B-alleles at a biallelic locus — representing the un-ordered genotype — equals the imprinting effect. The applicability to real data was demonstrated for about 1800 genotyped Brown Swiss bulls and their un-genotyped fattening progeny. Thus, this approach unlocks vast data resources in various species for imprinting analyses and offers valuable clues as to what extent imprinted loci contribute to genetic variability.Depending on their parental origin, alleles at imprinted loci are fully or partially inactivated through epigenetic mechanisms. Their effects contribute to the broader class of parent-of-origin effects. Standard methodology for mapping imprinted quantitative trait loci in association studies requires phenotypes and parental origin of marker alleles (ordered genotypes) to be simultaneously known for each individual. As such, many phenotypes are known from un-genotyped offspring in ongoing breeding programmes , while their parents have known genotypes but no phenotypes. By theoretical considerations and simulations, we showed that the limitations of standard methodology can be overcome in such situations. This is achieved by first estimating parent-of-origin effects, which then serve as dependent variables in association analyses, in which only imprinted loci give a signal. As a theoretical foundation, the regression of parent-of-origin effects on the number of  The existence of imprinting is well established in plants, insects and mammals2. In avian species, imprinting is not confirmed as studies have resulted in contradictory results6. In plants, imprinting has been established to occur in maize9, Arabidopsis thaliana14, rice16, sorghum17 and castor beans18. The majority of imprinted genes in plants have been found in the endosperm and only a few are known to be expressed in the embryo19. In mammals, less than 1% of all genes are thought to be imprinted20. Imprinting has, however, crucial functions in stem cells, neuronal differentiation and growth21. It is thus responsible for a wide range of diseases in humans. Well known examples are Prader–Willi syndrome22 and Angelman syndrome23. In livestock, imprinted genes have considerable effects on the expression of agriculturally important traits. Variance-component analyses have revealed significant contributions of imprinted genes to the total genetic variance of traits in beef cattle and pigs28. With respect to pigs, a pioneering discovery was a purely paternally expressed polymorphism within the porcine IGF2, which was found to affect muscle mass and fat deposition traits30. The gene was detected by applying a line-cross design, where lines in a P0 generation  are crossed to create an F1 generation of individuals being heterozygous at these QTLs (summarised in Sandor and Georges31). Intercrossing these individuals generates an F2 population with equal frequencies of the four ordered genotypes BB, Bb and bB, bb. When the average phenotypes of Bb and bB can be statistically distinguished, i.e. a difference can be observed, the existence of an imprinted QTL (iQTL) is indicated. This, however, requires the knowledge of the parental allele origin (ordered genotype). Ordered genotypes are also needed in genome-wide association studies of POEs. For example, to account for POEs, Belonogova et al.32 added a vector p — containing the difference between the numbers of maternally and paternally derived B-alleles — as a second step in a model called GRAMMAR (rapid association using mixed model and regression33). Ordered genotypes also form the basis for genomic relationship matrices that account for imprinting34. To determine the ordered genotype of an offspring, conclusions on the parental allele origin can usually be drawn from the genotypes of its parents. However, if both parents are heterozygous, it is not possible to determine the offspring’s ordered genotype32. Then, if available, markers adjacent to the considered locus (haplotype information) may indicate the parental allele origin and thus the offspring’s ordered genotype. Furthermore, to detect iQTLs, phenotypic information is necessary in addition to ordered genotypes. This is a common issue in livestock, where the traits of interest are often measured in progeny which are often ungenotyped (e.g. milk production traits35) in contrast to genetically influential parents, such as bulls in dairy cattle. Therefore, there is a large amount of existing data that could be used for imprinting analyses.Genomic imprinting is an epigenetic mechanism in which the expression of genes is partially or entirely limited to one of the two inherited alleles. The effects of imprinted genes can be considered parent-of-origin effects (POEs) as they appear as phenotypic differences between heterozygotes depending on their parental allele originimprinting model  that describes POEs as differences between two sex-specific transmitting abilities (TAs) for each parent. In the second step, the ePOEs are used as dependent variables in a model, where un-ordered genotypes of parents constitute the explanatory variable related to a particular fixed marker effect and a random polygenic effect accounts for the unconsidered genetic variability in the POEs. This novel approach does not require ordered genotypes or both genotypes and phenotypes from the same individuals. This principle is demonstrated in simulated data and is applied to empirical data consisting of genotyped Brown Swiss sires with ePOEs for slaughter traits. First, we provide theoretical justification by investigating the regression of POEs on the number of B-alleles at an imprinted locus in a random mating population.To overcome the limitations of the currently applied methods of analysis for the detection of iQTLs, we propose a novel approach where estimated POEs (ePOEs) of parents are exploited to map imprinted genes expressed in their progeny. In the first step, phenotypic information can be summarised by applying a mixed B-alleles as a population parameter for a biallelic imprinted locus in a random mating (Fisher-Wright) population without selection and mutation. The alleles B and b have respective frequencies of p and q = 1 − p. Differences between the phenotypic means of the ordered genotypes (a (a), the dominance effect d  and the imprinting effect i (i), as described in Knott et al.36, Mantey et al.37 and the review by Lawson et al.1. Note that a somewhat different parameterization has been given by Spencer38. Parent-specific allele-substitution effects39 are given for male parents as 40. In the presence of genomic imprinting, a locus exerts its effect on the offspring either under a male or a female expression pattern. In the former, the average phenotype of a parent’s offspring equals half of its breeding value ‘as father’ and in the latter, half of its breeding value ‘as mother’25. For the ordered genotypes BB, Bb, bB and bb, where the first allele is paternally derived, these breeding values can be expressed as functions of parent-specific substitution effects and allele-frequencies , we define genotype-specific POEs as differences between the two sex-specific TAs for each genotype or, equivalently, as half the difference between both kinds of breeding values. For the four ordered genotypes, the POEs are 2qi, (q − p)i, (q − p)i, and −2pi, in the same order as above  = p22qi + 2pq(q − p)i − q22pi = 0, and the variance is given by Var(POE) = p24q2i2 + 2pq(q − p)2i2 + q24p2i2 = 2pqi2, which is equal to the imprinting variance at the locus, as derived by de Koning et al.39. Moreover, we are interested in the relationship between the number of B-alleles , which has the expectation 2p and variance 2pq, and POEs. Their covariance can be derived as:For our purposes, we need to know the expectation and variance of the POEs in the population. The expectation is r = 4p2q2i2. In summary, for a single imprinted locus, we have the covariance matrix:which translates into a correlation of Finally, we arrive at the regression of the POEs on gene count, which is:B-alleles of the same locus equals the imprinting effect. Next, we demonstrate how estimates of this population parameter can serve for marker-based imprinting analyses of simulated and real data.This final result shows that the regression of the POEs on the number of 28 and, after a deregression step, be regressed on the number of B-alleles at a marker locus. In the light of the results for the single locus model, the resulting regression coefficient can then be interpreted as the imprinting effect of an iQTL in linkage and/or associated with the marker. Reliabilities of ePOEs are a prerequisite for deregression41. Only recently, their efficient calculation using mixed-model methodology has been described28.Importantly, POEs can be estimated for genotyped parents even when their phenotypes are not known, as it is often the case in livestock. In practice, ePOEs can first be obtainedWe simulated two types of populations; the first comprised two generations, while the second contained three generations. Phenotypes were always available for the last generation only, while parents and grandparents remained without known phenotypes. The two-generation population was simulated to prove the applicability of the principle. One hundred unrelated parents were drawn from a base population. These parents were then inter-mated in a cross-classified manner, resulting in 100 × 100 full-sib families of size three. In this way, each parent was mated as father to all 100 parents (including itself), which acted as mothers. Vice versa, each parent was mated as mother to all 100 parents (including itself), which acted as father. This gave rise to 100 × 3 maternal half-sibs per parent. Thus, imprinted alleles were passed from each parent to progeny with both of the two possible parental expression patterns.et al.42. Thus, deregressed and weighted ePOEs, free from the influence of the PA, were needed. The three-generation population was simulated to illustrate the effects of the PA-correction, deregression and weighting. Ten grandparents were randomly chosen from the base population and produced 100 full-sib families, whose variable size was chosen from a Poisson distribution with a mean of 5.0. This led to 514 parents in the second generation, which were again inter-mated in a cross-classified manner. The number of full-sibs per family in the third generation was also Poisson distributed with a mean of 5.0. Only a fraction of all possible progeny (3%) with phenotypes was retained so that 41,273 records remained for the analysis. The full-sib families contained one to four phenotyped offspring each.In the three-generation pedigree, sources of family information contributed to the ePOEs of the individuals in generations one and two. These sources were the parent-average (PA), records of the final progeny and records of the progeny’s final progeny. The naïve utilization of ePOEs as dependent variables would negatively influence the outcome of association studies as shown for breeding values in Ekine In both population types, 15 mutually unlinked marker genotypes were simulated, where five were in linkage disequilibrium (LD) with QTLs. The LD was created by first drawing the QTL alleles from a binomial distribution depending on their allele frequencies. The alleles of the adjacent markers were then drawn from a conditional distribution, where an initial LD of 0.1 among founders was assumed. The first QTL at marker locus two  was chosen to be biparentally expressed (Mendelian QTL) contributing 30% to a total additive