Gene expression changes contribute to complex trait variations in both individuals and populations. However, the evolution of gene expression underlying complex traits over macroevolutionary timescales remains poorly understood. Snake venoms are proteinaceous cocktails where the expression of each toxin can be quantified and mapped to a distinct genomic locus and traced for millions of years. Using a phylogenetic generalized linear mixed model, we analyzed expression data of toxin genes from 52 snake species spanning the 3 venomous snake families and estimated phylogenetic covariance, which acts as a measure of evolutionary constraint. We find that evolution of toxin combinations is not constrained. However, although all combinations are in principle possible, the actual dimensionality of phylomorphic space is low, with envenomation strategies focused around only four major toxin families: metalloproteases, three-finger toxins, serine proteases, and phospholipases A2. Although most extant snakes prioritize either a single or a combination of major toxin families, they are repeatedly recruited and lost. We find that over macroevolutionary timescales, the venom phenotypes were not shaped by phylogenetic constraints, which include important microevolutionary constraints such as epistasis and pleiotropy, but more likely by ecological filtering that permits a small number of optimal solutions. As a result, phenotypic optima were repeatedly attained by distantly related species. These results indicate that venoms evolve by selection on biochemistry of prey envenomation, which permit diversity through parallelism, and impose strong limits, since only a few of the theoretically possible strategies seem to work well and are observed in extant snakes. Single genes underlying major traits are the exception rather than the rule, and the dissection of polygenic trait variation has been at the forefront of biological research . Much ofG matrix), is one of the key questions in this field , from a list of 39 publications  online. λ values which denote the phylogenetic signal , snake venom metalloproteinase (SVMP), three-finger toxins (TFTx), and Kunitz-type serine protease inhibitor (KSPI), show very strong phylogenetic signals (>0.8) and narrow confidence intervals, indicating the presence of strong phylogenetic inertia.By limiting the range of responses to natural selection, the covariances between genes reflect constraints that shape a phenotype. The PCOV matrix accounts for the effect of phylogeny on the interrelationships between genes coding for the snake venom phenotype, providing an approximation of the presence or absence of constraint behind the evolution of gene expression levels. To estimate the PCOV, we used a phylogenetic generalized linear mixed model (PGLMM) under a Bayesian framework. The concept of PGLMM was devised in the early 90s as a method to infer evolutionary constraints of characters using only phylogeny and measures of phenotypes and is based on the animal model in quantitative genetics  . As an ec signal . Phylogec signal . The λ vcompositions R package  data, which has the potential of introducing spurious correlations. A range of common solutions to this problem involve log-transformations of the data , which a package  and impu package , to conf package  online.The PCOV is a measure of additive phylogenetic covariance, that can be used to estimate the direction of greatest adaptive phenotypic variation . We idenThe clustering of snakes on this phylomorphic venom space shows a clear association between family and the major component in the venom. For example, most elapids venoms form a cluster dominated by TFTx, which is the principal family found in their venom. On the other hand, vipers occupy a larger region of phylomorphospace because some have venoms dominated by SVMP, whereas others use different combinations of SVMP, SVSP, and PLA2. Finally, colubrid venoms are the most diverse in composition, employing all of the different strategies. A key observation in the PCA is that some distantly related species cluster together around the same envenomation strategy, suggesting parallel evolution.It is important to note that PLA2s in elapids (group I) and vipers (group II) are produced by different loci and have apparently evolved independently . In ordek and c, which represent refinement of the adaptive landscape due to convergence, and shifts toward convergent regimes occupied by multiple lineages respectively. Although both these measures represent convergence, we use shifts to convergent regime (c) to classify convergence, but report both. The final model included nine regime shifts and three distinct regimes (Δk = 3) and a c = 6 convergent shifts. The AIC improved from 298.4 to 229.5 in the forward phase, to a final AIC of 211.38 in the backward phase (S11) which indicated that the final model was a better fit than the initial ones. The SURFACE model revealed widespread convergent shifts as a result of optima  in elapids, vipers, and colubrids  obtained from our analysis than would be obtained by chance (pc = 0.038). This allowed us to reject the null hypothesis and conclude that species cluster together due to convergence toward some optima in the phenotypic adaptive landscape.We used the inbuilt simulation function in SURFACE to obtain a null distribution on a simulated data set using a Hansen model that lacked true convergence . CompariEchis and Bitis), to diversifying substantially in the Crotaline clade . The ASR suggests that high levels of PLA2 and SVSP (which is mostly restricted to vipers) are more recent additions to the venom. Although not shown in our analysis, PLA2 (both group I and group II) was most likely present at the common ancestors of both Elapids and Crotalids  analysis to estimate recruitment times of the major venom components into the venom arsenal, and how venoms have changed throughout the course of evolution. Because of the diversity and plasticity of the venom phenotype, confidence intervals at the root were very large, and the inference of the venom in the most recent common ancestor should be interpreted with caution, particularly concerning absence of individual toxin families. Of the four major toxins that are responsible for venom diversification, the ASR detected only SVMP in the most common ancestor of the snakes  . The ASRrotalids , but becrotalids  online, G matrix in quantitative genetics. Unlike the G matrix, which arises largely from pleiotropic interactions between genes, phylogenetic constraints may additionally include ecological, developmental, physiological, and other factors. Significant covariance between individual components would reflect constraints on evolutionary change and the total phenotypic space attainable by selection , as well as some colubrids. However, other toxin families were recruited (or increased in quantity) later in venomous snake evolution. For example, consistent with previous work that placed recruitment of TFTx before the divergence of modern elapids (Boiga irregularis), and to an extent in the king cobra (Ophiophagus hannah). With the proliferation of the TFTx family, elapids have largely lost their reliance on SVMPs.Being present in the ancestral venom, SVMP continued to be used as a major toxin by viperids and is still the dominant toxin family in some genera  about 20 Ma, but it was likely present at the common ancestor of elapids and maybe even colubrids given the convergent regime experienced by Pseudonaja textilis and Pantherophis guttatus, and its presence in many extant species. Interestingly, the recruitment of the two PLA2 families by elapids and viperids occurred at roughly the same time, perhaps as a result of convergent selection driven by radiations in prey lineages, such as mammals.Viperid and elapid subfamilies have convergently evolved greater reliance on PLA2 toxins (group I in elapids and group II in viperids) but have diverged in venom phenospace due to the previous co-option of different major components (TFTx for elapids and SVSP for vipers). The likely presence of PLA2 (group II) gene copies at the common ancestors of Crotalids raises questions about when the complex expanded in the course of snake evolution . From ouThe overall trend is that recruitment of major toxin families took place at different times, and has progressed along different trajectories in different lineages, with instances of both loss and heightened expression. Snakes have then shifted focus on specific toxin families, occasionally investing into new toxin categories for their arsenals . The increased concentration of specific venom components, relative to the ancestors, has most likely happened by increases in copy number of the specific gene families . InteresThe extent to which traits are constrained by their history, versus reaching their fitness optima has been a major debate in evolutionary biology. Numerous studies have relied on phylogenetic regression to estimate morphological covariation between traits while accounting for phylogenetic nonindependence . In our Toxin expression data were collected from 39 publications  online. We used a time-calibrated tree of squamate reptiles (snakes and lizards) based on two large data sets comprising of 44 nuclear genes for 161 squamates, and a data set of 12 genes from 4,161 squamate species, both these data sets represented families and subfamilies . The resVP) is a result of additive genetic variation (VA) and a residual variance from environmental effects (VR), where the additive genetic variance (VA) is the independent effect of inherited alleles on the phenotype.To familiarize the reader with the rationale behind how the model was constructed, we provide a brief introduction to the animal model and refer the reader to P) would be the sum of additive genetic covariance (COVA) and covariance of residuals (COVR). In the animal model, “breeding value” is used as an explanatory variable for a phenotypic trait such thatiy is our phenotypic trait of interest, μ is the population mean, ia is the breeding value, and ie is the residual error. Although ia is used as an explanatory variable, its actual value is unknown and thus cannot be used to fit the model. To overcome this, we can specify the above model as a mixed effects model, with ia being modeled as random effect (y) in the population. This allows us to obtain an estimate of among-individual variance in breeding values, which is defined as the additive genetic variance (VA)  . TherefoP would comprise of variances for both trait 1 and trait 2 along the diagonal  and covariance between the traits (COVP12) such that P = G + R, where G is the additive genetic covariance matrix (or in our case the phylogenetic covariance [PCOV]), and R is the residual matrix. Our model was similar to model (2) and written based on the description given in section 3 on the MCMCglmm vignette for modeling multiresponse traits (y).For a simple univariate trait thinking in terms of variance is sufficient, however, for multivariate models it is useful to think in terms of variance–covariance matrices. Thus, for a bivariate model of say trait 1 and trait 2, the phenotypic matrix e traits . The onlAlthough the genetic (or phylogenetic) effect has the potential to explain a substantial amount of phenotypic similarity, in actuality, a number of intrinsic and extrinsic variables may also be responsible. If there is speculation that such variables are important, they may be added to the model as fixed effects. This would allow us to interpret the resultant variance as having been conditioned on the specific fixed effect. However, if the additional explanatory variables are not associated with the pedigree (phylogeny in our case) then their inclusion would not alter the estimate of genetic (or phylogenetic) effect . In our Phylogenetic generalized linear mixed models allow for testing slightly complicated models, provide more than a simple qualitative estimate of the existence of phylogenetic structure, and have greater statistical power than typically used metric randomization approaches . The MCMk regime shifts, and k′ distinct regimes, in addition to the extent of convergence which is defined as the difference of these terms (Δk), c is used to represent shifts toward different convergent regimes in multiple lineages  were considered to be present at the root. Pie charts in the main figure were drawn by calculating the relative levels of each of the major toxins estimated by the ASR at the specific node. The ancestral states for each toxin was estimated separately, and thus could not capture any (unlikely) constraint between toxin families that might have been present in the past. The ancestral states were clubbed together to only give a representative picture of what venom configuration at a particular node might have looked like. Two images in the main were obtained from Wikimedia under the creative commons license (Elapidiae: Thomas Jaehnel and Colubridae: Carlo Catoni) image for Viperidae provided by Alexander S. Mikheyev.The default parameters for the  the ASR . fastAncMolecular Biology and Evolution online.msz125_Supplementary_DataClick here for additional data file.


