Reproductive efficiency has a great impact on the economic success of pork production. Gilts comprise a significant portion of breeding females and gilts that reach puberty earlier tend to stay in the herd longer and be more productive. About 10 to 30 % of gilts never farrow a litter and the most common reasons for removal are anestrus and failure to conceive. Puberty in pigs is usually defined as the female’s first estrus in the presence of boar stimulation. Genetic markers associated with age at puberty will allow for selection on age at puberty and traits correlated with sow lifetime productivity.n = 759) with estrus detection measurements ranging from 140–240 days were genotyped using the Illumina PorcineSNP60 BeadChip and SNP were tested for significant effects with a Bayesian approach using GenSel software. Of the available 8111 five-marker windows, 27 were found to be statistically significant with a comparison-wise error of P < 0.01. Ten QTL were highly significant at P < 0.005 level. Two QTL, one on SSC12 at 15 Mb and the other on SSC7 at 75 Mb, explained 16.87 % of the total genetic variance. The most compelling candidate genes in these two regions included the growth hormone gene (GH1) on SSC12 and PRKD1 on SSC7. Several loci confirmed associations previously identified for age at puberty in the pig and loci for age at menarche in humans.Gilts  contains supplementary material, which is available to authorized users. Puberty is the process of physical maturation of an animal to be capable of sexual reproduction. In humans puberty may be defined as age at first menses in girls, a milestone well-recalled and widely recorded. In pigs puberty is defined as age at first estrus when an animal will stand for breeding. With these definitions, puberty manifests as a spontaneous event. In reality, attainment of puberty is a complex maturation process that involves multiple body tissues and organ systems –3. The h2 = 0.38 to 0.46) [Gilts comprise a significant portion of breeding females and thus successful gilt development is critical to overall herd performance. Management decisions prior to first mating of gilts can affect productivity and later reproductive performance , 17; howto 0.46) , 20; butto 0.46) . A signito 0.46) –24. Withto 0.46) , genome-to 0.46)  and delato 0.46)  in the pto 0.46)  and are to 0.46) . The objGuide for Care and Use of Agricultural Animals in Agricultural Research and Teaching [Care and handling of all animals included in this study was according to procedures outlined in Teaching  and apprn = 759) were genotyped and used for this study.A composite population was developed in 2001 using maternal and terminal Landrace, Duroc, and Yorkshire lines. Full- and half-sib matings were prevented, otherwise matings were random. Twelve original sire-lines were maintained and semen from all sire-lines was used to produce approximately 600 litters per generation. Additional details of the development of this population were previously reported . Gilts bEstrus detection was performed daily from 140–240 days using 5–6 mature boars (>11 mo of age) placed in an alleyway between two pens of gilts, during which time herdsmen applied back pressure to gilts within each pen and observed them for estrous behavior. Age at puberty was defined as the date in which the first standing estrus was detected. Gilts that did not show signs of estrus by 240 days were harvested at the USMARC abattoir at an average age of 241 days, and the ovaries were inspected to determine whether they had not cycled and were classified as nonpubertal, or had cycled and were classified as behaviorally anestrus. Gilts that were observed to reach puberty before slaughter age had an average age of 200 ± 14.5 (mean ± SD) days at first estrus.Sus scrofa genome assembly 10.2 (http://www.ncbi.nlm.nih.gov/projects/mapview/map_search.cgi?taxid=9823).Genomic DNA was extracted from frozen tail tissue using the Wizard SV Genomic DNA Purification kit  for all phenotyped pigs. Samples of 300 ng at a concentration ≥ 75 ng/μl of DNA were genotyped using the Illumina PorcineSNP60 BeadChip containing 64,232 SNP  . Genotypn = 7) if > 5 % of SNP were missing or for failing a Mendelian segregation (parentage) test. After utilizing these quality control measures, a total of 41,148 SNP out of a total of 64,232 SNP on the array qualified for GWAS. A genotypic principal components analysis was done using genotypes of all 759 phenotyped animals with SNP & Variation Suite v8.4.1  [Any SNP with unknown chromosome positions, those located on SSCY, those with call rates < 95 %, or minor allele frequencies < 0.05 were excluded from the data set. Animals were eliminated (ix.com/) . The firhttp://archive.is/bigs.ansci.iastate.edu). Bayes C uses a common SNP variance that is reliably estimated from the data. The Bayes C has been explained previously by Kizilkaya et al. [The analyses were implemented with a Bayes C model averaging approach using version 4.61 GENSEL software , X is an incidence matrix of fixed effects (β), Z is a matrix of SNP genotypes that were fitted as random effects (u) distributed N , and e is the vector of random residual effects assumed to be normally distributed N . A fixed classification factor used in this statistical model was year-season of birth as all females born in the same season were uniformly managed and monitored for first