Juglans regia L.) varieties. The genetic control of these traits is still unknown in walnut, limiting the accuracy and rapidity of releasing new cultivars for commercial use. We studied the genetic architecture of five traits crucial for either marketing  or selection of individuals with specific phenology . By combining over 30 years of phenotypic data with genetic profiles generated using the latest Axiom™ J. regia 700K SNP array, we were able to identify and confirm major loci for all these traits. In particular, we revealed that a genomic region at the beginning of Chr1 controls both leafing and harvest date in walnut, consistent with the observed strong phenotypical correlation between these traits, and including candidate genes involved in plant development, leaf formation, and cell division. In addition, a large genomic region on Chr11 that includes genes with a central role in flowering control and shoot meristem growth underlies both lateral fruit-bearing and yield in walnut. We observed a more complex genetic architecture for pellicle color, strongly influenced by the environment (h2 = 0.43). We identified two marker-trait associations on Chr6 and 7 for pellicle color, where genes encoding a UDP-glycosyltransferase or involved in the response to oxidation were found. In conclusion, by combining classical quantitative trait loci (QTL) mapping and genome-wide association mapping, we deciphered, for the first time, the molecular pathways controlling walnut phenology, yield, lateral fruitfulness, and pellicle color. Our findings represent a further milestone in the transition from conventional to genome-assisted breeding in Persian walnut.Yield, nut quality, and ability to adapt to specific climate conditions, are all important factors to consider in the development and selection of new Persian walnut ( Juglans regia L.), native to the mountains of Central Asia, is widely cultivated in temperate regions extending from the Americas to Europe to Asia . In California, the first widely-planted cultivar to leaf out is “Payne,” with a bud-break in mid-March, while the latest is “Franquette,” which leafs out in the second half of April , was released and used to genotype a collection of 1,284 walnut accessions from the UCD-WIP  SNPs were used to test genotype-phenotype associations. SNP probes (71-mer) were mapped onto the new chromosome-level walnut reference genome (v2.0) (https://www.hardwoodgenomics.org/Genome-assembly/2539069) to obtain their chromosome locations. Specifically, a chromosome position was assigned to an SNP when its probe aligned uniquely on the genome with 98% identity and an E-value < 1e-20 for more than 95% of its length. The SNP dataset was then filtered for minor allele frequency (MAF > 5%) and missing rate (<20%). The genotypic dataset for this study can be found at https://hardwoodgenomics.org/Genome-assembly/2539069.The present research was based on 896 individuals of the UCD-WIP, which included several well-known walnut cultivars , advanced selections, and 34 full-sib families generated from controlled crosses in years 2004 to 2010. The largest family was “Chandler” x “Idaho” (CRxID) with 312 seedlings. Remaining families averaged 23 individuals each Table S1Historical phenotype data for leafing date (LefD), harvest date (HarD), lateral bearing (LTB), yield, and pellicle color were obtained from the UCD-WIP database. LefD is the time at which more than 50% of the terminal buds have begun to open. HarD is the time when 95% of the hulls have loosened from the shells. Both LefD and HarD were scored in Julian days. LTB is defined as the percentage of lateral buds flowering on elongated, 1-year-old shoots. Yield is based on visual evaluation with a score of 0 (no nut production) to 9 (highest yield). Pellicle color was scored using the official color chart of the Dried Fruit Association (DFA), where a score of one indicated extra-light, two—light, three—amber, and four—dark amber kernels. The averaged DFA score of 10 nuts per tree was then used as an individual record. Kinship relationships derived from the UCD-WIP pedigree  was usedYijklm is the m-th observation taken in the k-th year on the i-th tree of the j-th age class and located in the l-th block. In particular, ai is the additive genetic effect of the i-th tree on the trait, pei is the permanent environment contribution to the phenotype of the i-th tree, and eijklm is the residual term. The numerator relationship matrix was used to account for the covariance between additive genetic effects. A permanent environment effect was included in the model to account for the covariance between multiple observations from the same tree. For each trait, different models were fit, including both ai and pei, always as random effects, while age, year and block as random or fixed in a variety of combinations. The best model was then selected based on the Bayesian Information Criterion (BIC). Due to the categorical nature of yield, LTB, and DFA score, generalized linear mixed models were fit, relating the observed ordered categories to an underlying binomial density through a probit (yield) or logit (LTB and DFA score) link function. All models were fit and resolved using the REML estimation method implemented in ASReml v4 (h2) of each trait was then calculated as the ratio between the additive variance (σA) and the phenotypic variance (σP = σA + σPE + σe). Afterward, Pearson correlation value (R) between each pair of traits was investigated with R/GGally v1.4 . Also, Principal Component Analysis (PCA) based upon EBV values was performed using the built-in R function “prcomp.”where SReml v4 . The nar1 family “CRxID”   were removed. The linkage analysis was carried out using the R/ASMap package  using the Kosambi mapping function  . Markers package , which u package  to clustfunction . MapCharfunction  was usedp-value = 0.05) for each trait was determined with genome-wide permutation tests , and False Discovery Rate (FDR ≤ 0.05) were used to identify significant marker-trait associations.Five hundred eighty-four individuals, including all UCD-WIP families (except “CRxID”) and cultivars, were used to perform genome-wide association study (GWAS) for the five traits studied. GWAS was carried out by applying three different models implemented in R/GAPIT v3.0 : the Mulhttps://www.ncbi.nlm.nih.gov/genome/annotation_euk/Juglans_regia/100/) mapped onto the reference genome v2.0 to identify candidate genes for the studied phenotypes. We first inspected the LD landscape around the marker-trait associations identified in the same genomic regions by both QTL mapping and GWAS. By using the default method of confidence intervals implemented in Haploview v4.2 . LTB showed the highest h2 at 0.98, followed by LefD (0.88), yield (0.77) and HarD (0.68).Phenotypic records for all traits were collected by the UCD-WIP from 1988 to 2017 on trees ranging in age from one to 17 and distributed across 46 blocks. Both LefD and HarD were normally distributed , was appBased on individual breeding values estimated considering the entire walnut collection , the average HarD was 268.4 Julian days, with UC-06-005-8 the earliest tree (251 JD) and Scharsch Franquette the latest 290 JD; Table 1.R = 0.72; p-value < 0.001), suggesting that individuals with early leafing will also be early harvesting  with yield, suggesting higher yield would be expected in trees with early leafing and harvest dates. Also, the Pearson correlation analysis indicated that high-yielding individuals are generally lateral , and produce more extra-light kernels  spanned a total of 1,034.37 cM with 1,880 markers mapped into 16 LGs corresponding to the 16 walnut chromosomes Table 2.harD.1 explained 16.78% of the phenotypic variation , and also included the major QTL ltb.1 identified in the QTL mapping analysis. The trait with the second highest number of significant associations detected was LefD, with 14 SNPs found on Chr1, 4, 8, 10, 11, 12, 13, 16, and 17  and fell in two different LD blocks: the marker AX-170770379 formed a 5-kb LD block together with other two SNPs and was in strong LD with the most adjacent LD block, including 10 markers and spanning 25 kb  where no genes could be identified (The two SNPs on Chr1 associated with HarD were not in LD to each other r2 = 0.03 r2 = 0.03–0.35), except for the SNPs AX-171143099 and AX-170560823, which were moderately correlated (r2 = 0.53). The marker AX-170858858 formed a small LD block (< 1 kb) without any annotated candidate genes (r2 = 1) with four other SNPs, organized into only two haplotypes, GTCGG (frequency = 0.9) and TGTAC (frequency = 0.1). The other two most significant SNPs AX-171143099 and AX-170560823 fell in blocks of 43 and 13 kb, respectively. In the 43-kb block, four genes were identified . Six LD blocks of 75, 464, 49, 14, 300, and 151 kb were identified (5), 35 of which were also identified for LTB.Defining LD blocks was more complicated for LTB since the six most significantly associated SNPs covered a large genomic region of 12.5 Mb. Also, three SNPs  were in Hardy-Weinberg disequilibrium . Eight SNPs significantly associated with LTB fell in nine genes, encoding enzymes and transporters involved in carbohydrate metabolism processes, cellular signaling and ATP hydrolysis Table S4TMJ. regia 700K SNP array . Our study represents a further achievement in a long-term project of bringing molecular breeding in the UCD-WIP, which started with the release of the walnut reference genome  and moveNP array . Here weMalus domestica; Vitis vinifera L.; h2 estimates and those observed by h2 for LTB and yield, along with a more substantial proportion of lateral bearing individuals  and a higher average yield score. The value of h2 for HarD (0.68) was smaller than the one obtained by th) relative to the cv. Chandler (October 6th). We also estimate that 88% of the variability of LefD in our collection is heritable. A UCD-WIP goal is to release late leafing cultivars to avoid walnut blight, thus reducing the need for control measures   Table S22 ∼ 0) . Another2 ∼ 0) . HoweverBoth gene tagging strategies detected major QTLs for leafing and harvest date at the beginning of Chr1 4, S12During the spring, a complex signaling network mediated by plant hormones and transcription factors activates dormancy release, ending with bud break in response to warm temperatures . At thisAbout 1.7 Mb downstream from the candidate loci on Chr1 for LefD, we identified the protein TPX2-like gene as likely involved in HarD in walnut. The TPX2 protein is required for spindle assembly during mitosis . Walnut The strong selection exerted in favor of LTB and yield within the UCD-WIP during many years has created a large LD block on Chr11, where lack of recombination makes it difficult to select the best candidate gene for these two traits with precision.FLOWER LOCUS T-INTERACTING PROTEIN 1 (FTIP1), a key regulator of the transport of the FT protein from leaves to shoot apical meristems (SAM) for the initiation of flower development in response to day length and photoperiod , a DEAD-box helicase ATP-binding protein (OsABP) was upregulated in response to multiple abiotic stress treatments, including blue and red-light exposition  related to the use of EBVs as phenotypes for genetic mapping . The idehttps://hardwoodgenomics.org/Genome-assembly/2539069The genotypic dataset for this study can be found at AM coordinated the research, performed all the genetic analysis, and wrote the manuscript. GS assisted AM in analyzing and interpreting the data of pellicle color. CL provided the phenotypic data from the UCD-WIP database and his experience in walnut breeding to interpret the genetic results. HC contributed to fit the animal models for estimating breeding values and heritability. DN conceived and coordinated the research. All coauthors revised the manuscript.HC’s work is support by US Department of Agriculture, Agriculture and Food Research Initiative National Institute of Food and Agriculture Competitive Grant No. 2018-67015-27957.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.


