Linear mixed models (LMMs) are a powerful and established tool for studying genotype–phenotype relationships. A limitation of the LMM is that the model assumes Gaussian distributed residuals, a requirement that rarely holds in practice. Violations of this assumption can lead to false conclusions and loss in power. To mitigate this problem, it is common practice to pre-process the phenotypic values to make them as Gaussian as possible, for instance by applying logarithmic or other nonlinear transformations. Unfortunately, different phenotypes require different transformations, and choosing an appropriate transformation is challenging and subjective. Here we present an extension of the LMM that estimates an optimal transformation from the observed data. In simulations and applications to real data from human, mouse and yeast, we show that using transformations inferred by our model increases power in genome-wide association studies and increases the accuracy of heritability estimation and phenotype prediction. Linear mixed models (LMMs) provide a powerful method for studying genotype–phenotype associations. Here the authors present a LMM application that estimates an optimal transformation from observed data and increases the accuracy of heritability estimation and phenotype prediction. Linear mixed models (LMMs) are widely used in genetic studies of quantitative traits in humans and model organisms. This family of models is attractive because in addition to modelling the effect of individual genetic variants, the LMM effectively accounts for polygenic effects and confounding because of population structure or family relatedness. Important applications of LMMs include genome-wide association studies (GWASs)13567One of the core assumptions of LMMs is that the residual noise is Gaussian distributed, and deviations from Gaussianity can result in model misspecification111213Here we investigate the practical relevance of phenotype transformations in the context of key applications of LMMs in genetics. We propose the warped linear mixed model (WarpedLMM), a principled generalization of the standard LMM that allows to fit phenotype transformations while performing genetic analyses. We show how the likelihood principle can be extended to objectively assess alternative transformations in the light of the observed genotype and phenotype data. WarpedLMM can seamlessly be used in place of traditional LMMs, and it identifies transformations that are both parametric and invertible, thus permitting to predict phenotypic values on the original scale. This is not straightforward, for instance, when considering non-parametric transformations based on rank statistics (see Results).We investigate the practical utility of WarpedLMM in different genetic analyses, where we consider both extensive simulation studies, as well as real data from human, mouse and yeast. We compare WarpedLMM to established preprocessing approaches for phenotypes, such as Box-Cox transformationsg that links the latent phenotype to the observed measurements (f (where f=g−1) is needed. If we denote the observed phenotype for individual n as yn, an estimate of the latent phenotype zn can be obtained by applying the function f, optionally parameterized by ψ:Both, when specifying a phenotype transformation or when inferring it from the data , the implicit assumption is that the quantitative trait under genetic control is unobserved or latent, with the observed phenotype being determined by a nonlinear mapping urements . Thus, tf is determined by parameters ψ, which are inferred jointly with the remaining model parameters of the LMM. The most probable transformation can then be inferred by maximizing the sum of the standard log likelihood and a Jacobian term that accounts for the complexity of the fitted warping function. Several functional forms of the warping functions can be chosen (see Methods), differing in number of free parameters and in the complexity of the functions they can represent. In the following, we consider a particular family of functions initially proposed by Snelson et al.yn does not require a transformation, only the linear term will be used. Otherwise, the function will consist of both the linear term and one or more step functions.In WarpedLMM, these functions are constrained to be invertible and are termed ‘warping functions’. The functional form of g  and a completely nonlinear function (full transformation). We then compared the ability of the WarpedLMM and the LMM to estimate the true simulated heritability from the transformed phenotypes. We also considered an LMM applied to phenotypes pre-processed using a log transformation (Log-LMM) and a transformation fit using the Box-Cox method (Box-CoxLMM), both of which are commonly used in practice1620212223a priori defined set of pre-processing transformations can induce significant biases in the heritability estimates.When comparing the heritability estimates to the true simulated heritability, WarpedLMM consistently was more accurate than all the other methods, whereas the LMM tended to underestimate the heritability. In the most extreme cases, the LMM estimates had a downward bias of up to 30%, whereas WarpedLMM was close to unbiased (less than 1%). The overall accuracy of WarpedLMM for heritability estimation was remarkably robust to changes of the simulation parameters, including the simulated heritability level , the numP-value ≤0.05 from a paired t-test). In the majority of these cases (17 out of 18), WarpedLMM yielded higher heritability estimates than the standard LMM (up to threefold), again showing that the choice of phenotypic transformation can significantly affect heritability estimates.Next, we revisited data from a heritability study in a structured mouse populationUnlike in the simulated experiments described in the previous section, we lack an accurate gold standard to validate the heritability estimates on real data. To this end, we assessed the consistency of our findings by comparing both models in an out-of-sample prediction task. We performed a tenfold cross-validation experiment, where each model was repeatedly trained on 90% of the data to predict the phenotype from genotype on the remaining 10% of the samples. WarpedLMM was consistently more accurate in out-of-sample predictions than a standard LMM , even foet al.Finally, when comparing the transformations identified by WarpedLMM to those manually derived by Valdar In addition to heritability estimation and prediction, WarpedLMM can also be used to perform GWASs. To test this, we revisited genotype and phenotype data from the Northern Finland birth cohortP-value ≤5 × 10−8) for LDL cholesterol levels  correlations between these phenotypes, which can be important for multivariate genetic analyses with linear Gaussian models28Finally, we evaluated the genetic model fit by the WarpedLMM and compared it to a standard LMM using out-of-sample phenotype prediction. As the warping functions fit by WarpedLMM are invertible, we can assess the prediction accuracy of a genetic model on the natural scale of the raw phenotypic values, which is not feasible when using rank-based preprocessing methodsAlthough preprocessing methods are widely used in practice to approximately identify and invert an unknown phenotype transformation11121314172022232430ad-hoc preprocessing procedure. The objective function of the model can be derived from first principles, resulting in an extension of the mixed model that accounts for both the data likelihood and the complexity of the fitted transformation (see Methods). As a result, our approach can be directly applied to tasks commonly tackled using LMMs, such as GWAS, heritability estimation and phenotype prediction.Here we have shown how the classical LMM can be extended to estimate phenotype transformations directly from the data. Our experiments show that WarpedLMM is able to significantly improve accuracy and power in key genetic analyses and that unsuitable phenotype transformations can lead to profound analysis biases. Although an important application of WarpedLMM is the identification of phenotype transformation to improve downstream analysis, we emphasize that the model is more than an When applying WarpedLMM to studies in mouse and yeast, we found that the model tended to increase the estimates of heritability. Although in a minority of traits the heritability estimates decreased, we note that the model consistently improved out-of-sample prediction. This shows that inappropriate phenotype transformations can lead to biased heritability estimates and overfitting, an effect that has previously been reported by othersAlthough we have focused on some of the most established tasks in genetic analysis, WarpedLMM can easily be adapted to more specialized tasks. For example, it is straightforward to use the model in combination with multi-locus mixed models28Finally, we note that there may be settings where WarpedLMM does not achieve optimal results. Similar to other existing methods, the model estimates a transformation under the assumption that the noise level in the transformed phenotype space is constant. This assumption may be violated in some cases such as when dealing with count data or binary phenotypes. In such instances, it will remain appropriate to use generalized LMMs with non-Gaussian likelihoods that incorporate stronger assumptions about the nature of the datayn of each individual n with an unobserved normal distributed phenotype zn that results from transforming yn using a monotonic function f with some parameters ψ.We model the observed non-normal distributed phenotype zn can then be written asThe generative model for the normal distributed phenotype xn holds the covariates for individual n, β are fixed effects, S* loci and εn is independent normal distributed noise.where N-by-1 vector z=f  of transformed phenotypes for a sample of N individuals follows asGiven this LMM, the likelihood for K denotes the genomic relatedness matrixN × S matrix G:Here, while Instead of specifying a predefined static transformation, WarpedLMM identifies the most probable transformation et al.yn of each sample asThroughout this paper, we use the warping function first proposed by Snelson ψ=.where f is a sum over I nonlinear step functions, where the parameter ai controls the step size, bi controls the steepness and ci determines the location. Finally, the parameter d denotes the slope for the linear part (in yn) of the function. The only parameter that requires manual specification is the number of step functions I. We followed the recommendation in Snelson et al. and used I=3 step functions for all of our experiments. This specific choice appears to be remarkably robust and effective across a variety of experiments.In this parameterization, In principle, any parametric monotonic function can be used in place of the function suggested above. For instance, a warping function based on the popular Box and CoxThis classical warping function is controlled by a single parameter, and thus can be useful when the large number of parameters of the function proposed above is a concern. Other types of warping functions include shifted logarithmic transformations or shifted and scaled arsinh functions, which have been proposed in the context of variance stabilizing transformations for microarray data36ψ) are estimated by maximizing a form of LMM likelihood. By taking the logarithm of equation (4), the negative log likelihood L for the hidden normal distributed phenotype z is obtained asThe model parameters  with respect to the parameters of the LMM and the transformation.K can accurately capture the relatedness between individuals in the presence of many causal variants with small effect sizes, it does not necessarily do so when the genetic signal is mostly due to a small number