estrus.where Priors for variance components were taken from residual and additive genetic variance components from a preliminary analysis using MTDFREML . The mody represented a vector of observations; b was a vector of fixed effects; a was a vector of random additive genetic effects of animals, which was assumed to be distributed N , where A was the numerator relationship matrix among animals and e was a vector of residual effects, which was assumed to be distributed N  and where I was the identity matrix. Incidence matrix X related records to fixed effects and incidence matrix Z related records to additive genetic random effects. The fixed effects were those used in the Bayesian model above. The four generation pedigree file included 37 sires, 380 dams and 759 females with phenotypic data.where Bayes Cπ option of GENSEL was used to estimate After the Bayes C analysis, the Predict option of GENSEL was used to estimate the genetic variance of sliding windows of five consecutive SNP assigned by chromosome-position order beginning with the first five SNP on SSC1 and ending with the last five SNP on SSCX. There were 8111 non-overlapping five-SNP windows available in the whole pig genome for statistical testing. Based on our estimate of π, 267 SNP effects were expected to be important  = 267). Therefore we submitted 267 5-SNP windows explaining the greatest proportion of genetic variance, defined as putative QTL, for statistical testing utilizing the Bootstrap option of GENSEL.P-value was determined to be 0.001 < P < 0.002.To construct the distribution of the test statistic (genetic variance of a five-SNP window) for each putative QTL, bootstrap samples were produced using the posterior means of the 41,148 SNP. This involved creating 1000 bootstrap data sets –35. ThesMultiple testing was taken into account considering the proportion of false positives . This aphttp://ensembl.org/Sus_scrofa/Info/Index) and the UCSC Genome Browser (http://genome.ucsc.edu/cgi-bin/hgGateway) with the Sus scrofa Build 10.2 assembly.Intervals for candidate gene searches were defined as the 5-SNP window plus the 300 kb flanking regions in QTL peaks. Annotated genes contained in this window were identified using Ensembl BioMart tool (2) was estimated for the SNP using Haploview 4.0 software [http://www.broad.mit.edu/mpg/haploview/index.php). Haplotype blocks were based on pairwise LD values.Linkage disequilibrium  associated with age at puberty after bootstrap analysis . These adjacent groups of QTL may actually be due to a single quantitative trait nucleotide or gene in the region. High LD between markers in adjacent 5-SNP windows was observed in six QTL regions on SSC2 from 97.3–99.7 Mb, SSC6 from 88–89 Mb, SSC8 from 71.8–73.8 Mb, SSC9 from 93–96 Mb, SSC10 from 35.6–37.7 Mb and on SSC16 from 26–27.3 Mb  and chorionic somatomammotropin hormone (CSH1) gene cluster. Growth hormone and its receptor are necessary for the onset and normal course for attainment of puberty [PRKD1 and C14orf 23 loci. PRKD1 is associated with body-mass index (BMI) in humans [C14orf23 was previously reported to be associated with delayed puberty in relatives of the same population of pigs [The most significant QTL accounting for 9.7 % of the genetic variance was located on SSC12 at 15 Mb within the growth hormone ( puberty . There a puberty –45. A sen humans  and an S of pigs .CRTC1 (SSC2:59 Mb), PAPPA (SSC1:288 Mb), CCT6A (SSC3:17 Mb), CELF4 (SSC6:115 Mb), EDEM3 (SSC9:139 Mb), SMYD2 (SSC9:142 Mb), and XXYLT1 (SSC13:142 Mb). CCT6A expression was shown to be higher in sexually mature laying hen ovaries than in immature ovaries [For regions previously reported by Tart et al.  likely c ovaries .CRTC1 (SSC2:58.9 Mb) was associated with age at menarche in humans by Elks et al. [CRTC1 [IQCH located on SSC 1 at 183 Mb was associated with age at menarche in humans [IQCH form a haplotype associated with a major gene affecting ovulation rate in twinner cattle [RORA at 122 Mb on SSC1 was associated with age at menarche [RORA in staggerer mice causes delayed puberty, reduced oocyte number and accelerated reproductive aging [AQP8 at 22 Mb on SSC3 [GPRC5B at 27 Mb on SSC3 [NEGR1 at 130 Mb on SSC6 was associated with age at menarche and BMI [Six regions contained genes associated with age at menarche in humans, and identified by Tart et al.  as well s et al. . This ge. [CRTC1  through . [CRTC1 . IQCH lon humans , 23. In r cattle . RORA atve aging . Finally on SSC3  have bee and BMI .MTCH2 and ZNF608 on SSC2 at 16 Mb (BMI and obesity) [NEGR1 on SSC6 at 130 MB (obesity) [ADAMTSL3 and PRKD1 on SSC7 at 57 Mb (BMI and height) [NPFFR2 on SSC8 at 72 Mb (BMI) [CRTC1 [NEGR1 [MTCH2 [RORA [TBC1D1 [TBC1D1 and ZNF608 has been shown to be associated with fatness traits in pigs [Several loci that are associated with anthropometric traits in humans such as body-mass index (BMI) or its components, body mass (obesity) and height were also associated with pubertal age in pigs  , 52, andobesity) , 52, NEGobesity) , ADAMTSL height) , 55 and  height) , and NPFMb (BMI) . SeveralMb (BMI)  and obesMb (BMI) . Using MMb (BMI) , 62 or fMb (BMI)  reach puMb (BMI) , 64. MetMb (BMI) ,66 or thMb (BMI)  are cons) [CRTC1 , NEGR1 [1 [NEGR1 , MTCH2 [1 [MTCH2 , RORA [6H2 [RORA  and TBC1 [TBC1D1 . Variati in pigs , 72. An  in pigs  and an i in pigs . When li in pigs  owing to in pigs , 76. RedIGF1R on SSC1 at 153 Mb [ESRRG on SSC10 at 9 Mb [NELL2 (on SSC5 at 78.5 Mb) expression reduces GnRH release and results in delayed puberty [AFP) on SSC8 at 73.7 Mb is essential for female fertility [NPFFR2, ADAMTS3, ALB and AFP. Substance P encoded by the tachykinin gene (TAC1) on SSC9 at 85 Mb and activin receptor-like kinase 7 (ACVR1C) on SSC15 at 71 Mb are associated with delayed puberty in female knockout mice [Several other candidate genes were identified that are involved in pubertal development in other species. Two locations coincided with genes associated with puberty in cattle; t 153 Mb  and ESRR at 9 Mb . In rats puberty , 80. Alpertility  as mutanout mice , 83. Subout mice , which aout mice  where itout mice . Moreoveout mice . Given tout mice , these dAlthough rare monogenic mutations can disrupt normal pubertal development in humans through the GnRH axis, most loci contain common genetic variants that contribute to variation in pubertal timing and are involved in co-regulation of height, BMI or obesity  . ResultsAll relevant data are available within the manuscript and its Supporting Information files.


PTPN22 was also identified in the discovery cohort but replicated in only one independent cohort. Combining the three cohorts boosted power of vGWAS and additionally identified TYK2 and ANKRD55. Both PTPN22 and TYK2 had evidence of interactions reported elsewhere. We conclude that vGWAS can help discover interacting loci for complex diseases but require large samples to find additional signals.Genotypic variability based genome-wide association studies (vGWASs) can identify potentially interacting loci without prior knowledge of the interacting factors. We report a two-stage approach to make vGWAS applicable to diseases: firstly using a mixed model approach to partition dichotomous phenotypes into additive risk and non-additive environmental residuals on the liability scale and secondly using the Levene’s (Brown-Forsythe) test to assess equality of the residual variances across genotype groups per marker. We found widespread significant (P < 2.5e-05) vGWAS signals within the major histocompatibility complex (MHC) across all three study cohorts of rheumatoid arthritis. We further identified 10 epistatic interactions between the vGWAS signals independent of the MHC additive effects, each with a weak effect but jointly explained 1.9% of phenotypic variance.  Genome-wide association studies (GWASs) have been extremely successful in highlighting loci associated with complex diseases such as rheumatoid arthritis (RA)12145786One promising approach is genotypic variability based genome-wide association study (vGWAS) to search for loci with substantial genotypic variability as potential interaction signatures, i.e. differences of phenotypic variation across three SNP genotypes which tend to be small when only additive effects are important but large when non-additive effects such as interactions are important111315171920et al.et al.FTO in a vGWAS of body mass index in 170,000 samples from multiple GWAS cohorts, which is believed to interact with physical activity and/or lifestyleFTO in body mass indexLEPR in C-reactive protein levels and ICAM1 in soluble ICAM1 levelsSLC2A9 in serum urate1920262728There have been several successful applications of vGWAS in quantitative traits using either GWAS18191723So far vGWAS has been little exploited in complex diseases probably because phenotypes classified either as a disease case or a healthy control provide little continuous variation. This problem can be remedied by applying a two-stage vGWAS approach: firstly using a mixed model method implemented in software such as GCTA3132+), or seronegative (ACPA-) or unassigned. All participants provided written informed consent for participation. Further details of the sample collections in the three study cohorts can be found in the et al.We used the Rheumatoid Arthritis Consortium International for Immunochip samples recruited in the UK (RACI-UK), US (RACI-US) and Sweden  as described previouslyWe excluded SNPs on sex chromosomes and samples of non-European origin. RA cases that were either ACPA- or ACPA unassigned were also excluded in each cohort to avoid disease heterogeneity. A rigorous QC was conducted using PLINK31y; Zi = |yi-ỹgi| is the deviation of y of the ith sample (yi) and the median of y in samples with genotype g (ỹgi); N is the sample size and k is the total possible genotypes; nj is the number of samples with genotype j; Zj. is the mean deviation from the median for genotype j and Z. is the mean deviation from the overall median. When N is large, T2 is an approximate χ2 test taking two degrees of freedom.where the environmental residuals were the trait To be extra cautious about the impact of normality, we also compared the vGWAS results based on the raw environmental residuals with those based on fully normalized environmental residuals using rank transformation available in the GenABEL packageWe derived the significance threshold as 2.5e-05 based on permutation with 1000 iterations where a vGWAS was carried out using the randomly permutated environmental residuals and the lowest P value was recorded in each iteration . We perfFor comparison we also performed a conventional GWAS for each cohort using PLINK and following the previous study2) for all the identified SNPs and then only pairs of SNPs in low LD (i.e. r2 < 0.1)k selected