Single-step genomic BLUP (ssGBLUP), a single-step Bayesian regression model (ssBR), and P-AM were applied. Two base populations were defined: the first was the founder population referred to by the pedigree-based relationship (P-base); the second was the base population referred to by the current genotyped population (G-base).After the extensive implementation of genomic selection (GS), the choice of the statistical model and data used to estimate variance components (VCs) remains unclear. A primary concern is that VCs estimated from a traditional pedigree-based animal model (P-AM) will be biased due to ignoring the impact of GS. The objectives of this study were to examine the effects of GS on estimates of VC in the analysis of different sets of phenotypes and to investigate VC estimation using different methods. Data were simulated to resemble the Danish Jersey population. The simulation included three phases: (1) a historical phase; (2) 20 years of conventional breeding; and (3) 15 years of GS. The three scenarios based on different sets of phenotypes for VC estimation were as follows: (1) Pheno1 + 2) yielded biased estimates of additive genetic variance compared to the P-base model. When the phenotypes from the conventional breeding phase were excluded (Pheno2), P-AM led to underestimation of the genetic variance of P-base. Compared to the VCs of G-base, when phenotypes from the conventional breeding phase (Pheno2) were ignored, the ssBR model yielded unbiased estimates of the total genetic variance and marker-based genetic variance, whereas the residual variance was overestimated.In general, both the ssGBLUP and ssBR models with all the phenotypic and genotypic information (PhenoThe results show that neither of the single-step models (ssGBLUP and ssBR) can precisely estimate the VCs for populations undergoing GS. Overall, the best solution for obtaining unbiased estimates of VCs is to use P-AM with phenotypes from the conventional phase or phenotypes from both the conventional and GS phases. In animal breeding, the prediction of breeding values requires accurate and unbiased estimates of variance components (VCs). There are several approaches available for VC estimation depending on the practical conditions  . Among tBefore genomic information was available, Sorensen and Kennedy  showed tThe use of genomic selection (GS) has greatly enhanced genetic gains due to improved selection accuracy and shortened generation intervals ; this has led to faster changes in gene frequencies compared to traditional phenotype and pedigree-based genetic improvement programmes. In such situations, the extra selection acting on genomic information increases the challenges of obtaining unbiased VC estimates. Concerns have been raised about biased VC estimates caused by ignoring genomic information and selective genotyping . Hence, H). Thus, in contrast to typical genomic BLUP (GBLUP) [Single-step genomic BLUP (ssGBLUP) derived by –18 has p (GBLUP) , 20 usin (GBLUP) , 22. In  (GBLUP) , 24. HowThe compatibility between pedigree-based relationships and marker-based relationships is a crucial factor for ensuring unbiased estimation when using single-step methods , 25, 26.1), application of GS (Pheno1 + 2), and a lack of information from the previous conventional breeding scheme (Pheno2). Table 1 + 2) yielded biased estimates of the total genetic variance of P-base. Using P-AM with all the phenotypes (Pheno1 + 2) produced unbiased VC estimates and heritability of P-base. When the phenotypes from the conventional breeding phase were excluded (Pheno2), P-AM led to the underestimation of genetic variance (P < 0.01) of P-base. As expected, we obtained unbiased VC estimates and heritability when using P-AM with phenotypes only from the conventional phase (Pheno1).To determine the effects of GS on the estimation of VCs, we analysed data from three scenarios reflecting no application of GS  across all the scenarios (Table 1), the genetic variance was significantly underestimated, and the residual variance was significantly overestimated. Furthermore, when including phenotypes from the GS phase in the model (Pheno1 + 2), the genetic variance was significantly underestimated, although unbiased estimated residual variance was observed. In contrast to the VCs from G-base, when ignoring data from the conventional breeding phase (Pheno2), ssGBLUP significantly overestimated genetic variance, although an unbiased estimate of residual variance was obtained.For ssGBLUP, in general, the estimates of genetic variance were all biased , unbiased total genetic variance and residual variance were obtained. This led to an unbiased estimate of heritability. However, the marker-based genetic variance was significantly overestimated (P < 0.001) compared to the variance in G-base, resulting in a biased estimate of heritability. Conversely, when including phenotypes from the GS phase in the model (Pheno1 + 2), the marker-based genetic variance was unbiased, but the total genetic variance was significantly underestimated (P < 0.001). In contrast to the VCs from G-base, when ignoring data from the previous conventional breeding phase (Pheno2), ssBR yielded unbiased estimates of the total genetic variance and marker-based genetic variance, whereas the residual variance was overestimated.For ssBR, the convergence of the Gibbs sampler was assessed by estimating Monte Carlo error (MCE) (via batch means). The MCEs for the estimates of the total genetic variance and residual variance were at the level of 10ed Table . In contIn this study, we addressed the effects of GS on estimates of VCs. Two single-step methods (ssGBLUP and ssBR), together with the traditional pedigree-based animal model (P-AM), were used and compared based on simulated datasets that mimic dairy cattle populations. The first question addressed in this study was aimed at determining the impact of the choice of phenotypes from different phases of a breeding program on the estimation of VCs. The results showed that both the ssGBLUP and ssBR models led to biased VC estimates across all scenarios.1 + 2). We also demonstrated that when using phenotypes only from the conventional selection phase (Pheno1), P-AM produced unbiased VC estimates. The scenarios of Pheno2, which reflects current breeding programmes using GS, led to biased estimates of VC by using P-AM. This was mainly caused by ignoring the information from the selection decisions. Another possible cause of this bias might be explained by the negative LD between QTLs across the genome [We showed that P-AM yielded unbiased estimates of VC when including the phenotypes from the GS phase  resulted in biased estimates of VC.Reductions in genotyping costs have contributed to the comprehensive implementation of GS in many genetic selection programmes. This offers the opportunity to select for new traits that are difficult to measure or not yet among the breeding goals. In this situation, a new phenotyping strategy might be used, or new phenotypes may be more likely to be collected from populations under intense GS. In the present study, based on the scenario of Pheno2) were used, both ssGBLUP and ssBR yielded smaller genetic variance estimates compared with the VCs in P-base  would lead to smaller estimates of genetic variance than using P-base. Therefore, in this study, the G-base corresponding to the current GS phase was defined separately from P-base. Consequently, it may be improper to compare VCs estimated in the GS phase  with the VCs in P-base, which is generally referred to by the pedigree. This concern was initially raised by Powell et al. ; that isG and A22 matrices in ssGBLUP [In the present simulation study, we directly used the allele frequencies calculated from P-base to avoid the compatibility issue between the  ssGBLUP , 27, 33. ssGBLUP  by regre1), the estimated total genetic variance was unbiased; however, the marker-based genetic variance was biased upwards, although the allele frequencies from P-base were used. This result can be explained by the fact that a small proportion (1.2%) of animals (only progeny-tested bulls) in the pedigree were genotyped, resulting in poor imputation for non-genotyped animals and biased estimation of marker variance.As originally introduced by Fernando et al. , 22, theg1) given the breeding values of genotyped individuals (g2), i.e., ε) accounting for the remaining portion of the breeding values that could not be modelled by the imputed markers was added to the marker-based breeding values to obtain the final g1. The accuracy of this imputation quality depends on the genetic relationships between genotyped and non-genotyped animals; i.e., it is expected that less precise imputation will be achieved for old ancestors than for younger ones. More specifically, the imputation is based on a linear relationship between genotyped and non-genotyped individuals, which may not approximate the distribution of marker genotypes very well [g2, but M2; this indicates that the conditioning is on the observed marker information, and the conditional genetic variance estimated in ssBR is therefore actually only an approximation of the genetic variance.Apart from the estimated marker variance, the total genetic variance shows a relationship with the conditional variance of the breeding values of non-genotyped individuals (−1A21σg2 . With thery well ) for impThis study contributes to a better understanding of the effects of GS on VC estimation. The results show that neither of the single-step models (ssGBLUP and ssBR) can precisely estimate the VCs for populations undergoing GS. Furthermore, this study has demonstrated that when the complete data are analysed with both pre-GS data and data from the GS phase, the classic P-AM can yield unbiased estimates of VC. Therefore, an implication of these findings is that the best solution for obtaining unbiased estimates of VC is to use P-AM with phenotypes from the conventional phase or phenotypes from both conventional and GS phases.