of causal variants. To address this setting, several approaches333838Although the realized relationship matrix t, the conditional distribution of the latent phenotype z follows asAt iteration where the parameters zt using the current set of variance components as the relatedness matrix. A marker is selected if its q-valueIn each iteration, the SNP with the strongest individual effect is determined by fixed effects testingThe genetic effects incorporated in the model at the end of this procedure can in general be beneficial for certain tasks such as phenotype prediction. Here we only use them to better reconstruct the transformation function, and we do not take them into account while doing prediction or heritability estimation. Finally, it is important to notice that we model these individual genetic variants as random effects, placing a Gaussian prior over their effect sizes and integrating them out. If the number of selected genetic markers is small, they can alternatively be modelled as fixed effect covariates, for example, using restricted maximum likelihood.N individuals, we can use the parameter estimates under model (4) to compute the best linear unbiased predictor The fitted WarpedLMM model can also be used to predict the unobserved phenotype of a new individual indexed by * given the genotype alone. Assuming a fully observed sample of x* is a vector of covariates for the new individual, k* is a 1-by-N vector that contains the genomic relatedness between the new individual and all the individuals in the original sample.where f−1 to the best linear unbiased predictorTo get an estimate of the phenotype on the original scale, we apply the reverse transformation f−1 is obtained by numerically inverting f using Newton-Raphson updates, as previously proposed by Snelson et al.The reverse transformation h2 in the normal distributed scale by computing a chip heritability It is possible to obtain an estimate of the narrow-sense heritability where h2 from {0.1,0.20,0.40,0.70,0.9}, the number of causal variants from {5,20,100,500,1,000}, the number of samples from {200,400,600,800,1,000} and the variance explained by covariates from {0.0,0.25,0.5,0.70,0.9}. We can then recover the noise level conditioned on h2, and the covariates variance.The simulated data are generated taking genotypes from hapmap3 ref.  chromosof(y) from the set of transformations used in Valdar et al.y); results for alternative transformations are presented as z=t·y+(1−t) f (y), where t is a parameter that determines the intensity of the transformation and is sampled from {0.0, 0.25, 0.5, 0.75, 1.0}. We repeated this simulation procedure 50,000 times in order to have a sufficiently large sample size to investigate all the regimes described above.Finally, we pick a transformation et al.We used mouse data from Valdar et al.We used yeast data from Bloom et al.We used the data from Sabatti http://github.com/pmbio/warpedLMM.An implementation of WarpedLMM is available at O.S. and N.F. conceived the method. N.F., O.S. and C.L. designed the experiments. N.F. performed the experiments. N.F. and O.S. analysed the data. N.D.L., N.F., O.S. and C.L. contributed computational tools. O.S., N.F. and C.L. wrote the paper.How to cite this article: Fusi, N. et al. Warped linear mixed models for the genetic analysis of transformed phenotypes. Nat. Commun. 5:4890 doi: 10.1038/ncomms5890 (2014).Supplementary Figures 1-9, Supplementary Tables 1-3 and Supplementary References


A number of statistical methods for detecting gene-gene interactions have been developed in genetic association studies with binary traits. However, many phenotype measures are intrinsically quantitative and categorizing continuous traits may not always be straightforward and meaningful. Association of gene-gene interactions with an observed distribution of such phenotypes needs to be investigated directly without categorization. Information gain based on entropy measure has previously been successful in identifying genetic associations with binary traits. We extend the usefulness of this information gain by proposing a nonparametric evaluation method of conditional entropy of a quantitative phenotype associated with a given genotype. Hence, the information gain can be obtained for any phenotype distribution. Because any functional form, such as Gaussian, is not assumed for the entire distribution of a trait or a given genotype, this method is expected to be robust enough to be applied to any phenotypic association data. Here, we show its use to successfully identify the main effect, as well as the genetic interactions, associated with a quantitative trait. Recent advances in high-throughput genotyping techniques have produced massive volumes of genetic data. Although it is common to analyze single SNP effects extensively, such approaches cannot adequately explain the intricate genetic contributions to complex diseases such as hypertension, diabetes, and certain psychiatric disorders. Consequently there are still large amounts of genetic components that remain unexplained. Gene-gene interaction analysis may be one method to adequately address this missing heritability problem .For case-control studies, which formulate the measures for a binary trait, a number of statistical methods for detecting gene-gene interactions have been proposed. One of the most popular methods is multifactor dimensionality reduction (MDR)  that cont-test statistic [However, for quantitative traits such as the blood pressure, body mass index, and patient survival times, relatively few attempts have been made to analyze the genetic interactions. Because many phenotype measures are intrinsically quantitative, and categorizing a continuous trait may not always be straightforward and meaningful, association of gene-gene interactions with an observed distribution of such phenotypes needs to be investigated directly without categorization. To that end, introducing a new statistic is one way to tackle the problem . Extenditatistic . Howevertatistic , 13, andtatistic –19. Althtatistic . Howeverm-spacing [Here, we extend the usefulness of the information concept to quantitative traits by considering nonparametric estimates based on sample-spacing or -spacing –25 for t-spacing  to the q-spacing , our metIn the following sections, after a brief review of nonparametric entropy estimation, we describe a new method for modeling genetic interactions. A nonparametric entropy estimator is shown to successfully couple with genetic datasets through our modifying work in the Materials and Methods. Application of this information gain standardized (IGS) approach is evaluated for both simulation and real datasets in the Results and Discussions.X is a random vector with probability density function, f(x), its differential entropy is defined byf(x) is first estimated using a standard density estimation method such as a histogram or kernel density estimator, and the entropy is then computed. Integral, resubstitution, splitting data, and cross-validation estimates are among the usual plug-in estimates [Xk} be a set of independent and identically distributed real valued random variables, with corresponding order statistics of {Xn,k}. Here, n represents the total number of measured samples. For the arbitrary integers i and m satisfying the condition of 1 ≤ i < i + m ≤ n, a spacing of order m or m-spacing is defined as Xn,i+m − Xn,i. A density estimate, based on sample-spacing, m, is then constructed asx ∈ [Xn,(i − 1)m, Xn,im [n → ∞, m → ∞ and m/n → 0 [m increases, the correctional terms become negligible and the two estimators coincide. Our evaluation of the entropy of a phenotype, H(P), of a quantitative trait is based on this estimator.If stimates . Another, Xn,im . This de m/n → 0 . Several m/n → 0 , 24. Amo m/n → 0 :(3)Hm,n=function , 28:(4)Hn and m as parameters. In genetic association studies, the number of samples, n, of several hundreds is common. However, when the conditional entropy is estimated, there may be a minor allele that could have a much smaller number of samples corresponding to that allele. Moreover, the choice of the sample-spacing, m, should affect the resulting estimation of an entropy value. Therefore, it is required to have an entropy estimation scheme independent of the number of samples, without the need of choosing a particular value of the sample-spacing. To illustrate such a requirement, an ensemble of 3,000 sets of the random deviation from N was generated for each data point in m is fixed to 10 and 20 while n is varied. The analytic formula of the entropy for a normal distribution can be obtained as follows [e is Euler's number:σ above it. The obvious n-dependence of the estimator can be seen in this plot, where the estimation approaches the analytic value, as n increases with n is fixed to 400, while m is varied. In this plot, the estimated entropy again changes in value throughout the possible range of m. It is shown that the estimated value is always smaller than the analytically calculated value. Therefore, assigning a particular value to m such as n- and m-dependences, the estimator in , with three different σ's, are marked on the vertical axis on the right-hand side. Regardless of the value of σ, the differences between the analytically obtained value and the values given by the estimator stay essentially the same. Considering that the association study measures the difference between the entropy and the corresponding conditional entropy, the stability should be a more critical issue than the absolute value of the estimates. Therefore compensation of this Δ would not be necessary as long as it is stable. Furthermore, the underestimation of the entropy shown in the plot should have little effect on the association strength. Hence, an entropy estimator has been set up that should satisfy the practical n-independence without the need to find a proper sample-spacing.The estimator in  has boths number:H=lnσ2πeexpected . In Figul choice , would nG be a categorical variable assigned to each sample measurement Xk. G may be a genotype given by a measured SNP or a combination of SNPs, while Xk represents the measured value of a phenotype. For detecting the main effect of a single SNP, G consists of three categories of G = 0, G = 1, and G = 2. For detecting the interaction between SNPi and SNPj, G consists of 9 categories, such that G = 0 = , G = 1 = , G = 2 = , G = 3 = ,…, and G = 8 = . Detection of the higher order interaction can be performed in the same way with expansion of the categories of G. Then an estimator for each specific component of the conditional entropy, H(P∣G = g), can be constructed using the genotype-selected subset measurements {Xng,k}, along with an individual sample-spacing of mg. Extending , the difference would be lnc:i(1) denote the maximum IG of the ith permuted dataset. Then, the mean and standard deviation of IG1(1), IG2(1),…, IGn(1) can be computed as follows: n is the number of permuted datasets. Now IGS is defined as follows:Since the differential entropy values are scale-dependent, when the above estimators are calculated with {ntropies , should stimator . IG stanm-spacing method, a representative result is shown in m-spacing and GMDR, are plotted as horizontal and vertical coordinates, respectively. Filled triangles represent the main effects, while open circles are for the 2nd order interactions. Both methods identify the same single SNP pair having a prominent interaction plotted in the upper right corner. One of the SNPs was found to produce the main effect, in contrast to others. Again, the result is agreed by both methods. P values obtained by permutation are given in the boxes for those selected points. Association strengths of the 3rd order interactions are plotted with a plus sign. Because no 3rd order interaction is simulated into the