pairs of SNPs by fitting a pair of SNPs and their interaction terms as well as covariates of gender and the first 10 PCs derived from the GRM based on the subset of independent SNPs, with a significance of threshold defined as 0.05/(k*(k-1)/2); c) significant pairwise interactions were assessed while conditioning on the additive background of independent GWAS signals and unique pairs of interactions were identified using the forward selection approach above. Variance explained by the selected epistatic SNP pairs was calculated using a full logistic regression model fitting all the covariates, the additive background and the independent pairs of SNPs and their interactions. The identified epistatic SNP pairs were tested for replication individually in RACI-US and RACI-SE and the total variance explained was calculated following the approach above.We tested interactions between the identified vGWAS SNPs in RACI-UK as follows: a) PLINK was used to compute pairwise LD  and 107,144 SNPs in the vGWAS and GWAS. We quoted SNP genomic locations in the GRCh38/hg38 version throughout.+ RA was estimated as 24.7%   in the RACI-UK cohort where the Immunochip-wide heritability of ACPAas 24.7% . About 95.0e-08) . Forward5.0e-08) . The qua5.0e-08)  and GWAS5.0e-08)  analysesLCT in RACI-US  and 343 in RACI-SE (heritability estimated as 18.5%) under the same significance threshold, suggesting the two independent cohorts were underpowered probably due to the relatively small samples used . The QQ  RACI-US .PTPN22 in RACI-UK each had a direct replication only in RACI-SE with a P value of 3.3e-02 and 3.0e-02 respectively, suggesting genotypic variability within the locus was detectable only with a large sample size. The top vGWAS SNP rs2322659 within LCT in RACI-US had no replication in either RACI-UK or RACI-SE.We found that a quarter (i.e. 413 out of 1639) of the identified vGWAS SNPs in RACI-UK had direct replication in both the RACI-US and RACI-SE cohorts  and theyHLA-DRA and HLA-DRB5) was about 134 kb away from the most strongly associated GWAS SNP rs6931277 (near HLA-DRB1)  , and theLA-DRB1) . These r2 < 0.1. Based on a significance threshold of 4.2e-06 derived from Bonferroni correction, we found a large number of significant interactions all within MHC, of which 2,962 pairs of SNPs had a conditional interaction P value between 3.4e-07 and 5.0e-02 independent of the additive background. Applying forward selection to the 2,962 pairs and requiring a conditional interaction P < 1.0e-03 in each step, we identified 10 independent epistatic pairs of SNPs that spanned the entire MHC region and were replicated in both RACI-US and RACI-SE except for the rs9366778 - rs2239707 pair in RACI-US  and rs34536443 for TYK2 (P = 7.0e-06) both had only weak or no signals in individual member cohorts, i.e. the P values were 4.4e-03, 2.5e-02 and 7.9e-02 in RACI-UK, RACI-US and RACI-SE respectively for rs71624119; and 1.8e-04, 3.4e-01 and 2.1e-01 respectively for rs34536443. In contrast, the GWAS analysis identified additional 12 genome-wide significant loci that were insignificant in the vGWAS  and used high resolution imputation and a much increased sample size to fine map within-locus interactions29PTPN22404142432938Our results of multiple GxG interactions within MHC are in line with the recent reports that focused on a few preselected MHC loci (e.g. PTPN22) that tended to be involved in GxG and/or GxE interactions. We argue that co-existence of strong additive and non-additive effects in the major associated loci may be biologically importantOne major concern about vGWAS applications is potential conflation caused by the mean-variance correlation that is hardly disentangled, i.e. variance can be mathematically modelled as some function of the mean20PTPN22, suggesting that they are unlikely involved in strong interactions and thus require more samples to detectANKRD55 is associated with multiple diseases including RA and multiple sclerosis3TYK2 is also a pleiotropic gene associated with multiple autoimmune diseases and was found interacting with IRF5 in lupus but the interactions seemed weak and inconsistent4849vGWAS may be more fruitful in meta-analysis of multiple cohorts as demonstrated in the Combined cohort analysis. We showed that the newly discovered vGWAS loci, like those in GWAS meta-analysis, had weaker association signals than MHC or vGWAS is also useful to increase power of detection of interactions via an effective reduction of multiple tests concerning only the prioritized loci. For example, testing GxG interactions benefited from a much relaxed significance threshold as 4.2e-06 after filtering on vGWAS significant SNPs and then their pairwise LD in this study. Caution is recommended when using such filtering because vGWAS could miss true interacting loci with limited genotypic variability911This pilot study has a few limitations. Firstly, the low power of detection in individual cohorts (particularly in RACI-US and RACI-SE). In addition to sample size and SNP density, power of a vGWAS is also determined by the effect sizes of the interactions involved and the unobserved interacting factors113132How to cite this article: Wei, W.-H. et al. Major histocompatibility complex harbors widespread genotypic variability of non-additive risk of rheumatoid arthritis including epistasis. Sci. Rep.6, 25014; doi: 10.1038/srep25014 (2016).