− 5 for both markers and QTLs was set to establish mutation-drift equilibrium in the historical generations. The number of recombination per chromosome (per Morgan) was sampled from a Poisson distribution with a mean equal to the length of the chromosome, and crossovers were uniformly located along the chromosome. This part of the simulation was implemented with QMSim software [Populations that were similar to the Danish Jersey dairy cattle population in terms of the breeding scheme and population structure were simulated over a 35-year period with 5 replicates for each scenario. The simulation was conducted with the following three phases: (1) The historical phase, covering 3000 non-overlapping generations, was run to generate an initial linkage disequilibrium (LD) structure. The simulated genome consisted of 30 chromosomes of 100 centiMorgans (cM) each with 100 QTLs and 10,000 biallelic SNP markers. The QTLs and markers were uniformly distributed within each chromosome. This resulted in a total of 3000 QTLs and 300,000 markers across the whole genome. The offspring inherited alleles at these loci from their parents following Mendel’s rules allowing for mutation  and recombination. A recurrent mutation rate of 2.5 × 10software . Generatsoftware . For the1: phenotypes only from conventional phase (1–20 years) were used; (2) Pheno1 + 2: phenotypes from both the conventional phase and genomic selection phase (1–35 years) were used; (3) Pheno2: phenotypes from only the genomic selection phase were used (21–35 years). Within each scenario, the three single-trait models  were applied. An overview of the subsets used and the average number of individuals in the pedigree, phenotypes, and genotypes for each scenario over 5 replicates are shown in Table 2), the VC estimates needed to be compared with the VCs from G-base.Three scenarios based on the use of phenotypic information from different phases of breeding programs for the estimation of VCs were explored: 1) Pheno Pheno1:  phase 1–0 years wy represents the vector of phenotypes; β is a vector of fixed effects, i.e., herd-year-season effects: a is a vector of additive genetic effects following A is the numerator relationship matrix, and X and Z are design matrices relating phenotypes to fixed effects and random animal effects, respectively; and e is a vector of residuals following The classical animal model  using peH matrix that combines the marker-based (G) and pedigree-based (A) relationship matrices to replace the numerator relationship matrix (A) in the classical animal model. Therefore, the vector of GEBVs is assumed to be distributed as H matrix [G is constructed according to [Z is a centred marker covariate matrix containing 0 − 2pj, 1 − 2pj, and 2 − 2pj for genotypes of AA, AB, and BB, respectively; pj is the allele frequency at locus j, and m is the total number of markers. For the scenarios of Pheno1 and Pheno1 + 2, the allele frequencies were estimated from the animals in P-base, whereas for the scenario of Pheno2, the allele frequencies were estimated from the animals in G-base. The variance components of P-AM and ssGBLUP were estimated with REML [The model equation of the regular ssGBLUP model , 17 was H matrix :2\documrding to :3\documith REML  as impleith REML .y represents the vector of phenotypes; β is a vector including elements of herd-year-season effects; X and Z are design matrices; M2 contains observed marker covariates for genotyped individuals; M1 contains imputed marker covariates for non-genotyped individuals; the imputation is conducted from the following linear relationship: A12 and A22 are the sub-matrices of A; α is the vector of marker effects ε is the vector of imputation residual deviations, A11, A12, A22 and A21 are the sub-matrices of A; e is a vector of residuals, β, and normal priors are specified for α, ε, and e, with null mean and variance of να = 4, are assumed to be the prior distributions for g1 and g2 represent the vectors of GEBV for non-genotyped and genotyped individuals, respectively.An ssBR model  based onpj is the allele frequency at locus j and m is the total number of markers. Similar to ssGBLUP, for the scenarios of Pheno1 and Pheno1 + 2, allele frequencies were calculated based on the stored genotypes in the base population (P-base). For the of Pheno2 scenario, the allele frequencies were calculated based on the current genotyped population. In addition, an extra fixed effect (μg) was fitted in the model to account for the unknown expectation for genotyped individuals [The use of ssBR allows the inference of the additive genetic variance from two sources of information: first, the total genetic variance, approximated by the estimated imputation residual variance, ividuals . The ssBividuals , 43.


During the last decade, the interest to apply machine learning algorithms to genomic data has increased in many bioinformatics applications. Analyzing this type of data entails difficulties for managing high-dimensional data, class imbalance for knowledge extraction, identifying important features and classifying individuals. In this study, we propose a general framework to tackle these challenges with different machine learning algorithms and techniques. We apply the configuration of this framework on lung cancer patients, identifying genetic signatures for classifying response to drug treatment response. We intersect these relevant SNPs with the GWAS Catalog of the National Human Genome Research Institute and explore the Regulomedb, GTEx databases for functional analysis purposes.MAE, CEP104, PRKCZ and ADRB2 show relevant biological regulatory functionality related to lung physiology.The machine learning based solution proposed in this study is a scalable and flexible alternative to the classical uni-variate regression approach to analyze large-scale data. From 36 experiments executed using the machine learning framework design, we obtain good classification performance from the top 5 models with the highest cross-validation score and the smallest standard deviation. One thousand two hundred twenty four SNPs corresponding to the key features from the top 20 models  were compared with the GWAS Catalog finding no intersection with genome-wide significant reported hits. From these, new genetic signatures in We have defined a machine learning framework using data with an unbalanced large data-set of SNP-arrays and imputed genotyping data from a pharmacogenomics study in lung cancer patients subjected to first-line platinum-based treatment. This approach found genome signals with no genome-wide significance in the uni-variate regression approach  that are valuable for classifying patients, only few of them with related biological function. The effect results of these variants can be explained by the recently proposed omnigenic model hypothesis, which states that complex traits can be influenced mostly by genes outside not only by the “core genes”, mainly found by the genome-wide significant SNPs, but also by the rest of genes outside of the “core pathways” with apparent unrelated biological functionality.The online version of this article (10.1186/s12918-018-0615-5) contains supplementary material, which is available to authorized users. All human diseases are influenced to some extent by genitic variability, and yet much of these genetic consequences are still not fully characterized . The herInitial approaches mimicking Mendelian approaches, looking for driver genes of the diseases, consisted of analyzing a group of prior “candidate genes” and their effect to a certain trait. Other studies were based on family-based linkage, analyzing inheritance patterns in thousands of genomic markers. In 2003 the genome-wide association (GWA) method appeared as a promise to identify many of the genes involved in complex diseases. In these GWA studies (GWAS), hundreds of thousands of (mainly) single nucleotide polymorphisms (SNPs) are analyzed without priors. If GWAS is used as a case-control study, it is based on a comparison of allele frequencies between groups of affected and unaffected individuals from a population. A particular allele (the variant form of a given gene) is said to be associated with the trait  if it occurs at a significantly higher frequency among affected individuals as compared with those in the control group. This strategy has been applied with success to identify hundreds of variants   corresponding to the top CV F1 score minus 0.10. This criteria includes the top 20 pipeline models (CV F1 score >= 0.65). All of them have CV F1 score larger the mean of the same score of all the experiments (0.59). These models identify 1,224 unique SNPs.The pipeline model with the highest Table All intersections with both lists “GWAS cat LUNG” and “GWAS cat CANCER”, for the top 20 pipeline models were empty. Only for a couple of cases, the intersection with the “GWAS cat ALL” list gave non-empty results.p-value thresholds, generally below 10e−8.These results suggest that none of the SNPs identified as relevant by the combination of ML methods applied in this study, using the top 20 pipeline models, were previously identified by GWAS studies with low An interesting remark from the intersection analysis of the top 20 pipeline models is that sampling methods do not seem to affect classification methods that ultimately decide which SNPs are relevant to the model or not. Table rs13147602 , rs9424303  and one in CEP104 , rs6702916 . Furthermore, three variants are likely to affect protein binding one at PRKCZ (Protein Kinase C Zeta) (rs262669), and two at ADRB2  (rs4880878 and rs10903495). The former is likely to affect the RUNX3 protein, a candidate tumor suppressor in many human tumors such as NSCLC [SPI1, a transcriptor factor that may be related to NSCLC [CTCF protein, which regulates the TERT gene and its over-expression is important in lung cancer [From 1224 unique variants identified in the 20 top pipelines, 1159 with reported rs signature were explored with Regulomedb  obtained are very much in line with what has been reported in these articles. In our case, our best F1 score is 0.72, which is considered to be acceptable for the problem at hand and the amount of data available.The mple, in , 75, 76 CV F1 and Test scores. Specifically the class 0 Recall ), to keep track of low FN values. Remember we hope to obtain models with low FN values in order to avoid predicting that a certain patient responds to treatment, when in reality he/she does not.The general criterion for classifying individuals with the machine learning framework was to focus on the models with the highest CV F1 score >= 0.65). We believe that considering the rest of experiments with possible relevant functional variants are not appropriate for patient stratification because their CV F1 are close to or smaller than 0.50. It is worth to mention that most of the identified variants were under genome-wide significance and have not been reported  previously in the GWAS Catalog. Furthermore, only few of these variants are scored with a higher regulome score, having putative functional role as eQTLs in lung tissues or affecting binding proteins involved in well known lung cancer genes as RUNX3, SPI1 and CTCF.We identified 1224 SNPs as the most relevant key features from the top 20 pipeline models , we believe there is room for improvement when the different models are trained with a larger data-set.This study has the several limitations. Despite we obtained good classification measures, the sample size and therefore the size of the training data-set was small. We are aware that when applying the ML framework design, performing the “partial analysis” with the training and stability data-sets and later a separate “final analysis” with part of that same training data-set, introduces bias to the obtained results. We are also aware that the lack of an additional/independent sample to train and test the models is a limitation to stress the scores and the key features obtained. Given the difference in performance between the e−6), we obtained a robust classification model using large-scale genomic data, that enlighten new involved genes. The effect results of these variants can be explained by the recently proposed the omnigenic model hypothesis, which states that complex traits can be influenced mostly by genes outside not only by the “core genes”, mainly found by the genome-wide significant SNPs, but also by the rest of genes outside of the “core pathways” with apparent unrelated biological functionality [From our study, the machine learning approach is anticipated as an state-of-the-art, scalable and flexible methodology alternative to the classical GWAS analysis. Despite none of the SNPs identified as relevant by the combination of ML methods applied in this study were previously reported in the GWAS catalog General and class specific metrics of all 36 possible instantiations of pipeline using LC data-set. They are ordered by Additional file 2Detailed description of evaluation metrics used in our experiments. Description of columns in Table Additional file 3CV F1 score. (CSV 31 kb)1159 key features explored with Regulomedb database that are identified with the top 20 pipelines ranked by