dataset, the combinations of SNPs made by adding a single SNP to the causal pair are expected to have high association values. Those points are clustered near the identified causal pair in the upper right corner. In panel (b) of m-spacing and QMDR. Both comparisons show consistent results between the proposed m-spacing method and GMDR or QMDR. Note that IGS instead of IG was used. The distribution of the IG values from a dataset would shift to a higher direction, with increased order of interactions. Thus, the more conditions applied, the less entropy may be left to find. In other words, as the order of interaction increases, the conditional entropy H(P∣G) tends to decrease, while H(P) remains the same. Therefore IGS is vital if one needs to compare the association strengths between genotypes from different orders of interactions. To show the plausibility of the proposed m-spacing method, an extensive set of simulation data was necessarily generated. First, three types of quantitative trait distributions were considered. Two of them were normal and gamma distributions, and another one was a mixture of those two types. With single causal pair designed, 70 different penetrance models, based on [y, associated with two interacting SNPs was selected from a normal distribution, as defined by the penetrance values tabled for possible combinations of genotypes associated as follows:fij represents the penetrance values tabled for every model simulated and can be found in [i, j). In 70 different penetrance models, 14 different combinations of two different minor allele frequencies (MAFs) and seven different heritability values were considered. Specifically, we considered the cases when the MAFs were 0.2 and 0.4 and when the heritability was 0.01, 0.025, 0.05, 0.1, 0.2, 0.3, and 0.4. Three different values  of the variance, σ, were used independently for the high- and low-risk groups, resulting in 9 combinations. The grouping constraint for the generated event was set such that the averaged y of the high-risk group should be larger than or equal to the overall average. The averaged y of the low-risk group should be less than the overall average. In k and θ, were determined by fij and σ, using the relationship fij = kθ and σ = kθ2. Penetrance models were classified by 7 heritability values: 0.01, 0.02, 0.05, 0.1, 0.2, 0.3, and 0.4, resulting in 10 models for each heritability. The generated data files had a sample size of 400, with 20 SNPs. In all, 3 × 70 × 9 = 1,890 different conditions were set up, with 100 simulated data files generated for each condition.To examine the performance of the based on , were infound in . It is tm-spacing method, QMDR and GMDR were used to compare the results. m-spacing's performance was in between those of QMDR and GMDR for higher values of penetrance. However, in the range of penetrance less than 0.2, the m-spacing performs best. Note that the QMDR shows higher detection probability than the GMDR throughout the range. In the case of a gamma distribution, as shown in m-spacing, as well as the GMDR, stay better than that of QMDR and are comparable to each other. Note the switch of the GMDR and QMDR's performance ranks with the change of the phenotype distribution. What QMDR does is essentially the dichotomization of the observed values of the quantitative phenotypes. Therefore, it should do better with well-defined symmetric distributions, such as a normal distribution, than with an asymmetric one . The proposed m-spacing method is expected to be effective regardless of the shape of the phenotype distribution, because it makes no assumptions regarding the distribution and is therefore nonparametric, as demonstrated in Figures m-spacing outperforms the QMDR and the GMDR, throughout the whole range of heritability, in the case of the mixed form of phenotype distribution. Among the three methods examined, m-spacing was the most robust, performing consistently within the range of conditions for the simulation.The “hit ratio,” or detection power, of the IGS was evaluated and compared. Simulated data files described in the previous subsection were used. All of them had a single causal pair to identify. In addition to our proposed P values for a particular pair were obtained by permuting each dataset 1000 times. We took the significance level α as 0.05 to get the ratio of the permutation P values smaller than or equal to α. We report this ratio as the type I error rate in To estimate the type I error rate, the null datasets were generated under the same scheme as used for the detection power analysis except that there was no causal pair intended. Now there are 20 SNPs that none of the pairs are expected to have an association. Permutation m-spacing method. Among the available phenotypes, “height” was chosen with a sample size of 8,842 from the population-based cohort. The total number of SNPs was 327,872, spanning over 22 chromosomes. The “height” phenotype showed to be close to a normal distribution such that the m-spacing method may not take advantage of the shape of the phenotype distribution, as discussed in the previous subsection. m-spacing method (IGS), that had the strongest main effects. Out of 10 selected SNPs, rs2079795 and rs6440003 coincide with two previous reports [P values were estimated by permutation of the phenotype values to make null distributions. Permutations were iterated 100,000 and 10,000 times for the main effect and the interaction, respectively. A clear distinction between rs11989122 and the other selected SNPs can be seen in the IGS values. In A full-scale real dataset from the Korean Association Resource (KARE) project  was anal reports , 27, alt reports , but usim-spacing method for genome-wide association studies with a quantitative trait. The robustness of this method makes it useful for a wide range of sample sizes, while the original m-spacing method yields a reliable result only for datasets with a large sample size. Extensive simulation was performed to produce the datasets with different shapes of phenotype distributions, while varying the penetrance functions and adjusting the heritability as well. Causal pair detection probability was unaffected the most by the compared methods, based on the distribution shape and heritability, while GMDR and QMDR showed more dependency. The proposed m-spacing method is proven to outperform the others regardless of the shape of the trait distribution and also the range of lower heritability. In the higher heritability region, the performance of the proposed method is comparable to that of GMDR or QMDR, whichever shows better performance in that region. This would lead to versatile applicability of our nonparametric method for quantitative traits, with various characteristics. We applied this method to successfully identify the main effect and gene-gene interactions for the phenotype “height” with the full set of KARE samples. Although several of them overlapped with a previous report, new interactions were also found. Because “height” is presumed to be a trait with a normal distribution having a higher heritability, our method may be said to have performed successfully with no advantage over other methods. More extensive study is needed for quantitative traits, having various characteristics, to further demonstrate the expected robustness of our modified m-spacing method.In this paper, we present a modified


Recent technological advances have created challenges for geneticists and a need to adapt to a wide range of new bioinformatics tools and an expanding wealth of publicly available data . This wide range of methods and a diversity of file formats used in sequence analysis is a significant issue, with a considerable amount of time spent before anyone can even attempt to analyse the genetic basis of human disorders. Another point to consider that is although many possess “just enough” knowledge to analyse their data, they do not make full use of the tools and databases that are available and also do not fully understand how their data was created. The primary aim of this review is to document some of the key approaches and provide an analysis schema to make the analysis process more efficient and reliable in the context of discovering highly penetrant causal mutations/genes. This review will also compare the methods used to identify highly penetrant variants when data is obtained from consanguineous individuals as opposed to nonconsanguineous; and when Mendelian disorders are analysed as opposed to common-complex disorders. The colossal amount of information that is produced has led researchers to look for ways of reducing the time and effort it takes to analyse the resulting data whilst also keeping up with the storage needs of the resulting files, which are in the magnitude of gigabytes each. The recently emerged variant call format (VCF) has somewhat provided a way out of this complex issue . Using ahttp://www.genome.gov/gwastudies/). As whole genome sequencing (WGS) is prohibitively expensive for large genetic association studies [http://omim.org/) . For co studies  whereas ferences , 16 for ferences , findingIn this paper, our aims are to (i) provide a guide for genetic association studies dealing with sequencing data to identify highly penetrant variants (ii) compare the different approaches taken when data is obtained from unrelated or consanguineous individuals, and (iii) make suggestions about how to rank single nucleotide variation (SNV) and/or insertion/deletions (indels) following the standard filtering/ranking steps if there are several candidate variants, using annotated variants within VCF files as examples. To aid the process of analysing sequencing data obtained from consanguineous individuals, we have also made available an autozygosity mapping algorithm (AutoZplotter) which takes VCF files as input and enables manual identification of regions that have longer stretches of homozygosity than would be expected by chance. RSPH9 gene (the p.Lys268del mutation) was one of their a priori candidates [Before any genetic analysis, it is important to understand how the raw data were produced and processed to make better judgements about the reliability of the data received. Thorough quality control steps are required to ensure the reliability of the dataset. Lack of adequate prior quality control will inevitably lead to loss of statistical power and increase false positive and false negative findings. Fully comprehending each step during the creation of the dataset will have implications on the interpretation stage, where genotyping errors  may turndidates . This isAs far as WES projects are concerned, questions about coverage arise right from the start . Since kThe raw reads produced should then be aligned to a reference genome  and there are many open sources and widely applied tools . HoweverEffective variant calling depends on accurate mapping to a dependable reference sequence. If available, using a population specific reference genome would be most ideal to filter out known neutral SNPs existing within the region of origin of the analysed subjects . Inclusion of ambiguity codes  for known polyallelic variants to create a composite reference genome can also be useful .There are many tools available for the identification of SNVs, indels, splice-site variants, and CNVs present in the query sequence(s). Each variant calling tool has advantages and disadvantages and has made compromises relating to issues such as speed of analysis, annotation, and reliability of the output file . SeparatAs mentioned above, there are many tools available for the identification of variants present in the query sequence see . GATK 22 is one http://soap.genomics.org.cn/).SAMtools  is a varF = 0.0625) and 12.5% (F = 0.125) for offspring of double first cousins . These values will be higher in