Gilthead sea bream (Sparus aurata) is a teleost of considerable economic importance in Southern European aquaculture. The aquaculture industry shows a growing interest in the application of genetic methods that can locate phenotype–genotype associations with high economic impact. Through selective breeding, the aquaculture industry can exploit this information to maximize the financial yield. Here, we present a Genome Wide Association Study (GWAS) of 112 samples belonging to seven different sea bream families collected from a Greek commercial aquaculture company. Through double digest Random Amplified DNA (ddRAD) Sequencing, we generated a per-sample genetic profile consisting of 2,258 high-quality Single Nucleotide Polymorphisms (SNPs). These profiles were tested for association with four phenotypes of major financial importance: Fat, Weight, Tag Weight, and the Length to Width ratio. We applied two methods of association analysis. The first is the typical single-SNP to phenotype test, and the second is a feature selection (FS) method through two novel algorithms that are employed for the first time in aquaculture genomics and produce groups with multiple SNPs associated to a phenotype. In total, we identified 9 single SNPs and 6 groups of SNPs associated with weight-related phenotypes (Weight and Tag Weight), 2 groups associated with Fat, and 16 groups associated with the Length to Width ratio. Six identified loci  were present in genes associated with growth in other teleosts or even mammals, such as semaphorin-3A and neurotrophin-3. These loci are strong candidates for future studies that will help us unveil the genetic mechanisms underlying growth and improve the sea bream aquaculture productivity by providing genomic anchors for selection programs. The gilthead sea bream, Sparus aurata , is a teOne of the main avenues to genetically improve the cultured stock is to identify associations between genetic variants and traits of interest, such as growth, disease resistance, and fat content. Genome Wide Association Studies (GWAS) offer the way to accomplish this by comparing the genotypes of individuals having varying phenotypes for a specific trait of interest. GWAS have boosted the field of human genetics as well as plant and livestock breeding , leadingvia genetic marker utilization  . Howeverlization . Geneticlization . Althouglization .In this study, we sought to identify genetic markers associated with important phenotypes in sea bream. We used ddRAD sequencing to identify and genotype genome-wide single nucleotide polymorphisms (SNPs) in multiple sea bream families. We performed both GWAS and FS to test the association among a combination of loci and the phenotypes of fat, weight, tag weight, and length/width. Finally, genomic prediction of the phenotypes was tested using the selected polymorphisms to evaluate its potential in selection for improved phenotypic traits like weight in sea bream. Our ultimate goal was to construct a signature—a combination of genetic markers—that will lead to maximizing the sea bream aquaculture efficiency, by improving the selected phenotypic traits.The fish used in this study were a subset of a larger experiment with progeny from 66 male and 35 female brooders constituting 73 different full sib families from the breeding program of a commercial aquaculture company (Nireus Aquaculture S.A.). From those 73 full sib families, 14 families originating from 13 males and 11 females were selected (selective genotyping), based on their within-family variation of bodyweight at harvest, for genotyping with microsatellite markers in order to perform a QTL confirmation experiment . Seven male and six female brooders with 105 progeny in total, constituting six full sib families and one maternal half sib family (10 progeny on average per family), were used for ddRAD library preparation and sequencing. These seven families were those exhibiting the greatest family variation of bodyweight at harvest out of 14 total families included in the QTL verification experiment . All progeny were reared in commercial conditions, and after PIT tagging, they were transferred to sea cages at 220 Days Post Hatching (DPH) for the growth period. For all progeny, the weight at tagging (g) (205 DPH), weight at harvest (g) (750 DPH), percentage (%) of fat at harvest  as described by Individual DNA library preparation and sequencing of the samples, which were extracted using a modified salt-based extraction protocol based on We used FastQC v.0.11.5 software to check the quality control of the raw sequence data . To recoThe annotated reference genome of gilthead sea bream has been provided by Hellenic Centre for Marine Research (H.C.M.R.) (Accession Numbers: SRR6244977-SRR6244982) . To aligGenotypes of each sample were constructed using STACKS pipeline . For eacTo check family relationship and indicate possible pedigree errors, we used KING v.2.1 software . KinshipTo fit the mixed model for every phenotype, we used the command lmer from the lme4 R package . Random iy is the vector of measurements of the i-th family containing ni measurements with i is the overall constant term. The iτ is the random effect of the i-th family, the deviation of the i-th family from the overall constant a. The term jβ is the fixed regression coefficient of the variable jX, and ie is the vector of residuals of the i-th family. The model has two sources of variation: one stemming from the residuals and one stemming from the repeated measurements, where i = 1,…,K, with K denoting the number of families and variance . To compvariance . BIC att–4, which is the typical significance level a = 0.05 divided to the number of independent SNPs (497) based on linkage disequilibrium (LD)  . We usedium (LD) . Finallyium (LD)  library The typical GWAS pipeline reveals individual SNPs that are associated with a specific phenotype. One limitation of this pipeline is that it cannot produce signatures that contain combinations of variants. This problem is commonly referred as SNP to SNP interaction induction . The larCommonly FS algorithms aim to find a single group of features that has the highest predictive power. On the contrary, SES algorithm introduced by Orthogonal Matching Pursuit is an iterative algorithm. At each iteration, it selects the column-marker of the SNP data matrix, which has the greatest correlation with the current residuals . OMP updThe selection of the appropriate algorithm for each dataset is a challenging task. Commonly, a k-fold cross-validation (CV) is used in order to end up with the algorithm with the best fit in the examined dataset. Cross-validation is a model validation technique for assessing the results of a model. It is commonly used for estimating how precisely a predictive model performs in unknown data samples. The standard method of a prediction problem, where a dataset of known data is given, is to split data samples in folds and every time use the n-1 folds as training dataset and the one fold that is left, as test dataset (“unknown data”). The goal of cross validation is to estimate the expected level of fit of a model to a data set that is independent of the data that were used to train the model. This approach limits problems like over-fitting and gives an insight on how the model will generalize to an independent dataset . To compThe different models were assessed based on the sum or errors when assuming that the “unknown data” belong to each family (Equation 3). The model with the lowest mean sum of errors is selected as best model (Equation 4).iy(in + 1), ix(in + 1) and iz (in + 1) are, respectively, the outcome and predictors of the new observation in cluster i, and β and ib based on all the training data. This can be estimated by the leave-one-out cross validation,where β and ib based on the training data without subject j in cluster i  in any of the following species: Stickleback, Asian sea bass, Medaka, Asian swamp eel and Amazon molly, they were considered as conserved.To identify potential genes that might be affected by the retrieved SNPs, we searched the reference genome and classified the SNPs to those falling within a genic region (located within or in a window of 10Kb upstream or downstream of an annotated gene) and those that do not. If these regions were described as conserved at the genome browser of Gilthead sea bream , and Hierarchical clustering , and from each model, we extracted the median squared error as an evaluation metric Figure 2The selected variables/SNPs associated with Fat content (%) at harvest, retrieved from SES algorithm (threshold 0.01), recovered three SNPs, out of which two were located within or proximal to an annotated gene Table 2.Four selected variables associated with weight at harvest (800 g average weight at harvest) have been retrieved from SES algorithm with number of condition set equal to three. The first was found in chromosome 1 (chr1:16636968) on “ethanolamine phosphate cytidylyltransferase-like” gene, the second (chr6:12617755) in a conserved region upstream of “myosin-7-like” gene, the third (chr8:11613979) was located in “semaphorin-3A” gene  and upstream of ‘Piccolo’ gene, and another one (chr16:2232897) and the fourth on two overlapping genes acetylserotonin O-methyltransferase-like and LBH-like isoform X1. When lowering the significance threshold to 0.05, four SNPs were added to the signatures, retrieving two more annotated genes Table 3.Five SNPs were associated with Tag Weight, as retrieved from SES algorithm Table 4.Finally, five SNPs were associated with Length/Width ratio (at 750 DPH) as retrieved from SES algorithm Table 5.Here, we present a family-based approach for the discovery of genetic variants that are significantly associated with a set of phenotypes with economic importance for the farmed gilthead sea bream. The application of these methods on seven families, each measured on four phenotypes, revealed several genetic signatures that may be used for genomic selection. Various QTL affecting growth, morphology, and stress-related traits have been detected using microsatellite markers in gilthead sea bream . Some ofThe sample size of our study (N = 103) might indeed produce some artifacts of this kind. Nevertheless, the analysis pipeline that we apply (SES) is specially tailored for small or moderate sample sizes in order to detect statistically significant QTLs. We anticipate that a future study with greater sample size will refine our findings and might locate additional important QTLs.In GWA analysis after the LD-pruning, we found 497 independent SNPs. It expected the LD-pruning to reduce drastically the number of SNPs. Studies has shown that a strict LD filters like the one that we applied has minimal effect on the predictive accuracy of the remaining SNPs . In geneRegarding the loci associated with weight and tag weight, we identified 15 genes in total. Interestingly, although those two traits represent the same trait at different stages, we found no gene associated with both. There are many reasons for such result. One reason may be due to the low power of the experiment and the differences in variation in the weight of the fish at different ages. Another reason may be because different genes are affecting growth at different stages of development. A third reason is that may be the gene action is not only additive and epistatic effects exist. In any case, all these scenarios should be further investigated in a more powerful experiment, which would be necessary in any case. The outcome of our analysis revealed SNPs close to very important genes with a well-known role in weight gain–loss, such as Follistatin, myosin-7, and semaphorin (SEMA3A) genes. Follistatin binds and inhibits the activity of several TGF-family members in mice . StrikinThe compilation of an annotated reference genome for this species has been recently published by the Hellenic Centre for Marine Research (H.C.M.R).  