Genome-Wide Association (GWA) with population-based imputation (PBI) has been successful in identifying common variants associated with complex diseases; however, much heritability remains to be explained and low frequency variants (LFV) may contribute. To identify LFV, a study of unrelated individuals may no longer be as efficient as a family study, where rare population variants can be frequent in families. Family-based imputation (FBI) provides an opportunity to evaluate LFV. To compare the performance of PBI and FBI, we conducted extensive simulations, generating genotypes using SeqSIMLA from various reference panels for families. We masked genotype information for variants unavailable in Framingham 550 K GWA genotype data in less informative subjects selected by GIGI-Pick. We implemented IMPUTE2 with duoHMM in SHAPEIT (Impute2_duoHMM) for PBI, MERLIN and GIGI for FBI and PedBLIMP for a hybrid approach. In general, FBI in both MERLIN and GIGI outperformed other approaches with imputation accuracy greater than 0.99 for the squared correlation and imputation quality scores (IQS) especially for LFV, although imputation accuracy from MERLIN depends on pedigree splitting for larger families. PBI performed worst with the exception of good imputation accuracy for common variants when a closely ancestry matched reference is used. In summary, linkage disequilibrium (LD) information from large available genotype resources provides good imputation for common variants with well-selected reference panels without requiring densely sequenced data in family members, while imputation of LFV with FBI benefits more from information on inheritance patterns within families yielding better imputation. Genotype imputation derives from statistical inference of genotypes that are not directly assayed. In recent decades, genotype imputation has been commonly used in genome-wide association studies (GWAS) since it provides the same set of single nucleotide polymorphisms (SNPs) to collaborating studies, thereby enabling researchers to combine genotype-phenotype association results from participating cohorts using different genotyping platforms. Thus, genotype imputation efficiently increases the effective sample size and improves statistical power to detect disease variants with moderate effects. Genotype imputation strategies can be broadly classified into population-based methods, which use population linkage disequilibrium (LD) information, and family-based methods, which use inheritance information within pedigrees.2, represent most common genetic variation in human populations. LD or correlation between nearby SNPs is used to predict unobserved genotypes in a study sample with a sparser set of variants. For example, IMPUTE23 was developed as a population-based imputation method that improves upon previous approaches by using both the reference and study samples to inform haplotype phasing at observed markers. SHAPEIT2 duoHMM4 further improves upon phasing in family-based studies with a hidden Markov model for identity by descent (IBD), with results incorporated into an IMPUTE2 analysis.Population-based methods impute unobserved SNPs using a reference panel of subjects with complete observations on a more comprehensive set of SNPs. These reference panels, such as HapMap and 1000 Genomes5 and larger samples are needed to identify variants with weaker effects and/or lower frequency. Whereas we once thought that only a few genes/variants might be associated with disease, we have now reconfirmed the paradigm that the genetic determinants of many complex diseases derive from a polygenic model comprising many genetic variants with small effects9.The era of GWA with population-based imputation has been highly successful in identifying common variants associated with many diseases and their risk factors. Nevertheless, GWAS have not explained all genetic variation in association with the diseases and risk factors that affect large numbers of U.S. individuals. Much genetic variation remains to be explained10.To identify low frequency variants (LFV), a population study of unrelated individuals is no longer an efficient study design. Family studies offer an effective, and less expensive, option to pursue such variation with adequate power, as rare population variants will be more frequent in families where a founder has the variant. Further, multiple rare variants in a gene in several families may act in a similar fashion on traits. Hence, linkage studies or collapsed rare variant analyses in such families may have improved power compared to studies of unrelated individuals and also provide identification of those variants that are segregating through the family with the trait12 uses pedigree structure to identify inheritance vectors within a family, then propagates genotypes at high-density markers observed in a subset of individuals to others in the pedigree. GIGI (Genotype Imputation Given Inheritance)13 uses a two-stage procedure to infer inheritance vectors at sparse markers, then uses MCMC sampling to estimate genotypes of a dense marker set. With the growing availability of whole genome sequences, family-based imputation may provide improved strategies for imputing rare variants. In this paper, we compare two family-based imputation (FBI) methods to population-based imputation (PBI) as well as a hybrid version that combines FBI and PBI.Thus, imputation in family studies provides an opportunity to evaluate rarer variants and their effects on disease and associated risk factors. Several methods have been proposed for situations where some family members have been genotyped on a dense set of markers, and other members have only sparse marker genotypes measured. For example, Merlin14 using LD information from external panel data and IBD information from internal family data.We carried out a series of simulations to evaluate the performance of PBI and FBI strategies in several scenarios. Figure 16. For FBI, we implemented two approaches for imputation. One is GIGI, where imputation for each member of a family follows estimation of the pattern of genetic transmission within the family based on the observed genotype data17. We used MORGAN for this estimation of inheritance vectors18. The second FBI approach was implemented in MERLIN, which performs estimation of inheritance vectors for families and does not require an additional step for haplotype estimation12. Additionally, we considered a hybrid approach, PedBLIMP, which calculates the covariance matrix for LD information from an external panel and then estimates IBD for each locus to obtain the locus specific relatedness matrix14. We briefly describe each approach.We estimated unknown haplotypes from typed genotypes (e.g. GWA array variants), known as phasing, for each subject with SHAPEIT (both with and without using the duoHMM feature) and followed by genotype imputation for PBI implemented via IMPUTE24.Haplotype phasing and inheritance vector estimation are essential steps in PBI and FBI. We used SHAPEIT version v2-790 to pre-phase prior to PBI. SHAPEIT estimates haplotypes from directly measured genetic variants (e.g. array-based genotypes) before imputing genotypes for those un-typed variants from a denser reference haplotype panel. This pre-phasing step improves the imputation speed since the haplotype estimation needs to be done only once. We considered two scenarios in haplotype phasing. One ignored relatedness information within families and another improved phasing by incorporating family information through a hidden Markov model (duoHMM)For FBI, we used PLINK 1.9 to perform LD-based SNP pruning, with window size of 50 SNPs and shifted by 5 SNPs at each step, to construct a list of SNPs in approximate linkage equilibrium with pairwise LD r2 < 0.2 from available directly genotyped data. The SNPs in linkage equilibrium identified by this analysis were selected from simulated data and used to estimate the number of alleles shared IBD among relatives in a pedigree in MERLIN. We used the same SNPs to infer inheritance vectors summarizing the pattern of genetic transmission through pedigrees, based on estimated genetic locations of meiotic events with the gl_auto routine in MORGAN 3.1. The same process was used for PedBLIMP.19. Briefly, the algorithm used kinship coefficients for splitting and trimming each large pedigree into multiple smaller sub-pedigrees of a user pre-specified size . The basic steps started with clustering un-genotyped individuals with their un-genotyped first-degree relatives and then constructing sub-pedigrees based on these clusters and their genotyped relatives. The same procedure applied to the sub-pedigrees until their bit sizes meet the pre-selected size. Essentially, each sub-pedigree produced was centered on one or more un-genotyped individuals with as many closely related genotyped relatives as possible. In the case where an individual was included in multiple sub-pedigrees, imputation was performed using one sub-pedigree at a time and the imputations with the best quality for an individual were used for further analysis.An important property of MERLIN is that it can only evaluate smaller pedigrees. For the scenario where pedigrees exceed the computational limit for imputation in MERLIN, we used a pedigree splitting algorithm previously described3. IMPUTE2 can use either unphased genotype data or phased haplotype data to estimate unobserved genotypes. However, pre-phasing lowers the computational time significantly; hence we phased our data first with SHAPEIT before conducting imputation with IMPUTE2.We used IMPUTE2 v2.3.0 to impute genotypes for untyped (masked) variants using several reference panels20, in which posterior probabilities of the three possible genotypes at each SNV are calculated. MERLIN imputation can be very rapid and efficient in small pedigrees; however, the complexity of Lander-Green algorithm increases exponentially with pedigree size. Pedigree size 12 used in our study is sufficiently small for this algorithm21. For pedigree size 40, sub-pedigrees were constructed as described above.For FBI, we consider three implementations: MERLIN v1.1.2, GIGI v1.04, and PedBLIMP v0.2.0. MERLIN uses dense genotype data from a subset of individuals in a pedigree to infer missing genotypes in remaining relatives, who may or may not have sparse genotype data. It first uses low-density genotypes in all family members to estimate the number of alleles shared IBD in a pedigree. Then, with IBD and high-density genotype data in a subset of family members, unobserved high-density genotypes for remaining members can be imputed. The imputation implemented in MERLIN uses the Lander-Green algorithmGIGI uses a two-step procedure to impute dense genotypes in pedigrees where only a few members have high-density genotype or sequence data available, and most members have been genotyped on a sparse set of “framework” markers in linkage equilibrium. After summarizing the pattern of genetic transmission through the pedigree as inheritance vectors, using MORGAN, the second step uses the inferred inheritance vectors and all available dense marker sequence data to impute unobserved genotypes by estimating locations of meioses and filling in variants between framework markers.14 extends the population-based method BLIMP22, which uses conditional multivariate normal moments to impute genotypes with LD information from an external panel, by additionally taking the pedigree structure or IBD information into consideration. PedBLIMP first builds a precomputed shrinkage covariance and mean of genotypes from the reference panel data, and then imputes SNP data using the expected relatedness matrix calculated from the pedigree structure.PedBLIMPFigure 23 to generate genotype data for family members  and the 1000 Human Genome Metropolitan Panel ; H2: Haplotype information from UK10K only; H3: one-third of haplotype information randomly selected from UK10K   on chromosome 20 was selected as it contains variants with a full range of minor allele frequency (MAF) from 0.028% to 49.98%. The majority of variants were less frequent: the proportions of variants with MAF >5%, 1–5% and <1% were 19.3%, 9.2% and 71.4% in the H1 pool, respectively. In addition, we selected this region to be large enough to contain various LD