Genomic information can contribute significantly to the increase in accuracy of genetic predictions compared to using pedigree relationships alone. The main objective of this study was to compare the prediction ability of pedigree-based best linear unbiased prediction (PBLUP) and single-step genomic BLUP (ssGBLUP) models. Turkey records of feed conversion ratio, residual feed intake, body weight, breast meat yield, and walking ability were provided by Hybrid Turkeys, Kitchener, Canada. This data was analyzed using pedigree-based and single-step genomic models. The genomic relationship matrix was calculated either using observed allele frequencies, all allele frequencies equal to 0.5 or with a different scaling. To avoid potential problems with inversion, three different weighting factors were applied to combine the genomic and pedigree matrices. Across the studied traits, ssGBLUP had higher heritability estimates and significantly outperformed PBLUP in terms of accuracy. Walking ability was genetically negatively correlated to body weight and breast meat yield; however, it was not correlated to feed conversion ratio (FCR) or residual feed intake (RFI). Body weight showed a moderate positive genetic correlation to feed conversion ratio, residual feed intake and breast meat yield. Feed conversion ratio was strongly correlated to residual feed intake (0.68 ± 0.06). There was almost no genetic correlation between breast meat yield and feed efficiency traits. Larger differences in accuracy between PBLUP and ssGBLUP were observed for traits with lower heritability. Results of the three weighting factors showed only slight differences and an increase in accuracy of prediction compared to PBLUP. Slightly different levels of bias were observed across the models, but were higher among the traits; BMY was the only trait that had a regression coefficient higher than 1 (1.38 to 1.41). We show that incorporating genomic information increases the prediction accuracy for preselection of young candidate turkeys for the five traits investigated. Single-step genomic prediction showed substantially higher accuracy estimates than the pedigree-based model, and only slight differences in bias were observed across the alternate models. The traditional mixed model equations  are a veIncorporating genomic information in genetic evaluations was initially based on the two-step technique e.g., . This teA), the genomic relationship matrix (G) should be positive definite. Condensing the G matrix to remove duplicate rows and columns  that can be obtained as wG + (1 - w)A22, where A22 is the numerator relationship matrix among genotyped individuals. Such adjustment can be interpreted as the relative weight on the polygenic effect  and residual feed intake (RFI) in males; 170,844 records of body weight (BW) and walking score (WS) at 20 weeks for males  and 18 weeks for females ; 9,634 records for breast meat yield (BMY) in males as shown in P<1×10-8), had minor allele frequency lower than 5%, call rate lower than 90%, or were located in non-autosomal regions. After editing, the number of markers remaining for subsequent genomic analysis was 53,455. All animals had a call rate higher than 90%.A subset of animals in this population were genotyped using a proprietary 65K single nucleotide polymorphisms (SNP) panel  as shown in A traditional animal model procedure based on BLUP was used to obtain estimated breeding values for all animals in the pedigree across all traits. The following multi-trait model was used to estimate genetic parameters:y is a vector of observations of FCR, RFI, BMY, BW, and WS sorted within animals; b is a vector with the fixed effects of hatch week-year and sex for BW and WS and only hatch week-year for FCR, RFI and BMY; u is a vector of additive genetic effects , distributed as u ∼N, where A is the numerator relationship matrix including the inbreeding coefficients and R is the additive genetic variance-covariance matrix among traits; e is a vector of residual effects, distributed as Eiy indicates a mi×mi matrix corresponding to the traits that were present for animal i, and mi is the number of traits present for animal i; X and Z are incidence matrices for the respective fixed and random effects. Variance components and genetic correlations among the traits were estimated by restricted maximum likelihood (REML) and the procedure was carried out using the BLUPF90 family of programs  in the traditional animal model described above and the variance components were estimated based on the H matrix, which was created as follows:A combined pedigree and genomic relationship matrix H;  was creaw is a constant denoted as a weighting factor in this study as described later, G is the genomic relationship matrix, which was calculated as described in In the above, M is the matrix of genotypes, with columns representing markers and rows representing individuals. Each element in Mij was coded as 0, 1 or 2 if the genotype of individual i for SNP j was homozygous for the first allele, heterozygous, or homozygous for the second allele, respectively. P is a matrix with average allele frequencies calculated as 2(pi − 0.5), where pi is the frequency of the second allele at locus (column) i. If allele frequencies are not properly estimated, biased relationships and consequently biased genomic estimated breeding values (GEBV) may result (where y result . In this0=α/(α+β) is the expected allele frequency, q0=(1-p0), α and β are parameters of the beta distribution fitting the allelic frequency, and m is the number of markers. The two unknown parameters α and β were estimated using the method of moments  for all animals based on the PBLUP model (PBLUP full model). Second, approximately 10% of the youngest, phenotyped birds had their records set to missing (PBLUP reduced model). The estimated breeding values (EBV) for this 10% of animals were then estimated based on their parent average and comprised the validation group as shown in For PBLUP, the bias of predictions and their associated standard errors were assessed by the regression of each adjusted phenotype from the full PBLUP model in the validation subset on the corresponding EBV from the reduced PBLUP model. For ssGBLUP, the bias was evaluated as the regression of the adjusted phenotype from the full PBLUP model on the corresponding (G)EBV obtained from the reduced ssGBLUP model. Slope coefficients from the linear regression with values closer to one are preferred, as slope coefficients notably less than or higher than 1 reflect inflation and deflation, respectively .The three different allele frequency approximations  showed similar results in terms of accuracy and bias and hence the observed allele frequencies (GObsF) were considered for subsequent analyses.Estimates of heritability from multi-trait PBLUP and alternatively weighted ssGBLUP are shown in Accurate estimation of genetic correlations among traits is imperative for any breeding program . GeneticThese results indicate a moderate and unfavorable genetic correlation between WS with both BW and BMY, meaning that selection for increased BW and BMY may also increase leg problems. The genetic increase in body weight of turkeys starting at age 16 weeks was previously found associated with frequency of leg abnormalities . The maiAcross the studied traits, the ssGBLUP model outperformed PBLUP shown in Table 4.In practice, there could be a number of issues with single-step prediction. The genomic matrix can be singular if there are more genotyped animals than markers, or in the presence of clones . More geIn addition to the accuracy of prediction, it is important to examine potential bias when establishing a breeding program or comparing models. Although it does not change the ranking of animals from the same generation, systematic over- or under-estimation of genetic merit leads to consistent biases . Hence, In this study, we estimated heritability, genetic correlations and contrasted single-step genomic and pedigree-based models in terms of prediction ability using two feed efficiency traits, body weight, breast meat yield, and walking ability in turkeys. We showed that incorporating genomic information into breeding programs increased prediction accuracy for the five traits investigated. Single-step genomic prediction showed substantially higher accuracy estimates than the pedigree-based model. Slightly different levels of bias were observed across the alternate models, but a high variation in bias was observed across the traits. The five traits investigated are expensive to measure, therefore the use of genomic selection has strong potential to reduce the cost of turkey breeding programs, as the reliance on phenotypic, pedigree, and progeny information is reduced.Data that support the findings of this study are available from Hybrid Turkeys upon reasonable request, but restrictions apply to the availability of these data, which were used under a license of a material transfer agreement for the current study, and thus are not publicly available.This study was carried out in accordance with the principles of the Canadian Council on Animal Care, the Hendrix Genetics Animal Welfare Policy, and the University of Guelph Animal Care Committee. The protocol was approved by the University of Guelph Animal Care Committee .The author(s) have made the following declarations about their contributions: Conceived and designed the experiments: EA, FS, CB. Analyzed the data: EA, FS. Interpreted results: EA, CB, HE, FS, BW, OW, PV. Wrote the paper: EA, CB, FS, RV, BW.This study was conducted as part of the project entitled ‘Application of genomic selection in turkeys for health, welfare, efficiency and production traits’. This Project was funded by the Government of Canada through Genome Canada and the Ontario Genomics Institute (OGI-133) through the Genome Canada Genomic Application Partnership Program . This study was also financially supported by Hybrid Turkeys . The authors declare that this study received funding from Hybrid Turkeys. The funder was involved in providing datasets used in this study.BW and OW are employed by Hybrid Turkeys, Kitchener Canada. PV is employed by Hendrix Genetics, Boxmeer, Netherlands.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.