and is aIn this study, we employed two different approaches to identify variants associated with growth-related phenotypic traits. Our chosen selected panel combined with the vigorous bioinformatic analyses revealed the most significant SNP loci on the sea bream genome. The discovered candidates are located in the proximity of genes with known involvement in processes related to growth. The combination of these novel loci may lead to the selection of brooders based on specific genetic signatures and can have a great effect on the efficiency of the aquaculture. Moreover, these results could be used to verify or not putative QTL identified in previous studies and could also be used in order to fine map identified QTL in the same population using other types of genetic markers . Following this step, the use of these variants independently as individual SNP (or SNP haplotypes) and/or in combination with other marker information in a MAS program could be a form of direct application in the aquaculture breeding industry. When more dense SNP markers would be available  for the species and more families from more populations are genotyped , then the application of Genomic Selection will be more feasible and cost effective in terms of any selection accuracy benefits. Nevertheless, our study presents, in a small scale example, the feasibility of GS application as well as the availability of the tools necessary before its application  in an important Mediterranean aquaculture species such as gilthead sea bream.Animal welfare was achieved according to the “Guidelines for the treatment of animals in behavioural research and teaching”  . All fish utilized in the study were kept in registered and authorized facilities to maintain and perform animal experiments; rearing and sampling followed the guidelines of the Directive 2010/63/EU for the protection of animals used for experimental and other scientific purposes  . In addition, experimental sampling protocols were approved by the IMBBC’s aquaculture department committee and methods were in accordance with relevant guidelines and regulations approved by the Hellenic Ministry of Rural Development and Food and the Regional Directorate of Veterinary Medicine for certified experimental installations (EL 91-BIO-04) and experimental animal breeding . Laboratory personnel include accredited technicians by the Federation for Laboratory Animal Science Associations (FELASA).CT, GP, TM, AK, and DK conceived and designed the study. LP, DC, and CT designed and performed the family selection. AT performed the DNA extraction and ddRAD library preparation. DK performed the bioinformatic analyses with guidance from AK and TM. DK performed the statistical analyses with guidance from MT and IT. DK wrote the first draft of the manuscript. MT, AT, DC, AK, and TM wrote sections of the manuscript. All authors contributed to manuscript revision and read and approved the submitted version.Financial support for this study has been provided by the General Secretariat for Research and Technology (GSRT), Ministry of Education and Religious Affairs, under the National Programme for Competitiveness & Entrepreneurship (EPAN II) funded by National sources and the European Regional Development Fund for the gilthead sea bream. This research was supported in part through computational resources provided by IMBBC . Funding for establishing the IMBBC HPC has been received by the MARBIGEN (EU Regpot) project, LifeWatchGreece RI, and the CMBR  RI.Author LP was employed by company Nireus Aquaculture SA, Greece. 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.


It is extremely expensive to conduct large sample size array- or sequencing based genome scale association studies. For a quantitative trait, an extreme case-control study design may improve the power and reduce the cost of variant calling. We investigated the performance of extreme study design when various proportions of samples are selected from the tails of phenotype distribution. Using simulations, we show that when risk genotypes become rare in the population and effect size is relatively small, it is beneficial to carry out an extreme sampling study. In particular, the number of selected cases and controls can even be unbalanced such that power is further increased, compared with a balanced selection. Our application to two data sets: methadone dose data and yearling weight data, demonstrated that similar results for full data analysis can be obtained using extreme sampling with only a fraction of the data. Using power analysis with simulated data and an experimental data application, we conclude that when full data is unavailable due to restricted budget, it is rewarding to employ an extreme sampling design in the sense that there can be immense cost reductions and qualitatively similar power as in the full data analysis. As a result, considerable attention in recent years has turned to extremely large sample size array- or sequencing-based genome-scale association studies in the search for more undiscovered causal variants3. But it is notoriously expensive to genotype a large number of individuals, especially in sequencing studies. In addition, there is the need to adjust for multiple testing. The Bonferroni-corrected p-value, the significance threshold set to 0.05 divided by the total number of SNPs analyzed  SNPs), is generally applied to control the family-wise error rate. Therefore, low statistical power is a major concern in genetic association studies.Despite the successful application of genome-wide association studies (GWAS) in hundreds of traits, the genetic variants discovered so far explain only a small proportion of the total heritability of complex traits0) while the alternative hypothesis (HA) is true. To improve power, for a quantitative trait, it has been proposed that one cost-effective strategy for enriching the presence, or absence, of a causal allele in a sample and reducing the cost of variant calling is to only take extreme observations of the trait distribution and carry out a case-control study instead of a regular QTL mapping study. In a GWAS study of hypertension, Padmanabhan et al. used an extreme case-control strategy by taking the top 2% of the blood pressure distribution as cases and the lower 9.2% of the distribution as controls, and discovered a SNP in the uromodulin gene to be associated with hypertension4. Other researchers compared different thresholds in the distribution of body mass index, height and waist-to-hip ratio for anthropometric traits and this way identified 11 novel loci5. Schork et al. focused on theoretical calculations for the power of extreme sampling under different scenarios of LD strength and heritability6. For common variants, Huang and Lin (2007) proposed testing for associations between extreme continuous phenotypes and variants using the maximum likelihood method assuming a truncated normal distribution for extreme phenotype7. Uemoto et al. (2011) accounted for pedigree structure using selective genotyping strategy, and identified 32 loci associated with oleic acid (C18:1) in the intramuscular fat of the trapezius muscles in Japanese Black cattle8. Recently, Barnett et al. extend the extreme case-control methods to identify rare variants in Sequencing Association Studies9.Statistical power is the probability to reject a null hypothesis  in former heroin addicts undergoing methadone maintenance treatment (MMT) in Israel2. The genotype with mean value 1 is considered the reference genotype. Individuals with trait value y less than a threshold T1 are defined as control subjects and individuals with y > T2 are case subjects. We consider selecting individuals from the tails of the quantitative distribution so that we hopefully increase the proportion of sampled individuals with and without the risk allele in cases and controls, respectively, compared to the proportions in dichotomous disease groups with the threshold equal to the median of y. Note that the controls may not be controls in a strict sense in certain scenarios. From clinical point of view, both extremes may be interesting and can be defined as “cases” in case control analysis. In such situation, the definition of cases and controls can be tricky. In this study, controls refer to relatively healthy individuals obtained from a quantitative trait, or those that are cheaper and easier to recruit.Define a QTL locus with two alleles, A and B, with the B allele conferring risk. Under a dominant model, let the mean phenotypic value for individuals with genotype AA be 1 and the phenotypic values for individuals with AB and BB be δ, δ > 0. Similarly, under a recessive model, the mean phenotypic values for AA, AB and BB are 1, 1, and δ, respectively. Under a multiplicative model, the means should be 1, δ and δ12, and thus often used to be compared with13. Therefore, we choose the classical Fisher’s exact test to assess the association between the marker and disease status. Table Among various tools employed for determining significant markers, Fisher’s exact test is classical and largely acceptableUnder the null hypothesis of no association in the dominant model and given the observed margins, the probability of an observed table is hypergeometric,mentclass2pt{minim14.In addition to Fisher’s exact, we employ XP-GWAS to identify trait-associated variants. The method is developed in particular for individuals that have extreme phenotypes2, 2pq and q2. To generate a genotype, two alleles are drawn independently from a binomial distribution B. After SNP genotypes have been generated, we simulate phenotype data for individuals with a specific genotype. Phenotype data are generated from normal distributions with different specifications of mean values between genotypes under the various genetic models (See section Definitions and Models). We repeat this process 10,000 times.To provide a practical guide for choosing an appropriate threshold in selecting cases and controls, we conduct extensive simulations to study the relationship between power, fraction of selected samples, effect size and minor allele frequency (MAF). For a sample size of n = 300, we first generate genotype data under the assumption of HWE. Let the frequency of the minor allele B be p, so the frequency of the major allele A becomes q = 1 − p. The three respective genotype frequencies in the population are then p6, followed by extensive simulations comparing the performance of the QTL and threshold-defined case-control selection approach. For the quoted dataset, investigators collected blood samples from former heroin addicts who were all stabilized with methadone. One hundred