endogamous populations . Autozygosity could be checked by inspecting long runs of homozygosity (LRoH) for each individual by using tools such as Plink (for SNP chip data) [http://www.ensembl.org/Homo_sapiens/Location/Genome). AutoZplotter  that we developed takes VCF files as input, enabling easy and reliable visualisation and analysis of LRoH for any type of data . The code (written in the Python programming language) can also be adapted relatively easily for use in analyses of other species.For data obtained from consanguineous families, confirming expected autozygosity  would be an additional check worth carrying out. If the individual is the offspring of first cousins then the level of autozygosity would be approximately 6.25% (ip data) , EXCLUDEip data) , Agilentip data) , and Autip data)  and diviOnce the quality control process is complete and VCF files are deemed “analysis ready,” the approach taken will depend on the type of disorder analysed. For rare Mendelian disorders, many filtering and/or ranking steps can be taken to reduce the thousands of variants to a few strong candidates. Screening previously identified genes for causal variants is a good starting point. Carrying out this simple check will allow the identification of the causal variant even from a single proband thus saving time, effort, and funding. If no previously identified variant is found in the proband analysed, there are several steps which can be taken to identify novel mutations.http://www.hgvs.org/dblist/glsdb.html for a comprehensive list) and “whole-genome” mutation databases such as HGMD [Locus specific databases  and scores derived from mutation prediction tools  would enable assessment of the predicted impact of all rare mutations. It is important to understand what is assumed at each filtering/ranking stage; and comments are included about each assumption and their caveats in http://www.ensembl.org/info/docs/tools/vep/index.html) where VCF files are annotated [For individuals of European ancestry, a VCF file will have between eighty and ninety thousand variants for WES ; and apnnotated .These prediction algorithms are, as their name suggests, only there to make predictions about whether a variant is expected to be functionally disruptive or not. Thus their main purpose is to enable researchers to rank certain variants higher than others in order for them to be studied in a systematic way. Thus they do not “prove” anything about the causality of the variant. The variants predicted “deleterious” still require following up through replication and/or functional studies. Also disagreements amongst different tools can be observed which can lead to different interpretations about the evolutionary history of the variant . Users of prediction algorithms should be aware of how these algorithms derive their predictions and then decide whether the tool can be generalized to their datasets. For example, those interested in somatic mutations should choose cancer-specific algorithms for example, FATHMM-Cancer  and SPF-With current knowledge, there are approximately fifty synonymous mutations with proven causality, complex traits and Mendelian disorders combined . This isHighly penetrant (Mendelian or common-complex) disease causal variants are expected to be very rare; therefore most of them should not appear in publicly available datasets. However filtering all variants present in dbSNP which is common practice should not be carried out as amplification and/or sequencing errors as well as potentially causal variants are known to make their way into this database  as this can reduce the amount of variants present in the Ensembl VEP (or ANNOVAR) annotated files considerably (~5x fold). However, this can be a problem for genes where the canonical transcript does not contain all the exons present within the gene, as a mutation which falls in an exon which is not present in the canonical transcript will not be observed in the filtered file (coded “CANONICAL” in Ensembl VEP annotated variants).As many online tools are expected to keep logs of the processes undergoing in their servers, to protect the confidentiality of genetic information, downloading a local version of the chosen tools (or the VEP cache from the Ensembl website) is recommended. VEP also enables the incorporation of many other annotations , which will make the screening and filtering steps more manageable.https://genome.ucsc.edu/) is another useful tool for collating a candidate gene list as it groups genes according to several features such as protein homology, co-expression and gene ontology (GO) similarity. Uniprot's (http://www.uniprot.org/) Blast and Align functions can provide essential information about the crucial role a certain residue plays within a protein if it is highly conserved throughout many species. This is especially important for SNVs where the SNV loci itself should be causal .Having a candidate gene list based on previously published literature  and knohttp://www.genecards.org/) and NCBI Gene (http://www.ncbi.nlm.nih.gov/gene) for functional information, GEO Profiles (http://www.ncbi.nlm.nih.gov/geoprofiles) and Unigene (http://www.ncbi.nlm.nih.gov/unigene) for translational data about the gene's product; and if available, one can check if a homologue is present in different species using databases such as HomoloGene (http://www.ncbi.nlm.nih.gov/homologene) and whether a similar phenotype is observed in model organisms. For example, if the disorder affects the cerebral cortex but the gene product is only active in the tissues located in the foot, then one cannot make a good argument about the identified variant in the respective gene as being “causal.”An example of the filtering process for an autosomal recessive disorder such as PCD is depicted in There are many complications that may arise depending on the disorder such as genetic (locus) heterogeneity , allelicFor rare Mendelian disorders, familial information can be crucial. The availability of an extended pedigree can be very informative in mapping which variant(s) fits the mode of inheritance in the case(s) and not in the unaffected members of the family . This will provide linkage data where its importance is best displayed by Sobreira et al. where WES data from a single proband was sufficient in discovering the causal variants in two different families . Where aTraditionally a LOD score of 3 (Prob. = 1/1000) is required for a variant/region to be accepted as causal. Reaching this threshold requires many large families with many affected individuals. However this is not feasible for most disease causal variants (which are very rare by nature) and other lines of evidence such as animal knockouts, molecular studies and local sequence alignments (by using UniProt as mentioned above) are required to make a case for the causality of variants, especially mutations which are not stop gains .As mentioned previously, understanding the characteristics of a Mendelian disorder is important. If the disorder is categorised as “familial” , which are usually very rare by nature, then availability of familial data becomes crucial, as unaffected members of the family are going to be the main source of information when determining neutral alleles. Any homozygous (and rare) stop gains, splice-site acceptor/donor variants and start losses in previously identified genes would be prime candidates.Approach taken in families is different from the approaches taken when analysing common Mendelian disorders using unrelated individuals. For common Mendelian disorders , fitFor consanguineous subjects, the causal mutation usually lies within an autozygous region , thus cThere are several software which can detect long runs of homozygosity reliably (>5 Mb), however they struggle to identify regions that are shorter. Therefore we developed AutoZplotter which plots homozygosity/heterozygosity state and enables quick visualisation of suspected autozygous regions (requires Xming or other X11 display server). These regions can then be followed up in more detail if any overlaps with a candidate gene/region. The input format of AutoZplotter is VCF thus it suits any type of genetic data . AutoZplotter was used for this purpose in a previous study by Alsaadi et al. .There can always be exceptional cases  such as compound heterozygotes . This would require haplotype phasing and the confirmation of variant status  in the parents and the proband(s) by sequencing of PCR amplicons containing variant or genotyping the variant directly. Beagle and HAPI-UR are two widely used haplotype phasing tools for their efficiency and speed , 68.For common complex disorders, identifying causal variants in outbred populations has proven to be a difficult and costly process ; and these disorders can have many unknowns such as the significance of environmental factors on the disorder  andThe NGS era has brought data management problems to traditional geneticists. Many data formats and bioinformatics tools have been developed to tackle this problem. One can easily be lost in the plethora of databases, data formats and tools. “Which tools are out there? How do I use it? What do I do next with the data I have?” are continually asked questions. This review aims to guide the reader in the rapidly changing and ever expanding world of bioinformatics. http://omim.org/statistics/entry, true as of 15/07/14), future genetic studies have much to discover. However for these projects to be fruitful, careful planning is needed to make full use of available tools and databases  and most common-complex disorders are still waiting for their molecular basis to be figured out , which plots homozygosity/heterozygosity state and enables quick visualisation of suspected autozygous regions. This can be important for shorter autozygous regions where other autozygosity mappers struggle.S1: List of useful bioinformatics command, parameter and files for variant calling, annotation and analysis.Figure S1: Pedigree trees demonstrating examples of relevant consanguineous unions.Figure S2: Example of the routes taken when analysing complex disorders.