genetic variance of 1.35. A purely paternally and a purely maternally expressed QTL each contributed 5% to the total additive genetic variance and 25% to the total imprinting variance of 0.27. These were linked to the marker loci five (MAF = 0.5) and eight (MAF = 0.5). The marker loci 11 (MAF = 0.5) and 14 (MAF = 0.5) were both linked to partially imprinted QTLs with opposite POEs, which contributed 30% to the total additive genetic variance and 25% to the total imprinting variance. A residual variance of 2 generated a heritability of 0.40 for the simulated trait, and the imprinting variance overall accounted for 20% of the total additive genetic variance. The trait was created by adding additive and imprinting effects according to the simulated QTL genotypes. All genetic distances between associated markers and QTLs were set to 10 centiMorgans in the base population. For each of the two populations, 100 repetitions were simulated by drawing new genotypes and residual effects without altering family sizes or pedigree structures.43 was applied. Analysis 2B considered additive effects only by neglecting the imprinting effect.Next, we compared the results for imprinted and un-imprinted (Mendelian) QTLs under both our new and the traditional approach. Therefore, four different kinds of analyses, labelled 1A, 1B, 2A and 2B, were applied to the two-generation data. First, in analyses 1A and 1B, we made use only of the un-ordered genotypes and ePOEs and TAs of the 100 parents. Second, in two consecutive association analyses , we assumed that the phenotypes and ordered genotypes of the 30,000 offspring were available. To find associations with imprinted loci, in analysis 2A an adapted version of a measured genotype modelFinally, to illustrate the effects of the PA-correction, deregression and weighting, the ePOEs from the three-generation data were used for association analyses. In analysis 3A, ePOEs were left completely untreated, while in 3B they were deregressed and PA-corrected, and in 3C, the ePOEs were additionally weighted. A summary of the analyses is provided in Table et al.27. They were derived for up to 428,710 sires and dams based on the routinely recorded performance of their progeny, which were up to 173,051 fattening bulls (exact numbers vary from trait to trait). The imprinting variance contributed a significant proportion to the total genetic variance in the net body weight (BW) gain (carcass weight divided by age [g/d]), carcass muscularity and carcass fatness. While muscularity was described using five monetary grades reflecting price differences, fatness was categorised by scores ranging from 1 (lean) to 5 (very fat). Assuming these traits to be normally distributed, ePOEs were first generated applying a linear imprinting model (these traits are subsequently indicated with the subscript L). Then, ePOEs were generated applying a threshold imprinting model assuming the traits to be binomially distributed (subscript T). As data were routinely obtained, animal care guidelines were not obtained.The ePOEs and parental TAs as well as their reliabilities were derived from an imprinting analysis of Brown Swiss cattle slaughterhouse data published in detail in Blunk Upon agreement of all involved organisations, genotypes were made available from the central genome database, which is maintained for breeding purposes at LKV Bayern in Munich. Data retrieval was assisted by the Institute for Animal Breeding at the Bavarian State Research Centre for Agriculture. After quality control, 37,443 genotypes remained for 1,857 sires for the net BW gain and 37,433 genotypes remained for 1,831 sires for the muscularity and fatness traits.imprinting model), both kinds (TAs as sire and TAs as dam) were used as dependent variables. Both ePOEs and TAs were PA-corrected, deregressed and weighted adapting the approximate method published in Garrick et al.41 for breeding values. When their deregressed reliabilities were <3%, they were discarded. With regard to ePOEs, 1,793 remained for the net BW gain with an average reliability of 25.86%; 1,033 remained for muscularity(L) with an average reliability of 9.73%; 1,720 remained for muscularity(T) with an average reliability of 14.01%; 1,277 remained for fatness(L) with an average reliability of 10.63%; and 1,649 remained for fatness(T) with an average reliability of 12.51%. As discussed in detail later, the sensitivity to c, which was chosen to calculate the weighting of ePOEs and which defines the proportion of the imprinting variance not captured by markers41, was not particularly high in the simulation study. Therefore, c was limited to 0.1, 0.5 and 0.8. These values were only applied during the genome scan for ePOEs on the net BW gain to investigate the effect of changing c within a real data framework. A c of 0.1 was chosen to analyse the ePOEs on all other traits.The genome was scanned via single marker regression, where ePOEs, defined as deviations of the TAs as dam from the TAs as sire, were regressed on their marker gene counts individually. With respect to the TAs  did not significantly deviate from zero. As expected, the same pattern of signals was observed when phenotypes and ordered marker genotypes of offspring were used in a measured genotype model to detect iQTLs in analysis 2A  indicated the positions of iQTLs . At the fully imprinted marker loci (five and eight), the average p-values ranging from 0.002 to 0.011 indicated QTLs at all loci with a Mendelian component, i.e. purely Mendelian and partially imprinted loci , mean B, mean pimprinting model27, which can be either the genetic effect as father minus the genetic effect as mother or the reverse. Neither the estimation of the imprinting variance nor the detection of iQTLs depends on the sign of that difference as it has no effect on the absolute value of the marker effect and its estimate. When, in contrast to ePOEs, estimated TAs were used as dependent variables , the estimates were about half the magnitude of those observed when the model for phenotypes included an additive effect in analyses 2A and 2B  on the Bos taurus autosome (BTA) 11 was associated with ePOEs estimated in the net BW gain assuming a genome-wide false discovery rate (FDR) of 5%  was located on BTA11 and was found in a region harbouring iQTLs with an effect on weaning weight. However, this gene is located about 24.75 mega base pairs (Mb) away from the marker locus ARS-BFGL-NGS-101636. Furthermore, ARS-BFGL-NGS-101636 displayed low LD with its surrounding markers (r2 < 0.20). The highest LD (r2 = 0.34) was calculated for the SNP BTA-97072-no-rs, located in a non-coding region at 47.52 Mb , one SNP  were detected on BTA24  on chromosome 5 at 30.01 Mb is imprinted49.In addition to (L), two SNPs significant assuming a chromosome-wide FDR of 5%  were analysed. Instead, a significant SNP (chromosome-wide FDR of 5%) was found in a non-coding area on BTA7. As this marker is distantly located at 38.41 Mb, no relationship can be assumed to the SNP found on BTA7 when ePOEs on muscularity(L) were analysed.With regard to muscularity 5% Fig. ; Table 4(L), no significant SNPs were found. However, for fatness(L) the smallest number of records was available because 798 ePOEs were discarded from the analysis due to their low reliabilities. This might have considerably reduced the power to detect imprinted loci. With regard to fatness(T), 45 SNPs significant assuming a 5% chromosome-wide FDR were found on BTA5. As described in detail later, a series of these SNPs were also observed to be significantly associated with the parental TAs in fatness(L) and fatness(T). The strongest signals were displayed by SNPs surrounding TROAP and FAIM2. These genes are located in the regions from 30.65 Mb to 30.66 Mb and 30.15 Mb to 30.18 Mb, respectively. Some SNPs, being significantly associated with ePOEs, are located within or proximal to these genes , Zaitoun and Khatib50 did not find any indication that SLC38A4 is imprinted in cattle. Another fact giving rise to some uncertainty is that the SNPs found for fatness(T) on BTA5 were not observed when ePOEs on fatness(L) were analysed. However, as mentioned earlier, the lowest number of records and the smallest average of reliabilities were observed for ePOEs estimated in fatness(L). Furthermore, the heritability estimated for fatness(L) (h2 = 0.23) in Blunk et al.27 was far below the heritability estimated for fatness(T) (h2 = 0.46). These facts might have considerably reduced the power to detect imprinted loci when ePOEs on fatness(L) were analysed. With regard to fatness(T), another SNP significant assuming a 5% chromosome-wide FDR (ARS-BFGL-NGS-36861) was found in a non-coding region on BTA9  and to SNPs within IGF2R (r2 ≤ 0.02), however, suggests that ARS-BFGL-NGS-36861 is a fully independent signal. Another significant SNP (chromosome-wide FDR of 5%) was found in a non-coding region at 13.95 Mb on BTA29. An imprinting cluster is located on BTA29 incorporating the genes IGF2 and H19. However, this cluster is distantly located in the region from 49.32 Mb to 50.15 Mb.With regard to fatnessTo conclude, our results identify potentially imprinted genes on BTA5 and BTA11, affecting the carcass fatness and net BW gain, respectively. Their imprinting status cannot be established from the results of this study alone. Moreover, as ePOEs were used as dependent variables, it remains unclear whether their effects actually arose from genomic imprinting or another parent-specific genetic phenomenon . To answer this question, follow-up studies are necessary to gain deeper insights.Due to strong similarities between the results for the TAs as sire and the TAs as dam, findings for the latter are subsequently omitted from Tables. The same holds true for the results found in traits analysed via the threshold model. Moreover, only markers found to be significant assuming a 5% and 10% genome-wide FDR are listed Table .Table 5SWith regard to net BW gain, only one SNP, located in a non-coding region on BTA28, was found to be significantly associated with the parental TAs assuming a chromosome-wide FDR of 5% Fig. .Figure 4(L), six SNPs on BTA10 were associated with the parental TAs assuming a 5% genome-wide FDR . Three SNPs can be assigned to the gene UNC13C and one SNP to the gene AQP9. Their effects are of similar magnitude (Table (L) as well as for muscularity(T). Both genes are protein coding; however, their functions are still unclear in cattle. They are located in the regions from 52.15 Mb to 52.19 Mb (AQP9) and from 55.71 Mb to 56.41 Mb (UNC13C). Moderate lambdas (up to 1.042 for the TAs as sire) indicate almost no genome-wide inflation of p-values51, as shown for the muscularity traits in the Q-Q plot in Fig. r2 > 0.24 , a QTL associated with lean meat yield was found in Holstein-Friesian on BTA10 at 56.10 Mb, a region which is located within UNC13C53. Apart from the findings on BTA10, further markers significantly associated with the TAs estimated in the muscularity traits were found on BTA20, BTA23 and BTA28. Associations on BTA20 were only found for the TAs as dam assuming a chromosome-wide FDR of 5%. They cannot be assigned to genes. However, Doran et al.53 detected SNPs on BTA20, which were strongly associated with carcass conformation and were <1 Mb away from the gene GHR. In the current study, one of the SNPs on BTA20 is located only 41.75 Kb away from GHR.With regard to muscularityFDR Fig. ; Table 5de Table . This ho(L) and muscularity(T) with a 5% genome-wide FDR. However, it is located within a non-coding