structures, a strong LD block and a weak/mild LD block, and small enough to handle the multiple simulations in the current study. There are 26,308 variants in total within this region. To mimic reality, we assumed that dense genotypes were observed only for ‘informative’ family members. Informative family members were identified with GIGI-PickWe considered three scenarios for selecting which members of the pedigree have dense genotype information from the sequence data Fig. . The firFor reference panels for IMPUTE2, we considered: R1: combined haplotype information from 1000 G and UK10K; R2: 1000 G only; R3: one-third of UK10K without overlapping with H3 haplotype pool; R4: two-thirds of UK10K from the complementary set of the H3 haplotype pool. For PedBLIMP, we used R2:1000 G as the reference panel.24. Therefore, we used the squared correlation and IQS as measures of imputation quality for comparisons among different imputation methods.Several measures of imputation performance are available to evaluate imputation quality, for example, concordance, squared correlation and imputation quality score (IQS) with the true sequence genotypes. Concordance between imputed and true simulated genotypes uses the best guess genotype and thus, depends on the threshold of the posterior probability for the best guess. As a result, it overestimates the accuracy for rare or less common variants due to random chance of concordance. In addition, by using the best guess and ignoring the posterior probability for the best guess, it ignores the uncertainty of imputed genotypes that is reflected in the dosage. Prior literature has shown lower power in association analyses that use the best guess compared to those methods that use genotype dosage or take uncertainty of imputed genotypes into considerationThe squared correlation estimate for each SNP is the squared Pearson correlation between the masked true genotypes, which take values of 0, 1, 2, and the imputed dosages, which take values in the range . Squared correlation estimates are not very reliable measurements of the accuracy for rare variants. For example, the squared correlation of a SNP with low minor allele frequency is unmeasurable because either the true genotypes or the imputation dosages might be identical for all individuals. We used the squared correlation here to compare the different imputation approaches and to contrast with the IQS.et al.26. IQS measures the agreement between two classifications, adjusting for chance agreement. The calculation of IQS requires the posterior probabilities of imputed genotypes. Denote nij as the number of individuals with true genotype i and imputed additive genotype j, n.j as the total number of individuals with imputed genotype j, ni as the total number of individuals with true genotype i and n.. is the total sample size. IQS is calculated by subtracting the chance agreement Pc from the observed agreement Po and dividing by the maximum possible value of the numerator: We also consider the imputation quality score (IQS), originally inspired by Cohen’s Kappa statistic and developed by Lin et al.26.IQS incorporates the uncertainty of imputation by using posterior probabilities for genotypes instead of the best-guess genotype, thus avoiding potential bias caused by the selection of a threshold for posterior probability. IQS is useful for rare variants because it accounts for allele frequency and adjusts for chance agreement. IQS can be computed using dosages, yielding more information on imputation quality. Details of IQS can be found in Lin As described, genotypic data were generated from three sources ; imputation was performed using five imputation methods  along with four reference panels  for imputation  and IQS close to 1  performed worst even with the ideal reference panel except for variants with MAF greater than 20% where it slightly outperformed FBI. The variability of the estimated accuracy was larger in Impute2_unrel than other approaches. However, variabilities were consistently low, especially for MERLIN and GIGI. Hence, variability information is not provided hereafter. We also evaluated a larger pedigree of size 40, selected from the Framingham Heart Study, where MERLIN requires splitting the whole pedigree into sub-pedigrees. We evaluated two options for maxbit: 18 and 20. MERLIN with maxbit 18 retains imputation quality as good as GIGI while there is a clear drop in imputation quality for MERLIN with maxbit 20  and the reference panel (1000 G) Fig. . In addiWe further evaluated the imputation accuracy using different reference panels Fig. . The hapIt is not uncommon that DNA samples are unavailable for an earlier generation while other clinical variables are available for analysis. Including these individuals’ imputed genotypes will increase the sample size and power for downstream analysis. We evaluated the imputation results for the first generation individuals using the second and third generations’ genotype information (Supplemental Fig. We conducted intensive simulation to evaluate the performance of several strategies to impute missing genotypes. Our data demonstrated that FBI, specifically MERLIN and GIGI, provides better imputation quality in general when there are informative family members with available dense sequence data, while PBI, specifically Impute2_duoHMM, offers reasonable imputation quality for common variants especially when a closely related reference panel is used. In addition, MERLIN and GIGI produced imputation quality comparable to each other in small pedigrees; however, as a cautious point, MERLIN can only handle pedigrees of small or moderate size and requires splitting of large pedigrees, which has an observable effect on imputation accuracy. A separate effort to comprehensively describe the properties of MERLIN, especially the strategy on the splitting of large pedigrees, is needed.28. However, we still observed an apparent gap in the imputation accuracy compared to family-based imputation. Other studies suggest using a local reference or study-specific samples30, consistent with our observation in the ideal scenario for population-based imputation, an unusual case, where the haplotype sources are the same for target study samples and reference panel. The advantage for this type of approach comes from the potential population-specific haplotypes introduced by low frequency variants and a local reference panel can provide more precise haplotypes than publicly available reference panels of similar size. The information used for FBI shares similar merit as a local reference panel. However, the advantage of FBI is less likely to diminish even when publicly available reference panels grow with dense sequencing of more individuals as such an ideal scenario for population-based imputation may not be realistic. Additionally, imputation to family members, such as older generations, without genotype information is only applicable in a family-based approach.PBI has facilitated identification of common variants associated with complex diseases; however much genetic variation remains to be explained and less frequent variants may contribute. Various imputation approaches have been proposed to enhance imputation accuracy of rare variants. The growing size of available reference panels will provide better coverage of longer stretches of haplotypes32 showed that combining PBI and FBI of sequence data improves statistical power to detect rare variant associations. Lent et al.33 demonstrated that a sequential approach that uses PBI to increase the density of a sequenced reference panel before performing FBI further increases imputation accuracy. Results that are more powerful were observed through such approaches, but these only used information from LD and inheritance patterns indirectly. Recently, PedBLIMP14 uses both pedigree structure and LD information to define the genotype covariance matrix used in a linear prediction model. As observed in our simulation, the improvement of the imputation accuracy with this approach compared to the population-based imputation is obvious although there remains room for improvement compared to the family-based imputation.Leveraging the information from LD and inheritance patterns may improve genotype imputation. There may not always be enough family members with dense sequence data to obtain accurate inheritance vectors, although the family-based imputation clearly dominates the imputation accuracy. LD information from large publicly available genotype resources can provide imputation for common variants with a well-selected reference panel without requiring densely sequenced data in family members. Therefore, methods to use the strengths from both PBI and FBI may provide alternative strategies. Indeed, Saad and WijsmanOur study comes with several strengths and limitations. Among the strengths, first, we used UK10K plus 1000 G, the largest publicly available haplotype reference panel, at the time we started this project. The release of more dense reference panels will continue to improve PBI. Second, we conducted extensive simulations to systematically evaluate the accuracy of genotype imputation for FBI, PBI and hybrid strategies. Third, imputation to the earlier generation of individuals based on the available data in later generations was also evaluated. This evaluation provided useful information as it is relatively common to lack DNA data in earlier generations due to death or loss to follow up.Some limitations of our study include the fact that we primarily simulated a specific pedigree structure with three generations. This structure may provide more information in imputation than a trios study design but is less informative than more extended family pedigrees, such as family structures collected in the Framingham Heart Study. Larger pedigrees may affect the imputation accuracy for family-based imputation. However, MERLIN cannot be used in large pedigrees without splitting. We demonstrated this approach in one of our simulation settings. On the other hand, we assumed an ideal scenario that all informative individuals within the pedigree have dense genotypes, a circumstance that may not always be practical for various reasons such as cost or lack of DNA samples for genotyping. Considering information from related individuals, the imputation results and their downstream association analysis will depend on the selection of subjects to densely genotype. Third, to better evaluate imputation performance for rare variants, we conducted extensive simulations in a specific genomic region rather than simulating whole genome data, due to the computational constraints. However, the selected region has a wide range of allele frequencies and various LD structures; so we do not anticipate substantial changes in our findings should the simulation be done in the whole genome.32 where better imputed genotypes for each variant from either family-based or population-based imputation are used. Hence, an approach that can simultaneously use LD information from a large haplotype reference and extra information from related subjects may provide fruitful results in genotype imputation and identification of risk variants underlying complex disease.Imputation methods provide information on the distribution of possible genotypes at untyped variants for very little cost compared to direct genotyping or sequencing. As observed in our study, family-based imputation when informative individuals within a pedigree having dense genotypes outperformed population-based imputation even with haplotype phasing estimated using family relationships. This advantage was found in both common and LF variants while population-based imputation may provide relatively comparable results for common variants if closely ancestry-matched samples are available for the reference. Combining family- and population-based imputation data may provide an alternative option to improve imputation quality as suggested by Saad and WijsmanSupplemental Figures 1 and 2