ACE Ins/Del, ACTN3 Arg577Ter, AMPD1 Gln12Ter, CKMM 1170bp/985+185bp, HFE His63Asp, GDF8 Lys153Arg and PPARGC1A Gly482Ser) in a cohort of 196 elite athletes who participated in the 2008 Kona Ironman championship triathlon. Mean performance time (PT) was not significantly different in individual marker analysis. Age, sex, and continent of origin had a significant influence on PT and were adjusted for. Only the AMPD1 endurance-optimal Gln allele was found to be significantly associated with an improvement in PT . Individual genotypes were combined into a total genotype score (TGS); TGS distribution ranged from 28.6 to 92.9, concordant with prior studies in endurance athletes (mean±SD: 60.75±12.95). TGS distribution was shifted toward higher TGS in the top 10% of athletes, though the mean TGS was not significantly different (p = 0.164) and not significantly associated with PT even when adjusted for age, sex, and origin. Receiver operating characteristic curve analysis determined that TGS alone could not significantly predict athlete finishing time with discriminating sensitivity and specificity for three outcomes , though models with the age, sex, continent of origin, and either TGS or AMPD1 genotype could. These results suggest three things: that more sophisticated genetic models may be necessary to accurately predict athlete finishing time in endurance events; that non-genetic factors such as training are hugely influential and should be included in genetic analyses to prevent confounding; and that large collaborations may be necessary to obtain sufficient sample sizes for powerful and complex analyses of endurance performance.Polygenic profiling has been proposed for elite endurance performance, using an additive model determining the proportion of optimal alleles in endurance athletes. To investigate this model’s utility for elite triathletes, we genotyped seven polymorphisms previously associated with an endurance polygenic profile ( Human pstrength . Many ofRecent studies –7 have pACTN3 Arg577Ter polymorphism analysed in this cohort in a prior study [In this study we therefore investigate the utility of the seven-marker optimal endurance model  to distior study . These ret al. 2009 [ACE Ins/Del, ACTN3 Arg577Ter, AMPD1 Gln12Ter, CKMM 1170 bp/985+185bp, HFE His63Asp, GDF8 Lys153Arg and PPARGC1A Gly482Ser—were individually associated with performance time (both unadjusted and adjusted for significant demographic variables) or whether the combined influence of these polymorphisms as a total genotype score (TGS) could distinguish ‘faster’ from ‘slower’ performance time of the Ironman athletes. Each of the genes included in Ruiz et al.’s profile is a strong candidate for involvement in endurance performance and has been found to be associated previously with improvements in physical ability. The functions of these seven genes and the impact of the profile polymorphisms on gene function are outlined below.This study investigated whether the seven polymorphisms strongly associated with an endurance polygenic profile as described in Ruiz al. 2009 —ACE Ins/ACE 287bp Ins/Del polymorphism  is located in intron 16 of the gene angiotensin converting enzyme (ACE), which is heavily involved in the cardiovascular system, in particular with blood pressure regulation. The ACE gene encodes a zinc metallo-carboxypeptidase that converts the inactive angiotensin I peptide into the potent vasoconstrictor angiotensin II [ACE gene is associated with lower levels of ACE activity in serum and tissues, with the II genotype carriers having about half the activity level of DD carriers, while ID carriers have intermediate levels [The ensin II , 14, whiensin II , 15. Thee levels , indicatACTN3 gene encodes α-actinin-3, which is a tissue-specific actin-binding protein expressed in skeletal muscle fibers to assist in anchoring actin filaments of the sarcomere during muscle contractions. Although both α-actinin-3 and highly similar protein α-actinin-2 are both expressed in muscle, α-actinin-3 is only expressed in type II  muscle fibers, which have an increased contraction speed and contraction force compared to type I  fibers [ACTN3 Arg577Ter nonsense mutation  results in a truncated and non-functional protein which subsequently results in α-actinin-3 deficiency, and has been shown in knockout mouse models to decrease muscle strength and contraction force due to a decrease in the size of type II fibers. Presence of the R allele is therefore thought to improve strength and speed of contraction and has been shown to be significantly more common in sprinting athletes [The ) fibers . The ACTathletes . While tAMPD1 Gln12Ter polymorphism , also known as the C34T polymorphism, is located in the muscle-specific isoform of the AMP deaminase gene (AMPD1), which deaminates the adenosine monophosphate (AMP) that accumulates during exercise into inosine monophosphate (IMP) as part of the purine nucleotide cycle [AMPD1 thus assists in salvaging adenosine molecules and helping regulate the levels of IMP, AMP, adenosine diphosphate (ADP), and adenosine triphosphate (ATP) in skeletal muscles during exercise [The de cycle , 17. An exercise . Additioexercise , though exercise , the X aCKMM contains a NcoI RFLP in the 3’ untranslated region of the gene , resulting in two alleles named for their fragment lengths, the more common 985+185bp allele and the rarer 1170 bp allele [CKMM gene is a muscle-specific form of creatine kinase (CK) which catalyses the conversion of phospho-creatine (PCr) and ADP into creatine and ATP, as well as the reverse reaction. This CK/PCr energy buffering system acts as a temporal buffer for energy by ensuring that ATP can be quickly generated from cellular stores of ADP when required [CKMM 3’ UTR results in a change to the mRNA cellular localisation signal, which is important for correct CK/PCR shuttling [CKMM due to mRNA instability [2max (ml / kg • min) in response to endurance training, while the TT genotype results in 1.5- to 3-fold higher change in VO2max [The gene huttling  and whictability . Though n VO2max  and therGDF8 Lys153Arg polymorphism  is located in exon 2 of the growth differentiation factor 8 gene (GDF8), which is more commonly known as myostatin (abbreviation MSTN). Myostatin functions as a negative regulator of myoblast differentiation into muscle fibers, by signaling to increase p21, resulting in the inhibition of Cdk2 and thus the hyperphosphorylation of retinoblastoma (Rb), which then promotes cell cycle progression and thus myoblast proliferation [The feration , 23. It feration , 23, andferation . Myostatferation ; howeverHFE His63Asp polymorphism  is located in the hereditary haemochromatosis gene  which is a transmembrane protein with a key role in regulating iron absorption. The HFE protein is thought to regulate the interaction of other key molecules involved in iron uptake and circulation [TFRC and TRF2 genes), a transmembrane glycoprotein facilitating intake of transferrin-bound iron into cells; ferroportin (FPN1 or SLC40A1), a transmembrane protein located on the basolateral surface of gut cells macrophages, which allows transport of absorbed iron out of cells into circulation; and hepcidin (HAMP), a negative regulator of iron transport that competitively binds ferroportin, preventing release of iron from cells. HFE primarily interacts with TfR by decreasing the affinity of transferrin for the TfR, thus reducing the uptake of transferring-bound iron [HFE and the other key iron transport genes TRF2, FPN1, and HAMP [2max from HFE mutations [et al.’s polygenic profile [The culation , includiund iron , 27 as wund iron , 28. Theund iron , 27, 29.und iron , 29, eveand HAMP . Alternaand HAMP , despiteutations , 32. Theutations , the hetPPARGC1A Gly482Ser polymorphism  is located in the peroxisome proliferator-activated receptor-γ coactivator-1α gene (PPARGC1A), which is a coactivator of regulatory genes for the oxidative phosphorylation (OXPHOS) pathway for generation of ATP. As endurance athletes predominantly utilise aerobic energy generation through oxidative phosphorylation, requiring higher maximal oxygen uptakes (VO2max) compared to sprint and power sports, the PPARGC1A gene could potentially impact on energy availability [PPARGC1A is also involved in the activation of other pathways which may also equally be important for endurance athletes, including stimulating mitochondrial biogenesis through binding with nuclear respiratory factors NRF-1 and NRF-2 and mitochondrial transcription factors [MEF2), which occurs as a result of the normal response of muscle tissue to endurance training, improving oxidative capacity and resistance to fatigue [PPARGC1A expression peaking within two hours [PPARGC1A overexpression increases type I fiber ratio while knockout models show a decrease in type I and shift to type IIx and IIb fibers, and a recent study examining human muscle biopsies, which showed a lower level of post-training type I fibers in S carriers compared to G carriers, though mitochondrial density and activity, and intracellular lipid content was not different between different genotype groups [The lability . However factors , 35. PPA factors , 35. PPA fatigue . The impwo hours . The funwo hours , 35 and wo hours . This ise groups . These dEthical approval was obtained from the Human Research Ethics Committee (HREC) at Griffith University (Protocol No: MSC/06/05/HREC) and Queensland University of Technology  and written consent was obtained from each participant. The study population consisted of a previously described  cohort oet al., 2013 [Briefly, eligibility for the Kona Ironman championship is gained by earning a qualifying place in yearly qualifying half-Ironman or full-Ironman marathons run at differing locations worldwide. Approximately three-quarters of the participants were male  while about one-quarter were female . Athletes originated from various countries from around the world, and were grouped according to continent of origin. Although 83.7% of athletes originated from North America (N = 104) or Europe (N = 60), although a small number did originate from Oceania (N = 23), South America (N = 6), Asia (N = 2) and Africa (N = 1). Most participants were between the ages of 30 and 50 N = 123, 63.3%), with mean participant age 42.5 ± 11.4 yrs. Further detail on the cohort baseline characteristics and questionnaire data may be found in Grealy 3, 63.3%,ACE I/D polymorphism  was genotyped by PCR amplification using a previously published primer set [AMPD1 Q12X polymorphism  was genotyped by PCR amplification using a previously published primer set [HpyCH4IV. The GDF8 K153R polymorphism , the HFE H63D polymorphism , and the PPARGC1A G482S polymorphism  were all genotyped by PCR amplification using primer sets designed for this study, followed by restriction enzyme digestion with PspOMI, BclI, and MspI respectively. The ACTN3 R577X polymorphism  had been genotyped in this cohort previously [CKMM NcoI 3’-untranslated region polymorphism  was genotyped by PCR amplification using a HRM primer set designed for this study, followed by HRM analysis. Positive controls for each genotype were created for each assay, and were genotyped using both the original assay and an alternative assay method such as sequencing or RFLP. Both typing methods resulted in 100% concordance of genotypes, for all assays. Positive controls were subsequently included in all genotyping runs on cohort samples. Additionally, HRM assays were genotyped in duplicate, with samples re-typed in cases of disagreement between duplicates.Genotyping for the seven gene polymorphisms was performed by PCR amplification followed by various assays, including agarose gel electrophoreses (AGE), restriction fragment length polymorphism (RFLP) analysis, and high resolution melt (HRM) analysis (see imer set  slightlyimer set  followed2 tests or Fisher’s exact tests where appropriate. Performance time (PT) was analysed by one-way ANOVA tests to determine whether PT differed between genotype groups for individual polymorphisms in this cohort. PTs were also used to group the athletes into two extreme phenotypes, the top 10% performers (with fastest times) and the bottom 10% performers (with slowest times). Genotype frequencies in the top and bottom 10% groups were compared using Fisher’s exact tests. The combined effect of having multiple optimal alleles was assessed using the total genotype score procedure outlined previously [et al. assumed an additive effect of an advantageous allele, with homozygotes of the non-optimal allele assigned a score of 0 and heterozygotes with one copy of the optimal allele assigned a score of 1. The only marker that did not fit this pattern was the HFE H63D polymorphism, in which H/D heterozygotes were scored as 2 while the H/H homozygote was scored as 0 and the D/D homozygote was scored as 1. This was due to the prior finding that heterozygotes are significantly overrepresented in endurance athletes versus controls [et al., 2013) were also examined for association with PT.Genotype frequencies were tested for conformation to Hardy-Weinberg Equilibrium (HWE), and compared to HapMap reference population frequencies using χeviously . Brieflycontrols , 31. Gencontrols ). Due toReceiver operating characteristic (ROC) area under the curve (AUC) analyses were conducted to determine whether models with demographic and genetic variables could predict: (1) whether athlete performance time would be less than the median time; (2) whether athlete performance time would be less than the mean time; and (3) whether