amount of data used in this study are in Table For each line, we split the animals into two groups, based on a cut-off birth date. Animals born before or on the cut-off birth date were used as the training population, and animals born after the cut-off birth date were used as the validation population. This cut-off date was 31st January, 2017 for the sire line, and 31st December, 2015 for the dam line. Then, from the validation population, animals that met the following requirements were selected as validation animals: (1) none of their parents were in the validation population, and (2) the animals had phenotyped progeny. The first requirement ensured that the validation animals were from only one generation, and the second requirement enabled the comparison of the GEBV of the validation animals against their progeny yield deviations (PYD) . Since r–15), or had a minor allele frequency lower than 0.005. Table Our genomic data included genotypes of animals for about 21,000 single nucleotide polymorphisms (SNPs) that segregated in both lines, and were distributed across the 18 porcine autosomes. The SNPs were genotyped using a custom SNP chip. We used the Plink software  for all In our genetic evaluations, we used precorrected rather than raw phenotypes as records. Animals from different lines were sometimes raised together, so they shared some fixed and non-genetic random effects. Because we studied the impact of GPS within lines, it was necessary to correct phenotypes for all non-genetic effects before the data were divided into lines. Another motivation for using precorrected phenotypes is that the additional GPS scenarios (as described in detail in the next section) could result in some classes of the non-genetic effects to be left with only one or a few animals. Thus, correcting for these effects would be less accurate compared to correcting for them before implementing our additional GPS scenarios. To compute precorrected phenotypes (The (co)variance components used for this analysis were estimated, before separating the data into lines using the four-trait pedigree-based animal model of Eq.  in ASRemFor each line, we implemented a reference scenario and two scenarios that added layers of GPS. The reference scenario—against which the other scenarios were compared—only included the original GPS implemented by Topigs Norsvin. Thus, the subsequent ssGBLUP evaluations following the reference scenario used the entire available data until the validation generation. For the second scenario, called validation generation preselection (VGP) scenario, we implemented additional GPS only in the validation generation, by discarding all animals in the validation generation that had no progeny in the data, but that did have genotypes and/or phenotypes. For the third scenario, called multi-generation preselection (MGP) scenario, we discarded any animal in the validation and training generations without progeny in the data. Animals kept after each GPS scenario are shown in Fig. Following each GPS scenario, we implemented a subsequent ssGBLUP evaluation with all animals that survived the GPS. We call this evaluation ‘subsequent’ because it came after the initial evaluation that provided the GEBV used in preselection. The subsequent ssGBLUP evaluations were conducted with and without records (i.e. own precorrected phenotypes) on the animals in the validation generation   as a prohe trait . For conValidation accuracy was computed as a weighted Pearson’s correlation coefficient between PYD and GEBV of all validation animals, using the ‘cor.test’ function of the ‘stats’ package in R . We compWe computed two types of bias. The first type is level bias, which is a measure of whether estimated genetic gain is equal to true genetic gain. Level bias was computed as the weighted mean difference between PYD and half of the (G)EBV across all validation animals, expressed in additive genetic standard deviation (SD) units of the trait. We used the ‘weighted.mean’ function of the ‘stats’ package in R  to compuThe second type of bias that we computed is dispersion bias, which is a measure of how correctly relative differences in (G)EBV between animals are estimated, i.e. whether the scale of (G)EBV is correct. Dispersion bias was measured by the weighted regression coefficient of PYD on (G)EBV for all validation animals. We used the ‘lm’ function of the ‘stats’ package in R  to compuTable The results of the subsequent genetic evaluations conducted with ssGBLUP and with PBLUP are in Tables For both lines, the estimated heritabilities for ADGT and ADGL did not differ between the reference and VGP scenarios, but increased in the MGP scenarios. For backfat thickness, heritability estimates did not differ between the GPS scenarios, neither in the sire line nor in the dam line. For loin depth, heritability estimates did not differ between GPS scenarios in the sire line, but in the dam line they were higher in the MGP scenarios than in the reference and VGP scenarios. For all traits, the above trends in heritability estimates were observed regardless of whether records on animals in the validation generation were included or not when estimating heritabilities. Without records on animals in the validation generation in the subsequent ssGBLUP evaluations, all results (including estimated heritabilities) for the reference and VGP scenarios were the same. The increases in heritabilities observed with additional layers of preselection were generally due to decreases in residual variances with additional layers of preselection, while additive genetic variances generally did not differ between GPS scenarios  on accuracy and bias in subsequent ssGBLUP evaluations of preselected animals. We used data on production traits from one sire line and one dam line from a commercial pig breeding program in which preselection had taken place, and retrospectively implemented additional layers of GPS. For each line, we implemented three GPS scenarios and used precorrected phenotypes as records in the subsequent genetic evaluations, and progeny yield deviation (PYD) as the proxy for TBV. We conducted the subsequent genetic evaluations either with or without records on animals in the validation generation, and in all cases without progeny of validation animals. Validation accuracy decreased, or at least tended to decrease, with additional layers of GPS. Dispersion bias was largely absent, and the regression coefficient of PYD on GEBV—the indicator of dispersion bias—in all instances did not differ between corresponding GPS scenarios. Level bias was also