region, and markers found to be significantly associated with carcass conformation in Doran et al.53 are distantly located. Another marker significantly associated (chromosome-wide FDR of 5%) with both TAs estimated in the muscularity(T) was found on BTA28 within the gene KCNMA1 (32.82 Mb to 33.58 Mb). Its function with regard to the carcass conformation in cattle is unknown. However, Doran et al.53 identified a QTL with an effect on lean meat yield close to this gene at 33.60 Mb .A SNP on BTA23 was found to be significantly associated with both parental TAs estimated in muscularity(L), 22 SNPs on BTA5 were found to be associated with the TAs as sire assuming a genome-wide FDR of 5%. The smallest p-values (p < 2.6e-08) were displayed by markers surrounding TROAP located in a region from 30.65 Mb to 30.66 Mb. Overall, 41 further SNPs on BTA5 were significant assuming a genome-wide FDR of 10% or a chromosome-wide FDR of 5%. They were replicated for the TAs as dam as well as for the parental TAs estimated in fatness(T). Some SNPs are located within genes other than TROAP (Table 52), haplotypes with an effect on backfat breeding values are closely located to TROAP in a region from 32.6 Mb to 34.2 Mb54. Further significant SNPs (genome-wide FDR of 5% and 10%) were found on BTA2, BTA13, BTA16 and BTA19 when the TAs as sire estimated in fatness(L) were used as dependent variables . With regard to SNPs solely found when TAs as dam were analysed, a SNP significant assuming a 5% chromosome-wide FDR was revealed for fatness(T) on BTA29  and TROAP (BTA5). Scanning the genome for effects on TAs, which were estimated in the muscularity and fatness traits via linear and threshold models, led to results of high consistency. This suggests — at least for the categorical traits under consideration — that the linear and threshold models perform equally well at capturing the underlying genetic variation.33; measured-genotype approach43). Available marker information could, in principle, already be integrated in the estimation of ePOEs by replacing the numerator relationship matrix in the mixed model through a combined marker and pedigree-based relationship matrix H56. Following Wang et al.57, ePOEs of genotyped parents could then be transformed into marker effects and potential QTL-regions be made visible. However, significance testing of such marker effects has, to our best knowledge, not yet been described in the literature.From the single-locus population model with imprinting it was derived that the regression of true POEs on allele counts equals the imprinting effect. This was the foundation for our simulation study, by which estimates of POEs were related to marker alleles. In a two-step procedure, ePOEs and their reliabilities were first obtained by employing appropriate mixed models. In this way, information on parent-of-origin-specific genetic effects was extracted from un-genotyped offspring and summarised for genotyped parents. In a second step, the deregressed ePOEs then served as dependent variables to be regressed on allele counts of marker alleles, indicating the association of an iQTL with the marker. Most importantly, in this way, the complete lack of any genotype information for progeny and the phenotypes of the parents could be overcome. This is a substantial step forward compared to previously published methods for association mapping of imprinted loci, as these require data where phenotypes and ordered genotypes are known for the same individuals  and, to a certain fraction, may also be parents themselves . This calls for analyses of mixed data, where the vector of dependent variables contains ePOEs for genotyped parents, as a summary of information from un-genotyped progeny, and the phenotypes of genotyped progeny. Their respective counterparts on the explanatory side of the model are marker allele counts and ordered genotype information. Thus, including ePOEs in marker-based imprinting analyses enables researchers to make full use of available information which otherwise would remain un-accessible.The Brown Swiss beef traits data set is a meat animal example, where phenotype-providing progeny never become parents and remain un-genotyped. In livestock genetics, other candidate data show the same characteristics, e.g. in dual-purpose Simmental43 (with genotypes on progeny only) and our new approach compare depends on several factors. For the use of ePOEs sufficient data of adequate structure (sires and dams have to be related) are required to estimate variance components. Another important point is the average reliability of ePOEs. With genotyped progeny we also need to assign resources to the genotyping of their parents, otherwise we cannot derive the parental origin of marker alleles. In general, our new approach is obviously well suited for further studies of the importance of POEs in species where large progeny groups can be produced or are available and their phenotypic information can be combined into reliable estimates of parental POEs. This is especially the case in plants and some animal species with large half-sib families, such as horses, cattle or birds.How power and cost effectiveness of the measured-genotype approach61. Accordingly, ePOEs may pick up such effects, especially when not explicitly accounted for in the model for POE-estimation . Other potential confounders are Y-chromosomal and mitochondrial effects, which, however, seem to be negligible at least for beef traits62. However, if present, the latter would not show any signal of association with purely autosomal markers, as investigated in the Brown Swiss analysis. Moreover, model-specification is also important for the ability to find associations between different kinds of imprinted loci and markers. Models that account for all kinds of genomic imprinting simultaneously, no matter if paternal, maternal, fully or partial, have not been described in the literature before25. When such models are used for POE-estimation, all types of imprinted loci can, in principle, be located in the genome, as was successfully demonstrated in the simulation study. Nevertheless, follow-up studies are necessary, as for other approaches like mapping in line-cross experiments39, in order to confirm both genomic imprinting and its exact type.Some authors have stressed the fact that POEs may be caused by other phenomena than imprinting alone, e.g. by maternal genetic effectset al.42, preprocessing the ePOEs is necessary to achieve reliable marker effect estimates and to avoid large false-positive rates. With regard to the weighting, c was limited to 0.1 to analyse the muscularity and fatness traits. When the ePOEs on net BW gain were analysed, c was varied, which led to some changes in the p-values and estimated effects. As this indicates a degree of sensitivity to c, varying this parameter with regard to the muscularity and fatness traits might have resulted in the detection of additional associations. However, as no effect of the weighting was observed in the simulation study, it remains questionable whether changing c actually results in true associations or in an inflation of effects. Thus, whether the associations found on BTA24 for ePOEs on the net BW gain constitute true associations or false-positives remained unclear when c was set to 0.8. Analyses with greater amounts of data would help investigating the true imprinting status of loci, especially regarding the SNPs found on BTA24.As shown for breeding values in Ekine et al.41 did not allow the deregression of two genetic effects simultaneously, which would, however, be appropriate using models that consider imprinting by including two genetic effects. In an article on the international genetic evaluation of beef cattle weaning weight63, the separate deregression of direct genetic effects and maternal genetic effects was described. A correction was presented, in which the contributions of the second correlated effect to the variance of the first are eliminated, when the first genetic effect is deregressed. With the help of a λ-value, corrected heritability was computed both for the direct and maternal effect, which can be interpreted as equivalent heritability under a single trait model63. The same principle could be applied to the reduced imprinting model . However, using an adapted λ-value in the approximation method by Garrick et al.41 did not have any impact as the λ-value was cancelled out .Note that the approximate method of deregression and PA-correction according to Garrick 64. Apart from whole-genome scans, targeted analyses may also concentrate on associations in and around known imprinted genes. Further research will aim at more general analyses that include phenotypes from individuals also providing ordered genotype information. In any case, vast repositories of already collected phenotypes will now become accessible for imprinting analyses by applying our new approach.In summary, the possibility to detect imprinted loci by regressing ePOEs of parents on the gene counts of their un-ordered marker genotypes has not been recognised before. Fields of application are, in principle, all kinds of pedigreed populations, be it animals or plants, where genotyping of parents has become part of routine breeding procedures, or, possibly even in human populations with available detailed genealogiesimprinting model . Estimates for the TAs  were derived from a reduced animal model that assumes no imprinting . Then, the model:yi was either the ePOE  or the TA of individual i , μ was the general mean and ei represents the residual. The term BB, Bb and bb) of individual i at the particular marker under consideration and b is the regression coefficient. A significant test result of the hypothesis H0: b = 0 indicates the association of a marker with an iQTL in case the dependent variable is an ePOE  and the association of a marker with an additive QTL in case yi is a TA . Tests were done separately for each marker via a conditional Wald F-test using the ASReml-package (Release 3.065) and ASReml-R (Version 366). The random variable ui models the unaccounted genetic variability and was assumed to have a variance of Var(u) = Aσ2 with A as the numerator relationship matrix (derived from the pedigree), which was included to account for the stratification of the population into families. Note, in the analyses 1A and 1B, ui was not included because the individuals with genotypes were unrelated founders. A summary of analyses is provided in Table 43:yi is the observed phenotype. The regression coefficient ba can be interpreted as the additive effect of the locus. The regression coefficient bp delivers an estimate for the difference between the two types of heterozygotes Bb and bB, i.e. for the imprinting effect. The term BB, Bb, bB and bb, respectively. The association with an iQTL is equivalent to a test of H0: bp = 0. It was assumed that the random gametic effects G as the gametic relationship matrix68. These random gametic effects were included to account for the stratification of the population into families. Analysis 2B considered additive effects only by neglecting 0: ba = 0 was performed for each marker separately.To estimate the ePOEs  for each parent together with their respective reliabilities, the phenotypic information from the progeny in the last generations were summarised by applying a reduced et al.41 for breeding values, which is described in detail in the Supplementary Material for ePOEs. To define parameter c, which is needed to calculate the weightings, a grid search was