DRD4), and serotonin transporter (SERT). Studies of wild bird populations have shown that exploratory and bold behaviours are associated with polymorphisms in both DRD4 and SERT. Here we tested for polymorphisms in DRD4 and SERT in the Seychelles warbler  population on Cousin Island, Seychelles, and then investigated correlations between personality and polymorphisms in these genes. We found no genetic variation in DRD4, but identified four polymorphisms in SERT that clustered into five haplotypes. There was no correlation between bold or exploratory behaviours and SERT polymorphisms/haplotypes. The null result was not due to lack of power, and indicates that there was no association between these behaviours and variation in the candidate genes tested in this population. These null findings provide important data to facilitate representative future meta-analyses on candidate personality genes.Consistency of between-individual differences in behaviour or personality is a phenomenon in populations that can have ecological consequences and evolutionary potential. One way that behaviour can evolve is to have a genetic basis. Identifying the molecular genetic basis of personality could therefore provide insight into how and why such variation is maintained, particularly in natural populations. Previously identified candidate genes for personality in birds include the dopamine receptor D4 ( Between-individual differences in behaviour that are consistent through time/context are referred to as personality . PersonaDRD4), involved in the mediation of the hormone dopamine in the dopaminergic system, and the serotonin transporter (SERT), which controls the uptake of the hormone serotonin in the synaptic clefts of the neurones [DRD4 [DRD4 deficient mice [SERT [SERT deficient mice [The most promising candidate genes for human personality traits are the dopamine receptor D4  was identified and the genotype SNP830T correlated with faster exploratory behaviour in a novel environment in one of four populations of great tits, Parus major [Ficedula albicollis), where DRD4 SNP554 was linked with neophobia and DRD4 SNP764 with risk-taking behaviour [DRD4 SNP449 in two wild populations of invasive yellow-crowned bishops (Euplectes afer) was also found to be positively correlated with neophobic behaviour [Macaca mulatta) DRD4 polymorphisms have also been associated with bold behaviour [SERT in wild populations. Individuals heterozygous for SERT at SNP758 and SNP988 were more prevalent in rural, less neophobic populations of wild blackbirds (Turdus merula) when compared to urban populations, between 23–45 km apart in the same country [SERT genotype .It is important to investigate these associations in natural populations because, although human personality is not directly comparable to animal personality, cultural determinants of behaviour are thought to be less influential in natural animal populations and can provide insight into why individual variation exists . In captus major . A similehaviour . DRD4 SNehaviour . More reehaviour . Conflic country . In contDRD4 and SERT, are associated with variation in these respective behavioural traits in a wild population of Seychelles warblers . The Cousin Island population of Seychelles warblers should prove to be a good model for such a study, because adult individuals exhibit innate predator recognition behaviour [DRD4 and in SERT.Here we investigated whether polymorphisms in the candidate genes for exploratory and for bold behaviour , DRD4 anehaviour . Here weLocal ethical regulations and agreements were followed for fieldwork. Nature Seychelles permitted us to work on Cousin Island Nature Reserve. The Seychelles Department of Environment and the Seychelles Bureau of Standards authorized fieldwork and sampling (permit reference AO157).The Seychelles warbler is an endemic facultative cooperative breeding passerine that occurs on five islands within the Seychelles. Dominant breeding pairs are territorial and socially monogamous. Paternity is gained predominantly by dominant rather than subordinate males and around 44% of offspring have extra-group fathers ,26. Due At the study site of Cousin Island , during the winter (Jan-Feb) and summer (Jun-Sep) breeding seasons in 2010–15 the breeding status of each individual was identified, territories mapped and birds caught with mist nets, colour/BTO ringed if necessary, and a blood sample obtained from a brachial venipuncture. The blood sample was later used for pedigree analysis and molecular sexing ,31.Exploration behaviour was assayed in an Oxygen 4 tent . The tent contained three artificial trees and each tree had two branches that were 45 cm long (one attached at 95cm and one attached to the top of the trunk), and a trunk, 148 cm high. The number of flights, hops and total number of trees visited were recorded in five minutes .Bold behaviour was tested two minutes after the exploration assay to allow for habituation to the novel environment of the tent. A novel pink toy attached to a tree branch (95cm long) was inserted and positioned in the centre of the tent . We alsoDRD4 exon 3 sequences from the great tit DQ006802, the chicken Gallus gallus NP001136321, blue tit (Cyanistes caeruleus) JN986724.1 and blackcap Sylvia atricapilla (AEC22814.1), and SERT chromosome 19 sequences from the blackbird Turdus merula KC584781, collared flycatcher Ficedula albicollis AGTO02004766.1 and zebra finch Taeniopygia guttata ABQF01026424, were