largely absent, and mean PYD minus mean GEBV—the indicator of level bias—in most instances did not differ between GPS scenarios. The above results were observed in both lines, for all traits, and regardless of whether records on animals in the validation generation were included or not in the subsequent ssGBLUP evaluations.Empirically assessing the impact of preselection on subsequent genetic evaluations of preselected animals requires comparison of scenarios that take different approaches into account, including scenarios without preselection. Since some GPS had already taken place in the dataset that we used for this study, it was not possible to have a scenario without preselection. Thus, we had to find an alternate way to investigate whether ssGBLUP is able to estimate GEBV in the subsequent evaluation of preselected animals without preselection bias in our current dataset and by extension in real breeding programs. We hypothesized that if ssGBLUP in subsequent evaluations yields unbiased GEBV for preselected animals in spite of additional GPS in the current dataset (i.e. in our VGP and MGP scenarios), then it also yields unbiased GEBV for preselected animals in the subsequent evaluations with the current dataset (i.e. in our reference scenarios). This is why we developed the VGP and MGP scenarios that implemented additional layers of GPS over the regular GPS that had already been implemented in the commercial pig breeding program. While scenarios such as VGP and MGP do not occur in real breeding programs, implementing these GPS scenarios in our study enabled us to investigate the impact of GPS on subsequent genetic evaluations of preselected animals using real data, by including different amounts of pedigree, genomic and phenotypic information in the subsequent genetic evaluations. Our results show that ssGBLUP in subsequent evaluations of pigs can estimate GEBV of preselected animals without preselection bias. We believe that the findings of the current study can be extended to other animal breeding programs because preselection has similar effects, regardless of its type and intensity and in how many stages it is implemented, i.e. preselection ensures that only better-than-average animals are phenotyped for the traits measured at advanced stages of the life of animals. Our findings are in line with those from our previous studies that used simulated datasets, i.e. that ssGBLUP in subsequent evaluations estimates unbiased GEBV for preselected animals, regardless of the preselection type and intensity , 4. In , we showThe preselection that we implemented in this study and in  and 4]  4] are fOur results show that, for all traits and especially for ADGT and ADGL, which were highly weighted in the breeding goal and for which GPS was highly effective, the heritability estimates increased or at least tended to increase, with additional layers of GPS. This is because changes in residual variances were larger than the corresponding changes in additive genetic variances from the reference to the VGP and to the MGP scenarios EBV among validation animals) did not differ between corresponding GPS scenarios, regardless of whether ssGBLUP or PBLUP were used for the subsequent evaluations. Although we have not been able to find a definite explanation for the relatively small level bias observed in some scenarios in this study, we have reasons to believe that it was not caused by preselection. First, based on how we calculated level bias (i.e. as the mean progeny yield deviation minus the mean (G)EBV), level bias caused by preselection is expected to be positive, since unaccounted preselection underestimates MS terms and by extension breeding values of preselected animals, as shown by , 11, 12.Without selection, the expectation of the regression coefficient of PYD on (G)EBV is 0.5, because PYD only represents half of the breeding value of the parent. However, when validation animals are on average genetically better than a random sample of their age group, the expectation of the regression coefficient decreases in single-trait subsequent evaluations, depending on how much the validation animals deviate from the average of their age group e.g. , 38). In. In38]).Even in the dam line where the original GPS was at least numerically more intense and the ratio of males with records to females with records in any generation was about 20:80, in general, we observed no significant decrease in validation accuracy, or significant increase in level or dispersion bias across our GPS scenarios. However, we found that the corresponding validation accuracies for ADGT, ADGL and backfat thickness were always higher in the sire line than in the dam line, although the corresponding heritability estimates for ADGT and ADGL were in many cases higher in the dam line than in the sire line. These higher accuracies in the sire line than in the dam line may be explained by the relatively higher phenotyping and genotyping rates in the sire line than in the dam line Table , meaningFor the subsequent ssGBLUP evaluations without records on animals in the validation generation, results from the corresponding reference and VGP scenarios are exactly the same, at least up to two decimals Tables , 4. HoweIn real datasets as used here, it is difficult to completely rule out mistakes in pedigree recording and in genotyping. In the genomic data quality control stage in the current study, genotypes of a few thousand animals were discarded because the animals did not meet the genomic data quality standard (i.e. genotyped for at least 90% of the SNPs). This can, however, not completely rule out genotyping mistakes in the genomic data that passed quality control. Tables When subsequent genetic evaluations of preselected animals are based on ssGBLUP, genomic preselection in single or multiple generations decreases realized accuracy only slightly, and hardly causes level or dispersion bias. This conclusion is expected to hold regardless of whether records on validation animals are included or not in the subsequent evaluations, and regardless of the weight of the trait in the breeding goal. Although these conclusions were derived using data from a pig breeding program, we believe that they can be generalized to other animal breeding programs, because preselection is expected to have the same effect in any animal breeding program.Additional file 1: Table S1. Estimated heritabilities , genetic correlations  and phenotypic correlations  for the traits analysed in this study, using the full data from the sire line. Standard errors are in brackets.Additional file 2: Table S2. Estimated additive genetic and residual variances (standard errors in bracket) in the sire line.Additional file 3: Table S3. Estimated additive genetic and residual variances (standard errors in bracket) in the dam line.