conducted, where c was progressively increased with a step size of 0.05 according to a proposal in Gorjanc et al.69. The c-parameter generating the greatest log-likelihood was chosen for each considered marker.With regard to the analyses 3A, 3B, and 3C, the deregression, PA-correction and weighting of the ePOEs were achieved by adapting the approximate method published in Garrick et al.27. The reduced imprinting model was used to estimate the ePOEs as well as the TAs.The ePOEs and parental TAs as well as their reliabilities were derived from an imprinting analysis of Brown Swiss cattle slaughterhouse data published in detail in Blunk 70, genotypes were excluded based on low frequencies (MAF < 0.05) and a Hardy-Weinberg equilibrium test (p ≤ 10−5). Neither animals nor genotypes were dismissed due to bad genotyping quality as missing genotypes were imputed beforehand (BEAGLE version 3.3.271).Genotype information was acquired from two versions (v1 and v2) of the BovineSNP50 BeadChip . Thirty SNPs map to the same position (base pairs). Note that they were kept for the analyses. Using PLINK version v1.07F-test using ASReml (Release 3.065). To control the type I error rate, the significance threshold of p-values was adjusted according to the genome-wide FDR72. Weaker signals only exceeding a chromosome-wide FDR of 5% were additionally reported. The unexplained genetic variance due to the relationships between sires was captured by including the inverse of the additive genomic relationship matrix73. The matrix was constructed with all available markers, i.e. the marker tested was not excluded from the matrix74. As it was not of full rank, its blending73 with 5% of the numerator relationship matrix A was required. Matrix A only contained the relationships between the animals with genotypes and was generated using the kinship2 R-package version 1.6.475 in R76.The genome was scanned via single marker regression, where ePOEs (defined as deviations of the TAs as dam from the TAs as sire), the TAs as sire and the TAs as dam were regressed on their marker gene counts individually. The marker effect’s deviation from zero was tested by conducting a conditional Wald http://genome.ucsc.edu/) based on the Bos Taurus UMD3.1.1/bosTau8 (assembly date: Dec. 2009). Pairwise LD between SNPs was specified as r2 estimated using Haploview (version 4.277). Information about the known imprinting status of genes was derived from the geneimprint database49.Except otherwise specified, all positions of SNPs and further genetic information were obtained from the UCSC Genome Browser (Supplementary Information


Heterosis, a multigenic complex trait extrapolated as sum total of many phenotypic features, is widely utilized phenomenon in agricultural crops for about a century. It is mainly focused on establishing vigorous cultivars with the fact that its deployment in crops necessitates the perspective of genomic impressions on prior selection for metric traits. In spite of extensive investigations, the actual mysterious genetic basis of heterosis is yet to unravel. Contemporary crop breeding is aimed at enhanced crop production overcoming former achievements. Leading cotton improvement programs remained handicapped to attain significant accomplishments.1 hybrids derived from Line × Tester mating design were evaluated under 10 diverse environments. Heterosis, GCA and SCA were estimated from morphological and fiber quality traits by L × T analysis. For the exploration of elite marker alleles related to heterosis and to provide the material carrying such multiple alleles the mentioned three dependent variables along with trait phenotype values were executed for association study aided by microsatellites in mixed linear model based on population structure and linkage disequilibrium analysis. Highly significant 46 microsatellites were discovered in association with the fiber and yield related traits under study. It was observed that two-thirds of the highly significant associated microsatellites related to fiber quality were distributed on D sub-genome, including some with pleiotropic effect. Newly discovered 32 hQTLs related to fiber quality traits are one of prominent findings from current study. A set of 96 exclusively favorable alleles were discovered and C tester (A971Bt) posited a major contributor of these alleles primarily associated with fiber quality.In mentioned context, a comprehensive project was designed involving a large collection of cotton accessions including 284 lines, 5 testers along with their respective FHence, to uncover hidden facts lying within heterosis phenomenon, discovery of additional hQTLs is required to improve fibre quality. To grab prominent improvement in influenced fiber quality and yield traits, we suggest the A971 Bt cotton cultivar as fundamental element in advance breeding programs as a parent of choice.The online version of this article (10.1186/s12864-018-5129-4) contains supplementary material, which is available to authorized users. Gossypium covers economically sustainable and diverse amount of diploid as well as tetraploid cotton species grown in most of the regions worldwide  obtained via STRUCTURE with ΔK (ad hoc statistic), K value was precisely estimated . On the 2 of each pair of microsatellites was calculated using the software package TASSEL 2.1 based on rapid permutations in 1000 shuffles with rare alleles  treated as missing data [2 distribution for unlinked markers, which determined whether LD is due to physical linkage, was treated as the background LD level [2 values of each pair of microsatellites were plotted against map distance (Mbp), and LD decay was estimated. By utilizing Sigmaplot version 12.5 an inner fitted trend line i.e., nonlinear logarithmic regression curve was sketched in order to elaborate the affiliation between r2 and Mbp of microsatellites prevailing on single chromosome.To estimate LD pattern in Upland cotton genome, the weighted average of squared correlation coefficient ring data . Every lLD level . The r2 2 values of each significant association. The detail of genotypic and phenotypic data combinations used in the TASSEL analysis is given in Table Mixed linear model (MLM) was used to construct markers-fiber quality trait association tests using the TASSEL 2.0.1 software package . For theSignificantly, associated loci were further scrutinized for determining the favorable alleles respective of their targeted traits on the basis of association results previously obtained. This phenotypic effect value was calculated through comparison between the average phenotypic value over genotypes with specified allele and that of all genotypes:However,ai: phenotypic effect of the ith alleleij: phenotypic value over the jth accession with the ith allelexni: number of accessions with the ith alleleNk: phenotypic value over all accessionsnk: number of accessionsai came larger than zero then allele was considered with a positive effect, otherwise with negative effect.If value for Additional file 1:1s. (DOCX 19 kb)Estimates of the weighting coefficient (Eigen vector) associated with the principal components and different characters of Parents and FAdditional file 2:Summary of significant associations between markers and Phenotypic traits. (XLS 44 kb)Additional file 3:Association of fiber quality and agronomic traits with microsatellites (XLS 56 kb)Additional file 4:Association table displaying 46 microsatellites significantly (log10 > 3) associated with fiber quality and agronomic traits. (XLS 110 kb)


In this paper we analyzed whole-genome genetic information provided by GAW20 from the Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study for family data. Lipid levels such as triglycerides (TGs) and high-density lipoprotein (HDL) are measured at different time points before and after administration of an anti-inflammatory drug fenofibrate. Apart from that, the data contain some covariates and whole-genome genotype information. We propose 2 novel approaches based on Henderson’s iterative mixed model to identify associated loci corresponding to (a) inflammatory biomarkers like TGs and HDLs together over time, and (b) the response to fenofibrate treatment. We developed a mixed-model approach using both TG and HDL phenotypes at all 4 time points for a genetic association study whereas we used TGs only to study genetic association with response to the drug. We expect that use of complete family data in a longitudinal framework under a single model involving the appropriate correlation structures would be able to exploit the maximum possible information contained in the sample. Our analysis of whole-genome single nucleotide polymorphisms (SNPs) and genomic regions corresponding to drug treatment finds no significant locus after multiple correction. Arguably, the moderately small sample size of the data set, as compared to the sample size usually used in genome-wide association studies (GWAS), could be a reason for such a result. Nevertheless, we report the top 20 SNPs associated with the phenotypes, and the top 20 SNPs and genomic regions associated with a response to fenofibrate treatment. Application of our methods to larger GWAS and further functional validation of the reported top SNPs and genomic regions might provide important biological insight into the genetic constitution of the trait. Understanding the genetic architecture underlying complex phenotypes is crucial in decoding disease mechanisms as well as treatment and drug development. Genome-wide association studies (GWAS) have contributed significantly to the identification of associated variants with numerous traits. Although the sample size requirement of GWAS is high, the proportion of the disease risk explained by a single variant always remains low. However, availability of longitudinal data on multiple phenotypes might carry more information in identifying associated variants. The Genetics of Lipid Lowering Drugs and Diet Network (GOLDN) study provides a data set with triglyceride (TG) and high-density lipoprotein (HDL) levels at 4 time points for a fixed set of families with few missing observations during follow-up. Consequently, given a moderate sample size, reduction of the multiple testing burden and/or use of longitudinal information is required. Moreover, with available data on multiple interacting phenotypes, it is informative to study both the inherent environmental correlation and the genetic correlation.Increased levels of TG and decreased HDL levels are well-known causes of heart disease. So we developed one model that captures the genome-wide genetic association with interacting phenotypes, that is, TG and HDL, over time by introducing both a temporal covariance structure and a genetic covariance structure between phenotype measurements. Our method is expected to increase power as a result of the inclusion of more information through genetic and environmental correlation structures.On the other hand, fenofibrate is an antiinflammatory drug, well known for TG-lowering effects. Some studies report modulation of a lipid response to fenofibrate as the result of genetic variants involved in lipid metabolism , but the0) of no association. During imputation, we assumed constant heritability, and this value was from an existing study , gn is the genotype vector for n individuals at a single marker locus, uTG and uHDLare random effect vectors for n individuals, and ZTG = ZHDL = 14 ⊗ In is the corresponding matrix. Here K is the kinship matrix, Var(εTG) = ΣTG ⊗ In, Var(εHDL) = ΣHDL ⊗ In,where