Genetic improvement of honey bees is more difficult compared to other livestock, due to the very different reproductive behavior. Estimation of breeding values requires specific adjustment and the use of sires in the pedigree is only possible when mating of queens and drones is strictly controlled. In the breeding program of the National Registry for Italian Queen Breeders and Bee Producers the paternal contribution is mostly unknown. As stronger modeling may compensate for the lack of pedigree information, we tested two models that differed in the way the direct and maternal effects were considered. The two models were tested using 4003 records for honey yield, defensive and swarming behaviors of Italian honey bee queens produced between 2002 and 2014. The first model accounted for the direct genetic effect of worker bees and the genetic maternal effect of the queen, whereas model 2 considered the direct genetic effect of the queen without maternal effect. The analyses were performed by linear (honey production) and threshold (defensive and swarming behavior) single-trait models; estimated genetic correlations among traits were obtained by a three-trait linear-threshold model.For all traits, the highest predictability  was obtained with model 2, where direct genetic effect of queens was considered. With this model, heritability estimates were 0.26 for honey yield, 0.36 for defensive behavior, and 0.34 for swarming behavior. Multi-trait estimation resulted in similar or higher heritability estimates for all traits. A low, positive genetic correlation (0.19) was found between honey yield and defensive behavior, whereas the genetic correlation between honey yield and swarming behavior was moderate (0.41). A strong, positive genetic correlation was found between defensive and swarming behaviors (0.62). Predictability for multi-trait evaluations was higher for honey yield (0.46) and defensive behavior (0.30) but almost identical for swarming behavior (0.45) compared to corresponding single-trait predictability.Multi-trait evaluation using a model that accounts for the direct genetic effect of queen was the best approach for breeding value estimation of Italian honey bees. The results suggest a new direction for selection of linear and categorical traits in breeding programs where drone origin is unknown. Apis mellifera) represent a biologically and economically valuable species. They contribute to pollination of wild plants and crops and provide direct income to beekeepers who collect honey and other hive products from managed colonies. Programs for genetic improvement of honey bees have been developed and implemented  is as follows: E(r) = k × rEBV-BV, where k is a constant, being the ratio between standard deviation of true breeding values and that of phenotype ; and rEBV-BV is the correlation between true breeding value of the animal and the predicted (pedigree) breeding value.Models were compared for their fit and ability to predict future performance. For variance component estimates and heritabilities, standard errors were calculated. For ability to predict future performance, colony performance for 150 queens that had families with more than three members and known grandparents were removed from the dataset (reduced data). Estimated breeding values (EBV) were obtained using the reduced dataset for each tested model. Pearson correlation between EBV in the reduced data (− 12. The THRGIBBS1F90 program [− 12 for linear traits and THRGIBBS1F90, with an option to store solutions assuming variance components are known, for threshold traits.Honey yield was considered to be a continuous trait, whereas defensive and swarming behaviors were considered categorical traits with 5 classes. Because the origin of drones was not known in the considered breeding population, in preliminary analyses we introduced their influence using phantom drones or genetic groups in the pedigree file. These methods should allow more genetic ties between queens and colonies, but none of them improved estimation of genetic parameters and thus were not used. The AIREMLF90 software  was used program  was used program  was used program  and a co


SNP) density of genotyping arrays and relatedness between dogs on imputation accuracy due to the acknowledged genetic and pedigree structure of dog breeds. In this study, we simulated different genotyping strategies based on data from 1179 Labrador Retriever dogs. The study involved 5826 SNPs on chromosome 1 representing the high density (HighD) array; the low‐density (LowD) array was simulated by masking different proportions of SNPs on the HighD array. The correlations between true and imputed genotypes for a realistic masking level of 87.5% ranged from 0.92 to 0.97, depending on the scenario used. A correlation of 0.92 was found for a likely scenario , which indicates that genotype imputation in Labrador Retrievers can be a valuable tool to reduce experimental costs while increasing sample size. Furthermore, we show that genotype imputation can be performed successfully even without pedigree information and with low relatedness between dogs in the reference and validation sets. Based on these results, the impact of genotype imputation was evaluated in a genome‐wide association analysis and genomic prediction in Labrador Retrievers.The dog is a valuable model species for the genetic analysis of complex traits, and the use of genotype imputation in dogs will be an important tool for future studies. It is of particular interest to analyse the effect of factors like single nucleotide polymorphism ( The genomic relationship between dogs in the validation and in the reference sets was calculated for every scenario using gemma  Labrador Retrievers from the UK and has previously been used for studies of complex traits  software  were used for this study. Imputation accuracy was calculated using the most likely genotypes estimated by fimpute for all missing genotypes.To analyse the effects of genetic and pedigree characteristics on the performance of genotype imputation, scenarios were designed based on four criteria and are summarised in Table Size of the reference population: 10% (‘Ref10’), 50% (‘Ref50’) and 90% (‘Ref90’) of the dogs were randomly assigned to the reference population, and the remainder was assigned to the validation population.Use of pedigree information in imputation: Scenario 1 was repeated without pedigree information .n = 660). One offspring of each sire was randomly selected for the reference population, resulting in 206 dogs in the reference population and 454 dogs in the validation population (scenario ‘REL’). As a control, the same number of dogs as in REL was randomly sampled from the full dataset without considering pedigree information (‘REL‐C’).Relatedness between the reference and validation population: Only full‐sibs and paternal half‐sibs were used  the SNPs from the LowD array were masked as missing at 87.5% of the HighD array's SNPs. This was done by coding all SNPs as missing except every eighth SNP, when ordered by their position on CFA1. For these scenarios, the number of markers on the LowD array was similar to the number of markers on CFA1 on the 22K array that was previously available for dogs. The same masking procedure was applied for approach 4 but for different masking densities . Statistics describing the distribution of marker density on the HighD and LowD arrays are provided in Table For validation of imputation, 10 replicates were performed for all scenarios, except for REL, for which the dogs were randomly reassigned to either the reference or validation population and imputation was repeated. Each dog was used in the validation population a different number of times for the particular scenarios, for example, once out of 10 replicates for Ref90, five times for Ref50 and nine times for Ref90.Further, an analysis of variance was run for the measures of imputation accuracy to test for the effect of relatedness by comparing the REL to the REL‐C scenarios.sicurracy version 0.3.2  and the correlation between true and imputed genotypes (‘corr’) were computed to evaluate the success of imputation. The % correct was the proportion of correctly imputed genotypes out of all imputed SNPs. The corr measure was calculated using the R package  Edwards  as the Ps et al. , with alet al. . The SNPs were binned according to their MAF, as estimated in the HighD dataset, into the following MAF bins: [0, 0.025), [0.025, 0.05), [0.05, 0.075), [0.075, 0.1), [0.1, 0.2), [0.2, 0.3), [0.3, 0.4) and [0.4, 0.5), as described by Hickey et al. . The meaet al.  and the GWAS using imputed genotypes (GWASimputed), the correlation between the P‐values and the effect size of every marker was calculated. To estimate the breeding value with imputed genotypes of the same trait, the GBLUP method was applied using acta  were calculated for the imputed dataset and compared to that for the real dataset.A GWAS for the hip‐dysplasia‐related trait Norberg Angle right (NA_right), as described by Sánchez‐Molano et al. , and the  resulted in the highest percentage of correctly imputed genotypes (% correct = 98.6%) and highest correlation between true and imputed genotypes (corr = 0.95) when compared to scenarios with smaller reference populations (Ref50 and Ref10). Reducing the size of the reference population reduced % correct to 98.4% and 97.4% for Ref50 and Ref10 respectively Table . The corWhen imputation was carried out without pedigree information, both % correct and corr were reduced by a very small amount for all scenarios Table . For theP < 0.001). Moreover, corr (0.97) and % correct (98.8%) were higher for the REL scenario than for all other scenarios analysed in this study.Using the reference set of full‐ and half‐sibs (REL) increased % correct by 1% and increased corr from 0.926 to 0.972 compared to the control (REL‐C)  with a few outliers  ranged from 97.4% (Ref10NoPed) to 98.8% (REL) and the correlation between true and imputed genotypes (corr) ranged from 0.92 (Ref10NoPed) to 0.97 (REL).fimpute is a program that exploits pedigree information , relatedness between dogs in the reference and validation populations was maximised. Genotype imputation in the REL scenario performed better than in all other scenarios. This is consistent with previous studies in livestock, in which it has been shown that imputation accuracy is positively correlated with the number of genotyped ancestors  could be seen as a compromise between accurate imputation and a small number of SNPs to reduce genotyping costs. This would correspond to a genome‐wide ~22K array if our results are representative of the remaining chromosomes. Further work would need to be done on optimal spacing of markers on the LowD array, as some regions (e.g. the major histocompatibility complex region) might require denser coverage than others.et al. et al.  and improved as MAF increased. It is assumed that a low MAF hinders the construction of haplotypes, as only a small number of animals are carriers of the minor allele  to 117 dogs (Ref10) decreased imputation accuracy somewhat, in accordance with previous studies in livestock  and an ~22K array as a LowD array for the imputed population, reasonable imputation accuracies can be reached in dogs even without pedigree information and the weaker relatedness compared to livestock animals. In accordance, dogs with no relatives or unknown pedigree should be kept in the analysis because they may provide other valuable information. Nevertheless, our results and previous findings in livestock animals suggest that genotype imputation can be improved by informed assignment of dogs into the reference and validation populations.However, although genotype imputation from LowD arrays to HighD arrays is an appropriate approach for the identification of regions of interest in GWAS and genomic selection, genotype imputation from HighD arrays to WGS data should be considered for the dissection of complex traits and the analysis of rare variants.The authors declare that they have no conflict of interest.Table S1 Average genomic relationship between dogs in the reference and validation set for every scenario. For every dog in the validation set, the average and the maximum genomic relatedness  with the dogs in the reference set were calculated.Click here for additional data file.Table S2 Marker spacing (in kbp) on the HighD and LowD arrays for CFA1.Click here for additional data file.Table S3 Animal‐wise imputation accuracy (% correct and corr) for the 10 replicates of the control scenario REL‐C.Click here for additional data file.