aligned using Mega 5.2 [SERT exon), non-coding regions can alter the level of gene expression and behaviour [Mega 5.2  to desigMega 5.2 , and theMega 5.2 . The graet al. [DRD4 and, when this did not show any variation, we tested nineteen birds for the start region of DRD4. An additional twenty-eight birds measured once for exploratory behaviour were included in the SERT analysis, resulting in a total sample size of eighty-five. The number of individuals measured for bold behaviour was lower because bold behaviour was not assayed in earlier years.A power analysis  using thet al.  revealedet al. [2O per PCR reaction. The Sanger sequencing protocol was modified using 1/8 of the BigDye® Terminator Cycle Sequencing reagents 3.1 (Applied Biosystems). Sets of primers were used for sequencing on the ABI3730 sequencer.Blood samples were collected and stored in absolute ethanol. DNA was extracted using either a phenol extraction technique  or a salet al. ; modificwww.codoncode.com) and visually examined for polymorphisms. Note that 3 base pairs at position 80 were missing in two samples. Construction of haplotypes followed in DNAsp 5.10.1 [Sequences were aligned in CodonCode Aligner 5.1.4  as a factor for the overdominant model  and SNP as a continuous variable for the additive model . For the haplotype analyses, the independent variables were each haplotype as a factor for the overdominant model  and haplotype as a continuous variable for the additive model . Assay number, see A generalised linear mixed model, GLMM, was run in lme4 1.1–5  using thDRD4 was monomorphic, however four SNPs were identified in SERT at SNP147, SNP209, SNP446 and SNP467 in the non-coding end region. None of the four SNPs deviated from Hardy-Weinberg equilibrium  influenced by factors such as age or the external environment . Blue ti effects . In our  effects . It woulDRD4 polymorphisms and polymorphisms in the neighbouring DEAF1, involved in the regulation of the serotonergic system, in chickens [SERT polymorphisms, and bold behaviour and exploratory behaviour, because of higher linkage with other personality related genes close by.An association between candidate genes and personality does not always imply a direct functional effect . For exachickens . Althougchickens ,63, and chickens ,64. Addichickens ,65. HighBeing unable to identify the genes underlying focal traits is one disadvantage of the candidate gene approach. Additionally, the candidate gene approach is often biased towards genes with large effect sizes  and thisA future direction could be to employ a genome-wide study to look for signatures of selection on personality. The bottlenecked past of our study species may have left signatures of selection at other putatively adaptive relevant loci that genome-wide scans could detect. A candidate gene approach could then follow at these loci to investigate their association with personality ,68. HoweSERT variants and investigate underrepresented candidate genes that may have an additive or pleiotropic effect on personality. We emphasise the importance of studying personality throughout development in a controlled longitudinal study and the need for the publication of null findings to aid future meta-analyses on personality candidate genes.Understanding the molecular genetic basis of personality can ultimately help to explain why behavioural differences between individuals occur in populations. Studies in wild populations that experience natural selective pressures will allow us to address these questions. We found no association between these behaviours and variation in the candidate genes tested in our study population. Future work should account for age or environment effects on S1 FigNumbers at branching points represent bootstrap values inferred from 5000 replicates. The horizontal scale bar indicates 0.1 nucleotide substitutions per site.(TIFF)Click here for additional data file.S2 FigThe models are relative to homozygotes with the G/C/A SNP, subordinate is relative to dominant, male is relative to female.(TIFF)Click here for additional data file.S3 FigThe models are relative to homozygotes with the C/A SNP, subordinate is relative to dominant, male is relative to female.(TIFF)Click here for additional data file.S4 FigThe models are relative to individuals with no copies of the SNP, subordinate is relative to dominant, male is relative to female.(TIFF)Click here for additional data file.S5 FigThe models are relative to individuals with no copies of the SNP, subordinate is relative to dominant, male is relative to female.(TIFF)Click here for additional data file.S1 TableA linear mixed model (LMM) was run in lme4 1.1–5  with exp(TIFF)Click here for additional data file.S2 TableU is the degrees of freedom in the numerator. The sample size (N) is calculated by adding the degrees of freedom in the denominator, U and one.(TIFF)Click here for additional data file.S3 TableBold nucleotides indicate the SNPs.(TIFF)Click here for additional data file.S4 Table(TIFF)Click here for additional data file.S5 Table(TIFF)Click here for additional data file.S6 TableFalse Discovery Rate (FDR) p values control for running four SNP models and five haplotype models with alpha set at 0.05. d.f. = degrees of freedom.(TIFF)Click here for additional data file.S7 TableFalse Discovery Rate (FDR) p values control for running four SNP models and four haplotype models with alpha set at 0.05. d.f. = degrees of freedom.(TIFF)Click here for additional data file.