and ten SNPs from eleven genes encoding potential pharmacodynamic factors of methadone were analyzed. The study was approved by the Helsinki Committee of the Tel-Aviv Sourasky Medical Center and The Rockefeller University Hospital institutional review board, and all subjects signed informed consent for genetic studies .Analysis of real data can provide more relevant information than simulation. In analysis of real data, we first describe our analysis of a dataset on dose required for effective MMT11. The data set comprised 486 Hanwoo steers that were born between spring of 2005 and fall of 2007 in Hanwoo Improvement Center (HIC) of Nonghyup in Seosan, Korea. Yearling weights of the steers were measured in the HIC and the DNAs of the steers were provided by the HIC laboratory under the approval of the Hanwoo research committee of the Technology Development Program for Agriculture and Forestry, Ministry of Agriculture, Forestry and Fishers, Republic of Korea in 2010. The steers were genotyped with the 35,968 SNPs that were embedded in the Illumina bovine SNP 50 K beadchip and yearling weight traits were measured for the steers. Ethics committee approval for treatment of animals was not required, as all the blood samples and measurement of the trait were taken by veterinarians for routine purposes in HIC.The other data set comes from the genome-wide association study for yearling weight in Korean native beef cattlehttp://www.r-project.org). Code for simulation and evaluating power of the methods is available from the Supplementary Code.The program used to simulate and analyze the data has been written in the R statistical programming language  for all 110 SNPs are also not significant when adjusted for multiple testing.The enhancement in power is also illustrated through a real data application to analysis of methadone doses (MD) in former heroin addicts undergoing methadone maintenance treatment (MMT) in Israel1 = t-percentile and T2 = (1-tpercentile), meaning we take equal fractions of individuals from the tails of the distribution. Next, we vary T1 from the 10th to 50th percentile. The median number of significant SNPs is 6.5. When T1 = 32th percentile, the smallest p-value equals to 0.0026 for SNP rs10835210. SNP rs4358872 resides in intron 21 of gene NTRK2 (Neurotrophic Receptor Tyrosine Kinase 2) and rs10835210 is in intron 8 of gene BDNF (Brain Derived Neurotrophic Factor). These two SNPs have also been shown to be associated with MD10.We first examine the association between SNPs and methadone doses using the traditional QTL analysis. There are five statistically significant SNPs . The smallest unadjusted p-value from ANOVA is 0.027 . Let T15. Some of the results are indeed better than when we select equal fractions of extreme individuals. The number of significant SNPs and the smallest p-value is summarized in Table Next, we vary T1 between the 10th and 50th percentile and also T2 between the 50th and 100th percentile, because it is known that increasing the control-to-case ratio beyond 1:1 may result in higher poweret al.11. Among the 54,001 SNPs in the Illumina bovine beadchip array, 35,968 SNPs were available for tests. The 486 steers in this study represent a full sample  and the trait yearling weight can be assumed normally distributed in the population. The corrected phenotypes are estimated by the fixed effect , covariate (yearling age) and random additive polygenic effect. We therefore perform test using the high and low corrected phenotypic tails of the corrected phenotypic distribution in the population.Weight traits are considered the most economically important production traits in beef cattle. The animals are weighed at predefined times to comply with the respective breeding scheme, where common measurements are taken at 12 months, yearling weight. A genome-wide association study for yearling weight in Korean native beef cattle has been reported by co-authors Yi Li −6 for 35,968 SNPs). The smallest unadjusted p-value from ANOVA is 1.09 × 10−5 , which is not significant after Bonferroni correction. Then, we tested each SNP for association between genotypes AA, AB, BB versus yearling weight in extreme samples using the Fisher’s exact test. Let T1 = t-percentile and T2 = (1-tpercentile), meaning we take equal fractions of individuals from the tails of the distribution. When we vary T1 from the 10th to 50th percentile, there is one statistically significant SNP, Hapmap36817-SCAFFOLD245829_8774 . The SNP has a p-value of 1.77 × 10−7, obtained with T1 = 13th percentile. The SNP resides in gene FAT2  and SNP Hapmap36817-SCAFFOLD245829_8774 resides in gene GAS2 (Growth Arrest Specific 2). These two SNPs have also been shown to be associated with yearling weight10. Next, when we vary T1 between the 10th and 50th percentile and also T2 between the 50th and 100th percentile, the number of significant SNP remains one with multiple testing correction. If we relaxed the threshold of statistical significance to 10−4, we can detect two SNPs using full data, while 3–5 SNPs are detected under the extreme sampling design. The p-value for ARS-BFGL-NGS-105590 decreases to 6.07 × 10−7  with T1 = 26th and T2 = 85th. The smallest p-value of 3.00 × 10−8 is obtained for Hapmap36817-SCAFFOLD245829_8774  when T1 = 13th and T2 = 80th, in other words, the control-to-case ratio is approximately 1:2. It shows that similar results as for full data can be obtained using extreme sampling with only a fraction of the data.We first examine the association between SNPs and yearling weight using the traditional QTL analysis. We assume a conservative threshold value by using the Bonferroni correction to reduce type I error (p = 1.39 × 1017. Here the most optimal case-control ratio is not 1:5 or 1:4, because it would relax the threshold too much in selecting controls such that many individuals with risk genotype are mixed into the control samples.The cost of large-scale molecular studies is still relatively expensive and in some animal studies, it even has to kill cattle in order to measure the phenotypes. Therefore, researchers are attracted by potential gains in using extreme samples of population. However, practical guidance has not been well established. To provide some insights for large-scale association studies, we investigate the power of sampling the extremes and establish proper thresholds to select cases and controls with the changes of MAF and effect size. We show that when effect size is relatively large, it is beneficial to carry out an extreme sampling study. We confirm through extensive simulations that selecting between 20% and 40% of cases and controls, respectively, from the tails of the distribution could be as powerful as the full data analysis. Conventionally, adding more controls would yield more statistical power, but this effect is negligible above 4:1To avoid the multiple testing problem in searching for the threshold with the smallest p-value when the underlying genetic model is unknown, we would recommend researchers to go with the worst case scenario to avoid the problem of low power in detecting the associated risk allele. Worst case scenario refers to a genetic model where a relatively bigger sample size is required compared to the other genetic models, among dominant, recessive and multiplicative.18] and no need to consider unbalanced case control design.We demonstrate the application of the design through real data analyses. Note that although we arbitrarily define former heroin addicted individuals who needed extremely high MD in methadone maintenance treatment as cases, we should be aware that individuals with very low MD are not clinically healthy controls. It may partially explain that the lower/lowest p-value is observed when the number of cases is more than that of controls while according to the simulations, generally it is more powerful when the number of controls is more than that of case. It would be interesting to explore the biological mechanisms and factors that lead certain individuals to require only a very low MD in treatment. The idea of increasing the number of controls to increase power may come from situations in which the cost of obtaining controls is lower than the cost of obtaining cases, or in which cases may be difficult to find, while healthy controls are more easily available. If the definition of cases and controls is arbitrary, the oversampling idea should be applicable to both tails of the phenotypic distribution, or, consider oversampling the tail where it is much easier and cheaper to recruit individuals. When the total sample size is restricted due to cost and it is equally expensive to obtain cases and controls, the most powerful case-to-control ratio would be 1:1 [Jewell, 200410.In the real data demonstrations, the detected SNPs might be unstable and should be interpreted cautiously, since they are derived from a small sample size. The smallest p-values may correspond to different SNPs with different parameters, for example, with different genetic models. Nevertheless, it is noted that the SNPs identified in the real data analysis have been demonstrated to be related to the phenotype in literatureThe study has its limitations. Our conclusions are derived from a simulation study of limited scenarios. In the simulation, it is assumed that the minor allele increases the risk. Another scenario may be that the direction of effects of the minor allele is opposite or protective. But it would not change the conclusion of extreme sampling design being cost-effective, because the definition of cases and controls in quantitative traits can be arbitrary.Note that we would not recommend practitioners to blindly use extreme sampling approaches for power improvement when full data is available, but rather to propose an alternative way of study design before any samples are collected.In practice, it is cost-effective to employ an extreme sampling design, which achieves similar power as the QTL analysis in most situations except when effect size is relatively small. To maximize power, it may worth to explore the choices of an unbalanced proportion in selecting cases and controls.Supplementary Information