athletes would fall into the top 10% of performance times. Models included TGS only, demographic variables only, TGS and demographic variables, individual genes and demographic variables. The ROC curve is defined as a plot of test sensitivity or true positive rate (TPR) as the y coordinate versus its specificity or false positive rate (FPR) as the x coordinate. It is an effective method to evaluate the quality or the performance of an diagnostic test . The cliHFE (97.4% of samples successfully genotyped). The genotype distributions for all markers was found to conform with Hardy-Weinberg Equilibrium (HWE) in the overall cohort and in the subgroups of the 10% fastest and 10% slowest race performers (p > 0.05) for all groups and markers; see ACE rs4340. No data was available for ACE rs4340 in HapMap CEU population; data shown in et al. 2000, which is a UK study involving 5934 Caucasian myocardial infarction controls [2 p = 1.68 x10-6). Genotype distribution was not significantly different in males and females, athletes from different continents, or athletes of different ages ; for AMPD1, with a higher frequency of the Q/Q genotype in the top 10% performers (88.2% compared to 70.6%); and for CKMM, with a lower frequency of the G/G genotype in the top 10% performers (0.0% compared to 17.6%).Genotyping success rate ranged from 99–100% for all markers except ages see  Tables; ages see , particuACE I/I genotype (685 min); ACTN3 R/R genotype (697 min); AMPD1 Q/Q genotype (704 min); CKMM A/G (695 min); GDF8 K/R genotype (694 min); HFE D/D genotype (697 min); and PPARGC1A G/S genotype (704 min). For ACE and AMPD1, the fastest PT corresponded with the ‘optimal’ genotype for endurance. For CKMM, GDF8, PPARGC1A and HFE, the less optimal genotype had the fastest PT. Interestingly, for ACTN3, the fastest PT corresponded with the genotype optimally associated with speed/power (the R/R genotype), not endurance. For AMPD1, a trend of increasing mean PT for decreasing number of optimal alleles was observed; however, mean PT did not significantly differ between genotype groups for any of the individual polymorphisms in this cohort (p > 0.1).Mean performance time (PT) overall was 11 hr 44.4 min ± 1 hr 51.4 min; the fastest finishing time was 9 hr 5.3 min, while the slowest finishing time was 16 hr 55.2 min. Mean PTs and ANOVA comparisons for each genotype group are shown in et al. (2009), which is a percentage of optimal alleles obtained across all seven markers. In the total cohort of Ironman athletes, the mean ± SD of the TGS was 60.75 ± 12.95 , sex , and continent of origin  were statistically significant, accounting for most of the variance in performance time (35.1%). Regression models of individual markers followed an additive genetic model adjusted for age, sex, and continent of origin; shown in AMPD1 marker was significantly associated with PT . Each AMPD1 null allele  resulted in an increase of about 39 minutes in PT, with X/X genotypes having an average increase of 78 min in PT compared to Q/X genotypes. The model accounted for 37.3% of the variance in PT, which was a significant improvement  on the next best model of age, sex, and continent of origin alone (which accounted for 36.8% of the variance in performance). The regression model for total genotype score (AMPD1 genotype (37.3%).Performance time (PT) modelling using linear regression showed that clinical characteristics such as being a twin (n = 1), being a smoker (n = 1), and presence of a known disorder (n = 18) were not significantly associated with changes in PT. Occupational activity level and preferred exercise type were also shown to not significantly influence PT. There was a significant trend of decreasing mean PT with increasing estimated weekly exercise hours, with mean PT ± SD of 761 ± 126 min for athletes exercising at least 3–8 hrs per week, 701 ± 109 min for weekly exercise at least 8–12 hrs, and 682 ± 89 min for athletes exercising more than 12 hrs per week . However, this effect was not significant when weekly exercise hours was included in the PT regression model with other variables . Only the demographic variables of age . ROC AUC graphs for all analyses are shown in AMPD1 genotype was found to be the most significant for predicting whether athletes would finish in less time than both the mean and median , while the model with age, sex, continent and TGS was the most significant model for predicting whether athletes would finish in the top 10% . However, the model with age, sex, continent, and AMPD1 genotype had similar though slightly less significant results . Of all the ROC AUC analyses (age) + (79.90 • sex) + (-21.36 • continent) + (-0.42 • TGS) + 552.6, this would indicate that a North American male aged 35 yrs old would need a TGS of 51 or more in order to obtain the identified criteria cutoff of 672.28; however, a trade-off among the variables means that a lower TGS in combination with optimal values for the demographic variables would be equally likely to finish in the top 10%.Furthermore, ROC AUC analysis determined that TGS alone could not significantly predict whether an athlete would finish in (a) less than the median PT of 681.33 min ; (b) less than the mean PT of 708.39 min ; or (c) the top 10% fastest PT i.e. less than 593.7 min . However, models with the demographic variables of age, sex, and continent of origin only, demographic variables and TGS, and demographic variables and analyses , the modAMPD1 Gln12Ter genotype showed a significant result, with the endurance-optimal Gln allele decreasing mean performance time.Overall, although expected genotype frequencies corresponded well with expected Caucasian frequencies from HapMap, none of the individual polymorphisms had significantly different genotype frequencies in the top and bottom 10% performers. This is perhaps due to power limitations, given that the top and bottom 10% of performers consisted of only seventeen individuals in each group for this study. However, none of the individual polymorphisms were found to significantly impact performance time when unadjusted for confounding demographic variables. Interestingly, an age-, sex- and continent of origin-adjusted analysis of As previously reported , age, seIndeed, training variables are an additional important factor to account for in such studies, as different training types and durations can have hugely significant impacts on athlete capabilities. In this study, fitness training characteristics were determined only through estimated weekly exercise hours (determined by exercise frequency and duration questions). However, this data alone cannot meaningfully inform the effect of athlete training on performance, as even low volume exercise may potently increase athlete endurance performance for certain training types, such as high-intensity interval training (HIT). For instance, muscle mitochondrial capacity, resting muscle glycogen, and GLUT4 protein content were all found to be improved significantly by HIT in a 2010 study, despite the fact that the training was merely six training sessions of 8–12 x 60 second intervals (with interspersed 75-second recovery periods). Further2 = 40–60%) and while athletic status itself has also been reported to be highly heritable (h2 >50%) [at least half of the variance in endurance phenotype. This can be due to both shared environment  and non-shared environment . As genetic analyses show that each allele must contribute relatively small amounts of variance to the overall phenotype compared with environmental factors [AMPD1 Gln12Ter.These findings highlight the importance of including potentially confounding environmental factors in genetic analyses of athletic performance. This should not be surprising, given that while endurance endophenotypes have been shown to have high heritabilities h2 = 0–60% and factors , these tet al. 2009 (mean 62.43 ± std. dev. 11.45), the TGS distribution in the Ironman athletes was overall lower than for Spanish endurance athletes (mean 70.22 ± std. dev. 15.58). Similar to the reported results in Spanish endurance athletes by Ruiz et al. 2009, we observed multiple ‘peaks’ in the distribution of the endurance athletes. The first peak was observed at a TGS ~43 and was common to both top and bottom performers; the second peak was observed at a TGS of ~57 for the bottom 10% but ~64 for the top 10%; a possible third peak was observed for top 10% performers at TGS of ~79. The difference in frequency of higher TGS for top performers compared with lower TGS for bottom performers was more clearly observed when TGS distribution was grouped into 10-unit intervals. This might suggest that there groupings of optimal alleles, perhaps, the likelihood of an optimal allele for one marker increases the likelihood of having other optimal alleles (and vice versa). Thus far, this possibility has not been explored in relation to the TGS, as what all the currently existing TGS models have in common is that they represent the proportion or percentage of ‘optimal’ alleles for a particular phenotype, and assumes an additive genetic model of allele favourability for all polymorphism except HFE . Furthermore, the TGS follows a simple additive model of athletic advantage between different polymorphisms, which may not be the case if gene-gene and gene-environment interactions result in non-additive advantages for certain allele combinations. Several papers have already reported gene-gene interactions for small combinations of genes [NOS3 and BDKRB2 genes  [Another method of preventing polymorphisms with individual small effect from escaping statistical detection is to analyse their joint effects using the TGS system. This has been used to successfully show a significant difference in genetic profile ‘favourability’ between endurance athletes versus non-athlete controls for the seven-gene endurance profile  or a tenof genes , 48; of nations) . It is anations) , 49.These reasons may also partly explain why TGS was not significantly associated with PT in our cohort even when adjusted for age, sex, and origin and that ROC AUC analysis determined that TGS alone could not significantly predict whether an athlete would finish in less than the median or mean or the top 10% fastest PT. Alternatively, the TGS profile for ‘optimal endurance’ may not be an appropriate profile for examining event performance as an outcome, even an endurance event. Additionally, even differing types of endurance events may show different levels of association with ‘endurance’ genes; while acknowledged as one of the most gruelling endurance events in the world, the Ironman championships require a blend of cycling, running, and swimming skills, which makes them more of a complex phenotype than single-sport endurance events such as running. Triathlons may thus require different set of ‘optimal alleles’, emphasising not only endurance-associated genes but perhaps power-associated as well. “Success” in any kind of endurance event relies, in addition to endurance capabilities, on speed and strength to outperform competitors.ACTN3 Arg577Ter null allele (X) was coded as the ‘optimal’ endurance allele and the X/X genotype was given a genotype score of 2, the R/X genotype given a score of 1, and the R/R genotype given a score of 0. However, the R allele is highly associated with speed and power [et al.’s 2010 speed/power profile showed three common polymorphisms to the endurance profile , albeit with inverse allele coding [Thus, in the TGS profile we employed, the nd power , and thee coding . Thus, 3S1 Fig(TIF)Click here for additional data file.S1 Table(DOC)Click here for additional data file.S2 Table(DOC)Click here for additional data file.S3 Table(DOC)Click here for additional data file.S4 Table(DOC)Click here for additional data file.S5 Table(DOC)Click here for additional data file.