The interactions among genes and between genes and environment contribute significantly to the phenotypic variation of complex traits and may be possible explanations for missing heritability. However, to our knowledge no existing tool can address the two kinds of interactions. Here we propose a novel linear mixed model that considers not only the additive effects of biological markers but also the interaction effects of marker pairs. Interaction effect is demonstrated as a 2D association. Based on this linear mixed model, we developed a pipeline, namely PATOWAS. PATOWAS can be used to study transcriptome-wide and metabolome-wide associations in addition to genome-wide associations. Our case analysis with real rice recombinant inbred lines (RILs) at three omics levels demonstrates that 2D association mapping and integrative omics are able to provide a systems biology view into the analyzed traits, leading toward an answer about how genes, transcripts, proteins, and metabolites work together to produce an observable phenotype. Wenchao Zhang et al. developed a tool for analyzing traits using data generated from genome-wide, transcriptome-wide, and metabolome-wide association studies. They test their approach in rice, providing a systems biology view of identified traits. This type of analysis relies on statistical methods and tools to perform association mapping between causal genetic variants and resulting phenotypes, which can determine the heritability of a trait at a subset of genetic variants  and delineate regions of the genome that control the trait, thereby providing markers that can be utilized to accelerate breeding by marker-assisted selection2. Because of the great success of genome-wide association studies (GWAS), hundreds of SNPs conferring genetic variation of complex traits have been identified and reported3. However, the genetic structures of most traits remain unexplained, as associated SNPs detected from GWAS explain only a small fraction of heritability 4 and a much smaller percentage of the total phenotypic variance. This is mainly because a number of these studies employed only additive models that fail to account for epistasis, or the interaction between multiple loci and the environment6.Trait analysis, especially genome-wide trait analysis, is centered on how genetic variation gives rise to phenotypic variation7 proposed a new linear mixed model (LMM) for mapping quantitative loci (QTL) by incorporating multiple polygenic covariance structures. Based on this model, a pipeline for estimating epistatic effects (PEPIS) was developed to comprehensively estimate additive effects, dominance effects, and interaction effects between multiple genetic loci. PEPIS allows analysis of genome-wide genetic architectures, including genotype interaction effects (GxG), and can thereby explain more than 80% of phenotypic variance8.Xu et al.9. Recent work in Saccharomyces cerevisiae suggests that GxE can occur at the individual locus level and the group level for multiple loci, leading to environment-dependent epistatic interactions12. Although Muir et al.13 conceptualized the partitioning of GxE into two possible interaction types, our mathematical understanding of the genetic and molecular mechanisms by which GxE collectively gives rise to phenotypes is still incomplete14.Compared with standard GWAS tools that consider only additive effects, the PEPIS pipeline is equipped with a more complex polygenic linear model that can explain more phenotypic variance. However, neither of these methods can explain nearly 100% of phenotypic variance, as neither considers the interaction between genotypes and environments (GxE). Today, the predominant thinking in biology is that the orchestrated expression of many genes in different environmental conditions affects the transcriptome, proteome, and metabolome to produce a final observable phenotype15. The development of life science technologies enables transcriptomic, proteomic, and metabolomic events to be analyzed in detail within the same biological system, allowing the systematic study of a complete biological system16. Out of all the omic data from the same biological system, genomic data generally remain constant across environments, although the same genotype subjected to different environments can produce a wide range of phenotypes by triggering the expressions of different genes, downstream enzymes, and metabolites17. Most current association methods and analysis tools perform association mapping based on fundamental relationships between DNA sequence variation and phenotypic variation without addressing environmental variation. GxE can be understood by observing and measuring the expression of genes or metabolites. Harper et al.2 developed an associative transcriptomic approach to study complex traits in the polyploidy crop species Brassica napus by correlating trait variation with the quantitative expression of genes and sequence variation of transcripts, with the consistent physical positions of the two kinds of associative markers allowing the identification of high-confidence transcription factor candidates18. However, their method is based on a pure additive model only, and they make no mention of interaction effects between biomarkers or their contribution to phenotypic variation.The central dogma of biology is that the genome, transcriptome, proteome, and metabolome are cascading and connected to the end phenomeTo overcome the limitation of standard GWAS that fails to consider the GxG and GxE effects, we extend associative genomics and transcriptomics into a broader associative omics by systematically integrating all available omic data into one analytical model. Here we propose a new LMM and describe the development of a pipeline for analyzing traits through ome-wide association studies (PATOWAS) to implement the model. The proposed LMM considers not only the additive effects of each biological marker but also the interaction effect of each marker pair. The marker pairs’ interaction effect introduced here corresponds to two-dimensional (2D) association mapping, which is complementary to one-dimensional (1D) association mapping in regular GWAS. Consequently, the proposed model and PATOWAS pipeline are not limited to GWAS for genotype-to-phenotype mapping (G2P); instead, they are capable of performing multiple types of ome-wide association studies, such as transcriptome-wide association studies (TWAS) for transcript-to-phenotype mapping (T2P) and metabolome-wide association studies (MWAS) for metabolite-to-phenotype mapping (M2P).We submit a rice recombinant inbred line (RIL) dataset with three omics markers and two agronomic traits to PATOWAS for comprehensive analyses of associative omics. The results demonstrate that our proposed LMM and the pipeline PATOWAS can effectively address the GxG effect and the GxE effect, perform multiple-level associative omics in one platform, and innovatively provide a systems biology view into the traits analyzed.We aimed to systematically integrate multiple associative omic results to provide more biological insights into the phenotypic traits to be analyzed. We first collected a dataset of 210 rice RILs genotyped with 1619 marker bins, profiled with 22,584 transcripts and 1000 metabolites, and phenotyped with two agronomic traits Table –5 were bMotivated by our consideration of genetic epistasis and our desire to explain more phenotypic variance, we next proposed a statistical LMM that considers not only the additive effects of each marker variant but also the interaction effects of each marker pair. Based on this linear model, we developed a PATOWAS pipeline to analyze traits through multiple ome-wide association studies. Therefore, the proposed model and PATOWAS can be used to study not only GWAS for G2P but also TWAS for T2P and MWAS for M2P, which is progress toward an integrative omics Fig. .Fig. 1Bi10(p) values indicate markers or marker pairs that are more relevant to the phenotypic trait.To test this presumption and verify our consideration, we used PATOWAS to analyze the rice RIL datasets with two agronomic traits and three different omics markers. PATOWAS accepts 2D omics marker matrix data and 1D phenotypic trait data as inputs Fig. . PATOWASIn the present study, we sequentially submitted three omic marker datasets to PATOWAS to analyze the two field traits, YIELD and KGW. We downloaded the results after completion of the analyses. Based on these results, multiple associative omics and the biological insight can be compared and integrated. For example, the combination of 1D association mapping across G2P and T2P can help identify the genotype and expressed gene transcript markers with consistent physical positions; comparison of the metabolites from 1D M2P association mapping can uncover the biochemical relevance of tissue-specific metabolites and traits to be analyzed; and the investigation of major biomarker pairs from 2D association mapping can be used to build an association network. All these together provide a systems biology view into the analyzed traits, leading toward an answer about how genes, transcripts, proteins, and metabolites work together to produce an observable phenotype.Based on the variance component analysis results, we generated six pie charts displaying the three variance components of the two traits across associative genomics, associative transcriptomics, and associative metabolomics Fig. .Fig. 2PiWe found that the two biologically meaningful variance components accounted for nearly all of the phenotypic trait variance in associative transcriptomics and associative metabolomics but not in associative genomics. Also, YIELD was a more complex trait than KGW, as the two biologically meaningful variance components accounted for only 66% of the total phenotypic variance in associative genomics but nearly 100% of the total phenotypic variance in associative transcriptomics and metabolomics Fig. . These fHere we noticed that the marker number for transcripts was obviously one-order of scale higher than the other two. Consider the marker-by-marker interactions: The pairwise number of transcripts will reach to ~250 million, which is about two-order of scale larger than the other two kinds of omic markers.To test whether the higher ratio of biological explanatory components observed in the TWAS result is not due to the larger numbers of transcripts used in TWAS, we further produced a reduced transcript gene set with a number scale comparable to the genotypes and metabolites. We separately submitted the reduced transcript gene set to PATOWAS and checked the variance component analysis result.10(p) as the representative transcript of a genotype bin. Then we generated a reduced transcript gene set for each phenotypic trait, which essentially is a data matrix with a dimension of 1543 × 210 . We then used the HAT method23 to calculate the PREDs for all transcripts and metabolites  with the selected markers by PRED thresholding. We found that the number of