ρTG1, , ρTG2,  and ρTG3, . Similarly we define βTG and ΣHDL. Now, denoting ρg and ρε as genetic and environmental correlations respectively, we assume the correlation structure as:where We test the null hypothesis of no genetic association of an SNP with TG and HDL using a likelihood ratio test. The asymptotic distribution of the log-likelihood ratio statistic can be shown to follow a Y is the vector of changes in phenotype (measured as log-log of TG) before and after the drug treatment; X is the design matrix of covariates, namely, age, smoking status, and SNP/genotypes in a genomic region (not in linkage disequilibrium); β is the associated fixed effect parameter; Z is the design matrix of random components; u is the random effect of the family; and ε is the error component. We assume K is the kinship matrix and u. Hence, R appears in the variance-covariance matrix of ε.To address our second objective , we model our data using Henderson’s mixed-model approach with adequate modification. Incorporating correlation structure among family members, we propose our model asr2 > 0.5). The genomic regions are basically (a) the genic regions, and (b) the intergenic regions lying between 2 consecutive genes, that overlap the genotyped SNPs in our data. We use Henderson’s iterative procedure for mixed model approach  prov provY anH0 : Mβ = 0 for an arbitrary p × q matrix M with rank(M) = p. Thus, if n be the number of observations and rank(M) = p, the test statistic [So to test the association of (a) whole-genome SNPs and (b) genomic regions, with response to the drug treatment, our null hypothesis will be, tatistic ,4\documeWe developed the above procedure to test association of multiple SNPs (genomic regions), which reduces the multiple-testing burden. However, this test can be seen as a single-marker association test that we have used to perform our GWAS study with appropriate multiple-testing correction.TPTE2 in an intron. rs2880301 is reported to be associated with HDL particle diameter and low-density lipoprotein (LDL) particle diameter [p value in Table 1-antitrypsin level [With longitudinal information using multiple phenotypes we identified only 1 significant SNP  genic, that overlap the genotyped SNPs, and (b) intergenic, that lie between 2 consecutive genes and overlap the genotyped SNPs in the data set. After BH correction, none of the SNPs nor genomic regions showed significant association with the drug response  GWAS using longitudinal data and (b) GWAS/genomic region association with response to fenofibrate treatment based on a family-based design. These methods are agnostic to the choice of phenotype and can be generalized to any such study. Although we could not detect any novel biologically relevant locus that is significantly associated with response to fenofibrate treatment, we identified a few loci that are associated with TG and HDL levels. Our belief is that the primary reason for obtaining only a small number of significant association findings is the much smaller sample size in our analyses as compared to conventional GWAS. Validation in a larger sample might throw more light on the roles of the top few significantly associated SNPs and/or genomic regions in controlling TG and HDL levels. Nevertheless, this study emphasizes the effect of administering fenofibrate to individuals with specific genetic profiles.We pruned the available set of SNPs to an independent set of SNPs in our GWAS, primarily to reduce the multiple-testing burden. Because many studies impute SNPs, and hence augment the number of available SNPs, to explore association findings for previously reported SNPs that have not been genotyped, our strategy has a caveat in the sense of reduction in the overall power of the GWAS. Similarly, while our proposed method involves simultaneous testing of multiple SNPs within a gene in order to evaluate association at the gene level, it may yield lower powers compared to the usual single SNP analyses in GWAS.We imputed the missing phenotype data using a known heritability value  and haveAssociation findings based on any real data set are susceptible to being false positives. If these findings validate previous reports of association, they are more likely to be true positives. In case of novel significant findings, it is necessary to either validate them in an independent data set or, alternatively, to perform extensive simulations under similar genotype and phenotype structures to evaluate the false-positive rates of the underlying test procedures.


To understand the pathophysiology of complex diseases, including hypertension, diabetes, and autism, deleterious phenotypes are unlikely due to the effects of single genes, but rather, gene-gene interactions (GGIs), which are widely analyzed by multifactor dimensionality reduction (MDR). Early MDR methods mainly focused on binary traits. More recently, several extensions of MDR have been developed for analyzing various traits such as quantitative traits and survival times. Newer technologies, such as genome-wide association studies (GWAS), have now been developed for assessing multiple traits, to simultaneously identify genetic variants associated with various pathological phenotypes. It has also been well demonstrated that analyzing multiple traits has several advantages over single trait analysis. While there remains a need to find GGIs for multiple traits, such studies have become more difficult, due to a lack of novel methods and software. Herein, we propose a novel multi-CMDR method, by combining fuzzy clustering and MDR, to find GGIs for multiple traits. Multi-CMDR showed similar power to existing methods, when phenotypes followed bivariate normal distributions, and showed better power than others for skewed distributions. The validity of multi-CMDR was confirmed by analyzing real-life Korean GWAS data. In genome-wide association studies (GWAS), genotype data from a large number of single nucleotide polymorphisms (SNPs) are collected, to associate SNPs with traits of interest . Not onlIn many cases, a phenotype is considered, and there are various studies on statistical methods for finding GGIs, for univariate phenotypes. For studying qualitative traits, as in the case-control studies, one simple way for identifying genetic interaction is to fit a logistic regression model (LRM) that includes main effects and relevant interaction terms. However, LRMs perform poorly when there is a dimensionality problem. Another well-known approach is a multifactor dimensionality reduction (MDR) method , 4, whic t-test to compare the means of the two groups. More recently, cluster-based MDR (CL-MDR), which is less sensitive to outliers and distributional assumptions, was also developed , ∑k=13Mik = 1. Mik is the membership degree of the ith subject in group Ck, ck is the center of the cluster Ck, Mi3 is the membership degree of the noise cluster, m(>1) is the fuzzifier parameter which defines the group's fuzziness , and δ is a squared distance of each data point to the noise cluster. such that Step 2. Trim the data and calculate the global ratio.(i)C1 and C2. The membership degree of the ith subject in group Ck   is given byData are trimmed by removing all the samples in the noise cluster. The remaining samples have membership degrees for each of the two groups. Denote these two groups as  (ii) θ:Calculate global ratio Mik is the membership degree of the ith subject in cluster Ck.where Step 3. Divide the samples by N-folds.For N-folds, split the cross-validation (CV) samples randomly into N subgroups of equal size. Let N-1 sets of samples be the training dataset and let the remaining dataset be the test dataset used for evaluating the model. Step 4. Calculate the local ratio.(i)mth-order gene-gene interactions, select a set of m SNPs from a pool of SNPs. Calculate the local ratio θj for the jth genotype combination in the training set. θj is the ratio of the sum of membership degrees of the samples belonging to C1 to that belonging to C2:To find the Mijk is the membership degree of the ith subject with the jth genotype combination, in cluster Ck.where (ii)D1,” if θj ≥ θ, or “D2,” if θj < θ. Label each genotype combination either “Step 5. Calculate the test statistic.(i)T2 statistic, for both training and testing datasets, to test differences of the mean vectors between the D1 and D2 groups:Calculate Hotelling's  where n1 is the number of observations in group D1 and n2 is the number of observations in group D2; xi1 is ith observation of D1; xj2 is jth observation of D2.(ii) The model with the largest statistic in the training data is chosen as the best model. Statistics for the test data will be performed later. Step 6. Find the final best model and obtain the empirical p-value.(i)Repeat Steps 4 and 5 N times, for each fold, and count the number of specific SNP combinations for the best model. We call this cross-validation consistency (CVC).(ii) Find the best final interaction model, i.e., the one with the largest CVC.(iii) T2 statistics for the test data and let this statistic be T2test.Derive the final statistic for the best model by averaging N (iv)B permuted datasets by shuffling only the phenotype vector Yi across individuals while fixing the genotype vector Xi. This way of shuffling nullifies the association between the phenotype and genotype vectors, while preserving the correlation structures within their components. Perform the multi-CMDR and calculate T2 statistics for each permuted dataset. B test statistics are in T2null. The empirical p-value is calculated asTo evaluate the statistical significance of the best model, perform a permutation test and obtain the empirical p-value. Generate I(x) is indicator function, returning 1 if x is true, otherwise 0.where In this section, we conducted simulations to compare the performance of the proposed multi-CMDR method, with multi-QMDR and univariate QMDR methods. We also compared the performance of the two versions of multi-CMDR. One version is a nontrimmed version of multi-CMDR. That is, the noise cluster is not generated in the fuzzy clustering step. The other version uses k-means clustering, without considering membership score. For multi-QMDR methods, the First Principal Component (FPC) was used to classify each cell into high- or low-risk groups, as previously described . For a uWe then generated a multivariate normal distribution and a multivariate gamma distribution for phenotypes. We used 70 different penetrance functions that define a probabilistic relationship with disease-causal interaction. The models consisted of 7 different heritability values  and 2 different minor allele frequencies . A total of 5 models for each of the 14 heritability-minor allele frequency combinations were considered. Thus, a total of 70 models were generated. The details of the 70 penetrance functions are given in . For eveY = T, were associated with SNP1 and SNP2, respectively, and were generated from the bivariate normal distribution,fij is the element from the ith row and jth column of a penetrance function, representing the two functional interacting SNPs. From this, we considered 3 different ρ  s  :  ρ = 0, 0.25, 0.5. We used R software to generate simulation data. For multivariate normal distributed cases, we used mvrnorm function in MASS package in R.For the multivariate normal distributed case, two continuous phenotype values, The hit-ratios for each heritability values are reported in c represents the copula density, f1,f2 are marginal probability density functions, and g is joint density