Success in genome-wide association studies and marker-assisted selection depends on good phenotypic and genotypic data. The more complete this data is, the more powerful will be the results of analysis. Nevertheless, there are next-generation technologies that seek to provide genotypic information in spite of great proportions of missing data. The procedures these technologies use to impute genetic data, therefore, greatly affect downstream analyses. This study aims to (1) compare the genetic variance in a single-nucleotide polymorphism panel of soybean with missing data imputed using various methods, (2) evaluate the imputation accuracy and post-imputation quality associated with these methods, and (3) evaluate the impact of imputation method on heritability and the accuracy of genome-wide prediction of soybean traits. The imputation methods we evaluated were as follows: multivariate mixed model, hidden Markov model, logical algorithm, k-nearest neighbor, single value decomposition, and random forest. We used raw genotypes from the SoyNAM project and the following phenotypes: plant height, days to maturity, grain yield, and seed protein composition.We propose an imputation method based on multivariate mixed models using pedigree information. Our methods comparison indicate that heritability of traits can be affected by the imputation method. Genotypes with missing values imputed with methods that make use of genealogic information can favor genetic analysis of highly polygenic traits, but not genome-wide prediction accuracy. The genotypic matrix captured the highest amount of genetic variance when missing loci were imputed by the method proposed in this paper.We concluded that hidden Markov models and random forest imputation are more suitable to studies that aim analyses of highly heritable traits while pedigree-based methods can be used to best analyze traits with low heritability. Despite the notable contribution to heritability, advantages in genomic prediction were not observed by changing the imputation method. We identified significant differences across imputation methods in a dataset missing 20 % of the genotypic values. It means that genotypic data from genotyping technologies that provide a high proportion of missing values, such as GBS, should be handled carefully because the imputation method will impact downstream analysis. Marker-assisted selection (MAS) is a powerful tool for accelerating genetic improvement of plants and animals  through For genetic improvement and genetic studies in the post-genomic era, new genotyping platforms such as genotyping by sequencing (GBS)  and singde novo genotyping [Researchers have proposed a variety of procedures for adjusting genotypic data to impute missing values and correct SNP miscalls. Most imputation algorithms, such as Hidden Markov Models , linear notyping , 43.Incorporating genealogical information boosts the accuracy of genotypic imputation, phasing, and the power of association analysis , 23. Theth, 2014. SoyNAM is a soybean  maturity group III nested association panel composed of 40 bi-parental crosses sharing a common parent and inbred for five generations. The panel comprises 5,596 recombinant inbred lines, phenotyped in 18 combinations of year and location, for four agronomic traits: grain yield, plant height, days to maturity, and seed protein composition. The panel was genotyped with a designed 5 k SNP chip. After removing non-segregating markers, low quality SNPs based on marker heritability (0.99) [This study employed genotypes and phenotypes from the SoyNAM project (soynam.org), downloaded on September 10y (0.99)  and minoy (0.99) , we seley (0.99) . If diffWe compared imputation approaches using a variety of methods: a multivariate mixed model (MMM); Hidden Markov Models (HMM) implemented in three software packages commonly employed in genetic studies ; a logicWe adapted the multivariate mixed model method for imputation from Gengler et al.  and Yangyj) and its flanking markers (yi and yk) as response variables , coding them in an ordinal or continuous scale [If allele inheritance follows the pedigree, the marker should be perfectly heritable, except for Mendelian sampling error. Consequently, SNP heritability is an indicator of the gene content , 13, andus scale , and fitZ is the design matrices of the random effects, μ and γ represent the intercept and individual additive effect, and ε represents the residual term. The variances associated with the imputed marker are: ij, the genetic covariance between marker j and the flanking marker i; σik, the genetic covariance between marker j the flanking marker k; and where A is the additive numerator relationship matrix and I is an identity matrix. MMM uses restricted maximum likelihood (REML) to estimate genetic covariances and then replaces missing values for the central position by the multivariate empirical Bayes estimate [where estimate , also reestimate . The modThis study used the software BLUPF90 , 33 to ct to change state given the previous marker Mt − 1. In genetic terms, the four possible states for a diploid organism with alleles M1 and M2 for locus M, are: M1M1, M1M2, M2M1 and M2M2.The HMM method is commonly employed in genetics and genomics for stochastic modeling of Markov processes (such as the computation of haplotypes). Assuming ordered markers, the HMM estimates the most likely path of states (i.e. genotype) based on the transition probability of marker MThis study evaluated three HMM software programs: fastPHASE , Beagle This method is implemented in the program findhap.f90 . The proFindhap.f90 first generates a list of possible haplotypes, then adds a genotype into the haplotype list and searches for a matching haplotype, then finds the second haplotype by subtracting the first haplotype from the genotype. It then compares each genotype to the haplotype list and imputes unknown alleles from the haplotypes. The first two iterations use population-wide genotypic data, and subsequent iterations locate matching haplotypes from pedigree data .kNN is a non-parametric method commonly used for prediction and classification. kNN is a memory-based learning algorithm based on voting . It reliM = UDVT. SVD uses the most significant eigenvectors (columns of U) to predict missing values. We performed SVD imputations by chromosome using the bi-cross-validation algorithm described in Owen & Perry [SVD relies on orthogonal expression of the genotypic matrix  from the & Perry  and impl & Perry .Random Forest  is a non-11 [Imputation errors impact the reliability of breeding values , 43 and -11 . The ICCY2 = σA2 + σE2 + σC2 + σε2; where σA2 is the additive genetic variance, σE2 is the variance due to environment, σC2 is the variance due to microenvironment (i.e. controls), and σε2 is the residual variance. In genetic terms, ICC represents narrow-sense heritability, which is defined as the amount of genetic variation that alleles can transmit to the following generation, and it quantifies the population response to selection [given the phenotypic variance σelection . The ratelection , 34. Genelection .ijkl = μ. + τi + βj + γk + εijkl; where yijkl is the heritability of the ith imputation method  with jth percentage of missing loci  of the kth trait  in the lth observation; μ. is the overall mean; τi represents the imputation method; βj is the percentage of missing loci; γk represents the trait; and εijkl is the residual of the ijkl observation. In this model, imputation method is the parameter of interest while blocking trait and percentage of missing. Levene’s test determined the equality of variances [p-value of F test was significant (<0.05). Results shown in Fig. To compare the effect of imputation methods on heritability, we performed analysis of variance (ANOVA) following the linear model yariances . The Shathod i = , …, 8 wiThis study evaluated imputation accuracy by determining the proportion of data imputed that was identical to the standard dataset . For eacTo measure prediction accuracy in the context of genomic selection, we used the correlation of observed and predicted values in a five-fold cross validation divided by the square root of the heritability as described by Lehermeier et al. . We usedp-value < 0.01) between heritability values (yijkl) and all terms in the statistical model: imputation method (τi), percentage of missing values (βj) and agronomic trait (γk). The fitted model provided a coefficient of determination R2 = 0.95 and a coefficient of variation CV = 6.72. The group means procedure  after imputation with the HMM implementations. MaCH and Beagle Fig.  also incThe third measure of accuracy of imputation and data correction is the difference between the observed and expected proportion of heterozygosity in the data. The expected proportion of heterozygosity in this dataset is 6.25 % of loci given that the parents were homozygous and the plants were genotyped in the F5 generation (i.e. after 5 generations of selfing), in which the expected inbreeding coefficient is 93.75 %. The results show that the proportion of heterozygous loci tends to increase as the proportion of missing data increases Fig. . We obseThe mean heritability for traits in this study was 0.81 ± 0.04 for plant height, 0.77 ± 0.04 for days to maturity, 0.79 ± 0.06 for seed protein content, and 0.37 ± 0.08 for grain yield. Grain yield is considered minimally heritable while the other three are highly heritable. Imputation method had the greatest impact on the trait with the lowest heritability (grain yield) when compared to the impact on traits with high heritability . However, it appears that the genotypic data imputed with RF may have a slightly better performance. Whole-genome regression methods did not provide statistically significant differences in prediction accuracy (data not shown).The prediction accuracy across traits ranged from 0.606 (MMM) to 0.628 (RF), but did not differ significantly , and the population structure allied to the pedigree information simultaneously, while forward-backward HMM algorithms work one direction at time using just a subset of random samples . ImputatProperties of the methods are summarized in Table For GBS and other technologies where a high percentage of missing values is expected, our results support the use of MaCH, fastPHASE, and RF, methods that have shown insensitivity to the percentage of missing loci. In a similar study, ) observeQuality of the imputation disturbs the genetic variance captured by the genotypic data. We were able to show that the imputation of genotypic data in the case where proportion of missing values as low as 20 % can affect the quality of the genotypic representation by the SNP panel. This results must be seen as a word of care for technologies based on low-coverage genotyping, such as GBS, where the amount of missing information commonly achieves values of 80 %. Yet, for the scenario in study it was not possible to identify significant impact of imputation method on genomic prediction. Thus, based on imputation accuracy and genetic variance captured by the SNP panel, the imputation method choice is hidden Markov models and random forest for general analysis. Pedigree-based methods of imputation were recognized to enhance the heritability of grain yield, the lowest heritable trait in this study.This study employed genotypes and phenotypes from the SoyNAM project (soynam.org). Data is available through the R package SoyNAM  and USDA