Cucurbita moschata grows well in various ecosystems. It is not a very exigent plant and has an inherent capacity for plasticity that underlies its large variability. An assessment of the accessions of C. moschata in Cote d’Ivoire shows that the plant exhibits large morphological and phenological variability for all the 28 measured traits. There are outliers among most measured traits. Further analysis indicates the emergence of three ecotypes in congruence with the three distinct ecosystems and their respective bioclimatic characteristics. In the savannah region, characterized by a short rainy season followed by a long dry season, a total yearly rainfall of 900 mm, an elevated daily temperature of 29 °C, and a high relative humidity of 80%, the cline of C. moschata is long and thin, with small leaves, small peduncles and small fruits. It has a high growth rate and accelerated phenology. The mountain region has a very long rainy season followed by a short dry season, a total pluviometry of 1400 mm, an average daily temperature of 27 °C and a relative humidity of 69%. The cline of C. moschata in the mountain region is characterized by a delayed flowering and a delayed fruit maturity, large number of small seeds and large fruits. The forest region has a favorable climate for the growth of C. moschata in Cote d’Ivoire. It has two rainy seasons that alternate with two dry seasons of unequal durations, an annual rainfall of 1200 mm, an average daily temperature of 27 °C and a relative humidity of 70%. The cline of C. moschata in that region has a large girth size, large dimensions of the leaves, long peduncles and larger and heavier fruits. The seeds are also large but in small number. It appears that the anatomy and physiology of the clines are differentiated primarily in response to soil water content and availability for the ontogeny of the plant.With its predisposition to adapt to different environments,  Their persistence in the new environment along with natural selection result in their adaptation, and other time, increase their fit to the environment9. The processes leading to the fitness of the species in the new environment involve natural random mating and genes transfer from parents to progeny10, mutation and genes recombination which result in an assortment of genotypes with dominance, co-dominance, and recessive individuals. Natural selection eventually removes the purely recessive genotypes from the population as they often cannot survive in the new environment. These processes occur gradually and lead to genetic variability. An illustration is the different degrees of resistance to pesticides or heavy metal toxins12.The migration of species in a new environment means that the environment offers favorable conditions for the species’ survival and accommodation. Such migration and accommodation are often accompanied by the expression of different phenotypes depending on the environment and the interaction between genotype and environment19. It makes the genetic resources available for undertaking the breeding program for crop improvement. For example, the introgression of quantitative trait loci on southern leaf blight resistance in maize hybrids20 was feasible due to the genetic variation for the disease. Modern biotechnology tools can be used to introduce foreign genes into the genome of an individual21, thereby enhancing the genetic variability of the species as the introduced genes are heritable and can be passed to the progeny. With the importance of genetic variability in a breeding program, germplasm collection, maintenance and regular assessment have been an important part of the activities in research institutions24. The current study concerns the Cucurbita moschata germplasm in Cote d’Ivoire, precisely its morphological characterization as part of a program of Cucurbita moschata improvement.Genetic variability is the driving force of species persistence and evolution. It is the natural insurance policy as it provides an insurance for the species survival against the unexpected. Natural random mating allows the transfer of genes from individuals to others. In addition to the gene transfer, the recombination of genes and genetic mutation are the main cause of genetic variability that insures the survival and the evolution of species. In agricultural research, genetic variability is the backbone of cultivar improvementCucurbita moschata originated from Latin America26 and was an important crop for the indigenous people who first cultivated the crop for its edible seed and fruit27. From Latin America where it is first cultivated, Cucurbita moschata migrated to the Caribbean Islands where it adapted to the local ecosystems and further diversified29. After the discovery of America and through the intercontinental voyages that followed, Cucurbita moschata was spread to Europe, Asia and Africa and became naturalized to those continents, with increased genetic diversity in the new environments30. The diversification that resulted from the adaptation and acclimation of C. moschata to the diverse regions of the world created geographical subspecies31. Other studies add support to the geographical subspecies formation with the identification of distinct clusters based on geographic origins33.C. moschata is an annual crop that grows well in warm tropical areas36. It is even called “tropical pumpkin”35. It is very well suited to the climatic conditions of Africa. Unfortunately, it is not yet an important revenue-generating crop in Africa and it is neglected across the whole continent. This neglect is especially true in Cote d’Ivoire. Cote d’Ivoire is a country where agriculture occupies more than 60% of the active population and contributes up to 35% to its gross domestic product. However, most of the agricultural research activities and crop promotion are focused on cash crops for export. Food crops for local consumption have received very little attention from the public authorities. And C. moschata has totally been ignored in agricultural research programs until now. In Cote d’Ivoire, C moschata is sparsely cultivated by small-scale farmers. To date, they are the only ones with any information on the vegetable crop. Given its lauded nutritional and medicinal importance34, consumption of the fruit pulp, the seed, the leaves and the flowers in diverse