Genomic Selection (GS) has been proved to be a powerful tool for estimating genetic values in plant and livestock breeding. Newly developed sequencing technologies have dramatically reduced the cost of genotyping and significantly increased the scale of genotype data that used for GS. Meanwhile, state-of-the-art statistical methods were developed to make the best use of high marker density genotype data. In this study, 14 traits from four data sets of three species  and five influential factors that affect the prediction accuracy were evaluated, including marker density (from 1 to ~600 k), statistical method , minor allele frequency (MAF), heritability, and genetic architecture. Results indicate that in the GBLUP method, higher marker density leads to a higher prediction accuracy. In contrast, BayesR method needs more Monte Carlo Markov Chain (MCMC) iterations to reach the convergence and get reliable prediction values. BayesR outperforms GBLUP in predicting high or medium heritability trait that affected by one or several genes with large effects, while GBLUP performs similarly or slightly better than BayesR in predicting low heritability trait that controlled by a large amount of genes with minor effects. Prediction accuracy of trait with complex genetic architecture can be improved by increasing the marker density. Interestingly, for simple traits that controlled by one or several genes with large effects, higher marker density can cause a lower prediction accuracy if the QTN is included, but leads to a higher prediction accuracy if the QTN is excluded. The quantity of genetic markers with low MAF would not significantly affect the prediction accuracy of GBLUP, but results in a bad prediction accuracy performance of BayesR method. Compared with GBLUP-A, GBLUP-AD didn't show any advantages in capturing the non-additive variance for the traits with high heritability. The factors that affected prediction accuracy are discussed in this study and indicate that a combination of either GBLUP or BayesR method with moderate marker density and favorable polymorphism single nucleotide polymorphisms (SNPs) (~25 k SNPs) would always produce a good and stable prediction accuracy with acceptable breeding and computational costs. The plant and animal breeding history experienced a long period of phenotypic selection and the genetic evolution progress was relative slow. In 1950s, Henderson developed Best Linear Unbiased Prediction(BLUP) method that can estimate the breeding value of each individual and had been widely used in livestock breeding  estimate the effects of genetic markers, and then (2) accumulate the effects to get the estimated breeding values (EBV) of each individual. The representative methods are ridge regression BLUP (RRBLUP) method and Bayesian alphabet methods , heritability, and genetic architecture of target trait. Along with the development of cost-effective genotyping technology, high density marker genotype are used in GS and tell more information, this may increase the prediction accuracy , days to silking (DTS), and anthesis-silking interval (ASI). All samples were planted under eight environments and DTA, DTS, and ASI were measured and calculated as described by Buckler et al. . Samplesp-values < 10−4. A total of 42,551 SNPs were remained after the data quality control and used in this study. Estimated breeding values of three traits are provided to validate the GS-relevant factors: milk fat percentage (MFP), milk yield (MY), and somatic cell score (SCS). MFP, MY, and SCS are representatives for traits with different genetic architectures: (1) one gene with large effect (major gene) and a large number of genes with small effects (MFP), (2) several genes with moderate effects and many genes with small effects (MY), and (3) many genes with small effects (SCS).The cattle dataset contains 5,024 German Holstein bulls and all the bulls were genotyped using the Illumina Bovine SNP50 Beadchip  with five traits  and BayesR method was performed by BayesR software (http://cnsgenomics.com/software.html).As GBLUP is the most widely used statistical method in GS, BayesR is well-known for its high prediction accuracy and always has similar or higher prediction accuracy than other Bayesian alphabet methods  and σEBVσy is amplified. The other reason is that the skewed phenotype distribution of SSK easily introduced a large sampling error in the cross-validation processes.Where In this section, various marker densities are designed to evaluate the prediction performances in AMES, NAM_US, Cattle and Pig-PIC populations. The results are shown in Three traits of AMES dataset are GDD, SSK, and YWK. All three traits have very high prediction accuracies because of the high heritabilities. Among three traits, the genetic architecture of GDD is relatively complicated and controlled by a big amount of genes. The prediction accuracy of GDD is increased with marker density in all three methods.Unlike GDD, both SSK and YWK are affected by one or two genes with very big effect. The prediction accuracies of SSK and YWK are increased with marker density when using GBLUP-A and GBLUP-AD methods. However, as the marker density increases, the prediction accuracy of BayesR method fluctuates up and down and not performs as well as GBLUP methods. One potential reason is that prediction accuracy of BayesR is limited by the premature convergence of MCMC iterations. The total number of MCMC iterations is set to 200,000 and BayesR needs a much more MCMC iterations to reach the convergence. The prediction accuracy of the SSK trait is improved with the increased number of maximum MCMC iterations and more detailed information can be found in All three traits in NAM population have high heritabilities and complex genetic architectures. The hypothesis of GBLUP model fits the complex traits well, GBLUP-A and GBLUP-AD perform better than BayesR in ASI trait and three methods perform similarly in DTA and DTS traits. For all three traits, prediction accuracies of all methods increased with marker density.Three traits in cattle population represent three distinct types of traits. MFP has high heritability and controlled by one major gene  and plenty of genes with minor effects; MY has medium heritability and also controlled by DGAT1 gene and some genes with medium and minor effects; SCS is a low heritability trait and controlled by a big amount of genes with minor effects. As the marker density of cattle data is moderate, the MCMC iterations reached convergence in all 10 replicates of cross validation procedure. The results indicate that BayesR outperforms GBLUP in the traits of MFP and MY and performs similarly with GBLUP in SCS trait. Prediction accuracies of three methods are increased with marker density in all three traits.Five traits in pig population of PIC have medium or low heritabilities. BayesR performs slightly better than GBLUP in predicting most traits and shows more advantages in T2 as it is controlled by several genes with big effects. Prediction accuracy slightly increased with marker density for each trait.Genetic architectures of SSK, YWK, and MFP traits are relatively simple and controlled by one or several genes with very large effects. However, the prediction accuracies of the “simple” traits are increased with marker density as well and this doesn't comply with common sense. To find out the reason, we simulated two traits for AMES and cattle populations with heritability equals one and only controlled by one QTN. Two scenarios were simulated, including “QTN included” and “QTN excluded.” The results are shown in All of SSK, YWK, and MFP traits are affected by large effect genes and the hypothesis of BayesR is better suited for the genetic architectures of three traits than GBLUP. But BayesR only outperforms GBLUP-A in MFP trait while GBLUP-A performs better in SSK and YWK traits. Higher marker density causes MCMC iterations hard to converge, and this results BayesR a bad performance in prediction accuracy. However, for SSK trait, when the maximum number of MCMC iterations was more than 300 k, the prediction accuracy became steady and it was still not comparable with GBLUP. Therefore, there may be some other factors affected the prediction accuracy of BayesR method.If there are plenty of genetic markers with low MAF included in the genotype data, more mistakes would be produced during evaluating the marker effects. SSK trait and 200 k genetic markers that have the lowest prediction accuracy were selected for this study. Genetic markers were filtered by five MAF thresholds, including 0.01, 0.03, 0.05, 0.1, 0.2, and the same amount of randomly selected genetic markers were also used in this study for comparison. The maximum number of MCMC iterations and burn-in iterations were set to 200/50 k. The results indicated that the MAF significantly affected the prediction accuracy and low MAF genetic markers would reduce the prediction accuracy performance of BayesR method. Filtered SNPs by MAF <0.2, BayesR method reaches the same prediction accuracy as GBLUP. In contrast, prediction accuracy of GBLUP was slightly affected by the low MAF genetic markers .Previous studies indicate that prediction accuracy increases with marker density and a moderate marker density is always enough. Our results showed that prediction accuracy would continuously increase with marker density in GBLUP methods, especially when the marker density is low . However, in the BayesR method, higher marker density requires much more MCMC iterations for the program to converge and get reliable prediction values. The default setting of BayesR parameters are 50,000 MCMC iterations with 20,000 burn-ins, this is usually enough for SNPs <50 k, but the risk of slow convergence or even no convergence increases with marker density.Statistical methods significantly affect the prediction accuracy. Whittaker et al. assume that all genetic markers contribute to the trait and the effect follows a same distribution that all marker effects have the same variance, and the method is called Ridge Regression BLUP (RRBLUP)  and a most commonly used marker effected based method (BayesR) for comparison. The results indicate that BayesR outperforms GBLUP for the trait with high or medium heritability and controlled by genes with large effects, such as the MFP trait in cattle data. However, in results of SSK and YWK traits that controlled by large effect genes, GBLUP performs better than BayesR. One reason is that the high marker density makes BayesR