function. The Gaussian copula density is then defined as follows:ui = Fi(yi), i = 1,2, and Φ−1 is the inverse cumulative distribution function of the standard normal distribution; F1, F2 are marginal cumulative distribution functions. The forms of two gamma distributions, f1(y1) and f2(y2), are as follows:ρ s  :  ρ = 0, 0.25, 0.5. For multivariate gamma distributed cases, we used mvdc,normalCopula,rMvdc functions in copula package in R.For the skewed distribution, we generated bivariate gamma distribution using Gaussian copula . In the In To sum up, the power of proposed multi-CMDR is similar to that of multi-QMDR, for symmetric distribution while it outperformed multi-QMDR for the skewed distribution. Moreover, the powers of the two different versions of multi-CMDR were also slightly better than those of multi-QMDR, in skewed phenotype distributions. For all situations, multivariate methods performed better than univariate methods. Results for each combination of two minor allele frequency (MAF) values and 5 models are presented in the supplemental materials  project , were cost and 2nd-order SNP combinations, identified by the proposed multi-CMDR. In addition to the best model, which has the highest CVC, We then applied the proposed multi-CMDR to search for the best second interaction model, again by using 10-fold CV. st-order analysis, rs1106280 was selected as the best model with the highest CVC. rs11066280 was identified as significantly associated with metabolism, TGs, and HDLs [nd-order analysis from univariate analysis of HDL using QMDR [−3.For 1and HDLs , 15 and ing QMDR . The thind-order analysis, the proposed multi-CMDR identified the best two SNP combinations, rs11216126 and rs4244457, where rs11216126 is reported to be related to HDL [st- and 2nd-order analysis, using a multi-QMDR method for testing association with LDL [nd-order interactions.For 2d to HDL . rs42444with LDL , 19. EacD1, if the local ratio is greater than or equal to the global ratio; otherwise the observations are assigned to D2.For GGI analysis for multiple quantitative traits, we proposed multi-CMDR. Analyzing correlated multivariate phenotypes was shown to have higher power to detect susceptible genes and GGIs, by using more information from data . The maiT2 statistic were used to select the best model. In the simulation study, we showed that the proposed multi-CMDR could be used effectively in case of bivariate gamma distribution. While the proposed method did not seem to have advantage of computing time over the multi-QMDR method, it was higher for the skewed distribution. In real-life data analysis, multi-CMDR detected the best SNPs and 2-way interactions for lipid-related traits . The best SNPs, selected by our method, have been reported to associate with similar traits [This proposed multi-CMDR was shown to be less sensitive for outliers and nonsymmetric distributions than other methods. 10-fold cross-validation and Hotelling's r traits , 15–19. nd-order interaction, while multi-CMDR took 19.3947 seconds on average. That is, when the number of SNPs is small, the difference in computation time is small. R program to conduct multi-CMDR is available at our github repository (https://github.com/stat17-hb/Multi-CMDR).In terms of computation time efficiency, multi-QMDR was slightly faster than multi-CMDR. Using an AMD Ryzen 2700x desktop machine with 16G RAM, multi-QMDR took 145.8841 seconds on average (100 repetitions) to conduct real data analysis for the first-order interaction, whereas multi-CMDR took 162.7906 seconds on average. For simulation dataset with 400 sample size and 20 SNPs, multi-QMDR took 17.3334 seconds on average to conduct the 2For the analysis of GGIs associated with multiple quantitative traits, we proposed a new extension of the MDR algorithm that includes clustering. Using fuzzy k-means clustering, we divided samples into two groups and trimmed outliers in noise cluster. By fuzzy k-means clustering, we can capture numerous attributes of multivariate data. Therefore, this is a very productive way to use values calculated from clusters to set thresholds to assign observations to specific groups, in that the proposed multi-CMDR uses a fuzzy k-means clustering method. Unlike k-means clustering, where each observation is assigned to only one cluster, fuzzy k-means clustering provides each observation with a degree of membership to each cluster. Fuzzy k-means clustering is especially useful when the cluster boundary is not clear, and it also allows outliers to be clustered into a noise cluster and reflects individual membership degrees of elements in the same cluster. We expect that multi-CMDR would improve the identification of gene-gene interactions associated with numerous multifactorial human pathologies.


Gadus morhua), four large chromosomal rearrangements have been associated with ecological gradients and migratory behavior in regional analyses. However, the degree of parallelism, the extent of independent inheritance, and functional distinctiveness of these rearrangements remain poorly understood. Here, we use a 12K single nucleotide polymorphism (SNP) array to demonstrate extensive individual variation in rearrangement genotype within populations across the species range, suggesting that local adaptation to fine‐scale ecological variation is enabled by rearrangements with independent inheritance. Our results demonstrate significant association of rearrangements with migration phenotype and environmental gradients across the species range. Individual rearrangements exhibit functional modularity, but also contain loci showing multiple environmental associations. Clustering in genetic distance trees and reduced differentiation within rearrangements across the species range are consistent with shared variation as a source of contemporary adaptive diversity in Atlantic cod. Conversely, we also find that haplotypes in the LG12 and LG1 rearranged region have diverged across the Atlantic, despite consistent environmental associations. Exchange of these structurally variable genomic regions, as well as local selective pressures, has likely facilitated individual diversity within Atlantic cod stocks. Our results highlight the importance of genomic architecture and standing variation in enabling fine‐scale adaptation in marine species.Genomic architecture and standing variation can play a key role in ecological adaptation and contribute to the predictability of evolution. In Atlantic cod ( Understanding parallel evolution in wild populations has long been central to evolutionary biology; genomic evidence has recently indicated an important role for chromosomal structural variation in parallel adaptation. Atlantic cod show repeated evidence of local adaptation across diverse marine habitats, with recent evidence implicating the involvement of a series of chromosomal rearrangements. We explore the distribution and trait and environmental associations of these chromosomal rearrangements within populations range‐wide. We find that across the North Atlantic contemporary adaptation and individual‐based biocomplexity in Atlantic cod is frequently underlain by shared chromosomal rearrangements. Understanding the processes underlying parallel genomic adaptation is a fundamental goal in biology and can clarify to what extent evolution is deterministic , a heavily exploited, demersal, broadcast spawning marine fish, provides a study system well suited to investigate the extent of modularity and parallelism among genomic architectural features. Atlantic cod exhibit high connectivity and dispersal, but also show divergent adaptation and genetic structuring associated with genomic architectural variation  individuals genotyped at 6,669 informative SNPs genotyped in all populations, corrected for strand flips, and filtered to remove SNPs with ambiguous genotype coding across datasets.To identify population structure and genome architecture variation across the range of Atlantic cod, we combined five datasets that were previously genotyped using the same 12K SNP array, along with additional samples from the Flemish Cap genotyped using the same array  and t‐distributed stochastic neighbor embedding (t‐SNE), a nonlinear machine‐learning clustering algorithm , as the goal of the previous study was to identify the primary driver of individual genetic structuring within the Northern cod stock around Newfoundland and Labrador.To quantify individual genetic variation, we separated individuals into geographic groups from Canada North, Canada South, Gilbert Bay, Flemish Cap, Iceland and Northeast Artic, and Coastal Europe Figure a,b. Thes2.4parallelstructure . Because categorization of chromosomal orientations into rearranged and nonrearranged categories requires phylogenetic comparison across multiple species to test the origin of rearranged regions, we use “rearranged” genotype and “nonrearranged” genotype designations only to characterize alternative chromosomal states, but follow designations used by Berg et al.  between each SNP using plink 1.9 , Canada South (n = 490 SNPs), Iceland and Northeast Arctic (n = 618 SNPs), and Coastal Europe population clusters (n = 730 SNPs). We visualized linkage between outlier SNPs using an LD heatmap in the superheat R package  scores exceeding a threshold identified by MDA drop‐off inferred from binning of MDA scores. SNPs with MDA values below this threshold exhibited low power in predicting environmental features. Random forest regressions were conducted using the We explored genetic associations with migration phenotype for all individuals in Europe using all 6,669 SNPs, following the association methods used in Kess et al.  in Northp < .05, as the goal of this test was to quantify direction of association.To determine the direction of association between environmental and migratory variables and rearrangement frequencies, we calculated Pearson's correlation between the frequency of each rearrangement and each environmental variable. We assessed significance at a lenient 2.7r2) between each SNP and all environmental variables: principal component, minimum, maximum and mean values for salinity, temperature, and dissolved oxygen. We calculated separate correlations for each SNP that was identified as significantly associated with environment in RDA in Europe and in North America. We then produced a separate pairwise Euclidean distance matrix for Europe and North America from distances between SNPs and their associations across variables and carried out hierarchical clustering on each matrix using Ward's hierarchical clustering algorithm in R using the hclust function. Loci that exhibit shared patterns of association across multiple environmental variables will be found in the same cluster using hierarchical clustering; these clusters represent proxies for functional modules. The R package superheat was then used to visualize patterns of shared associations using paired dendograms and heatmaps.We examined patterns of SNP co‐association to uncover groups of loci that exhibited similar patterns of associations across multiple environmental variables. As in Lotterhos et al. , we calc2.8FST and XYd across linkage groups LG1, LG2, LG7, and LG12 between individuals with each rearrangement genotype in North America and Europe and calculated nucleotide diversity (π) separately for each rearrangement genotype in North America and Europe. FST calculations were carried out in the diveRsity R package , concentrated in four known rearrangements on LG1, LG2, LG7, and LG12  indicated