dishes is growing in Cote d’Ivoire and necessitates programs for the collections of the various accessions of C. moschata, the characterization, the conservation and the improvement of C. moschata genetic resources in Cote d’Ivoire. We conducted the present study to determine the agro-morphological characteristics of the different accessions of C. moschata collected from the main growing regions of Cote d’Ivoire and a region in Burkina Fasso. Because the environmental conditions of the growing regions are strikingly different, we evaluated the possibility of ecotypes of C. moschata in relation to those ecosystems. All the inferences in this study are based on the quantitative measures of the vegetative, phenological and yield traits.The process of data management included the computation of mean squares for the assessed phenological, vegetative and yield traits of the accessions with the sampling habitats considered as the treatment factor. The error mean squares served in the multiple comparison of means reported in Table Regarding the phenological traits, the accessions from the habitat of Zh have the longest period from seeding to first male (102.39 d) and first female (108.14 d) flower appearances, and the longest period from seeding to physiological maturity (153.95 d). For those traits, the accessions from Tiassale and Soubre are not significantly different from those of Zh. And, accessions from Tiassale and Zh have the longest periods from seeding to 50% flowering. On the other hand, accessions from Korho, Ferke, Bondu and Burki develop their first male and female flowers and attain 50% flowering in a very short period. They also reach physiological maturity faster. Accessions from Korho, however, have the longest period from seeding to 50% emergence (6.07 d) and accessions from Bondu have the longest period from first female flower appearance to physiological maturity (53.04 d).For the vegetative traits, accessions from Tiassale and Soubre have the largest girth size . Accessions from Tiassale have the longest (24.98 cm) and widest (19.94 cm) leaves, the longest male (16.2 cm) and female (4.03 cm) peduncles and the longest petioles (34.94 cm). The measures for those organs on accessions from Soubre rank second to those of Tiassale. On the other hand, accessions from Korho, Ferke, Bondu and Burki are characterized by smaller girth size, smaller leaves, smaller petioles and smaller peduncles of male and female flowers. But the accessions from Bondu are the tallest (586.91 cm) followed by the accessions from Ferke (489.20 cm). And the accessions from Zh are the shortest (417.38 cm).For the flowering and yield traits, accessions from Tiassale and Soubre show the largest numbers of male  and female  flowers per plant, largest numbers of fruits per plant  and largest measures of all fruit-related traits. Their seeds are very large, but in small numbers. In contrast, accessions from Korho, Ferke, Bondu and Burki have the smallest numbers of male and female flowers per plant, the smallest numbers of fruits per plant and the smallest measures of fruit-related traits. They have large numbers of seeds, but their seeds are smaller, except the seeds of the accessions from Burki. Refer to Table C. moschata. All the evaluated traits showed very wide ranges of distribution of the observations. Some conspicuously wide ranges of traits include number of days to 50% flowering (DTF) that goes from 52 to 152 d, plant height with a minimum of 48 cm and a maximum of 1510 cm, diameter of the fruit that is between 5.8 cm and 35 cm, weight of the fruit that varies between 150 g and 10,930 g and number of seeds per fruit that spreads in the interval from 32 units per fruit to 729 units per fruit. Excluding the number of days to 50% emergence (DTE), all the other assessed traits have remarkably wide ranges of phenotypic expressions  showed highly significant variations between accessions for the assessed traits. They all yielded p-values less than 0.01, providing additional support to the evidence of large variability among the accessions of C. moschata of Cote d’Ivoire. The computed standard deviation, and median absolute deviation for each trait are additional evidence. We should note that in most cases, the mean squares associated to year (data not reported) were not significant, indicating the relative stability of the assessed traits.Table lme4 package37 used in the determination of the components of variance, does not provide p-values in the analysis of mixed or random models. The reported quantities in Table The components of variance, the quantitative genetic differentiation, the overall mean, and the coefficients of variation are reported in Table CV) is another statistic that measures variation. It is actually the dispersion of a trait per unit measure of its mean, which can be used to compare variations of traits with different measurement units or different scales. As a rule-of-thumb, a coefficient of variation greater than 20% is indicative of large variation for the trait. The phenotypic coefficient of variation is considerably high for 25 of the 28 assessed traits. Only the number of days from seeding to physiological maturity, the first and second longest axes of the dry seed show coefficients of variation less than 20%. Traits with very large phenotypic coefficients of variation include the peduncle length of female flowers  with the phenotypic coefficients of variation. From that observation, we may conclude that the variations in the phenotypic expressions of the vegetative traits are largely due to the variations within morphotypes. For the flowering and yield traits, all the residual coefficients of variation are greater than 20%, except the first and second longest axes of the seed. The genotypic coefficient of variation is less than 20% for all the phenological and vegetative traits except the peduncle length of male flowers with a coefficient of variation of 33.01%. On the other hand, 13 of the 15 flowering and yield traits have genotypic coefficient of variation greater than 20%. Among them, are the weight of the pulp with a genotypic coefficient of variation of 90.26%, the volume of the fruit with a genotypic coefficient of variation of 84.20% and the weight of the fruit with a genotypic coefficient of variation of 75.12%. Besides, for the flowering and yield traits, the genotypic coefficients of variation are highly correlated  with the phenotypic coefficients of variation in a near-perfect linear trend  accounted for most of the observed phenotypic variationDrosophilla melanogaster from