require more MCMC iterations. However, for SSK trait, when the maximum number of MCMC iterations is increased to more than 300 k, the prediction accuracy becomes steady and it is still not comparable with GBLUP. MAF significantly affected the prediction accuracy of marker effect based method—BayesR while slightly affected on the relationship based method—GBLUP. The results in Not surprisingly, traits with higher heritability have higher prediction accuracy. Interestingly, we find that the increased marker density significantly affects the prediction accuracy of traits with simple genetic architecture that affected by one or several genes with large effects. As we know, the DGAT1 gene significantly affects MFP trait in cattle and the YWK trait is controlled by Y1 gene in AMES maize data  Increased marker density leads to a higher prediction accuracy of GBLUP methods, meanwhile, it also increases the risk of slow convergence and no convergence of MCMC iterations in BayesR method and this may result in a low prediction accuracy; (2) Statistical methods have their advantages when the genetic architectures of traits being predicting meet the hypothesis. BayesR outperforms GBLUP for the trait with high heritability and affected by one or several genes with large effects, while GBLUP performs similar or slightly better than BayesR for the trait with lower heritability and controlled by a big amount of genes with minor effects; (3) Prediction accuracy of trait with complex genetic architecture can be improved by increasing marker density. For simple traits that controlled by one or several genes with large effects, higher marker density can also lead to a higher prediction accuracy if the QTN is unknown and not included; (4) Including low MAF genetic markers would cause a bad performance of prediction accuracy when using BayesR method while GBLUP method has more tolerance and affected little by the MAF; (5) As most of the tested traits in this study have high heritabilities, GBLUP-AD performs similarly with GBLUP-A and doesn't show any advantages by capturing the non-additive variance. The understanding of GS related factors may help the breeders to design a more powerful and efficient genomic breeding plan. A combination of either GBLUP or BayesR method with moderate density (~25 k) and favorable polymorphism SNPs would always generate a good as well as stable prediction accuracy with acceptable breeding and computational costs.https://onlinelibrary.wiley.com/doi/full/10.1111/tpj.13174 (maize-NAM_US), https://genomebiology.biomedcentral.com/articles/10.1186/gb-2013-14-6-r55 (maize-AMES), http://www.g3journal.org/content/5/4/615.long (cattle), and https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3337471/bin/supp_2_4_429__index.html (pig).Publicly available datasets were analyzed in this study. The datasets can be found at XL, HZ, and XY conceived the study. HZ and LY wrote the codes and did the data analysis. XL, MW, HZ, and LY drafted the manuscript and all authors contributed to finalizing the writing.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The structural equation modeling analysis revealed a heritability estimate of 0.52 for the CTC connectivity, suggesting a moderately strong genetic effect. Moreover, using an independent schizophrenia cotwin sample , we observed a significant linear relationship between genetic distance to schizophrenia and the connectivity strength in the CTC circuitry . The present data provide converging evidence that increased connectivity in the CTC circuitry is likely to be a heritable trait that is associated with the genetic risk of schizophrenia.Our recent study has demonstrated that increased connectivity in the cerebello-thalamo-cortical (CTC) circuitry is a state-independent neural trait that can potentially predict the onset of psychosis. One possible cause of such “trait” abnormality would be genetic predisposition. Here, we tested this hypothesis using multi-paradigm functional magnetic resonance imaging (fMRI) data from two independent twin cohorts. In a sample of 85 monozygotic (MZ) and 52 dizygotic (DZ) healthy twin pairs acquired from the Human Connectome Project, we showed that the connectivity pattern of the identified CTC circuitry was more similar in the MZ twins ( At the neural level, the genetic risk of schizophrenia embodies the dysregulation of behavior-specific neural circuits, which in turn increases the risk of developing corresponding behavioral defects3. Such neurobiological changes  have offered a valuable avenue to understand the pathogenesis of psychosis and to probe for effective prediction and intervention strategies.Psychotic disorders such as schizophrenia possess a strong genetic basis. Empirical data from research on twins and relatives have revealed an estimated heritability of ~80% and a 10-fold increase of risk in first-degree relatives of patients6. Such alteration can be reliably detected across multiple functional magnetic resonance imaging (fMRI) paradigms in individuals both at clinical high risk (CHR) and with chronic illness, suggesting a “trait” brain functional abnormality that is robustly present across the entire course of psychotic disorders. These findings highly suggest that increased connectivity in the CTC circuitry may be caused by genetic predisposition to psychosis.Our recent study has demonstrated that increased connectivity in the cerebello-thalamo-cortical (CTC) circuitry is a state-independent “trait” alteration that may potentially predict the onset of psychosis and distinguish the patients from the healthy population7), including a total of 85 monozygotic (MZ) healthy twin pairs and 52 dizygotic (DZ) healthy twin pairs. Using this sample, we examined the heritability of the connectivity of the CTC circuitry using structural equation modeling (SEM). The second data set was drawn from the Swedish Schizophrenia Twin Study , which included 40 schizophrenia discordant cotwins  and 32 healthy control twins. We specifically tested the relationship between genetic distance to schizophrenia and the CTC connectivity in this sample. We expected that the CTC connectivity is heritable in healthy twin pairs and is associated with degree of genetic risk of schizophrenia in schizophrenia cotwins (schizophrenia MZ cotwins > schizophrenia DZ cotwins > control twins).In this study, we tested this hypothesis using two independent twin data sets with multi-paradigm fMRI data. The first data set was part of the Human Connectome Project  and have genotyping data available. Among these twin pairs, 85 were MZ  and 52 were DZ . The STAR sample comprised of 40 schizophrenia discordant cotwins  and 32 healthy control twins , each assessed with a battery of two fMRI paradigms . The zygosity in both data sets was determined by genotyping data from subjects’ blood samples. The STAR participants were recruited through the Swedish Twin Registry and were evaluated by psychiatrists using the Structured Clinical Interview for DSM-IV9. The exclusion criteria for control twins included prior history of neurological or psychiatric disorders, head injury, substance dependence in the last 6 months, mental retardation, and inability to read or comprehend Swedish. All schizophrenia discordant cotwins were free of any psychotic disorders according to the DSM-IV criteria. The participants provided written informed consents and the research protocol was approved by the Regional Ethical Review Board in Stockholm. For sample details, see Tables Two independent twin data sets were used in this study: the HCP twin sample11. Notably, the resting-state paradigm was scanned with four sessions spanned across two consecutive days, and the other paradigms were scanned with two sessions on a single day. To balance the amount of data across paradigms and to avoid overrepresentation of resting state in the following cross-paradigm computations, we only used the resting-state data from the two sessions acquired on the first day. The STAR data set used two fMRI paradigms that have been described previously13. In brief, the spatial working memory task used an event-related design where subjects were asked to encode the location of three target circles and to indicate whether the ensuing probe circle appeared at the same location as one of the target circles. During the block-designed emotional face processing task, subjects were shown a series of emotional faces and geometric shapes and were instructed to match either the target faces or the target shapes.A total of eight fMRI paradigms were employed in the HCP project. For details on these paradigms see previously published work2, 2 mm slice thickness, 72 slices, multiband factor = 8. Of note, unlike the commonly applied phase-encoding directions along the “anterior-posterior” axis, the HCP fMRI data were acquired using left-right and right-left phase-encoding directions to accelerate scan time and to minimize image distortion11. Each paradigm was scanned with two sessions, with each direction per session. In addition, T1-weighted and T2-weighted images were acquired using 3D-MPRAGE and 3D-T2-SPACE sequences with 0.7 mm voxel size and 224 × 224 mm2 FOV. The T1 images used a TR of 2400 ms and TE of 2.14 ms, and the T2 images used a TR of 3200 ms and TE of 565 ms.The HCP data were collected from a customized 3T Siemens Connectome scanner equipped with a 32-channel head coil. BOLD images were acquired using a multiband GRE-EPI sequence with the following parameters: TR = 720 ms, TE = 33.1 ms, FA = 52°, FOV = 208 × 180 mm3. T2-weighted images were scanned using a spin-echo sequence with 4000 ms TR, 82 ms TE, and 4 mm slice thickness.The STAR data were acquired from a 1.5 T GE scanner equipped with a standard 8-channel head coil. GRE-EPI sequence was used for functional imaging: TR = 2500 ms, TE = 40 ms, FA = 90°, 3.5 mm slice thickness, voxel size 3.44 × 3.44 × 4.5 mmhttps://db.humanconnectome.org). The preprocessing procedure followed the standard HCP preprocessing pipeline including five major steps: PreFreeSurfer, FreeSurfer, PostFreeSurfer, fMRIVolume, and fMRISurface14. In brief, images were corrected for gradient nonlinearity induced distortion, head motion, and phase-encoding related distortion, registered to individuals’ T1-weighted images, and normalized to the MNI space. The STAR data were preprocessed using the standard pipeline implemented in the Statistical Parametric Mapping software , including slice timing, head motion realignment, functional-structural image coregistration, MNI