Septoria linicola) is a fungal disease causing major losses in seed yield and quality and stem fibre quality in flax. Pasmo resistance (PR) is quantitative and has low heritability. To improve PR breeding efficiency, the accuracy of genomic prediction (GP) was evaluated using a diverse worldwide core collection of 370 accessions. Four marker sets, including three defined by 500, 134 and 67 previously identified quantitative trait loci (QTL) and one of 52,347 PR-correlated genome-wide single nucleotide polymorphisms, were used to build ridge regression best linear unbiased prediction (RR-BLUP) models using pasmo severity (PS) data collected from field experiments performed during five consecutive years. With five-fold random cross-validation, GP accuracy as high as 0.92 was obtained from the models using the 500 QTL when the average PS was used as the training dataset. GP accuracy increased with training population size, reaching values >0.9 with training population size greater than 185. Linear regression of the observed PS with the number of positive-effect QTL in accessions provided an alternative GP approach with an accuracy of 0.86. The results demonstrate the GP models based on marker information from all identified QTL and the 5-year PS average is highly effective for PR prediction.Pasmo ( Pasmo, rability . Developrability  and is qrability . Large vrability . Phenotyrability . Howeverrability ,4.With the advancements in molecular marker development over the last decade, efforts to use marker-assisted breeding strategies have been pursued. One such strategy involves identifying quantitative trait loci (QTL) in biparental mapping populations and using markers to efficiently backcross QTL into elite breeding materials . This soFusarium head blight (FHB) in wheat, a typically quantitatively inherited trait with predominantly additive genetic variation, where GP had a significantly higher accuracy than pedigree-based information alone [In GP, a training population (TP) is genotyped with genome-wide markers and phenotyped for the trait(s) under selection; statistical models that best predict the breeding values from the marker data are then applied to select non-phenotyped germplasm. GP has been used to select for disease resistance in several crops such as on alone . GP feason alone . The impon alone . Despiteon alone .p) and sample size (n) in a given population, there are many more p effects to be estimated than the n, leading to an infinite number of possible marker effect estimates [p, small n problem” (p >> n) when applying markers to predict phenotypes [p >> n setting, LASSO will select at most n − 1 variables and set the effects of the remaining predictors at zero [Lolium perenne demonstrated GWAS’s ability to identify and rank markers, which enabled the identification of a small subset of single nucleotide polymorphisms (SNPs) that could achieve predictive abilities close to that attained using the complete marker set [The fast-evolving genotyping platforms have been a game-changer in the implementation of GP, allowing the production of large numbers of genome-wide markers, whereas progresses in phenotyping were not associated with similar cost reduction or quantum leaps in throughput. Given the number of markers  were much higher than the Pearson correlations between individual years (r = 0.31–0.62) (PS ratings at green boll stage or maturity across five consecutive years were similar but on average PS ratings in 2014 and 2016 were higher than those in other years . They ha31–0.62) , implyin−5 probability level [Four marker sets were used for GP of pasmo resistance. The first marker set contained 52,347 genome-wide SNPs (SNP-52347) that were correlated to the five-year average PS and the PS of the five individual years at a 10r) and relative efficiency (RE) using a five-fold random cross-validation scheme  ranging from 0.71 to 0.81 and RE values of 1.42 to 1.62 were obtained when predicting PS for individual years  and predicted PS (x): y = 1.0522x − 0.3267 (R2 = 0.96) (A prediction accuracy as high as 0.98 and a cessions . A linea = 0.96) a. Based  = 0.96) a.r = 0.86 or R2 = 0.73) was observed (y = −0.0262x + 11.934) of the observed PS (y) to NPQTL (x) had a large standard deviation for each prediction value, with an average prediction interval width of 2.70, nearly three times the average prediction interval width of the GP model; that is, the NPQTL model had a higher prediction error than the GP model.NPQTL in the 370 accessions for the 500 QTL set was tallied. Significant linear correlation between PS-mean and NPQTL (observed b. This cobserved . Howeverr between observed and predicted PS). Similarly, a linear regression model of observed PS (y) to NPQTL (x) of the 277 accessions (the same TP as GP) produced y = −0.026x + 11.902  and different levels of resistance, we randomly chose 20% of the 370 accessions in the population, that is, 93 accessions  as validation dataset, that is, a five-fold random cross-validation set. To predict the PS of these 93 accessions, a RR-BLUP model using the SNP-500QTL set and the PS-mean of the remaining 277 accessions as TP set was built to predict PS. The predicted results are shown in + 11.902 , which w+ 11.902 b. Using + 11.902 . The pre+ 11.902 .Cross-validation remains the most popular method to evaluate GP accuracy ,28. Our Three sets of QTL markers  and a genome-wide SNP marker set (SNP-52347) were evaluated here. GP models built using SNP-500QTL consistently outperformed models derived with any of the other three marker sets , lendingp, small n” issue.Surprisingly, the GP models built using SNP-52347 generated a lower prediction accuracy than the models with SNP-500QTL , regardlG × E interactions, which affects the accuracy of trait assessment, are common for plant traits. A strong G × E interaction was observed in flax PR . As a coSome studies report that prediction accuracy of GP is highly affected by the size of the TP. In general, the prediction accuracy increases with TP size ,34,35,36A variety of statistical methods have been proposed to estimate marker effects for GP. In general, GP methods are based on additive genetic models and their accuracies may vary depending on genetic architecture of target traits. According to the assumptions for statistical distributions of the marker effects, two groups of GP models have been proposed. The first group of models, such as RR-BLUP, genomic BLUP (GBLUP) and BRR, assume that all markers have some effects on the target trait and the same variance, that is, all makers contribute to the variation of the trait. The second group of models, including BayesA, BayesB, BayesC and BL, assume a specific variance for each marker. Some of these models such as BayesB, BayesC and BL, also allow variable (marker) selection when some of markers have very small or no effects. Based on these assumptions, the first group of models are expected to be useful for complex quantitative traits that have a polygenic architecture, while the second group of models are suitable for traits that controlled by a small number of genes or QTL with large effects. Several studies have shown better performance of BayesB for traits controlled by a few of genes with large effect ,48,49,50r = 0.86 or 2R = 0.73) between NPQTL and PS  was used to analyse correlations between different PS datasets and draw histograms and scatter plots.All flax accessions were assessed for PS in the same pasmo nursery from 2012 to 2016 at the Morden Research and Development Centre, Agriculture and Agri-Food Canada (AAFC), Morden, Manitoba, Canada . A type-http://med.stanford.edu/tanglab/software/frappe.html) was used to estimate the population structure of the 370 accessions for other six multi-locus models. GEMMA does not require a Q matrix. The threshold of significant associations for all three single-locus methods  and the multi-locus method FarmCPU was determined by a critical p value (α = 0.05) subjected to Bonferroni correction, that is, the corrected p value = 1.93 × 10−7 , while a log of odds (LOD) score of three was used to detect robust association signals for the remaining six multi-locus models. The R package MVP (https://github.com/XiaoleiLiuBio/MVP) was used for GWAS analyses for the GLM, MLM and FarmCPU, the GEMMA software (https://github.com/genetics-statistics/GEMMA) for GEMMA and the R package mrMLM (https://cran.r-project.org/web/packages/mrMLM/index.html) for the additional six multi-locus models. The details of GWAS analyses were described in Reference [2 test with Yate’s continuity correction to detect all SNPs significantly associated with PS using a 10−5 probability level. The three QTL sets and the genome-wide SNP set were used to construct the GP models. Thus, GP models with the 24 combinations of the four marker sets and the six phenotypic datasets were built and compared.A total of 258,873 SNPs were obtained from the 370 accessions after pruning by removing redundant SNPs . The miseference . A totaleference . These tThree statistical methods RR-BLUP ,17,20, Br) was defined by the Pearson’s simple correlation coefficient between the genetic values predicted by GP and the observed phenotypic values. The relative efficiency of genomic prediction over phenotypic selection (RE) was estimated using |r|/RE was used as a criterion to compare the response to one cycle of genome-wide selection versus one cycle of phenotypic selection. Means of r and RE of the 500 samplings for each marker set, GP model and PS dataset were used to describe the prediction accuracy of GP and the efficiency of one GP cycle relative to one phenotypic selection cycle, respectively. To compare different marker and PS datasets, a joint analysis of variance with Tukey multiple pairwise-comparisons was performed to test the statistical significance of differences in r and RE using R. As a case study, we randomly selected 20% of all 370 accessions as validation dataset and used the remaining 277 accessions as training dataset to build a GP model for genomic prediction of unknown germplasm.Two validation methods were used to evaluate prediction models generated from combinations of statistical models, marker sets and PS datasets. The first method was a five-fold random cross-validation. The 370 flax accessions were randomly partitioned into five subsets. For a given partition, each subset was in turn used as validation or test data and the remaining four subsets made the training dataset. This partitioning was repeated 500 times. In this manner, a total of 2500 training data sets were created to build GP models and estimate marker effects. These were used to predict the breeding values of the individuals in the corresponding 2500 test/validation datasets. The accuracy of the genomic predictions (g |r|/H2 ,27, wherThe second cross-validation approach involved comparisons across different PS datasets, that is, each of the six complete PS phenotypic datasets were used as training datasets to build GP models that were applied to itself and to the other five phenotypic datasets. The same set of markers for all 370 accessions was used for training and validation. This method tests the relevance of models built based on single year phenotypic data to predict phenotypes measured in different years. The phenotypic variation explained by all markers in various marker sets, denoted ar model  implemenar model . The detar model .Using a diverse worldwide flax core collection of 370 accessions as a training and test population with 500 QTL identified by GWAS, the 5-year average PS data and the RR-BLUP statistical model, we developed a highly effective GP model with a prediction accuracy as high as 0.92 for pasmo, a low heritability and high inheritance complexity trait. This is the highest reported accuracy value of all GP models for plant disease resistance traits and comparable with previously published results. As an alternative, we developed a linear regression prediction model based on NPQTL that also produced a high prediction accuracy of 0.86. The GP model and the NPQTL-based regression equation were validated and deemed to be applicable to the evaluation of flax germplasm including parent selection for PR. The use of all potential QTL associated with a target trait would be beneficial because the exclusion of a large proportion of unrelated markers would facilitate the construction of highly accurate GP models.