The MRMLM is a multi-locus model including markers selected from the RMLM method with a less stringent selection criterion. Due to the multi-locus nature, no multiple test correction is needed. Simulation studies show that the MRMLM is more powerful in QTN detection and more accurate in QTN effect estimation than the RMLM, which in turn is more powerful and accurate than the EMMA. To demonstrate the new methods, we analyzed six flowering time related traits in Arabidopsis thaliana and detected more genes than previous reported using the EMMA. Therefore, the MRMLM provides an alternative for multi-locus GWAS.Genome-wide association studies (GWAS) have been widely used in genetic dissection of complex traits. However, common methods are all based on a fixed-SNP-effect mixed linear model (MLM) and single marker analysis, such as efficient mixed model analysis (EMMA). These methods require Bonferroni correction for multiple tests, which often is too conservative when the number of markers is extremely large. To address this concern, we proposed a random-SNP-effect MLM (RMLM) and a multi-locus RMLM (MRMLM) for GWAS. The RMLM simply treats the SNP-effect as random, but it allows a modified Bonferroni correction to be used to calculate the threshold  The mixed linear model (MLM) method1et al.Most complex traits are controlled by several major loci plus numerious undetectable loci with small effects . The one-dimentional scanning GWAS will never recover the true model due to the intrinsic limitation of the model. Multi-locus models are better alternative methods for GWAS; these include Bayesian LASSO9et al.et al.If the number of markers is small or moderately large and can be handled by one of the multi-locus approaches, we should consider a multi-locus method for GWAS, otherwise, a combination of the single locus genome scanning and multiple locus analysis may be considered. In the first stage, markers are scanned and selected with a low criterion of significance test. In the second stage, a multiple locus method is implemented for markers that have passed the initial screening. Statistical tests and marker effect estimation are then based on the multiple locus model. The MLM method of GWAS in the initial scanning stage treats marker effects as fixed. Goddard In this study, we developed an efficient algorithm to estimate variances of the markers and predict effects of these markers. This method is called the random-SNP-effect mixed linear model (RMLM). The result of RMLM can either be treated as the final result of GWAS or used to select markers for the second stage analysis. In the second stage of GWAS, the selected markers are simultaneously evaluated in a single model using an EM empirical Bayes approachp value for the MRMLM method was 0.0002 . The corresponding threshold p value for the RMLM method was me). The threshold p value for the EMMA method was m is the total number of markers. For each QTN, power was defined as the proportion of samples where the QTN was detected . In the first simulation experiment where no polygenic variance was simulated, the MRMLM method has the highest power for all six QTNs simulated, followed by the RMLM method and the EMMA method  along the EMMA method. The significance threshold A method . On one powerful . On one powerful  with an We used the mean squared error (MSE) to measure the accuracy of an estimated QTN effect for a particular method. We evaluated the accuracies for all the six simulated QTNs from all three methods. The MSE’s are demonstrated in The empirical Type 1 error rates of the three methods from the three simulation experiments are illustrated in A useful way to compare different methods for their efficiencies in the detection of significant effects is the receiver operating characteristic (ROC) curve comparison. An ROC is a plot of the statistical power against the controlled Type 1 error. The higher the curve, the better the method. When sixty-one probability levels for significance, between 1E-8 to 1E-2, were inserted, the corresponding powers were calculated in the first simulation experiment. When performing GWAS on the simulated data, we first scanned the genome by the single-locus RMLM method to find the association between each SNP and the trait of interest. This process took 12.78 hours  in the first simulation experiment. The MRMLM took an additional 0.51 hours to conduct the multi-locus analysis. Although the MRMLM method requires more computing time, the high power and small MSE relative to the RMLM method are good justifications for the improved method. The EMMA method took 68.77 hours for completing the analysis for the first simulation experiment.Arabidopsis thaliana population published by Atwell et al.We analyzed six flowering time related traits of the We found that 6, 4, 6, 2, 3 and 5 genes previously reported to be associated with the six traits are in the proximity of the SNPs detected by the MRMLM method. The corresponding numbers of genes in the vicinity of the SNPs detected by the RMLM method are 3, 3, 2, 1, 1 and 2, respectively, for the six traits. Only 2, 2, 1, 0, 0 and 1 genes are in the neighborhood of the SNPs detected by the EMMA method , the work of Atwell et al.181920212223Arabidopsis thaliana GWAS results of his study appear to be reliable.Atwell interest  and S7. et al.In the study of GWAS methodology, real genotypes in natural population are frequently used to conduct Monte Carlo simulation studies12p value for significance tests. The MRMLM is a multi-locus model including markers selected from the RMLM, and all the effects in the model are estimated by an EM empirical Bayes method. Results from real data analyses and simulation studies show that the MRMLM has the highest power for QTN detection, the best fit for genetic model, the minimal bias in the estimation of the QTN effect, and the strongest robustness, as compared with the RMLM and the EMMA.The RMLM simply treats the SNP effect as random, and includes new matrix transformation, fixing the polygenic-to-residual variance ratio and estimating residual variance after the variance of QTN effect is obtained. Meanwhile, it allows a modified Bonferroni correction to be used to calculate the threshold y be a vector of phenotypic values for all individuals. The mixed linear model isLet X is an incident matrix for fixed (non genetic) effects, kth SNP that are