space normalization, and spatial smoothing. All preprocessed images were further scrutinized for head motion using the measure of frame-wise displacement (FD15) to ensure data quality. All subjects in both data sets had a mean FD < 0.5 mm.The HCP data were downloaded after the completion of imaging preprocessing , white matter and cerebrospinal fluid signals, the 24 head motion parameters , and the FD. The corrected time series were then temporally filtered  to account for scanner and physiological noise. Subsequently, a 270 × 270 pairwise connectivity matrix was generated using Pearson correlation for each subject during each paradigm and scan session.The overall processing pipeline of this study is presented in Fig. 11, we averaged the derived connectivity matrices across the two sessions for each paradigm to boost signals, generating eight paradigm-specific connectivity matrices for each subject in the HCP data and two paradigm-specific connectivity matrices for each subject in the STAR data. The matrices for each subject were vectorized, concatenated across paradigms, and then decomposed into a set of principal components (PCs) using singular value decomposition (SVD). The first PCs generated from the analysis represented the shared CPC and were thus extracted. From these CPC matrices we further extracted the identified CTC network based on our prior work6.Following prior suggestions20. Specifically, using the SEM toolbox OpenMx implemented in R (https://openmx.ssri.psu.edu/), we decomposed the total variance of phenotype into additive genetic effects (A), dominant genetic effects (D), and unique environmental effects (E). In general, the MZ twins share 100% of additive and dominant genetic effects, while the DZ twins share 50% and 25% of additive and dominant genetic effects, respectively20. Based on this information, we estimated the squares of each path coefficients  that reflect the proportion of phenotypic variation attributable to the A, D, E effects, respectively. This was done by iteratively maximizing the log-likelihood between observed and predicted covariance matrices. The goodness-of-fit of the estimated model was quantified by −2 times the log-likelihood  as well as the Akaike Information Criterion , and was compared to the saturated model in which all covariances were treated as free parameters using Chi-squared test. A non-significant P value ( > 0.05) indicates a good model fit. Moreover, the full ADE model was further compared with nested AE, DE, and E models, and the most parsimonious model was determined by the one with the smallest −2LL and AIC values. Heritability (h2) was subsequently quantified as the proportion of phenotypic variance attributable to genetic effects in the most parsimonious model.The HCP data were employed to quantify heritability of the CTC connectivity. We first calculated the similarities of the MZ and DZ twin pairs using intra-class correlations. A larger correlation coefficient between MZ pairs compared with that between DZ pairs indicates a potential genetic effect. Since the MZ correlation was larger than twice of the DZ correlation in our sample (see Results section), we estimated an ADE model using structural equation modeling (SEM). This is due to the fact that dominant genetic effects (D) would decrease the DZ correlation relative to the MZ correlationWe examined the association between CTC connectivity and genetic risk of schizophrenia in the STAR data. Specifically, a linear regression model was employed where CTC connectivity was included as dependent variable and genetic proximity to schizophrenia , age, sex, and FD were included as regressors. A significant regression coefficient for genetic proximity indicates that CTC connectivity is associated with schizophrenia genetic risk. Since the size of STAR sample was relatively small, we further included all twins in the HCP sample as controls in the regression model. To control for discrepancy between the two data sets, cohort was included as an additional regressor in the model for the combined sample.P = 0.12 and 0.46, respectively). The intra-class correlation coefficients for CTC connectivity among MZ and DZ twin pairs in the HCP sample were 0.54 and 0.22, respectively, suggesting a genetic effect , and 48% was attributable to unique environmental effects (e2 = 0.48). In contrast, dominant genetic effects were estimated to be negligible (d2 < 0.001). There was no significant difference in comparison between the ADE model and the saturated model , indicating a good model fit for the present data. Moreover, the further comparison of the full ADE model with the nested models showed the smallest −2LL and AIC for the AE model , suggesting that the AE model is the most parsimonious and should be accepted as the model that best fits the data.There were no significant differences in the mean and variance of CTC connectivity between MZ and DZ twins in the HCP sample (P = 0.84). The regression analysis revealed a significant linear relationship between genetic proximity to schizophrenia and CTC connectivity in the STAR sample , which further supports the idea that CTC hyperconnectivity is likely to be a heritable trait that is associated with genetic predisposition to schizophrenia.The Levene test showed an equal variance of CTC connectivity between the three examined groups , suggesting a very trivial genetic effect. This supplementary analysis indicates that the heritability in CTC connectivity is unlikely to be driven by the heritability in head motion.Previous study has reported that head motion is moderately heritable during resting-state fMRI scansa2 = 0.38), 62% was attributable to unique environmental effects (e2 = 0.62), and common environmental effects were negligible (c2 < 0.001). This supplementary analysis again suggests that the variations in CTC connectivity are mainly caused by additive genetic effects and unique environmental effects.In this study, an ADE model was chosen to estimate heritability since the correlation of CTC connectivity between the MZ twins was larger than twice of that between the DZ twins. In a supplementary analysis we also estimated heritability using an ACE model. The ACE model showed a heritability of 0.38 (95% CI: 0.17–0.56). In particular, similar to the results from an ADE model, 38% of total variance was attributable to additive genetic effects . The power increased to 0.9 when comparing SZ-MZ cotwins and HC twins , suggesting that the present sample, although small, is likely to have been adequately powered.Because the STAR sample in this study was relatively small, we performed a power analysis to determine whether the study was adequately powered to detect the observed effect sizes. The power to reject the null hypothesis of no group difference was 0.7 for the comparison between SZ-MZ cotwins and SZ-DZ cotwins  signaling. Large-scale genome-wide association studies (GWAS) have identified a set of common genetic variants in glutamatergic genes in patients with schizophrenia, including, for instance, GRM3, GRIN2A, GRIA1, SRR, CLCN3, among others39. Gene expression and brain imaging analyses suggested a converging effect of these genes on brain structure and function, especially in the prefrontal cortex43, hippocampus43, and thalamus43. Moreover, pathway analysis also revealed a significant association of genetic variants in NMDAR complex and glutamate metabolism pathways with the pathogenesis of schizophrenia45. In addition to common variants, rare genetic mutations such as copy number variation have also been found to be highly enriched for genes involved in the glutamatergic and GABAergic neurotransmission48. These lines of evidence suggest that neurotransmission-linked schizophrenia genetic factors may affect excitation–inhibition balance in the human brain that further sets an over-excitatory tone for the overall brain connectivity. Such altered brain connectivity, especially in a CTC circuitry, is therefore presented as a “trait” abnormality that can be reliably detected across various states and phases of schizophrenia.Since CTC hyperconnectivity may reflect a downstream phenomenon of N-methyl-D-aspartate receptor (NMDAR) deficits50. Notably, dopamine system plays a key role in error processing in the brain. It is assumed that the prediction errors, which reflect the mismatch between the priors and outcomes, are encoded by the phasic dopamine neuron firing in the ventral-tegmental area (VTA) of the midbrain52. The activity of the VTA dopamine neurons alters the dopamine input to the mesolimbic and mesocortical pathways, which in turn, modulates a variety of human behaviors such as cognition, reward processing, reinforcement learning, and social activity55. Previous studies have shown that dopamine-related genes such as DRD2, DRD4, COMT, and DAT influence error-related negativity58 and increase the risk for schizophrenia59. As a result, genetic variants involved in dopamine signaling may regulate error processing associated behaviors via the regulation of the CTC circuitry.Other genes that may relate to the connectivity in the CTC circuitry are those associated with dopamine signaling, given the essential role of this circuitry in error processingOne major limitation of our study is the relatively small sample size, especially for schizophrenia cotwins. Although we showed that this small sample is still likely to have reasonable statistical power, further fMRI studies with larger twin samples are encouraged to replicate these findings. Second, different fMRI paradigms were used in two studied samples. While including different paradigms would strengthen the argument that CTC hyperconnectivity is a heritable “trait” rather than a “state-dependent” change, such differences may to certain degree influence the outcome individual “trait” networks between samples. Third, while we only included schizophrenia discordant cotwins without psychotic disorders in this study, some of the cotwins were diagnosed with other types of mental disorders (in particular major depressive disorder, see Table In sum, using multi-paradigm fMRI data from two independent twin cohorts, our study shows the first evidence that increased connectivity in the CTC circuitry is likely to be a heritable trait related to the genetic risk of schizophrenia. These findings echo our previous work on CTC hyperconnectivity as a biological trait for psychosis prediction and overall highlight the critical role of CTC circuitry in the pathogenesis of schizophrenia.