In this paper, we extend multi-locus iterative peeling to provide a computationally efficient method for calling, phasing, and imputing sequence data of any coverage in small or large pedigrees. Our method, called hybrid peeling, uses multi-locus iterative peeling to estimate shared chromosome segments between parents and their offspring at a subset of loci, and then uses single-locus iterative peeling to aggregate genomic information across multiple generations at the remaining loci.Using a synthetic dataset, we first analysed the performance of hybrid peeling for calling and phasing genotypes in disconnected families, which contained only a focal individual and its parents and grandparents. Second, we analysed the performance of hybrid peeling for calling and phasing genotypes in the context of a full general pedigree. Third, we analysed the performance of hybrid peeling for imputing whole-genome sequence data to non-sequenced individuals in the population. We found that hybrid peeling substantially increased the number of called and phased genotypes by leveraging sequence information on related individuals. The calling rate and accuracy increased when the full pedigree was used compared to a reduced pedigree of just parents and grandparents. Finally, hybrid peeling imputed accurately whole-genome sequence to non-sequenced individuals.We believe that this algorithm will enable the generation of low cost and high accuracy whole-genome sequence data in many pedigreed populations. We make this algorithm available as a standalone program called AlphaPeel. In this paper, we extend multi-locus iterative peeling to provide a computationally efficient method for calling, phasing, and imputing sequence data of any coverage in small or large pedigrees. In the past few years, the use of genomic data has expanded greatly. The widespread genotyping of animals empowers breeding via genomic selection , 2 and pAlthough the cost of producing whole-genome sequence data for an individual has decreased substantially, it is still prohibitively expensive to obtain high coverage whole-genome sequence data on tens of thousands of individuals. An emerging strategy in breeding populations is to obtain a mix of high and low coverage sequence data on a subset of individuals, and then to propagate that information between related individuals to call whole-genome sequence genotypes for all members of a population, some of which may have only single nucleotide polymorphism (SNP) array genotype data . This stPast methods for using mixed coverage sequence data to call, phase, and impute genotypes have primarily exploited linkage disequilibrium (LD), e.g., MaCH , Beagle Single-locus and multi-locus peeling are two pedigree-based methods that model an individual’s haplotypes based on the haplotypes of its parents and offspring and the individual’s genotype data. There is a large body of literature on peeling methods in genetics e.g., , 23–28 aIn this paper, we present a hybrid peeling method that is scalable to whole-genome sequence data on tens of thousands of individuals. In hybrid peeling, segregation probabilities are calculated at a subset of loci , and then fast single-locus style peeling operations are used at the remaining loci . This approach exploits the benefits of using linkage from multi-locus peeling while still being able to scale to whole-genome sequence data on thousands of animals. In the following, we first present the hybrid peeling method, and then the results of its performance on a synthetic dataset based on a real commercial pig population with 65,000 animals on a single chromosome with 700,000 segregating loci.Peeling is a method for inferring the genotypes and underlying haplotypes of an individual based on their own genotype information and the genotype information of their ancestors and descendants. In this context, we refer to ‘calling an individual’s genotype’ to describe the process of inferring the genotype of an individual based on their own genetic information and the genetic information of their relatives. Furthermore, we use the term ‘phasing’ for determining the parent of origin for each allele at a heterozygous locus. Peeling is computationally intractable when considering whole-genome sequence in the context of large multi-generational pedigrees with loops , 29, 34.Peeling relies on a model of the transmission of genetic information between a parent and their offspring. Single-locus and multi-locus peeling differ in how they model this transmission. In single-locus peeling, both parental alleles are assumed to be inherited with equal probability at all loci. In multi-locus peeling, it is assumed that there is a high probability that the alleles at nearby loci are inherited jointly from the same parental haplotype. To share information between loci, multi-locus peeling estimates the segregation probabilities at each locus. These probabilities indicate which parental haplotypes were inherited at a given locus. Hybrid peeling is a computationally efficient approximation of multi-locus peeling. Like multi-locus peeling, it uses information from nearby loci to infer which parental haplotype was inherited at a locus. Unlike multi-locus peeling, it estimates segregation probabilities at a subset of loci only, and linearly interpolates segregation probabilities at the remaining loci.For completeness, we describe these peeling operations in detail below. For single-locus peeling, we follow the previous work of Kerr and Kinghorn , and foraa, aA, Aa, AA), where the first allele in each pair is inherited from the father and the second allele is inherited from the mother. For brevity, we use the term phased genotype and genotype interchangeably. The probability that individual i has genotype gi is:Following Kerr and Kinghorn , in singWe examine each of these terms separately.gi is consistent with the genotype called by the SNP array, and ε accounts for a small error rate in SNP array genotype data. If we have sequencing data with a, and A, then:δ accounts for a small error rate in sequence data. By default, penetrance terms for an individual will not sum to 1, and so must be normalized to sum to 1.The penetrance term gives the conditional probability of the available genomic data, i.e., SNP array data or sequencing data, given the individual’s genotype. If no information is available, we set the penetrance term to a constant value, i.e., p, to calculate the anterior probabilities:gm and the father has phased genotype gf excluding any information from individual i. The “tr” term (a shorthand for “transmission”) is a function that gives the probability that the child inherits genotype gi given their parent’s genotypes, i.e., i. This gives:gm, independent of shared children with f. The second line calculates the probability of the father’s genotype, gf, independent of shared children with m. The third line calculates the probability of both parents’ genotypes based on their shared children except for individual i.The anterior probability captures the information about an individual’s genotype garnered from their parents’ genotypes. If the parents of the individual are unknown, then we use the minor allele frequency, mentclass2pt{minimc, inherits genotype gc, based on its parent’s genotypes, marginalized over the genotypes for c, and multiplied across all children. We then calculate m marginalized over their possible genotypes:There are two types of posterior terms. First, The remaining terms are calculated by removing the individuals that relate to them in the equations:Together the posterior, anterior, and penetrance terms give the probability of an individual’s genotypes Eq. . InformaDue to the dependence of the anterior terms and posterior terms on the anterior and posterior terms of other individuals in the population, the order in which they are updated is important and can decrease the overall number of peeling operations that need to be performed. We follow the updating pattern given in . At the p, and error rates, ε and δ. We found that an easy way to update these is by setting them equal to their observed values after each pair of peeling (up and down) operations. For the minor allele frequency, p, we average allele dosages for all the founders in the population :n founders and i has genotype g based on the current estimates  or maternal (m) haplotype at a locus. We can then build the transmission function by marginalizing over segregation states:i has segregation s at locus j. gi given its paternal genotypes and their segregation , using information only from the markers before (or after) j. We set the loci-to-loci transmission function to:s and γ is recombination rate, i.e., In Eq. , the fir. In Eq. , we expl Goddard , since h Goddard  infer thj, as follows:The middle term, i to the joint posterior term of their parents.The first line is the probability of the individual’s genotype, the second is the probability of the mother’s genotype, the third is the probability of the father’s genotype, and the fourth is the joint probability of the parents’ genotype. It is worth noting that none of the posterior or anterior terms in Eq.  rely on mentclasspt{minimap, error rates, ε and δ, and recombination rate, γ. The minor allele frequency and error rates are updated as in single-locus peeling. The recombination rate is updated by estimating the number of recombinations that occurred between loci by examining the difference between the segregation estimates at adjacent loci:Multi-locus peeling is performed as a combination of forward–backward operations over loci and up-down operations over individuals. Forward–backward operations update segregation probabilities between loci for each individual, while up-down operations update anterior and posterior terms and genotype probabilities for each individual. At the end of each pass, we update the minor allele frequency, Similar to the error rate, we found that using a locus-specific recombination rate slightly increased accuracy, and thus, we used a locus-specific recombination rate. Pilot simulations found that the genotype probabilities converged at around 10 to 20 cycles in large multi-generational livestock pedigrees with 60,000+ members, and thus we ran the algorithm for a fixed number of 20 cycles.Hybrid peeling is a computationally efficient approximation to multi-locus peeling. In a preliminary analysis, we found that the primary computational cost of multi-locus peeling stemmed from updating the segregation probabilities, Eq. . When evj and j + 1 are the loci in the set A that flank locus k, and a is the proportional distance between locus k and locus j:More formally, we divided the set of loci into two sets, A and B, with the size of A being much smaller than B, |A| ≪ |B|, e.g., A are the loci on a high-density SNP array and B is the entire set of segregating loci obtained from whole-genome sequencing. We performed multi-locus peeling on the loci in A to calculate segregation probabilities and then single-locus peeling