two geographically isolated regions are linked to cytological differences, one caused by a variation in cell number and the other one by both cell number and cell size, attributable to diverse genetic mechanisms48. In this study, the three clines of C. moschata evolved as the result of local adaptation through natural selection in order to thrive in the ecologically different environments. The clines differ mostly in sizes of organs and phenology as responses to what each environment can allow for the full completion of the ontogeny of the accessions. Obviously, anatomical and physiological differences in response to the environments resulted in the observed differences in sizes and weights of organs, and phenology of the accessions of C. moschata. To meet local environmental conditions, accessions of C. moschata developed different genetic mechanisms which underlie the observed genotypic divergence. Clearly, the accessions are pre-disposed to survive and adapt to the new ecosystems in order to do so and to persist. Pre-existing variation for plasticity permitted the accessions to persist under the new environments and over time, the persistence allowed new genetic variation to arise through mutations and/or recombination8 that led to the adaptive divergence of the accessions and the emergence of the ecotypes of C. moschata.Differences in the size of the organs may be due to differences in cell numbers and/or cell sizes. For example, divergence in the body size of Cucurbita moschata is a native crop of Latin America that spreads to Africa, Asia and Europe with its predisposition for adaptation to various ecosystems. In Cote d’Ivoire, C. moschata grows in several habitats and expresses large morphological and phenological variability along with outliers. Three clines of C. moschata are distinguished and their developmental needs, their morphology and their phenology are in congruence with the three distinct ecosystems and their respective bioclimatic parameters. The allopatric formation of the three clines is likely conditioned by soil water availability for the ontogeny of the plant.Cucurbita moschata maintained in the germplasm bank of University Nangui Abrogoua. They are collected from six sites in Cote d’Ivoire and one site in Burkina Fasso  and was composed of 5 rows. The space between rows, and between plants within a row was 3 m, resulting in a planting density of 1190 plants ha−1. Each year a total, 335 plants were randomly sampled, followed from emergence to physiological maturity, and used for all observations and measurements. Figure C. moschata of the current study. All agricultural practices were followed according to recommendations.The experiment was conducted at the experimental station of University Nangui Abrogoua, Abidjan , Cote d’Ivoire, in 2019 and 2020. The climate of Abidjan is characterized by two rainy seasons from April to July and October to November and two dry seasons from December to March and August to September. But, this pattern of alternating seasons has been disturbed in recent years. The annual rainfall in Abidjan is over 1200 mm, the daily mean temperature is 27 °C, and the average relative humidity is 70%. The vegetation is characterized by a dense forest and the ferralitic soil is rich in organic matter. The seeding date for the first year of the experiment was September 10th, 2019. Due to changing weather patterns, the usually short rainy season started in early September of that year and sparsely extended to December. The seeding date for the second year of the experiment was April 20th, 2020, at the onset of the long rainy season. The experiment was arranged in a randomized complete block design with three replications and covered a total area of 0.816 ha in both 2019 and 2020. The accessions were randomly assigned to different plots in each block and the blocks were randomized. Each plot occupied an area of 288 mThe assessed agro-morphological characteristics are reported in Table lme4 package37 of the R statistical software39, we obtained the genotypic variance , genotypic coefficient of variation (CVg) and environmental coefficient of variation (CVe) are respectively computed as follow: tidyverse package50 was used for data management. We computed the mean effect of each trait per sampling habitat, and used the Fisher’s least significant difference (LSD) procedure to separate means that are significantly different.The factors, block, accessions and year were considered random and we fitted a random effects model to get a better assessment of the components of variance. We used the following model:hclust function in the stat package of R, version 4.2.139 with the “ward.D2” method51. We then used the phylo function of the ape package41 for visualization of the structure of the populations of C. moschata in Cote d’Ivoire. The NbClust package40 helped to determine the number of clusters, based on the majority rule. For the purpose of clarity, we used the averages of the accessions of the 34 morphotypes. We then conducted a principal components analysis (pca). The pca is a technique for reducing the dimensionality of a large data set while preserving most of its variability. It does so by creating new uncorrelated variables called principal components and concentrates the maximum variance in the first few components52. The technique increases interpretability and allow low-dimensional graphical representation of the data set. With those advantages of the pca, we graphically presented the accessions along with the variable vectors in the two axes formed by the first two principal components that have the largest variances. This graphical representation helped to assess the morphological traits that best characterize the accessions grouped together according to their similarities in the attempt to identify the ecotypes of C. moschata in Cote d’Ivoire, along with their particularities. We used the ggbiplot package53 for the visualization of the biplot.The segmentation procedure used to regroup closely related accessions is the hierarchical agglomerative clustering. With this procedure, each accession is assigned to its own cluster. The distances between clusters are computed and the clusters with the shortest distance are merged to form a new cluster, as they are the closest to each other. The distances are then recomputed and the process is repeated until all accessions are regrouped in one cluster. We used the For the sampling of the accessions of Cucurbita moschata, all procedures were conducted in accordance with the guidelines. And permission was given to collect the accessions from the sampling sites of this study.Supplementary Information.Supplementary Table S1.Supplementary Table S2.