selected markers continued decreasing as the PRED threshold increased; however, the broad-sense H provides us with a very different perspective of different traits and different associative omics. It needs only ~1000 and fewer than 100 transcripts to explain more than 97% of the phenotypic variance in traits YIELD and KGW, respectively. In associative metabolomics, only 30 metabolites are enough to explain more than 90% of the phenotypic variance. In general, trait KGW is more conserved than trait YIELD, and associative metabolomics is more conserved than associative transcriptomics.First, the predictabilityVariance component analysis provides us with a big picture by partitioning the phenotypic variation into three components. The two biologically meaningful components for individual markers’ direct effects and the marker pairs’ interaction effects can be further illustrated by 1D and 2D association mapping, respectively.1D association mappings from PATOWAS across different associative omics can be combined, integrated, and compared, providing biological insights in trait analysis on both system and molecular biology levels.24, GCTA1, and PLINK25 can build associations between genotypes and phenotypes by calculating and outputting a p-value or −log10(p) value for each genotypic marker. The linear model adopted usually considers only the marker’s direct effect, which is mostly additive. This process essentially is 1D association mapping. PATOWAS is based on our proposed LMM, which considers not only the additive effect for each marker but also the additive × additive interaction effect for each marker pair. Therefore, PATOWAS calculates and outputs a p-value for each marker and a p-value for each marker pair, which essentially provides both 1D and 2D association mapping.Conventional GWAS tools such as TASSEL26. We submitted the same RIL rice genotype and two phenotypic trait data to PATOWAS and TASSEL. We compared the 1D p-values returned from both tools and found that the results are very consistent. The Manhattan and Q–Q plots using the same genotype and phenotypic trait data from PATOWAS and TASSEL are illustrated in Supplementary Fig. Regarding G2P mapping, 1D association mapping using PATOWAS can be compared with other GWAS tools2 developed an associative transcriptomic approach to analyzing traits of the polyploid crop B. napus. Their method combines SNP-based and gene expression-based association results to identify high-confidence transcription factor candidates. As mentioned before, the 1D p-values returned from PATOWAS correspond to the additive effects for the individual markers, and can be used to generate a 1D Manhattan plot. To generate comparable plots between associated genotypic markers and transcript gene markers along their chromosomal position, we first mapped transcript genes to genotype bins and then selected the minimum p-value as the representative p-value of a bin  values along the markers’ chromosomal positions.Harper et al.10(p) values in both G2P and T2P.We could easily find the positional consistency between genotype and expressed gene markers Fig. . For YIE10(p) values, we focused on trait YIELD and picked up the top 10 transcript gene markers for a deep molecular function investigation. The top 10 transcript gene markers are distinguished with a unique index and can be identified by its gene locus ID. Through a literature search, we found that at least five of the top 10 transcript markers have been reported to biologically affect rice YIELD (Supplementary Table LOC_Os01g62860) was reported to be related to seed shattering27; marker T_3229 (LOC_Os01g67580) was reported to be related to drug resistance28; and markers T_6368 (LOC_Os03g03070) and T_13429 (LOC_Os06g11330) were reported to control or delay flowering time30. Marker T_11921 (LOC_Os05g31040) in particular acquired the highest significance value (−log10(p) = 7.53) and was reported as the CKX9 plant hormone gene that could lead to the accumulation of cytokinin and the increased tiller number32. All these literature-validated gene markers demonstrate that our PATOWAS has the capability to perform trusted association mapping between causal expressed transcript variants and the resulting phenotypes. We annotated and marked these five genes to the 1D T2P association mapping plot and found that most of them belong to high association peaks  ≥ 3.0) metabolite markers from leaf than from seed for YIELD  ≥ 3.0) metabolite markers from seed than from leaf for KGW  ≥ Significance_Th) leaf and seed metabolites. Considering that there are 683 and 317 metabolites from leaf and seed, respectively, we set 0.683 and 0.317 as two meaningful ratio thresholds for significant metabolites from leaf and seed. From Table n < 25, significant leaf metabolites against total top n metabolites always have a ratio higher than 0.683; and (2) for KGW, when top n < 500, the significant seed metabolites against the total top n metabolites usually produce a ratio higher than 0.317.Further, we picked up variable top 34. This could be explained by the fact that the photosynthesis process takes place mainly in leaf tissue and is the main factor determining rice yield35.All these results suggest that leaf metabolites are more relevant to YIELD, while seed metabolites are more relevant to KGW, which is consistent with the findings of Xu et al.36.Further, we focused on the top 10 significant metabolites for deep molecular function investigation. Based on a literature search, the identification and classification of the top 10 metabolites are summarized in Supplementary Table The biological interpretation of 2D association mapping for marker pairs’ interaction effect can be illustrated by visualizing the 2D association matrix directly, significance thresholding, and constructing weighted association networks, etc.37.For trait YIELD, three 2D association mapping results were analyzed, and each association matrix was illustrated as a scaled image with pseudocolor Fig. . By comp10(p) ≥ Significance_Th) marker pairs instead of all the marker pairs. Similar to 1D association mapping, we could set a significance threshold to generate a binarized version of the 2D association matrix  value and its significance measured by −log10), which shows how much the omics marker pair is relevant to the phenotypic trait to be studied. If we pinpoint a marker pair  to the image illustrated for 2D association mapping, there surely are two specific lines recorded by 1D association significance values  values can be considered relevant regulators of that specific marker. Then an association network centered on the specific omics marker could be constructed. The tie connecting two omics marker nodes has an assigned association significance values. This could be called a weighted association network, which is very different from the co-expression-based gene regulation network38 due to it having a direct biological meaning with the phenotypic trait to be studied.Further, if we focus on one specific omics marker and set a significance threshold, its interactive pairs along the vertical or horizontal axes with higher −logAccording to the marker pairs’ significance values, we picked up top 10 associative transcript and metabolite marker pairs. To acquire a deep molecular-level investigation, we conducted a comprehensive literature search and function annotation for two types of associative omics marker pairs (Supplementary Tables LOC_Os03g45280). Therefore, a hub transcript T_8111 (LOC_Os03g45280)-centered expressed gene association network has been tentatively constructed  = Xβ, and the variance isKa and Kaa are marker-generated additive and epistatic kinship matrices with values calculated by formulas ..E(y) = Xσ2, which can be estimated by the restricted maximum likelihood (REML) method for dissection of phenotypic variance.The model involves three variance components, E(y) = Xβ, and the variance isThe model to estimate variance component isThe restricted log-likelihood function isσ2, we can solve for β byGiven Substituting Eq.  into Eq.Therefore, the defined likelihood function has three unknowns. Calling any optimization subroutine, we can obtain the REML estimates of the three variance components.After the three variance components are acquired, we fix the variance ratio Zi as shown below:We define model I and use it to estimate the additive effect of marker The expectation of this model isWij as shown below:We also define model II and use it to estimate the interaction effect of marker pair The expectation of this model isλa,λaa) are fixed, the two models are fixed models and can be solved using the weighted least-squares method. The variance of each model can be written asWhen  are fixed, the following matrix is a constant matrix and can be simplified using Eigen decomposition:D  holds the eigenvalues of H, and U (a matrix) holds the eigenvectors of matrix H. The inverse of D + I is simplyTherefore,Rewriting Eq.  gives23\r(P) = 2 and r(P) = 4 for model I and model II, respectively. The variance matrix of the estimated effects isThe residual error variance is estimated using0: ai = 0 isFor model I,0: γij = 0 isFor model II,p-value for a marker’s additive effect or the interaction effect of a marker pair is calculated usingThe p-value scanning for all markers’ direct additive effects, and a third for 2D p-value scanning for all marker pairs’ interaction effects. The four modules are designated km_cal, vc_anal, ps_main, and ps_inter, respectively. The modules were coded with C/C++ using Code::Blocks in a Linux environment and compiled into four separate executable commands. Several Perl and Linux C shell scripts were developed to function as a wrapper to streamline the complete analysis pipeline. Briefly, when the coded genotype data, transcript gene expression data, or metabolite abundance data are provided, module km_cal calculates and delivers the corresponding kinship matrix. When phenotypic quantitative trait data are provided, module vc_anal estimates and delivers the three variance component ratios utilizing both the quantitative trait data and the available kinship matrices. After performing various information aggregation procedures, including kinship matrix weighing and matrix eigen-decomposition, modules ps_main and ps_inter calculate and return 1D p-values for all markers and 2D p-values for all marker pairs, respectively  values for the markers’ additive effects and marker pairs’ interaction effects can be visualized and further analyzed.PATOWAS accepts 2D omic marker matrix data and 1D phenotypic trait data in.csv format as inputs Fig. . After dely Fig. . The PATcts Fig. . Based oTo increase the flexibility of analyses, users are allowed to run only a portion of the PATOWAS pipeline according to the input data and user-configured parameters . Such configuration flexibility enables users to utilize PATOWAS to generate specific data, such as a kinship matrix, for their own genetic data analysis.8, PATOWAS was implemented in C/C++ programming