The European Food Safety Authority (EFSA) mandates two sets of statistical tests in the comparative assessment of a genetically-modified (GM) crop: difference testing to demonstrate whether the GM crop is different from its appropriate non-traited control; and equivalence testing to demonstrate whether it is equivalent to conventional references with an history-of-safe-use. The equivalence testing method prescribed by EFSA confounds the so-called GM trait effect with genotypic differences between the reference varieties and non-traited control. Critically, these genotypic differences, which we define as a ‘control background effect’, are the result of conventional plant breeding. Thus, the result of EFSA equivalence testing often has little or nothing to do with the GM trait effect, which should be the sole focus of the comparative assessment. Here, an integrated method is introduced for both difference and equivalence testing that considers the differences of the three genotype groups  as a two-dimensional random variable. A novel statistical model is proposed, called the trait model, that treats the effects of the GM and control materials as fixed for their difference, and as random for their common background. For significance testing, the covariance structure of the three genotype groups is utilized to decompose the differences into the trait effect and the control background effect. The trait difference is then derived as a conditional mean, given the background effect. The comparative assessment can then focus on the conditional mean difference, which is independent of the control background effect. Furthermore, the trait model is flexible enough to include various types of genotype-by-environment (G×E) interactions inherent to the experimental design of the trial. Numerical evaluations and simulations show that this new method is substantially more efficient than the current EFSA method in reducing both Type I and Type II errors (protecting both the consumer and producer risk) after the background effect is removed from the test statistic, and successfully addresses two major criticisms  that have been raised. In the European Union, the safety of a genetically-modified (GM) crop and derived food/feed is established, in part, using a proof-of-equivalence approach . Under tAt least three linear mixed models have been proposed for this design  denote genotype group differences of the test versus control, control versus references, and test versus references, respectively. Let  be the sample estimates and The Test-Control-Reference (TCR) trial is the experimental base of EFSA’s prescribed two-step difference and equivalence testing methodology. Despite differences in the number of sites, reference varieties, etc., all TCR trials share some common properties. Let , must exist for the best measure of the GM trait difference, without confounding by the background effect.Notice in property [a] that the differences of the three genotype groups are two dimensional: one dimension is the control background effect; the other dimension is the GM trait effect. While both ΔDCR and DTR, respectively, and should be equal due to the paired arrangement in the field and the common background effect. Similarly, the covariance of DTC with DTR should be the same as with DCR. Other relationships can also be derived among variances and covariances.Property [b] is a direct result of the field arrangement. For example, The control material is the result of conventional plant breeding and there is no obvious preference for one control over other commercially-available varieties. Thus, the control background effect should be considered as random, and its potential value is no different from any individual reference in the reference genotype group. The random control background has been considered by , 5], an, an5], aThe remainder of this section addresses three fundamental questions: (1) how do we define the GM trait effect for a given background; (2) how do we model the random background effect in addition to other factors; (3) what is the sample performance of the estimation procedure?TR, a mixture of the GM trait- and background effects can be decomposed using conditioning or regression. Under the assumption of a bivariate normal distribution of , consider the following hypothetical model:Given ΔDTC and DTR given DCR. Using the notation of conditioning or regression, the model can be specified as: β depends on the correlation. The two equations in this model are linearly related, thus only one model equation is necessary since DTR = DTC + DCR. This implies that, given DCR, evaluation based on both DTC and DTR would be the same, and can be replaced by the evaluation of the intercept TR  on ΔCR (the control background effect). This is achieved by making use of the estimated background effect.Let DTC and DCR. The following equations are direct applications of bivariate normal theory . This is the familiar form of a simple regression: the intercept, say α, is equal to (μy − βμx) : the GM trait Y is the observed response; μ is overall mean; [S and B(S)] are environmental effects for site and block within each site, g is the background effect, and e is the residual. G and T(G) are main effects, and GS and TS(G) are corresponding interactions. Based on property [a] of the TCR trial, the background effect is defined as:The trait model can be expressed as:μ, G and T(G) are assumed to be fixed; all other factors are random and assumed to be independently distributed with mean 0 and corresponding variance. One advantage of the expression of Only g, that the random control background is identical for the control and the test, and has the same variance as the references, which is part of property [a] of the TCR trial. Second, there are three possible types of interactions in the TCR trial: the GM trait-by-site TS(G), the control background-by-site GS, and the reference-by-site. Inclusion or exclusion of each or all of them is optional depending on the data. G and (G), and interactions GS and TS(G), The primary factor differentiating ns denote the number of sites, nb the number of blocks and nsg the number of references at each site, and ng the total number of references.GS and TS(G), g and e, respectively, in The components of variances and co-variances are as follows in a design with the same number, but different varieties of references, at each site. Overlapping references among sites will be discussed later. Let nbnsgns))where σGnbnsgns))where σGResults in  show thadTC, dCR, dTR) are the sample means. Let When fitting to Eq in , the samdTR is the estimate of ΔTR given DCR at its observed value dCR. It simply says that, given the control background as dCR, the observed trait difference dTR would be a sum of two correlated differences dTC and dCR, which is what EFSA uses in their equivalence testing , dCR is random and follows a distribution with mean zero and variance Note that |DCR2 in  with eacDTR and DCR are the respective differences from the same reference mean, the regression of DTR on DCR is then equivalent to the regression of the test mean on the control mean. The conditional mean DCR at any value other than zero. Furthermore, the sample variance Since both iance of  and 4),,DTR and R2. Both  and 9)  DTR and Now, the following hypothesis can be tested using a t-test:R|DCR=0≠0tDTR|DCR2/4sdCR2)with degns = 8, nb = 4, ngs = 4. For illustration of the conditional method, all references were assumed different, i.e. ng = nsngs. The variation setting was defined as the ratio between the reference (or genetic) versus residual variances In this section, the asymptotic and sample performance of the conditional method is evaluated for a wide range of parameter values. Simulations are conducted on selected parameter sets to compare the conditional method and trait model with the EFSA method. Lastly, the EFSA example  on maizeFirst, the conditional and unconditional variances are compared, and the correlations are examined as functions of the variation settings. From Eqs  and 8),,8), the σg: σe. A few results are worth noting. In general, DTC and DTR. Even though the variation of DTR is mostly larger than that of DTC due to the background effect, it is actually smaller when σg is small. When genotypic variation is negligible, the residual becomes the main source of variability even among references. As the total number of replicates of references is larger than that of the control (a common case in practice), d by Eqs  and 7)..σDTR andDTR and DCR, all scaled by DTR, shows positive parallel change with DCR due to the common background, as long as a DTR as a test statistic, is mostly testing the background effect, as long as nonnegligible reference variation exists. In contrast, the conditional method using Sample performance of the conditional mean is examined in In this section, the practical performance of the difference testing methods is compared using the following hypotheses:Although hypotheses  are for α = 0.1 . Unlikeme as in  and assuH02: ΔTR = 0 and H02: ΔTR = 0 is often the least efficient. When H01: ΔTC = 0 and All three methods performed as expected with the Type I error being around the nominal level (approximately 7 to 13% except one case 2:σe2=0) . Slight DTR often makes the testing H02: ΔTR = 0 very inefficient with extremely low power, regardless of the trait difference. This implies that, when the trait difference is small, large variation in DTR will result in a failure to reject the non-equivalence hypothesis at a rate much greater than the nominal α = 0.10 level. Alternatively, a large trait effect might confound with the background variation, resulting in a rejection of the non-equivalence hypothesis.Results in post hoc testing of the trait-by-site interaction.The two-step difference and equivalence testing approach was illustrated with a maize grain composition example , 3. The post hoc procedure, as recommended by EFSA [In the re-analysis with the trait model, SAS PROC GLIMMIX  was used by EFSA .sg estimated from the corresponding model, the standardized differences dTR/sg of the seven analytes under the EFSA model are all greater than or close to 2.0 (from 1.92 to 2.75) in absolute value. Under the trait model, five of the seven show a background effect dCR/sg greater than 2 in absolute value. Obviously, the inability to reach conclusions on equivalence is the result of large control background effects, and has nothing to do with the GM trait itself. In the conditional difference testing, nine analytes showed a statistically-significant difference at the α = 0.10 level. The standardized differences EFSA could not reach a conclusion on equivalence for nine of the 53 analytes  . Among tTC in difference testing and ΔTR in equivalence testing. Second, if the control background effect is large, the result of EFSA equivalence testing has little or nothing to do with the trait effect, which should be the sole focus of the comparative assessment. The proportion of background variation in the test-reference difference can be estimated as the variation reduction from the conditioning:The equivalence testing method prescribed by  assessesFor example, when ervation . They plThe lack of a genotype-by-environment interaction term is one of the main concerns highlighted by Ward et al. . In factper se. It is, however, a component in the covariance structure, and will affect the standard error of the estimated background effect. The impact of this interaction must be determined on a case-by-case basis.The control background-by-site interaction may not be of interest to the GM safety assessment The reference-by-site interaction is different from the above two types of interactions. First, the TCR design does not require overlapping references among sites. Without overlapping references, this interaction cannot be properly estimated, and a good estimate of the interaction depends on a large degree of overlap. Second, the reference-related interaction will confound with the reference variation when absent in the statistical model. Such confounding should not have any consequence on the comparative assessment.The equivalence of the test and references should be determined in the context of natural variation, i.e. reference variation, when reference variation is a significant part of the total variation. When the reference variation is estimated as zero, EFSA Click here for additional data file.