We used data from a yield trial of 250 barley lines to estimate variance components and genome-wide effects. These parameters were used as basis for simulations. The simulations included multiple crossing schemes, population sizes, and varying sizes of the components of the masking variance. The genotypic values g of the selection candidates were obtained by genetic simulations, the phenotypic values p by simulating evaluation in the field, and the genomic predictions y by RR-BLUP effect estimation from the phenotypic values. The correlations r were greater than the correlations r for all investigated scenarios. We conclude that using genomic predictions for selection among candidates tested with low intensity in the field can proof useful for increasing the efficiency of barley breeding programs.Genomic prediction has been established in breeding programs to predict the genotypic values of selection candidates without phenotypic data. First results in wheat showed that genomic predictions can also prove useful to select among material for which phenotypic data are available. In such a scenario, the selection candidates are evaluated with low intensity in the field. Genome-wide effects are estimated from the field data and are then used to predict the genotypic values of the selection candidates. The objectives of our simulation study were to investigate the correlations  Genomic selection between candidate genotypes that were not tested in field trials has been implemented successfully in breeding programs of major crops  is greater than the correlation r. To our knowledge there are no studies in barley that are investigating the use of genomic predictions to select between selection candidates that were evaluated in field trials.From a statistical point of view, this procedure is in analogy to the following example from linear regression. Assume for a given set of r and r with simulations based on an experimental barley data set. In particular, our objectives were to (i) estimate the correlations r and r for replicated and unreplicated trials based on simulations, (ii) investigate the effect of the mating scheme, population size, and the components of the masking variance on the correlations, and (iii) demonstrate that genomic selection among barley lines in unreplicated trials can be superior to phenotypic selection based on replicated trials.The goal of our study was to investigate the correlations We used an experimental data set of winter barley  lines which were derived from 25 crosses of 10 parental lines. Five of the parental lines were elite lines and five were resistant donors. The derived lines and the parental lines were evaluated for yield at five locations in two years. The field trial was layed out as an augmented design with five blocks. In each block, 50 of the derived lines were tested together with the 10 parental lines that served as checks. In the first year, each of the derived lines was tested unreplicated in four locations, in the second year each of the derived lines was grown in two replications at five locations.To estimate the adjusted treatment means of the of the parental lines and the derived lines we used the linear modell is the effect of the line, e is the effect of the environment, l:e is the genotype-by-environment interaction, r:e is the replication within environment effect, b:r:e is the block effect nested within replication and environment, and ε is the residual. The genotype was analyzed as a fixed factor, the remaining factors of the model were random. The adjusted treatment means ranged from 69.4 to 99.3 dt/ha (adjusted to 15% moisture), the standard errors of the means were 2.7 for the 10 check genotypes in the augmented design, and 3.1 for the 250 genotypes with one replication per block. The heritability for unbalanced trials, according to Equation (19) of Piepho and Möhring  chip . SNPs with more than two recorded alleles, more than 10% missing values and a gene diversity smaller than 0.1 were excluded from the analysis, as well as genotypes with more than 15% missing information. After preprocessing the marker data, 9,597 SNP markers and 259 genotypes  remained for the analysis.cf Reif et al., The pairwise modified Roger's distances  and one plot per genotype (R = 1). The second investigated design was a replicated trial with three environments (E = 3) and two replications per environment (R = 2). The variance components mcl and thus the simulated phenotypic values pcl for the two different field trial designs.We considered two different field trial designs for the evaluation of the 250 simulated DH lines in order to compare unreplicated and replicated trials. The first investigated design was an unreplicated trial with one environment  and replicated  field trials, we ran a set of replicated simulations with 2,000 simulation runs for each parameter setting. In addition to the original factorial crossing scheme of 5 × 5 lines, we also simulated a diallel mating scheme. In the diallel mating scheme, all 10 pairwise crosses between the 5 elite lines were carried out.In order to investigate the effect of varying the variance components E = 1, R = 1) and a replicated  field trial.In the factorial mating scheme we simulated either family sizes of 10 DH lines per cross, resulting in a population of 250 lines, or family sizes of six lines per cross, resulting in a population size of 150 lines. For the diallel mating scheme, we generated 25 DH lines for each of the 10 crosses, resulting in a population size of 250 lines. Thus, we investigated three different mating schemes, all of which were evaluated in both an unreplicated , r, and r.For each of these six scenarios, we considered five different sets of variance components For the first set of variance components, we used a setting that is close to the variance components of the experimental design: p assessed in field trials are used as estimates for the genotypic values g of the selection candidates. The correlation r depends on the heritability and determines the response to selection. The response to genomic selection is determined by the correlation r between the genomic predictions y and the genotypic values g. The correlation r is referred to as prediction accuracy .The R code used to carry out the simulations is available at Github , in the second year two replications were grown in each location . In the retrospective analysis we regarded the data from each of