language. Furthermore, its computationally demanding analysis modules were implemented using parallel computing techniques, which effectively divide large computational tasks into smaller jobs that are distributed to nodes on networked Linux clusters to accelerate computing.Similar to PEPISn be the number of individuals and m be the number of omic markers. The total number of effects is m + C = m(m + 1)/2. According to the kinship matrix calculation formula7 and complexity analysis8, the multiplications to calculate the kinship matrix Ka and Kaa are mn(n + 1)/2 and m(m−1)n(n + 1)/4, respectively. These calculation complexities demonstrate the enormity of the multiplication demand associated with kinship matrix calculations, especially when both n and m are large. However, the procedure used to calculate each matrix cell value is the same; thus, all n(n + 1)/2 loops for matrix cell calculation can be parallelized.Let p-value scanning module needs m Chi-square calculations and Wald tests, and the 2D interaction effects p-value scanning module needs m(m−1)/2 Chi-square calculations and Wald tests. However, the procedure to calculate the p-values is the same, so the m times additive effect p-value calculation and m(m−1)/2 times interaction effect p-value calculation can also be parallelized. The strategy utilized in the PATOWAS for parallel high-performance distributed computing is summarized in Table The variance component analysis module essentially needs only one optimization for a three-parameter log-likelihood estimation. The 1D additive effects 46. The 210 RILs were derived by single-seed descent from a cross between the Zhenshan 97 and Minghui 63 rice hybrids. Field phenotypic data pertaining to YIELD and KGW were collected from replicated field trials on the Huazhong Agricultural University Experimental Farm in Wuhan, China.We analyzed YIELD and KGW from 210 RILs of rice described by Hua et al.41. Each bin was treated as a new synthetic marker for association studies, and the bin map was constructed by genotyping the RIL population sequences.Ome-wide quantitative marker data consisted of bin-based genotype data, Affymetrix RNA microarray-based gene expression data, and mass spectrometry-based profiling metabolite abundance data. Over 270,000 high-density SNP markers were used to infer recombination breakpoints (crossovers), which were then used to construct a total of 1619 genotype bins2-transformed before analysis47. Of the 24,994 genes, 22,584 were clearly matched to 1619 genotype bins. We found only minor and inconsequential differences between the analysis results for 24,994 versus 22,584 genes.The transcriptomic data originally consisted of 24,994 expressed genes, which were sampled and measured from flag leaves for all 210 RILs in 2008. Each line had two biological replicates, but RNA extracted from the two replicates was mixed at a 1:1 ratio before microarray expression profiling. The original expression levels were then log48. Metabolomic data were collected in 2009 and 2010. Before mass spectrometry-based metabolic profiling, germinated seeds were sampled in one biological replicate in 2009 and one in 2010, and flag leaves were sampled in two biological replicates in 2009. For both tissues, the abundance level of each metabolite was log2-transformed. For each line, we took the average of two replicates’ abundance levels as the measurement of the metabolite.The metabolomic data consisted of 683 metabolites measured from flag leaves and 317 metabolites measured from germinated seedsm × n = 1619 × 210, m × n = 22,584 × 210, and m × n = 1000 × 210, respectively (Table m and n represent the number of markers and individuals, respectively.In summary, the bin genotype data, microarray-based gene expression data, and mass spectrometry-based metabolite data were acquired and stored in three matrices as dimensions of The PATOWAS pipeline and source code are freely available at http://bioinfo.noble.org/PATOWAS/. In addition, the source code of PATOWAS has been deposited into the public repository GitHub at https://github.com/ZhaoBioinformaticsLab/PATOWAS. We are committed to maintaining and improving the specific function modules per user comments and suggestions.Supplementary InformationDescription of additional Supplementary DataSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5Supplementary Data 6Supplementary Data 7Supplementary Data 8Supplementary Data 9Supplementary Data 10


Menidia menidia) as the model system. Over a 3‐year period, a total of 542 families were used to estimate the genetic covariance in length at age from hatch through maturity. The function‐valued trait approach was employed to estimate the genetic covariance functions. A Bayesian hierarchical model was used to account for the unbalanced design, unequal measurement intervals, unequal sample sizes, and family‐aggregated data. To improve mixing, we developed a two‐stage sampler using a Gibbs sampler to generate the posterior of a well‐mixing approximate model followed by an importance sampler to draw samples from posterior of the completely specified model. We found that heritability of length is age‐specific and there are strong genetic correlations in length across ages that last 30 days or more. We used these estimates in a hypothetical model predicting the evolutionary response to harvesting following a single generation of selection under both sigmoidal and unimodal patterns of gear selectivity to illustrate the potential outcomes of ignoring the genetic correlations. In these scenarios, genetic correlations were found to have a strong effect on both the direction and magnitude of the response to harvest selection.Natural selection is inherently a multivariate phenomenon. The selection pressure on size  and the age at which selection occurs is likely to induce evolutionary changes in growth rates across the entire life history. However, the covariance structure that will determine the path of evolution for size at age has been studied in only a few fish species. We therefore estimated the genetic covariance function for size throughout ontogeny using Atlantic silversides ( When growth is allowed to evolve in these models, it is usually a single parameter that evolves rather than the shape of the growth trajectory  in the next generation is given by ΔZ¯=Gβ, where β=∇Z¯ln[W¯] is the selection gradient vector of mean fitness with respect to the trait mean =Gi,iβi+∑j≠iGi,jβj, which is the sum of the direct response and the indirect effects of selection on other ages. In the presence of strong genetic correlations, or a large number of correlated traits, the indirect effects can outweigh the direct response. In this case, predicting evolution from a scalar heritability estimate may underestimate the rate of change or even get the sign wrong.One approach to modeling the influence of genetic correlations on the evolution of size at age in harvested populations might be to treat size at a set of discrete ages as a vector‐valued trait. In studies of multivariate evolution, the additive genetic covariance matrix, n Lande, . For a vn Lande, . At a spfunction rather than a covariance matrix. For classical multivariate traits, there is no a priori structure to the dependence among size at each age. In contrast, continuity and smoothness require that the sizes at nearby ages be highly correlated. Thus, one of the main advantages of the FVT approach is that it retains information about the ordering and spacing of a set of data points, while this information is ignored in a classical multivariate analysis.Despite the potential utility of a multivariate approach, age is really continuous and discretizing age to obtain a vector‐valued trait may introduce artifacts. Genetic variation in traits with a continuous index such as age can instead be modeled via a function‐valued trait approach (FVT)  as a model organism to investigate the genetic basis of growth trajectories over the entire growing season from birth through maturation. M. menidia is an annual fish  from two sites on the north shore of Long Island  and two south shore sites . The north shore and south shore sites exchange only a limited number of migrants each year , each individual was injected with a Visible Implant Elastomer Tag (Northwest Marine Technology) underneath the skin adjacent to the dorsal fin. After tagging, fish from each family were subdivided into two groups and transferred into randomly selected 3,785‐L polyethylene tanks. There were 15 such tanks in total, and each tank contained individuals from ~9 families. As with sea tables, tank assignments were stratified by family such that no family occurred in only one tank allowing us to separate family and tank effects. Overall, 542 families of fish were reared over the 3‐year period.Artemia nauplii (Brine Shrimp Direct). During the juvenile and adult stages, fish were fed a combination of dry food  and frozen adult brine shrimp. Further details of the rearing protocol are described in Present and Conover . During the larval period, fish were fed to satiation daily using a combination of dry feed  and freshly hatched  Conover .2.2During the larval stages from days 1 to 15, the fish were measured using several approaches, including digital photography (batches 1 and 2) and calipers (batch 3). Repeated measurements of 100 individuals indicated that there are no systematic biases in any of the measuring approaches and that they each had comparable levels of precision. During the juvenile and adult stages, the lengths all of the fish in each replicate were estimated using digital photography. Specifically, a 100‐megapixel digital camera (Canon 40D with Canon 60 mm Macro lens) was used to photograph the fish from a fixed height at a shutter speed of 1/250 s. Larvae were held in a Petri dish with a shallow layer of water and photographed from 55 cm. Juveniles and adults were held in an 18‐L bucket with a 4 cm layer of water and photographed from a fixed height of 140 cm. The images were then measured in Image Pro Plus 6.0 (Media Cybernetics).2.3The results of the three rounds of experiments were combined via Bayesian modeling. Silversides are an obligate schooling fish that require ample swimming space and do not grow normally in isolation. However, space constraints limited the number of tanks we could use and several hundred fish were reared in each tank. Since only eight tag colors were available, individual fish could not be tracked throughout the study. Therefore, although we have sizes of each fish in each family at every measurement, we have no way to rigorously connect individual identities through time. In addition, not all individuals survived to the end of the experiment so that the numbers of individuals in each family were not constant. To circumvent these difficulties, we develop novel methods for estimating the genetic covariance function from these family‐level data (see Supporting Information). We note that this is, in effect, a repeated‐measures design with longitudinal data