on the loci in B using Eq.  as the tThe distance can be calculated in number of base pairs, centiMorgans, or number of intermediary loci. The exact measure of distance should only have a minimal impact on performance: if a sufficiently large number of loci is used in set A then adjacent segregation probabilities should be nearly equal, i.e., ding Eq.  to reducThe aim of the hybrid technique is to make multi-locus peeling more computationally tractable when applying it to large pedigrees. We evaluated the performance of this algorithm on a synthetic dataset.We examined the performance of hybrid peeling for calling, phasing, and imputing sequence data of different coverages in pedigrees. To perform these analyses, we simulated genomes for 65,000 animals using a multi-generational pedigree derived from a real commercial pig breeding line. We assumed that some animals had high-density or low-density SNP array genotypes from routine genomic selection. In addition, we generated mixed coverage sequence data for a subset of focal animals. Then, we carried out three sets of analyses. First, we analysed the performance of hybrid peeling for calling and phasing in disconnected families, these are subsets of the pedigree, which contained only a focal animal and its parents and grandparents. Second, we analysed the performance of hybrid peeling for calling and phasing in the context of the full general pedigree. Third, we analysed the performance of hybrid peeling for whole-genome sequence imputation. In the following, we describe in detail how we simulated and analysed the data.8 base pairs, a per site mutation rate of 2.5 × 10−8, a between-site recombination rate of 1 × 10−8, and an effective population size (Ne) that varied over time in accordance with estimates for a livestock population [Genomes were generated using the Markovian Coalescent Simulator (MaCS)  and Alphpulation . The resWe used AlphaSim to drop the base haplotypes through a multi-generational pedigree of 65,000 animals from a real commercial pig breeding line. We assigned SNP array data to animals, in line with routine genotyping for genomic selection in the population; 45,000 animals were genotyped with the high-density SNP array, 10,000 animals were genotyped with the low-density SNP array, and 10,000 animals were not genotyped.We generated sequence data, in line with the strategies implemented in the population. The goal was to use roughly $300,000 worth of sequencing resources to sequence and impute the entire population. First, the top 475 sires  were sequenced at 2x coverage. Second, AlphaSeqOpt  was usedfocal identified with AlphaSeqOpt, (2) the focal plus low coverage sires which also included the top 475 sires, and (3) focal plus all low coverage individuals, i.e. all the sequenced animals. A breakdown of the total cost and sequencing coverage by these sets is in Table In total, we generated sequenced data for 1912 animals at a range of coverages for a cost of $289,312. We partitioned this data into three sets: (1) the γj) of each of the 700,000 loci along the genome was sampled from a gamma distribution, with shape and scale parameters respectively equal to γi,j) per individual i at locus j was sampled from a Poisson distribution with a mean equal to xi was the targeted coverage for individual i. Third, sequencing reads were generated by randomly sampling alleles from the two gametes of individual i at locus j, accounting for a sequencing error  from the full pedigree, and analysed the effect of sequencing coverage on our ability to call and phase the individual’s genotypes. To perform this, we ran the hybrid peeling when the focal individual was sequenced at 1x, 2x, 5x, 15x, or 30x coverage, and when its parents or grandparents were sequenced at 0x, 1x, 2x, 5x, 15x, or 30x coverage. We generated data for each of these scenarios separately. We assumed that all the parents or all the grandparents were sequenced at the same coverage, and that all family members had high-density SNP array data.To call genotypes and phase alleles, we extracted the phased genotype probabilities generated by hybrid peeling and made a call if the probability of a genotype was higher than a pre-defined threshold. For all analyses, we used a probability threshold of 0.98. Scenarios were compared on the percentage of called genotypes (genotype yield) and phased alleles (phase yield).focal and all low coverage condition (see the Data subsection). We compared the genotype and phase yield between runs and compared the correlation between individual’s genotype dosages and the true genotypes (genotype accuracy) and correlation between individual’s allele dosages and the true alleles (phase accuracy) between runs.Next, we tested the ability of hybrid peeling to call genotypes and phase alleles in sequenced individuals using information from the full pedigree. To perform this, we ran hybrid peeling twice. First, we ran it separately for each disconnected family that consisted of an individual, its parents, and grandparents, with  SNP array and sequence data. Second, we ran it with SNP array and sequence data on all individuals in the pedigree. The sequencing coverage for each individual was the same as its coverage in the focal, focal and low coverage sires, or focal and all low coverage conditions.Last, we tested the ability of hybrid peeling to impute whole-genome sequence for non-sequenced individuals in the full pedigree. We ran hybrid peeling on all the individuals in the full pedigree. The multi-locus step used the high-density SNP array loci to estimate segregation probabilities. Then, hybrid peeling was run on the sequence data using all available sequence and SNP array data. Hybrid peeling was run three times, using either the sequence data from the Imputation accuracy was measured as the correlation between an individual’s imputed genotype dosages and the true genotypes. This measure of imputation accuracy has been reported to give imputation accuracies that are higher than the resulting genomic prediction accuracy . CorrectTo provide a comparison to hybrid peeling, we also tested findhap v4 , a combiSimulated genotype and sequence data are available from the authors upon request.http://www.alphagenes.roslin.ed.ac.uk). The code for generating simulated sequence data from genotype data is available from the authors on request.To perform hybrid peeling, we used the software package AlphaPeel, which is available from the AlphaGenes website .We obtained a similar pattern of results when evaluating phasing yield. In this case, although an individual’s own sequencing coverage was an important determinant for phasing yield, high coverage on both the parents and the grandparents was needed to phase the alleles. If neither the parents nor the grandparents of an individual were sequenced, then phasing yield was 0.7% at 1x, 6% at 2x, 35% at 5x, 59% at 10x, and 70% at 30x. The low phasing yield at 30x is due to the inability to phase heterozygous loci without information from relatives. Sequencing the parents at high coverage substantially increased phasing yield, and continued to do so even if the individual was sequenced at high coverage. If the parents of the individual were sequenced at 30x, then phasing yield was 72% at 1x, 74% at 2x, 82% at 5x, 89% at 10x and 94% at 30x. If both the individual’s parents and grandparents were sequenced at 30x, then phasing yield increased to 94% at 1x, 95% at 2x, 96% at 5x, 98% at 10x, and 99% and 30x. In all cases, the percentage of correctly phased alleles was higher than 0.989 (median 0.999).We examined the effect of using all sequence data from the full pedigree on percentage of called genotypes and phasing yield and accuracy of sequenced individuals. The gains in yield and accuracy in comparison to using data from disconnected families are plotted in Fig. 2 = 0.37), but is a weak predictor for the phase accuracy of those individuals in the full pedigree (r2 = 0.13). In contrast, adding the sequencing coverage on all ancestors increased the ability to predict accuracy when assessing the phase accuracy in the full pedigree (r2 increased from 0.13 to 0.42), compared to when assessing the phase accuracy in the disconnected families, (r2 increased from 0.37 to 0.55). The higher overall r2 for disconnected families is likely due to performance in a disconnected family being easier to estimate because of the limited interaction between coverage levels for distant ancestors. We found a similar pattern of results for genotype accuracy and the percentage of called genotypes and phasing yield.The gains in phasing accuracy were also not equal for all individuals in the pedigree; some individuals had only a small gain in accuracy, whereas others had a large gain in accuracy. This difference was particularly pronounced for individuals sequenced at 1x where the mean phasing yield increased from 0.11 to 0.67, but the standard deviation of the phasing yield increased from 0.13 to 0.28. If all individuals were influenced equally by including the full pedigree, we should expect an increase in mean but not a corresponding increase in standard deviation. The increased variability is a consequence of the different sequencing coverages on relatives who are outside of the immediate family. We found that the amount of sequencing coverage on immediate relatives (parents and grandparents) is a good predictor of the phase accuracy of individuals sequenced at 1x in the disconnected family  and the entire pedigree. Finally, we analysed the ability of hybrid peeling to impute whole-genome sequence data to all non-sequenced individuals in the pedigree. Figure focal plus all low coverage sequencing set, the imputation accuracy for the first quintile was 0.908, compared to the average imputation accuracy of 0.970. This decrease in imputation accuracy is due to the lower average sequencing coverage of ancestors for individuals in the first quintile  and the smaller number of individuals with high-density SNP array data (0.2% in the first quintile compared to the population average of 70%).We observed three trends in imputation accuracy. First, individuals in the first quintile had on average a lower imputation accuracy then the rest of the population. When we used the Second, increasing the amount of sequencing resources increased accuracy for all individuals in the population. The largest contribution came from using focal individuals and their parents and grandparents, which yielded an imputation accuracy of 0.945. Furthermore, adding low coverage sequence data of top sires increased imputation accuracy to 0.963. Finally, adding sequence data of top dams and of the remaining low coverage individuals increased imputation accuracy only to 0.970, but had a proportionally larger influence on individuals in the first quintile where imputation accuracy increased from 0.885 to 0.908. This effect is likely because 78% of the top dams and top-up individuals came from the first quintile.Third, imputation accuracy for an individual