the four environments in year one as an unreplicated trial . This results in four sets of phenotypic values. We denote the sets of phenotypic values obtained from these unreplicated trials with p*.Our experimental data was collected in two years, in the first year one plot per genotype was planted in each of four locations . These phenotypic values were then regarded as estimators for the genotypic values ĝ*.We then used the four sets of phenotypic values p*, y*, and ĝ* we determined the correlations r between the phenotypic values and the estimate of the genotypic value, and r between the genomic prediction and the estimate of the genotypic value.For each of the four sets of values z-test with the alternative hypothesis HA: r < r was carried out with the R package cocor , r, and r between phenotypic values p, genotypic values g and genomic predictions y were consistently lower for the unreplicated trial than for the replicated multi-environment trial  = 0.53, r = 0.72, and r = 0.87 in the unreplicated trial, and r = 0.82, r = 0.88, and r = 0.97 in the replicated trial. The correlation r in the unreplicated trial thus surpassed the correlation r in the replicated trial, even though the unreplicated trial used only one sixth of the field plots of the replicated trial.In the illustration example that was based on the parameter settings and variance components from the experimental data set, the pairwise correlations nt trial . The corr, r, and r  and highest for r. The correlations r were consistently lower than both r and r for all investigated scenarios  between phenotypic and genotypic values ranged from 0.33 to 0.54 for the unreplicated trials and from 0.61 to 0.80 for the replicated trials  between genomic predictions and genotypic values ranged from 0.76 to 0.91 for the unreplicated trials and from 0.89 to 0.96 for the replicated trials  . All cor r  than for r . The difcenarios . In the y over the phenotypic values p persisted when the total population size of the factorial mating designs was reduced from 250 to 150 DH lines  in the unreplicated trials were higher than the correlations r in the corresponding replicated trials  in the unreplicated trials and r in the replicated trials diminished when the total population size was reduced to 150 DH lines. For example, in the scenario that was close to the experimental data set, r in the unreplicated trial was 0.88 and r in the replicated trial was 0.80 with a population size of 250 DH lines  in the unreplicated trial diminished to 0.86, while r in the replicated trial remained at 0.80  decreased with increasing r increased. For example, in the factorial mating scheme with 10 DH lines per cross, r decreased from 0.91 to 0.88 to 0.85, while r increased from 0.67 to 0.69 to 0.71  increased, while the correlation r decreased  was lowest and the correlation r was highest for r remained approximately constant with increasing The masking variance for the simulation of the phenotypic values r, r, and r for all investigated mating schemes  in the factorial mating scheme with a population size of 250 in the replicated trials. It increased slightly when Increasing the error variance  l. 9 of . Furtherr, r, and r were consistently much lower in the diallel mating schemes than in the factorial mating schemes  ranged from 0.11 to 0.20 in the unreplicated trials and from 0.24 to 0.38 in the replicated trials  ranged from 0.26 to 0.52 in the unreplicated trials and from 0.52 to 0.79 in the replicated trials  in the unreplicated trials was higher than or comparable to r in the corresponding replicated trials  was always lower than r, r was higher than r for a higher cross-by-environment/line-by-environment variance ratio and larger environmental variances in the unreplicated trials  between genomic predictions and genotypic values were for all four sets of data greater than the correlations r between the phenotypic values from the unreplicated trial and the genotypic values  between genomic predictions y and phenotypic values p is often used as a measure for the precision of prediction  between the genomic predictions y and the true genotypic values g remains unknown. Some authors divide the correlation r by the square root of the heritability  and r between the phenotypic values p and genotypic values g and between the genomic predictions y and the genotypic values g, respectively. This allows the comparison of the selection criteria p and y with respect to their precision to predict the true unknown genotypic values g of selection candidates. Moreover, it facilitates the investigation of quantitative genetic factors that affect the two correlations.In experimental evaluations of genomic prediction, the correlation y and p with the true genotypic values g. In addition, the genetic structure of the parental lines can be assumed to have an effect on the size of the estimated genomic marker effects.The genomic marker effects and the components of the masking variance from our experimental barley data set were used as the basis for the simulations. This methodology implies simplifying assumptions, the most important of which we point out here briefly. The purely additive genetic model neglecting epistasis as well as the estimation method for genomic marker effects might have an effect on the results. It is neglected that a certain SNP variant might be in linkage disequilibrium with alleles having different genomic effects in breeding material that originates from genetically different sources. Moreover, we assume that the genomic effects of SNPs were estimated in the original barley data set without a residual error. In particular this simplification might result in an overestimation of the correlations of We used genome-wide effects estimated from an experimental data set as the basis for our simulations. An alternative approach is to use genetic effects that were drawn with a random number generator from a probability distribution. A prominent example for this methodology is Meuwissen et al. . We haveIn consequence, the results reported here can only illustrate the concept of using genomic predictions of tested material. Further research is needed on the basis of other experimental data sets or quantitative genetic scenarios to confirm the transferability to other situations of the results reported here.r between the phenotypic values p and the genotypic values g in an unreplicated field trial was 0.53 , the correlation between the phenotypic and the genotypic values amounted to r = 0.82, which should allow for efficient selection with reasonable selection