for each family. An appropriate statistical framework for such data must account for persistent differences among families, which is captured in the function‐valued trait approach.2.4The classic animal model  or tank (ages 30–276 days) estimated independently at each time point. The grand mean and fixed effect functions were piecewise linear, effectively taking independent values at each age for which we had data. The gs and gd functions represent the genetic contributions of the sire and dam, respectively, and ဓ represents the unexplained “environmental” contributions to size.where μ is the grand mean growth trajectory and βCst,t′=Egstgst′ and the environmental covariance function, Cϵt,t′=Eϵtϵt′. The covariance function for dams, Cdt,t′=Egdtgdt′, is also of interest but includes both genetic and maternal effect contributions to offspring . The environmental deviation term is modeled similarly, using the same basis set. Note that the basis expansion approach to modeling a function‐valued trait is equivalent to a classical multivariate approach, albeit in the abstract “trait space” of the basis coefficients. As such, the basis coefficients are assigned their own covariance matrices, which we denote by Cs, Cd, and E for the genetic contributions of sires, dams, and the environmental basis coefficients. The number of basis functions, K, determines the maximum rank of the inferred covariance functions and is equivalent to the effective number of “traits” in the analysis. We tested models where K ranged from 2 to 8. Similar results were found for both K = 7 and 8, with AIC favoring K = 7  is found by integrating mortality from birth to reproduction, that is,With these assumptions, the fitness of a given size trajectory, Wy=φexp-∫0TMytdt. However, fecundity is typically size dependent and likely to covary with size at several ages due to trade‐offs between growth and reproduction yT-μT+(φ″/φ-(φ′/φ)2)[yt-μt]2Wy where φ′ and φ″ represent the first and second derivatives of fecundity evaluated at the mean length at time T and W (y) is the approximate fitness from Equation ϕ = cyd, φ′φ=dy, and φ″φ-φ′φ2=-dy2. Moreover, the covariance between fecundity and length at age would then be driven by the covariance between terminal size and the length at earlier ages. However, this is a simplifying assumption that we do not pursue any further.For sake of completeness, note that had we included fecundity in our fitness model and assumed that fecundity is solely a function of size at maturation, say yt-μt=∑k=1Khkt(γk+ϵk), Equation zk be the sum of genetic and environmental components for the kth coefficient, that is, zk = γk + εk Plugging this in to Equation M¯=∫0TMμtdt is the total mortality for the mean size trajectory, mk1=∫0TM′μthktdt is the projection of mortality gradient on the kth basis function, and mk,l2=∫0TM″μthkthltdt is the projection for the second derivative.Using the basis expansion, E (zk) = 0 and the covariance matrix for z = {z1, …, zK}T is given by P = Cs + E (since we have assumed that Cs = Cd). Moreover, since the basis coefficients are multivariate normal, we can use the standard formulae for multivariate evolution to find that the mean for z = {z1, …, zK}T after selection isRecall that before selection and the mean in the following generation is given bym1)th element is mk,l2.where Δy¯∗t=∑k=1Khktz¯k∗ and the evolutionary response, that is, the change in the population mean in the next generation, is given by Δy¯t=∑k=1KhktΔz¯k. We used these approximations to calculate the response to selection for both the sigmoid and unimodal gear selectivity. To examine the relative importance of fishing versus natural mortality, we repeated these calculations over a range of values for m and f.Inserting these results into the basis expansion, we find that the change in mean length at age t following selection is given by 2.6In order to clarify the role of the genetic covariances in the response to selection, we consider two alternative models for the genetic basis of body size. In the first alternative model, we assume that size at age has constant heritability. As we show below, this is analogous using a single evolving trait to model fisheries‐induced evolution. The second alternative treats the size at each age as an independent character. Although we are unaware of analogues for this second assumption in the fisheries‐induced evolution literature, this model is the opposite extreme in terms of genetic constraints. Hence, the FVT approach based on the estimated genetic covariances is intermediate between these two alternatives.Vp (t), to be the same as for our baseline model by setting Vgt=h¯2Vpt, where h¯2 is the mean heritability over all ages. Note that this implies that the environmental variance is Vϵ(t)=(1-h¯2)Vp(t) . To connect this with the general model, note that this is precisely the same as rewriting Equation g~ and ϵ~ are constants representing the genetic and environmental components, scaled such that V(g~)=h¯2 Moreover, this is equivalent to setting K = 1 and using single basis function given by h1t=[Vpt]1/2. Since K is analogous to the number of traits in the analysis, we refer to this as the “single‐trait” model.For our first genetic alternative, heritability is constant across ages. But in order to make the results directly comparable with our baseline model, we constrain the phenotypic variance at age, Csonet,t′=Vg~[VptVpt′]1/2 and Cϵonet,t′=Vϵ~[VptVpt′]1/2. This implies the correlation  between size at any pair of ages is 1. Moreover, since there is only one component in this model, Equation Z¯∗=-m1/1+m2 and Δz¯=h¯2z¯∗ where m1=∫0TM′μt[Vpt]1/2dt and m2=∫0TM″μt[Vpt]1/2dt. Hence, the response to selection in the single‐trait model is determined by a weighted average of the selection applied to each age.The genetic and environmental covariance functions for the single‐trait model are dLdt=a-bL, where a represents anabolic processes and bL represents catabolic processes  = a (1 − ebt‐)/b. Decomposing a into genetic and environmental components and making the analogy with Equation μt=a¯1-e-bt/b, gt=ag1-e-bt/b, and ϵt=aϵ1-e-bt/b, from which we can derive the covariance and other functions. For example, the genetic covariance in size at age is Egtgt′=Varag+Varaϵ1-e-bt1-e-bt′/b2 and the variance in length at age t is Vpt=Varag+Varaϵ1-e-bt2/b2. Putting these together, the heritability for size at age is constant at h2=Varag/Varag+Varaϵ. From this, we can see that under some circumstances, assuming genetic variation in a single parameter is the same as using Equation b would also have resulted in a rank 1 covariance function, but without the tidy additive decomposition in Equation At first glance, the single‐trait model might seem like an unreasonably oversimplified abstraction. To put it into a more familiar context, consider what happens if we assume von Bertalanffy growth in length, Δy¯t=h2tΔy¯∗t.For our second alternative genetic model, we assume that the size at each age is an independent trait. Although this is physiologically impossible, it is the polar opposite of the single trait alternative in terms of evolutionary flexibility. Under this model, we keep the genetic and environmental variances the same as in our baseline model, but force the covariances to be 0. Under this model, the age‐specific heritabilities are the same as for the baseline model and evolution of size at each age follows a univariate breeders equation, that is, 3Cs and Cd).The growth trajectories from each of the three experimental batches are presented in Figure L = bt, the covariance in length 2 days apart would be Var(b)[t2 +2t]. This covariance clearly increases with age obscuring the fact that the lengths at all ages are perfectly correlated. The genetic correlation function circumvents this by scaling out the change in variance through time, for example, Rst,t′=Cst,t′/Cst,tCst′,t′1/2  = [dy/dt]−1 is the time spent at size y. Hence, all else being equal, we expect evolution to favor growth trajectories that minimize the time over which an individual is exposed to harvesting.Our hypothetical sigmoid and unimodal selectivity curves generated qualitatively different responses to selection. Under sigmoid selectivity, simulated length trajectories with the greatest fitness are those that stop growing by 80 mm, at which point the fishing mortality is still less than 20% of its maximum Figure b,f. In cThe predicted evolutionary responses to a single generation of selection under these two gear selectivity patterns depend heavily on the genetic covariance between size at different ages. Under our sigmoid selectivity scenario and the full genetic covariance model, offspring length is predicted to increase for the youngest fish up to about 40 days and decrease at all ages thereafter in a roughly parabolic manner Figure d, consisUnder our unimodal selectivity scenario and the full genetic covariance function, the predicted response is somewhat more complicated Figure c. Offsprm and F to evaluate the relative importance of natural and harvest selection , genetic correlations among ages were estimated for free‐living individuals from birth to 5 years old and positive covariances were found throughout ontogeny , significant positive genetic correlations for length at age were found  if the net selection is positive (negative). This is clearly different than what was observed with the full covariance function under unimodal selectivity, where the shape of the growth trajectory changed such that length at some ages increased while others decreased. In light of this, we suggest that future simulations of fisheries‐induced evolution would benefit from a more flexible representation for the genetic basis of growth.In contrast, treating length at each age as a sequence of independent traits virtually eliminated any response to selection in this modeling exercise. Given previous theory on how genetic correlations can constrain evolution Roff, , this waCompared to most of the commercial species with overlapping generations and size‐dependent fecundity, our model is oversimplified. However, it does illustrate that the response to selection on body size depends heavily on the particular ages over which selection acts and that this is driven by a combination of the size specificity of selection and the time spent at a given size. This is particularly relevant since rapid evolution of harvested populations has been widely documented , statistical approaches invariably truncate the expansion to some relatively small number of functions. As noted by Griswold et al.  that shrinks coefficients toward zero. In this way, we might avoid potential biases in the evolutionary inferences drawn using the function‐valued trait approach.In addition, we note that fixing K places a hard upper bound on the rank of the estimated genetic covariance function. This is the same thing as determining None declared.https://doi.org/10.5061/dryad.tq2f566.Data available from the Dryad Digital Repository:  Click here for additional data file.