Drosophila melanogaster and its closely related species are morphologically very similar, but the shapes of the posterior lobe, a cuticular projection on the male genital arch are distinct from each other, representing a model system for studying the genetic basis of male genital morphology. In this study, we used highly inbred whole genome sequenced strains of D. melanogaster to perform genome wide association analysis on posterior lobe morphology. We quantified the outline shape of posterior lobes with Fourier coefficients obtained from elliptic Fourier analysis and performed principal component analysis, and posterior lobe size. The first and second principal components (PC1 and PC2) explained approximately 88% of the total variation of the posterior lobe shape. We then examined the association between the principal component scores and posterior lobe size and 1902142 single nucleotide polymorphisms (SNPs). As a result, we obtained 15, 14 and 15 SNPs for PC1, PC2 and posterior lobe size with P-values smaller than 10-5. Based on the location of the SNPs, 13, 13 and six protein coding genes were identified as potential candidates for PC1, PC2 and posterior lobe size, respectively. In addition to the previous findings showing that the intraspecific posterior shape variation are regulated by multiple QTL with strong effects, the present study suggests that the intraspecific variation may be under polygenic regulation with a number of loci with small effects. Further studies are required for investigating whether these candidate genes are responsible for the intraspecific posterior lobe shape variation.Male genital morphology of animals with internal fertilization and promiscuous mating systems have been one of the most diverse and rapidly evolving morphological traits. The male genital morphology in general is known to have low phenotypic and genetic variations, but the genetic basis of the male genital variation remains unclear.  Gerris lateralis and G. lacustris [Onthophagus taurus [Dryomyza anilis [Male genital structures of animals with internal fertilization and promiscuous mating systems have been one of the most diverse and rapidly evolving morphological traits, whereas female genital structures have been relatively invariant during evolution . Althougacustris ,5, dung s taurus , and flya anilis . To datea anilis ,8; howevDrosophila melanogaster, one of the best studied model insects, and its closely related species are morphologically very similar; however, the shapes of the posterior lobe, a cuticular projection on the male genital arch are distinct from each other [Drosophila flies, but they also observed that slight artificial alteration to the posterior lobe shape significantly reduced copulatory success, suggesting that the posterior lobe shape is under precopulatory sexual selection. Although the association between the male posterior lobe morphology and mating success is still under investigation, posterior lobes of the D. melanogaster species group represent a model system for studying reproductive isolation via the lock-and-key mechanism of secondary sexual structures.ch other . The posch other , suggestch other . Masly &ch other  have revch other  experimeD. simulans and D. mauritiana [D. sechellia and D. simulans [D. melanogaster strains; this study reports three autosomal QTL, contributing to the difference in the posterior lobe shape between two inbred strains of D. melanogaster. Although a high-resolution fine-mapping QTL approach was adopted, the three QTL encompass 2085 protein coding candidate genes. Higher resolution mapping is necessary for identifying the genes and genetic pathways responsible for the intraspecific variation in the posterior lobe shape.To understand the evolutionary divergence of the posterior lobe morphology, it is necessary to characterize both the inter- and intraspecific genetic variation and elucidate the selective forces acting on it . Till dauritiana ,16 and bsimulans  using a simulans  describeD. melanogaster strains , providing a great opportunity to assess the genetic architecture of quantitative traits at a fine-scale resolution; because DGRP contains a representative sample of naturally segregating genetic variation and has a limited population structure, it is ideal for performing genome-wide association mapping [Mackay et al.  have seq mapping . In the D. melanogaster strains, comprising more than 200 inbred lines derived from the Raleigh, USA population. We randomly selected 155 strains from DGRP and obtained them from the Bloomington Drosophila Stock Center . We then removed the flies and reared the larvae until eclosion. The emerging adult males were collected from each vial and preserved in 70% ethanol; four replicate vials were set up for each line.We sampled up to 8 males from each line by pooling the individuals emerged from replicate vials . The abdomen was dissected from each male and boiled in 0.1 M KOH for 30 min at 60°C to dissolve tissues other than the cuticular exoskeleton. Further, the genital arch on the right side of the body was dissected from each abdomen and mounted on a slide glass in Hoyer’s medium. The posterior lobe was flattened by a coverslip to obtain a two-dimensional shape. We then captured the images of the posterior lobe using an optical microscope  with a 40× objective lens and CCD camera . Each posterior lobe image was manually outlined using Image J  Fig 1)..Fig 1). x and y coordinates were acquired for each posterior lobe outline and were further translated into a chain code. Before applying EFA, all the outlines were subjected to generalized Procrustes alignment using the artificial baselines for normalizing the size and configuration of the outlines and render the locations of all the posterior lobe outlines comparable. As a result of EFA for each posterior lobe, we obtained 200 Fourier coefficients (50 harmonics of the Fourier series), providing a nearly perfect reconstruction of the original posterior lobe outline. Because we performed generalized Procrustes alignment prior to EFA, we did not employ the Fourier coefficient normalizing procedures suggested by Kuhl & Giardina [Because no reliable homologous landmarks are definable for the posterior lobe, we performed elliptic Fourier analysis (EFA) to describe the outline shape . Series Giardina .The 200 Fourier coefficients were treated as variables describing the shape of the posterior lobe and were analyzed by principal component analysis (PCA). Among the 155 DGRP strains used in the present study, the first principal component (PC1) explained approximately 78% of the total variation while the second principal component (PC2) explained approximately 10% in the 200 Fourier coefficients. Based on the explanatory power distribution among the principal components, we used PC1 and PC2 as the two major shape descriptor variables for further analyses. All shape analyses were performed using the Momocs package , and PCAR) [R determines the proportion of variance due to variation between individuals where R = 0 indicates that all variance is attributable to variance within individuals (100% measurement error) whilst R = 1 indicates all variance is found between individuals (0% measurement error). As a result, both PC1 and PC2 scores showed consistently high repeatability regardless of the number of harmonics  to obtain PC1 and PC2 scores, but high number of harmonics in EFA can capture small asperity of the outline and that may result in larger measurement error. To examine this possibility, we obtained outlines of 104 flies from 13 DGRP strains twice, and calculated PC1 and PC2 scores using two to 50 harmonics. We evaluated the measurement error in the PC scores using a repeatability index (R) . Based oarmonics , indicatTo evaluate posterior lobe size, we used the number of pixels encompassed by the outlines obtained as described above.Wolbachia pipentis, which is a maternally inherited bacterium [http://dgrp2.gnets.ncsu.edu/). Because infection of Wolbachia pipensis is known to affect various fitness traits in D. melanogaster [Wolbachia infection on genital morphology. To assess whether the Wolbachia infection status influenced the male genital morphology, we used the following ANOVA model:I is the infection status (fixed effect), S is the DGRP strain (random effect), and ε is the error variance.Approximately half of the DGRP strains are infected with acterium ; the infnogaster , we testbetween − MSwithin)/, where MSbetween is the mean square of the between-genotype component, MSwithin is the mean square of the within-genotype component, and MStotal is the sum of these mean squares.To evaluate the broad-sense heritability of the posterior lobe shape quantified with the PC1 and PC2 scores and posterior lobe size, we calculated intraclass correlation coefficients (ICCs) ,26 by paD. melanogaster, they have a limited population structure and overall low linkage disequilibrium (LD) [SNP is the SNP genotype effect. We defined an arbitrary threshold P-value as 10-5, and the SNPs with lower P-values were treated as SNPs with a significant effect. Because of the LD effect, individual SNPs are not completely independent and it is difficult to apply adjustment for multiple test properly. In the current study, for descriptive purposes, we assumed independence between SNPs and applied the Benjamini–Hochberg procedure to control the false discovery rate (FDR) [Q-values (d) for each candidate SNP to draw more robust conclusion than interpreting the results only using P-values. The allelic correlation between those candidate SNPs was quantified with r2. We considered protein coding genes located within 1 kb of the significant SNPs as the candidate genes. In this study, the genotype–phenotype association was analyzed using the GWAS analysis pipeline [Because the DGRP strains are a collection of inbred lines derived from a wild population of ium (LD) , which ate (FDR)  and calcQ-values  Tables. pipeline .Wolbachia infection on PC1 and PC2 scores were not statistically significant . The broad-sense heritability estimates for PC1, PC2 and posterior lobe size were 0.247, 0.563 and 0.615, respectively, showing moderate to high genetic variation.We found widespread PC scores among the DGRP strains , indicatP-values smaller than 10-5  showed relatively high effect size although they did not show strong LD with other candidate SNPs in association with protein coding genes. Those intergenic SNPs may correspond to a genetic variation in the non-coding RNA [GluRIB, Invadolysin, CG34303, CG43693, Nrx-IV, Rh7 and bru-3) were located within the two QTL for the posterior lobe shape of D. melanogaster identified by McNeil et al. [sano, CG13024) were identified to express differentially between sexes in genital imaginal disc in D. melanogaster [mal, Hel25E and blow) were identified to express differentially between male genital discs of two Drosophila species with morphologically very different posterior lobe shape (D. mauritiana and D. sechellia) [Pde1c was associated with the SNP with third largest effect size for PC1, and was the only candidate gene that has been previously associated with fertility and male mating behavior in D. melanogaster [Pde1c is one of the six genes that code for cyclic nucleotide phosphodiesterases (PDEs) [Pde1c mutant males as unacceptable and tried to reject them, Pde1c mutant males revealed a reduced copulation rate and longer copulation latency [Pde1c is required for normal copulation behavior, while its non-neuronal expression was suggested to be necessary for fertility [Pde1c in the morphogenesis of the posterior lobe; however, because Pde1c is primarily expressed in the olfactory epithelium [D. melanogaster [Pde1c may affect the posterior lobe shape by modifying their foraging behavior. Except Pde1c, none of the candidate genes were previously suggested to be associated with posterior lobe morphogenesis or copulation behavior. Further studies are required for investigating whether these candidate genes are responsible for the intraspecific posterior lobe shape variation.As a result of genome-wide association analyses, we found 32 SNPs associated with PC1 or PC2 scores or posterior lobe size. Those SNPs were distributed to all the major chromosomes of l et al. , the thrding RNA  or cis-rl et al. . Two of nogaster . Three ochellia) . Althougs (PDEs) ,32. Becaithelium , it can P-value as 10-5 and identified 32 SNPs with significant association, but there were many more SNPs with slightly higher P-values , suggesting that there are many SNPs with small effects on the posterior lobe shape. Previous studies on the intra- and interspecific posterior lobe shape variation were based mainly on QTL mapping approaches and identified multiple QTL with strong effects: three autosomal QTL for intraspecific variation in D. melanogaster [D. simulans and D. mauritiana, respectively [D. simulans and D. sechellia [D. simulans and D. mauritiana. In addition to the previous findings showing that the intra- and interspecific posterior shape variation are regulated by a multiple QTL with strong effects, the present study suggests that the intraspecific variation is under polygenic regulation with a number of loci with small effects.The present study set the threshold nogaster ; 15 QTL ectively ; and 20 echellia . Furtherechellia  reportedP-value to evaluate the significance of SNPs. It was partly because of the non-independence of the linked SNPs. As Mackay et al. [r2 = 0.2 on average within 10 base pairs on autosomes and 30 base pairs on the X chromosome in DGRP strains, suggesting that there was relatively weak LD structure in our data. If we apply Benjamini–Hochberg procedure under the assumption of independence of the SNPs, no SNPs analyzed showed smaller Q-values than 0.05, suggesting that there may be false positive SNPs in our candidate SNPs. The effects of the candidate SNPs and genes need to be examined using mutants or RNAi screening in future studies.In the current study, we did not correct for multiple tests and use adjusted y et al.  describeIn future studies, a genome-wide association approach should be applied to the intra- and interspecific variation in the posterior lobe shape variation to reveal their underlying genetic architecture at a higher resolution.S1 Fig(TIF)Click here for additional data file.S2 Fig(TIF)Click here for additional data file.S3 Fig(TIF)Click here for additional data file.S4 Fig(TIF)Click here for additional data file.S5 Fig(TIF)Click here for additional data file.S1 Table(XLSX)Click here for additional data file.S2 TableP-values > 10-3, ID, minor and major alleles, minor allele frequency (MAF), minor allele count, major allele count, P-value and Q-value are listed.For SNPs with (XLSX)Click here for additional data file.S3 TableP-values > 10-3, ID, minor and major alleles, minor allele frequency (MAF), minor allele count, major allele count, P-value and Q-value are listed.For SNPs with (XLSX)Click here for additional data file.S4 TableP-values > 10-3, ID, minor and major alleles, minor allele frequency (MAF), minor allele count, major allele count, P-value and Q-value are listed.For SNPs with (XLSX)Click here for additional data file.