gain. However, the increase in precision in comparison to the unreplicated field trial comes at the cost of a six-fold increase of the resources required for the field trial.In a field trial in three environments with two replications  between the genomic predictions and the true genotypic values amounted to r = 0.87 in the unreplicated trial  reached by the replicated field trial with E = 3, R = 2. This enables an efficient selection of genotypes with high performance which results in a high selection gain.In contrast, the correlation ed trial . Hence, From an applied point of view, the costs of genotyping a line might equal roughly the costs of one field plot. In consequence, our results suggest for the investigated data set that using one field plot and in addition genotyping the lines can realize a selection gain roughly corresponding to that of a replicated trial, but requires only a third of the resources.r for unreplicated trials reached values that surpassed the correlations r for the corresponding replicated trials for all investigated scenarios  = 0.88 for the unreplicated trial  = 0.80 for the replicated trial  = 0.86 of l. 11 of r = 0.80 presented in l. 16 of The lower limit for the population size that is required to apply the proposed approach of predicting tested lines is not yet reached with 150 individuals. This conclusion is supported by the r decreased while the correlation r increased. This result suggests that a large genotype-by-cross variance might render the assessment of prediction accuracy using the correlation r difficult as there might be situations in which changing parameters of a genomic selection program increases r without actually increasing r.In our analysis we divided the genotype-by-environment interaction variance into two components, the cross-by-environment variance r decreased considerably. The correlations r remained above 0.75 nevertheless in the factorial mating schemes. This suggests that even when the correlations between the phenotypic and genotypic values of an unreplicated trial get low, using genomic predictions instead can still enable successful genomic selection of candidate genotypes.With increasing error variances and increasing genotype-by-environment variances  of 0.19 or 0.20  of 0.37 to 0.52.In the diallel mating scheme of the elite lines, the genetic variance was only a fraction of the genetic variance in the complete factorial. This observation might be caused by the contrasting yield of the two parental groups in the factorial mating scheme. The small genetic variance in comparison to the components of the masking variance in the diallel mating scheme results in a low heritability in the unreplicated trial accompanied by a correlation y of the genotypic values might be preferable over using the phenotypic values p directly for a wide range of variance components and populations sizes with our data set.These comparisons suggest that using genomic predictions g and their genomic predictions y observed in this study might be explained by the replicated evaluation of chromosome segments in different lines. Due to the replicated use of the parental lines, the parental chromosome segments are present and evaluated in the field in a large number of derived lines. The amount of this pseudo-replication of chromosome segments strongly depends on the degree of relatedness between the evaluated lines and the crossing scheme that was used to develop them.The high correlation between the true genotypic values From a quantitative genetics point of view, the approach suggested here can be related to older best linear unbiased prediction (BLUP) approaches. Assuming a large number of markers with small genomic effects of similar size, the genomic prediction model converges to a GBLUP model that employs the realized relationship matrix between the tested genotypes. Those type of prediction models showed a good performance in maize  at many locations  are required. The precision of the field trial used to collect our experimental data can be considered as sufficient in applied breeding programs, but it does not provide highly precise estimates of the genotypic value. In consequence, this data set can not be used for a rigid experimental validation of our simulation results. Nevertheless, it can be used to demonstrate the potential usefulness of our approach.* from three locations with one plot per genotype in the first year and five locations with two replications per genotype in the second year. The fourth location in the first year was considered as a “preliminary yield trial”  than r. Hence, the genotypic predictions from single-plot experiments approximated the genotypic values better than the original phenotypic values of the experiments.For all four data sets, which correspond to the four single-plot experiments in the first year, we observed a greater correlation Our investigation focused on the research question whether genomic selection between genotypes tested with low intensity in a field trial can be superior to phenotypic selection. We conclude, that for breeding material where parental lines are used in several crosses and from each cross several lines were derived, genomic predictions can have a greater correlation to the true unknown genotypic values than the phenotypic values. Hence, genomic selection has the potential to increase the efficiency of breeding programs that use low-intensity field trials.biometry.popgen@uni-giessen.de. The R code used for the simulations is available at https://github.com/JT-Giessen/Terraillon_2022.Simulated data are available from the authors on request. Requests to access these datasets should be directed to MF and FO conceived the study. HJ, MS, LC, KK, SB, AH, DK, and AS collected the data of the barley experiment. KCF and CZ-P analyzed the data of the barley experiment. JT and MF carried out the simulations. JT, CZ-P, and MF wrote the manuscript. All authors read and approved the final manuscript.via the Federal Office for Agriculture and Food (BLE) under the innovation support programme (FKZ 2818203515).The project was supported by funds of the Federal Ministry of Food and Agriculture (BMEL) based on a decision of the Parliament of the Federal Republic of Germany HJ was employed by Saatzucht Josef Breun GmbH & Co. KG. MS was employed by KWS Lochow GmbH. LC was employed by W. von Borries-Eckendorf GmbH & Co. KG. KK was employed by Limagrain GmbH. SB was employed by Ackermann Saatzucht GmbH & Co. KG. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. 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