that variation in principal components of salinity, oxygen, and temperature was strongly associated in with LG1, LG2, LG7, and LG12 rearrangements in both North America and Europe Figure a,b. RandRedundancy analysis and random forest classification have been previously used to identify an association between migratory behavior and the LG1 rearrangement in North America  and rearranged genotype individuals in LG12 , but were not significantly different in LG2. Nonrearranged genotype individuals also exhibited reduced FST in the structurally variable region of LG7 . In contrast, LG12 nonrearranged genotype individuals  values differed between rearranged and nonrearranged groups on LG1; rearranged genotype individuals in Europe  and North America  had lower nucleotide diversity than the remainder of the chromosome  and North America .Observed nucleotide diversity (e Figure e–f. We f4Genomic architecture and standing variation can be crucial in determining evolutionary trajectories, particularly for instances of parallel evolution (Bolnick et al., We demonstrate low interchromosomal linkage of rearranged regions, suggesting independent evolutionary trajectories for each rearrangement. These results are contrary to previous findings of high interchromosomal linkage between rearranged regions (Bradbury et al., We found a shared pattern of migratory association of the LG1 rearrangement in independent polygenic association tests in Europe and North America. Associations of LG1 with migratory phenotype found here are consistent with past genome scan studies using migratory and nonmigratory ecotypes from waters around Europe (Berg et al., Consistent with past studies using single‐locus association methods, we also find polygenic association of rearrangements with temperature, salinity, and oxygen availability in North America and Europe (Barney, Munkholm, Walt, & Palumbi, Pinus contorta, indicating physical separation among loci is not always necessary for adaptation to different environmental variables (Lotterhos et al., Using multivariate co‐association and clustering, we show that SNPs within each rearrangement exhibited similar patterns of environmental co‐association. However, some SNPs overlapped in environmental associations between the rearrangements, suggesting a subset of loci are adapted to a shared set of environmental variables across rearrangements. This observation is consistent with these SNPs exhibiting functional modularity despite physical linkage. A similar pattern has also been observed among environment‐adapted genomic regions in Atp1a1 gene, although the stickleback study focused specifically on multiple derived populations (Roesti, Gavrilets, Hendry, Salzburger, & Berner, We find signatures of adaptation from shared variation across the Atlantic for chromosomal orientations specific to each chromosome. Using differentiation‐based and genetic distance comparisons, we show low trans‐Atlantic differentiation between the rearranged orientation of LG1, and LG12, and the nonrearranged orientation of LG7, suggesting selection on shared variation in these regions in both Europe and North America. These patterns of localized reduced differentiation are consistent with incorporation of these genomic regions into the genetic architecture of adaptive traits from shared variation (Barrett & Schluter, Pitx1 regulatory regions (Chan et al., Astyanax cavefish has also arisen from independent deletions within the Oca2 locus (Protas et al., FST and XYd, suggesting diversity‐reducing sweeps in these regions. However, low precision due to low density of SNPs, ascertainment bias, and high variance in XYd when applied to SNP data may bias measures of diversity and divergence (Wakeley, We also uncovered elevated trans‐Atlantic differentiation in the nonrearranged orientations of LG1 and LG12, indicating distinct evolutionary histories of these chromosomal regions in Europe and North America. The identification of elevated trans‐Atlantic divergence within rearranged LG1 and LG12 genotype individuals suggests gene content in these regions may be amenable to repeated selection during ecological specialization in Atlantic cod. Repeated divergence of the same genomic region has been found to underlie parallel evolution of pelvic spine reduction in threespine stickleback through repeated deletions within Wakeley, . Future Shared, modular, structural variation is hypothesized to be integral to ecological adaptation and may facilitate repeatability of the genomic architecture underlying parallel adaptation. We show that modular, shared chromosomal rearrangements are associated with ecological adaptation within Atlantic cod. Additionally, we show that separate divergence in LG12 and LG1 rearrangements has occurred in North American and European populations, revealing a nonparallel component to adaptation within the same, structurally variable region of the genome. Our findings here also provide new understanding of biocomplexity organized at different spatial scales within this species. Substantial cryptic variation is mediated by these rearrangements, indicating different adaptive potentials among cod stocks. Understanding and conserving this variation may be crucial in mitigating anthropogenic impacts on Atlantic cod such as those imposed by climate change and overharvest.None declared.TK, SJL, IRB, and PB designed the study. TK, EVAS, and RF carried out statistical analyses. PB, IRB, MS‐W, MPK, and SL provided the molecular data. TK drafted the manuscript, and all authors contributed to writing and editing of the final manuscript. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file. Click here for additional data file.


AQP4 and KCTD1. However, neither this locus nor the other 16 suggestive loci reached a significant p-value in the validation cohort. The h2 estimate was 0.54 (sd: 0.30) and was significant . The top three genetic correlations of IHI were with traits representing either intelligence or education attainment and reached nominal P< = 0.013.Incomplete hippocampal inversion (IHI), also called hippocampal malrotation, is an atypical presentation of the hippocampus present in about 20% of healthy individuals. Here we conducted the first genome-wide association study (GWAS) in IHI to elucidate the genetic underpinnings that may contribute to the incomplete inversion during brain development. A total of 1381 subjects contributed to the discovery cohort obtained from the IMAGEN database. The incidence rate of IHI was 26.1%. Loci with P<1e-5 were followed up in a validation cohort comprising 161 subjects from the PING study. Summary statistics from the discovery cohort were used to compute IHI heritability as well as genetic correlations with other traits. A locus on 18q11.2  showed a significant association with the presence of IHI. A functional annotation of the locus implicated genes  Human hippocampi are small structures, one in each temporal lobe that belongs to the brain’s limbic system and is known to be mainly involved in memory processes such as long term memorisation and spatial navigation . The limGiven that recent evidence implicates developmental processes in the aetiology of IHI and the observation that the structure and shape of subcortical structures, including the hippocampus, are under genetic control , we aimehttp://www.chd.ucsd.edu/research/ping-study.html). PING was launched in 2009 by the National Institute on Drug Abuse (NIDA) and the Eunice Kennedy Shriver National Institute Of Child Health & Human Development (NICHD) as a 2-year project of the American Recovery and Reinvestment Act. The primary goal of PING has been to create a data resource of highly standardized and carefully curated magnetic resonance imaging (MRI) data, comprehensive genotyping data, and developmental and neuropsychological assessments for a large cohort of developing children aged 3 to 20 years. The scientific aim of the project is, by openly sharing these data, to amplify the power and productivity of investigations of healthy and disordered development in children, and to increase understanding of the origins of variation in neurobehavioral phenotypes. Access to the dataset was granted through a Federal Wide Assurance (FWA). For up-to-date information, see http://www.chd.ucsd.edu/research/ping-study.html and [Subjects were investigated from two cohorts: IMAGEN  and PINGhtml and . All metth and the 5th temporal lobe convolution (https://github.com/cclairec/viewerIHI_java). During scoring each criterion received a score between 0.0 and 2.0. The first three criteria have a step size of 0.5, the fourth criterion is binary (0 or 2), and the 5th criterion, assessed between 0 and 2, has a step size of 1.0. The sum of those criteria forms the overall IHI score ranging from 0.0 to 10.0. This is a semi-continuous score (with a step of 0.5), where an IHI score of 0.0 indicates the total absence of IHI, and a score of 8.0 represents a very pronounced presentation of IHI. In their previous study [The procedure for scoring IHI , which hvolution ; (3) thevolution . Each crus study  establisFor this genetic study, the phenotype was IHI in either left or right hippocampus. To determine IHI, we applied the same cut-off of 4.0 for left and right hippocampi and used, for the IMAGEN cohort, the previously processed data from the IMAGEN study .http://www.well.ox.ac.uk/~wrayner/tools/). Haplotype reference consortium (HRC) v1.1 [https://imputation.sanger.ac.uk) using EAGLE2 [IMAGEN subjects were genotyped from blood samples on 610-Quad SNP and 660-Quad SNP arrays from Illumina. Genetic data was available for 1,841 subjects. In a first round of quality control (QC) we performed subject-level QC by removing subjects with mismatching self-reported sex and genotype inferred sex (N = 10) or where more than 10% of SNPs were missing (N = 0). Next, we performed ancestry matching based on the HapMap3 data . PopulatRC) v1.1  SNPs werg EAGLE2  for pre-g EAGLE2  for impuping-dataportal.ucsd.edu). Ancestry and admixture proportions in the PING participants were based on the ADMIXTURE software [PING subjects were genotyped from saliva samples on Human660W-Quad arrays from Illumina. After QC, genetic data for 1,391 participants was suitable for analysis. Individual SNPs of the PING dataset were accessed through the PING data portal (software  and downsoftware ). We reshttps://analysistools.nci.nih.gov/LDlink/) was used to identify a proxy in LD (r2) within +/- 50kb of the top SNP’s location. Association with single SNPs was tested in R using the glm function; the logistic model was corrected for age and sex.The genome wide association study was carried out with Plink v1.9  assuminghttp://fuma.ctglab.nl/). In order to elucidate the functional consequences of genetic risk loci, FUMA approaches the mapping in two separate steps: first, lead SNPs are identified and mapped to relevant genes on the basis of strand proximity, expression quantitative trait loci (eQTL) and chromatin interaction; second, the reprioritized genes returned by the first step are annotated with respect to expression levels and overrepresentation in differentially expressed gene sets among a wide range of human tissues.The GWA summary statistics were annotated using the web-based version of the FUnctional Mapping and Annotation (FUMA) tool  (http://2>0.6 in the 1000 Genomes Phase 3 EUR panel) and with a minimum MAF of 1%. Positional mapping was performed by linking lead SNPs to genes in a 50kb window. Mapping based on eQTL was performed by using only SNP-gene