A majority of known genetic variants associated with human-inherited diseases lie innon-coding regions that lack adequate interpretation, making it indispensable tosystematically discover functional sites at the whole genome level and preciselydecipher their implications in a comprehensive manner. Although computational approacheshave been complementing high-throughput biological experiments towards the annotation ofthe human genome, it still remains a big challenge to accurately annotate regulatoryelements in the context of a specific cell type via automatic learning of the DNAsequence code from large-scale sequencing data. Indeed, the development of an accurateand interpretable model to learn the DNA sequence signature and further enable theidentification of causative genetic variants has become essential in both genomic andgenetic studies.We proposed Deopen, a hybrid framework mainly based on a deep convolutional neuralnetwork, to automatically learn the regulatory code of DNA sequences and predictchromatin accessibility. In a series of comparison with existing methods, we show thesuperior performance of our model in not only the classification of accessible regionsagainst background sequences sampled at random, but also the regression of DNase-seqsignals. Besides, we further visualize the convolutional kernels and show the match ofidentified sequence signatures and known motifs. We finally demonstrate the sensitivityof our model in finding causative noncoding variants in the analysis of a breast cancerdataset. We expect to see wide applications of Deopen with either public or in-housechromatin accessibility data in the annotation of the human genome and theidentification of non-coding variants associated with diseases.https://github.com/kimmo1019/Deopen.Deopen is freely available at Bioinformatics online. Over the past decade, genome-wide association studies (GWAS) have provided genome-wideprofiles about the genetic basis of complex traits and common diseases a. SystemPutative accessible regions in the genome often work together with transcription factors(TFs), RNA polymerases and other cellular machines to regulate gene expression , a computational framework that applies a hybrid deep convolutional neural network(CNN) to learn regulatory sequence code and predict chromatin accessibility at the wholegenome level. Through comprehensive experiments, we demonstrate that Deopen not onlyachieves state-of-the-art performance in the chromatin accessibility classification problem,but also successfully recovers continuous degree of chromatin accessibility for an inputsequence, thereby filling the gap of predicting DNA accessibility signals in continuousvalues. To make Deopen more understandable, we propose a strategy to visualize motifsdiscovered by our model and successfully find their counterparts in the JASPAR database. Todemonstrate applications of Deopen, we focus on a GWAS dataset of breast cancer and show theability of our method to explain functional implications of putative disease-associatedsingle nucleotide polymorphisms (SNPs). We finally summarize that Deopen, as an effectivepredictive model for learning DNA regulatory code, could shed light on the understanding ofgene regulation mechanisms and the deciphering of genetic basis of human complexdiseases.In this article, we introduce Deopen (In order to learn DNA sequence codes that determine accessible (open) and inaccessible(closed) chromatins, we randomly select 50 DNase-seq experiments  and a typical three-layer feed forward network . The deeM the size of thesliding window, N the number of input channels, kth convolutionkernel with size N isequal to 4. For other layers, N is equal to the number of convolutionalkernels of the previous layer. ith sample, respectively, , the cross entropy of n the number of training samples. Weuse Adam (The convolution operation in CNN could be denoted as use Adam  as theoL is the length of a region (1000 bpfor Deopen) and iSFor the Deopen regression model, instead of binary label, we define openness as belowThere are two major differences in the neural network architecture in Deopen regressionmodel. (i) The output layer directly applies a linear transformation as We implement the above models using the Theano framework (https://github.com/davek44/Basset). Second, we download gkm-SVM (https://github.com/Dongwon-Lee/lsgkm). Default parameters are used for bothmethods.We use two baseline models in classification. First, we download Basset, a deep learningmethod for predicting the genome accessibility  from the Scikit-learn library also surpasses both Basset(0.863) and gkm-SVM (0.851) see . With ak-mer features to Deopen,respectively, we performed a model ablation analysis where we ran Deopen in the same 50cell lines without CNN or k-mer features  and closed (inaccessible), of an input DNA sequence. However, degrees ofaccessibility of DNA sequences may differ from each other even when they have the samebinary labels. Such difference in the degree of accessibility implicates that binaryclassification models are unable to discriminate putative open regions with differentaccessibility. To address this problem, we built a Deopen regression model to furtherrecover the degree of accessibility of a DNA sequence. With the consideration that theaccessible regions tend to contain more mapped reads. We define ‘openness’ (see formula inMethods), the degree of accessibility of a region, as the average reads mapped back to theregion, thus providing a continuous measure for chromatin accessibility. We then modifiedthe structure of our Deopen model by replacing the softmax layer with a lineartransformation layer. Besides, we use mean square error (MSE) as the loss function, thusforming the Deopen regression model.Similar to the experiments in classification, we used Deopen regression model to recoverthe openness of input DNA sequences with the same datasets. Note that accessible regionsof human genome only cover a small proportion . The obvSince people are more interested in the degree of accessibility for open regions, weremoved negative samples in test datasets and directly predicted openness for the positivesamples . Due to k-mer feature as the input of the three baseline models. For regressionwith mixed samples, Deopen outperforms three baseline methods by a large margin with anaverage PCC 0.809 . We then comparedthese motifs with known Vertebrates motifs in the JASPAR database (r2 > 0.8) withthe 29 SNPs.To demonstrate the application of Deopen to GWAS, we collected a set of genetic variantsassociated with breast cancer from a previous study . In contrast, deltaSVM, a similarscoring method proposed in gkm-SVM  in the ENCODE project and trained a Deopenregression model using DNase-seq data of this cell line. We then calculated functionalimplication scores for these SNPs and drew box plots for the 29 and 1057 SNPs,respectively. As shown in Among the 29 SNPs, rs4784227 is believed to disrupt the binding of FOXA1 . In contFurthermore, it has been shown that the risk allele, rs4784227[T], yields a 9% affinityincrease when compared to the reference allele, rs4784227[C] (6.24 versus 5.73) ,hardware (GPUs) and genomic big data have enabled drastically performance boost on suchproblems. Specifically, we introduced Deopen, an open source framework that integrates adeep convolutional neural network (CNN) and a feed forward neural network, to automaticallylearn the regulatory code of DNA sequence and implicate nucleotide driving activities. Ourmodel has substantially surpassed the present state-of-the-art methods in the predictionaccuracy. The downstream applications have already given us two scenarios withconsiderations of both genomics and genetics. Researchers can not only use our method tolearn the chromatin accessibility code of different cell lines but also evaluate geneticvariants with potential influence on the accessibility.Besides, we have designed a series of extra experiments to verify the extensibility,scalability and robustness of Deopen. First, we further test Deopen on MNase-seq datasetswhich supposed to be more accurate than Dnase-seq datasets. Our method also achieves higherperformance than all baseline methods see . Second,Certainly, our model can further be improved from many aspects. First, the great ability ofDeopen to capture the regulatory code of DNA sequence could help us to identify otherfunctional elements in genome, including enhancers, silencers, repressors, insulators and soforth. Second, Deopen could also be generalized to predict the impact of mutations andprioritize functional variants, thereby facilitating both research and practice of precisionmedicine. Third, our current model mainly focuses on the identification of accessibleregions in a cell line, with the incorporation of informative data from biologicalexperiments such as RNA-seq and ChIP-seq, it is hopeful that our model can be generalized tomake cross cell-type predictions of regulatory elements. Finally, our motif analysis hasshowed that the first layer convolutional architecture is an effective motif discoverer.Researchers could use our method to learn the complex grammar of TFs binding in specificcell lines. It is also interesting to see whether higher layers of CNNs contain informationabout interactions of motifs.To sum up, with Deopen, researcher could perform a single sequencing assay  of the cell type with interests. Then, one can simultaneouslylearn the regulatory code of genome and annotate the impact of every possible mutation inthe genome. Using large-scale pubic data, one could train an accurate and interpretablemodel to predicting the impact of genetic variants associated with human diseases,especially the variants that lack enough interpretation in non-coding regions. We hope ourapproach could help unveil the regulatory mechanism underlying genetic signals andcontribute to understanding the potential functions of SNPs.Supplementary DataClick here for additional data file.