depended on its SNP array genotype status. A comparison of the imputation accuracies depending on their SNP array density is in Table Compared to findhap, hybrid peeling consistently yielded a higher accuracy, both in the first quintile, but also in the remaining four quintiles. Hybrid peeling outperforms findhap on individuals genotyped at high density (0.987 vs. 0.958), low density (0.967 vs. 0.892), and non-genotyped individuals (0.881 vs. 0.702). Similar to hybrid peeling, the performance of findhap was substantially lower in the first quintile, compared to the final four quintiles (mean of 0.777 vs. 0.915), but also was low in some regions, likely due to the presence of a large number of low-density or non-genotyped individuals clustered in certain portions of the pedigree.focal plus all low coverage sequencing set. We found that the initial multi-locus peeling step took 823 min and 41 GB of memory to process 2000 SNPs on 64,598 individuals, which translates to 6.3 h per 1000 individuals per 1000 loci. The hybrid peeling step was split across 1000 jobs of 700 SNPs each. Each job took on average 40 min and 2.3 GB of memory, which translates to 53.5 min per 1000 individuals per 1000 loci and a total of 40,344 min (roughly 28 core-days). The total computation time for findhap was 5.14 h and it required 101 GB of memory.Computational requirements were much less for hybrid peeling than for multi-locus peeling. We compared the time necessary for multi-locus peeling to process the high-density SNP array with 2000 markers used as an initial step of hybrid peeling to the time necessary for hybrid peeling to process the remaining sequence with 700,000 segregating loci when using the In this paper, we present a hybrid peeling method for calling, phasing, and imputing sequence data of any coverage in large pedigrees. This method is computationally efficient and enables the benefits of multi-locus peeling to be realised for datasets with tens of thousands of individuals on tens of millions of segregating variants. We evaluated the performance of hybrid peeling for calling and phasing sequence data in a livestock population and for imputing that sequence data to the non-sequenced individuals in the population. Hybrid peeling successfully used the pedigree to propagate information between relatives to call genotypes and phase alleles for individuals with low and high sequencing coverage. Furthermore, calling and phasing these individuals were most effective when the full pedigree was used. Hybrid peeling was also able to impute whole-genome sequence information to 65,000 animals with an accuracy higher than 0.98. We discuss these results in more detail below.We found that hybrid peeling effectively used pedigree information to call genotypes and phase alleles in a population of sequenced individuals. When using hybrid peeling, sequence data from an individual’s parents and grandparents increased the yield and accuracy of called genotypes and the yield and accuracy of phased alleles compared to just using an individual’s own sequence data. We also found that further increases could be gained by using more distant relatives. The benefits of using the full pedigree were most apparent for individuals that had low coverage sequencing data (1x and 2x), for which in some cases the total genotype yield could rise from 0.1 based on the individuals own sequence data to over 0.9 using the sequence data from the entire pedigree. These results suggest that hybrid peeling could be used to increase the yield of calling and phasing sequence data in pedigrees. The application of hybrid peeling is not limited to individuals with whole-genome sequence data, but may also be useful when handling data that are generated through genotyping via a reduced-representation sequencing . Hybrid peeling has the potential to open the door to the routine utilization of whole-genome sequence in large pedigreed populations, increasing the accuracy of genomic prediction and the power to detect quantitative trait loci.This paper presents hybrid peeling, a computationally tractable multi-locus peeling algorithm for whole-genome sequence data. We demonstrated the effectiveness of hybrid peeling in calling, phasing, and imputing whole-genome sequence in a large livestock population. We found that hybrid peeling could effectively use multiple generations of variable coverage sequence data to increase easily the yield and accuracy of called genotypes and phased alleles compared to using an individual’s own sequence data. We also found that hybrid peeling could accurately impute whole-genome sequence into non-sequenced individuals. We implemented a version of this method in the software package AlphaPeel, which is available from the AlphaGenes website (


NOD2 variants and two taxa: the Roseburia genus and the Faecalibacterium prausnitzii species. By exploring the overall association patterns between genes and bacteria, we found that IBD risk alleles were significantly enriched for associations concordant with bacteria-IBD associations. To understand the significance of this pattern in terms of the study design and known effects from the literature, we used counterfactual principles to assess the fitness of a few parsimonious gene-bacteria-IBD causal models. Our analyses showed evidence that the disease risk of these genetic variants were likely to be partially mediated by the microbiome. We confirmed these results in extensive simulation studies and sensitivity analyses using the association between NOD2 and F. prausnitzii as a case study.Several bacteria in the gut microbiota have been shown to be associated with inflammatory bowel disease (IBD), and dozens of IBD genetic variants have been identified in genome-wide association studies. However, the role of the microbiota in the etiology of IBD in terms of host genetic susceptibility remains unclear. Here, we studied the association between four major genetic variants associated with an increased risk of IBD and bacterial taxa in up to 633 IBD cases. We performed systematic screening for associations, identifying and replicating associations between  In this study, we used observational data to explore associations between host genetics and the commensal microbiome in inflammatory bowel disease cases. Our analysis identified four associations involving two genes and four bacterial taxa and replicated two of these associations in independent cohorts. Then, we developed a counterfactual framework to assess the fitness of a few parsimonious gene-bacteria-IBD causal models. These analyses confirmed the robustness of the identified associations and highlighted microbiota mediation as a potential mechanism underlying the association between IBD and those genetic variants while ruling out reverse causation and arguing against a bacteria-IBD association resulting from a shared genetic effect. Most genetic analyses and twin studies published to date support a genetic component of inflammatory bowel disease (IBD) phenotypes . Recent CARD9 affected the composition and function of the gut microbiota by altering the production of microbial metabolites and increasing the risk of intestinal inflammation . The bacterial level was simulated using a negative binomial distribution were the dispersion parameters of each replicate were chosen so that the proportion of zero value vary from 0% to 95% across replicates. The case-control status was drawn from a binomial distribution with probability derived using a logit function with parameters matching the each of the four models. For each replicate, a subset of 200 cases was randomly chosen and used to test for association between the genotype and the bacteria using standard linear regression. The left (a) and middle (b) panels show the signed explained variance obtain from this experiment before and after applying an inverse-rank based normal transformation of the bacterial level, respectively. The red line shows the trend derived using local fitting as implemented in R loess function with default parameters. The right panels (c) present median p-values from the latter experiment derived over bins of replicates with a range of percentage of zero-values.We simulated series of 20,000 replicates each including 10,000 individuals. For each individual, we generated a genetic variant, a bacteria and a case-control status following the four models  from (TIF)Click here for additional data file.S15 FigG, a bacteria B and two case-control status, CD, which was defined based on the four causal models  from Fig 3, and UC, which was drawn independently of other variables. The two diseases were merged to form the IBD status. The genotype was simulated using a binomial distribution with frequency of the risk allele randomly drawn in . The bacterial level was simulated using a negative binomial distribution while randomly drawing the dispersion parameter so that the proportion of zero-value ranges in . The case-control status was drawn from a binomial distribution with probability derived using a logit function. All parameters from the simulation were set so that it match estimates from the literature and our primary results. The three lower panels show empirical distribution of those parameters estimated in the whole population. Disease prevalence, genetic effect and bacteria-disease association matched both in direction and magnitude for all causal models. We then randomly sampled from each replicate, a subset of 200 cases tested for association between G and B using standard linear regression, and after applying an inverse rank-based normal transformation of B. The test was applied in the sub-sample of IBD cases, but also in the sub-group of CD cases only and the sub-group of UC cases only.We simulated series of 10,000 replicates each including 30,000 individuals. For each individual, we generated a genetic variant (TIF)Click here for additional data file.S16 FigB as a function of g in the population , in cases only (light grey points and trend in red), and again, in cases only but after adjusting the bacteria for severity . In model a) the effect of g on severity is mediated by B; in cases the effect of g on B is underestimated because of the oversampling of participants carrying risk alleles (e). In model b) the genetic variant influences both severity and B, inducing a correlation between severity and B which is observed in both the whole sample and cases only (f). In model c), g and B act independently on severity and are therefore not associated in the population, however g and B are positively correlated in case-only samples because of biased selection (g). Finally, in model d) the effect of g on B is mediated by severity; the indirect association between g and B observed in the general population is still present in cases only, but is canceled when adjusting bacteria for severity (h).We performed a simulation similar to (TIF)Click here for additional data file.S17 FigWe performed the same analysis as for (TIF)Click here for additional data file.