pairs significant at FDR<0.05 in all tissues/cell types from 4 data repositories ; the avnes from . We alsones from . The Maj2 Read Per Kilobase per Million (RPKM+1)) of protein-coding genes in 53 tissues from GTEx v6 were visualized through heat maps, allowing for comparison of expression level across genes and tissue types. Candidate genes were tested for overrepresentation in sets of differentially expressed genes (DEG), as well as sets of genes up- and down-regulated, across 53 specific tissue types from GTEx v6 using hypergeometric tests. The same gene-set enrichment analysis strategy was applied to test for overrepresentation of biological functions among the prioritized genes, using gene sets from the Molecular Signatures Database version 5.2 [After mapping lead SNPs to relevant genes, we performed annotation of the prioritized genes in biological context, mainly with respect to tissue-specific expression levels. Average expression levels .Given the reported higher prevalence of IHI in patients with epilepsy, we used LD score regression to compute the genetic correlation  between http://www.brainspan.org/rnaseq/search/index.html). The data comprises post-mortem gene expression data of 42 subjects at ages spanning from prenatal development (eight post conception weeks) till adulthood (40 years). Brains were sampled across 26 brain structures. Gene expression was measured using RNA-sequencing and expression levels for each gene were provided as reads per kilobase of exon model per million mapped reads (RPKM). We analysed this data using a linear mixed effects model implemented in the lme4 package in R. In these analyses, the gene expression level was the target variable, subject ID and structure ID were random effects, while an indicator variable for age less than 25 weeks post conception was the fixed effect. We tested for the significant effect of age<25 post conception weeks (pcw) on gene expression. This threshold was selected based on the estimated occurrence of hippocampal inversion between pcw 20 and 30 [In order to explore the transcription pattern of two candidate genes, we downloaded their expression values from BrainSpan through the web interface  were statistically significantly enriched  in overexpressed genes in hippocampal and caudate tissue from GTEx v6  for seven loci, intermediate (0.25 < r2 < 0.9) proxies for five loci and weak proxies for the remaining five loci (r2 < 0.25). None of the selected candidate SNPs showed a nominal significant association (uncorrected p < 0.05) with IHI in this cohort. The top SNP from the discovery cohort, rs9952569, was not significant in the validation sample and showed an effect in the opposite direction  and statistically significant using a one-sided test . We next sought to identify genomics regions or cell type marker genes that show enriched heritability. However, none of the tested genomic regions or gene sets showed statistically significant enrichment after FDR correction  between IHI and epilepsy susceptibility. The estimate of rg was -0.0854 (0.2612) which did not reach statistically significance .FDR<0.05). A total of 20 traits reached nominal significance  100 are depicted in KCTD1 remains rather stable across the entire time frame, while the expression of AQP4 starts very low and increases with the progression of brain maturation and reaches its peak around the time of term birth (pcw 37–40). Gene expression was significantly different before and after pcw 25 for both KCTD1 (p = 3.115e-04) and AQP4 (p = 2.424e-07) when limited to data acquired before pcw 40.We extracted the gene expression levels in the developing brain for KCTD1 and AQP4. Of note, the locus showed consistently strong association with continuous scales of the IHI phenotype. Furthermore, a genome-wide screen of those continuous scales revealed two genome-wide significant loci  gene negatively regulates the AP-2 family of transcription factors and the Wnt signalling pathway, which controls normal embryonic development, cellular proliferation and growth [KCTD1 have been linked to Scalp-Ear-Nipple syndrome [KCTD1 has the ability to influence developmental processes. Thus, it is conceivable that more benign variation in KCTD1 may play a role in the generation of IHI. Furthermore, KCTD1 is a potassium channel gene and various members of the potassium channel gene family have been linked as causes of epilepsy [KCTD1 gene reached p-values as low as 0.0003758  gAQP4) is a bidirectional water channel that is found on astrocytes throughout the central nervous system  and drastically lowered the statistical power to detect differences (power of 35% for just the top variant). Larger validation cohorts are needed to confirm the association of the identified locus with IHI: e.g., to validate the top variant with 80% at least N = 500 subjects are required. Although there are growing imaging and genetic datasets, e.g., the UKBB that aims at 100,000 participants with genetics and brain imaging data, few studies focus on healthy younger subjects , which is beneficial for the validation in order to exclude confounding by disease processes or age-related atrophy. One such option is the Philadelphia Neurodevelopmental Cohort (PNC) . Howeverh2 = 0.54; the estimate was subject to high uncertainty as reflected by the high standard deviation of 0.3, which is likely a direct reflection of the low sample size of the discovery cohort. Analysis on twin data, such as the healthy young adult twins participating in the Queensland Twin IMaging (QTIM) study [h2 is comparable to recently published estimates on the heritability of hippocampal volume and shape from more than 3600 subjects [h2 ranges from 0.08 to 0.337 depending on hemisphere and structural measure, with heritability of volume being generally the lowest. Given the impact of IHI on hippocampal shape and appearance together with the high prevalence of IHI in nearly 25% of healthy subjects, it is likely that the observed heritability of hippocampal shape reported by [We estimated heritability of IHI based on the state-of-the-art LD score regression method that operates on the GWAS summary statistics. The inferred heritability was substantial with M) study , can be subjects ; h2 rangWe used the generated genome-wide summary statistics for two additional explorations. First, we sought to investigate if heritability was enriched in any particular region of the genome, characterized by its function or by marker genes for specific cell types. None of the investigated categories achieved statistical significance after FDR correction. Second, we computed genetic correlations with other traits. We hypothesized that there may be genetic link with epilepsy, however the resulting correlation was non-significant and negative, i.e., people with IHI were less likely to be affected by epilepsy, thereby contradicting earlier reports. The exploratory analysis with 832 additional traits highlighted a positive genetic correlation between IHI and intelligence and education attainment. There are various reports highlighting the contribution of the hippocampus and its subregions to various mental aspects that collectively are referred to as intelligence, e.g., spatial processing  and workIn conclusion, we presented the first genome-wide association study of IHI, where we identified a genome-wide significant locus. Additional exploration of the resulting summary statistics revealed a high heritability and suggested positive genetic correlation of IHI with traits linked to intelligence and education attainment.London: Psychiatry, Nursing and Midwifery (PNM) Research Ethics Subcommittee (RESC), Waterloo Campus, King's College London. Nottingham: University of Nottingham Medical School Ethics Committee. Mannheim: Medizinische Fakultaet Mannheim, Ruprecht Karl Universitaet Heidelberg and Ethik-Kommission II an der Fakultaet fuer Kliniksche Medizin Mannheim. Dresden: Ethikkommission der Medizinischen Fakultaet Carl Gustav Carus, TU Dresden Medizinische Fakultaet. Hamburg: Ethics board, Hamburg Chamber of Phsyicians. Paris: CPP IDF VII (Comité de protection des personnes Ile de France), ID RCB: 2007-A00778-45 September 24th 2007. Dublin: TCD School of Psychology REC. Berlin: ethics committee of the Faculty of Psychology. And Mannheim's ethics committee approved the whole study. All informed consents have been obtained from a parent and/or legal guardian. Written informed assent and consent were obtained, respectively, from all adolescents and their parents after complete description of the study. For the PING dataset, written parental informed consent was obtained for all PING subjects below the age of 18, and child assent was also obtained for all participants between the ages of 7 and 17. Written informed consent was obtained directly from all participants aged 18 years or older.S1 FigThe panels show pairwise scatter plots for the first five principal components of the genetic relationship matrix. The HapMap3 subjects are represented as filled circles and color coded by population (see legend in the top left panel). IMAGEN participants are represented by black open circles; red open circles indicate subjects that were excluded based on distance to the CEU+TSI European ancestry.(TIF)Click here for additional data file.S2 FigQQ plot for the genome-wide association study. The xaxis shows the expected -log10 while the y-axis shows the study -log10. There was no evidence of p-value inflation λ = 1.017.(TIF)Click here for additional data file.S3 FigUpper plot: Result for the sum of the five criteria and then maxed over left and right hippocampus. Two loci exceed the genome wide significant threshold: on chromosome 6 rs35806781  and on chromosome 9 rs186025034 . Lower plot: Result for the global criterion presenting 3 classes: 0 = non IHI, 2 = IHI, 1 = partial IHI, and taking the max over left and right hippocampus. One locus exceeds genome-wide significance on chromosome 9: rs186025034 .The y-axis depicts the -log10 of the association between SNP and presence of IHI assuming an additive model in the discovery cohort. The SNPs tested in the study are ordered along their chromosomal position on the x-axis. The red horizontal line donates genome wide significance at the Bonferroni threshold (P = 5e-8), while the blue horizontal line marks the threshold for suggestive association (P = 1e-5). (TIF)Click here for additional data file.S4 FigLeft: chromatin interaction plot, mapping the genome-wide significant locus to six genes on chromosome 18. Right: expression heatmap (average log2(RPKM) in 53 GTEx tissues) for the four mapped protein-coding genes.(TIF)Click here for additional data file.S5 FigThe four prioritized genes are tested for enrichment in tissue-specific gene lists for 53 tissue from the GTEx dataset. Each list of differentially expressed genes is split into overexpressed and underexpressed genes. P-value threshold for significance was the Bonferroni corrected threshold for 3 * 53 tests (p<0.000314). Tissues showing significant enrichment are indicated by red bars.(TIF)Click here for additional data file.S6 Fig(TIF)Click here for additional data file.S7 FigThe x-axis shows the subjects’ age in weeks post conception (pcw). The y-axis depicts the mean of the log2 RPKM (reads per kilobase per million) provided by BrainSpan. AQP4 and KCTD1 are indicated by different colors.(TIF)Click here for additional data file.S8 Fig(TIF)Click here for additional data file.S1 Table(CSV)Click here for additional data file.S1 File(DOCX)Click here for additional data file.