coded as 1, 0 and −1, for one of the two homozygotes, the heterozygote and the other homozygote, respectively, k with an assumed normal distribution of mean zero and variance K, ε is a vector of residual errors with a y is where where λ is only estimated once under a pure polygenic model (the null model) prior to the marker scanning stage. The estimated variance ratio, In the single-locus RMLM, the polygenic variance ratio K so that U is an n × n matrix for the eigenvectors. Let Let us perform eigen decomposition for The expectation of σ2, we have the following profiled restricted log likelihood function,where q is the rank of matrix X andwhere λk. The Newton algorithm for λk isThis likelihood function contains only one unknown parameter λk, denoted by Once the iteration process converges, the solution is a single-locus RMLM estimate of σ2 areGiven k is also the conditional expectation of γk given The best linear unbiased prediction (BLUP) of γThe conditional variance isλk and scan all markers by testing λk = 0 for each SNP. The null hypothesis test for Under the single-locus RMLM approach, we first estimate The p-value of this Wald test is calculated usingwhere p value for genome-wide significance testsp value is Because the estimated marker effects under the random model are shrunken towards zero, we are able to use a modified Bonferroni correction to find the threshold is the effective number of markers.p values smaller than 0.01. In addition, consecutive markers passing the 0.01 threshold around an already selected marker  are eliminated to reduce collinearity among selected markers. Only these selected markers are included in the muti-locus model for further evaluation, including estimation of marker effects and significane tests. Due to the shrinkage nature, the majority of markers will be eliminated in the intitial screening. Therefore, the number of markers left in the second stage analysis is often a small subset of all markers, say a few hundred or a few thousand at most. Among the remaining markers, all those that passed the modified Bonferroni correction are used to conduct a likelihood ratio test (LRT), and the others are treated as random. If the LOD score for one marker in the LRT is more than 1.50, this marker is treated as fixed, or it is viewed as random. This small number of surviving markers are then included in a single multi-locus model. We propose to use the EM empirical Bayes (EMEB) methodThe single marker RMLM method described above can also be considered as an intial screening step for a new multi-locus random effect mixed linear model (MRMLM) that is described here. We use a less stringent criterion for the initial stage screening from RMLM for all markers that have http://mouse.cs.ucla.edu/emma/). The threshold of p value was set as m is the number of markers.This is an existing method for GWASet al.et al.p value is smaller than the designated threshold p value. A QTN detected within 1 kb of the simulated QTN was considered a true QTN. Empirical Type 1 error for each method was defined as the proportion of significant markers (excluding the markers overlapping with the six QTNs) over all markers with zero effects. In addition to power and Type 1 error, we also evaluated the mean square error (MSE) for each of the six simulated QTNs. For the ith QTN for In the first four simulation experiments, all the SNP genotypes were derived from the 216130 SNPs in Atwell i from the jth sample and i. A method with a small MSE is generally more preferable than a method with a large MSE.where h2), average, residual variance, and other values were the same as those in the first simulation experiment.To investigate the effect of the polygenic  background on the MRMLM and RMLM methods, the polygenic effect was simulated by multivariate normal distribution h2), average, residual variance, and other values were also the same as those in the first simulation experiment.To investigate the effect of epistatic background on the MRMLM and RMLM methods, three epistatic QTNs each with Arabidopsis thaliana data published by Atwell et al.http://www.arabidopsis.usc.edu/. We developed our own software to implement the data analysis (see Software S1).We also analyzed the well-known How to cite this article: Wang, S.-B. et al. Improving power and accuracy of genome-wide association studies via a multi-locus mixed linear model methodology. Sci. Rep.6, 19444; doi: 10.1038/srep19444 (2016).


The genome-wide association (GWA) approach represents an alternative to biparental linkage mapping for determining the genetic basis of trait variation. Both approaches rely on recombination to re-arrange the genome, and seek to establish correlations between phenotype and genotype. The major advantages of GWA lie in being able to sample a much wider range of the phenotypic and genotypic variation present, in being able to exploit multiple rounds of historical recombination in many different lineages and to include multiple accessions of direct relevance to crop improvement.Solanum melongena L.) association panel, comprising a mixture of breeding lines, old varieties and landrace selections originating from Asia and the Mediterranean Basin, was SNP genotyped and scored for anthocyanin pigmentation and fruit color at two locations over two years. The panel formed two major clusters, reflecting geographical provenance and fruit type. The global level of linkage disequilibrium was 3.4 cM. A mixed linear model appeared to be the most appropriate for GWA. A set of 56 SNP locus/phenotype associations was identified and the genomic regions harboring these loci were distributed over nine of the 12 eggplant chromosomes. The associations were compared with the location of known QTL for the same traits.A 191 accessions eggplant  contains supplementary material, which is available to authorized users. Solanum melongena L.) ranks third in commercial importance among the solanaceous crops after potato and tomato, and it is cultivated in many countries, particularly in southern Asia, middle East and Northern Africa. Global production in 2012 was about 48 Mt [Capiscum[Ralstonia solanacearum resistance [Eggplant . In a bi-parental population, only the polymorphisms between the two parents can be queried, whereas in a GWA population the number of polymorphisms is determined by the genetic diversity of the entire germplasm panel. In a GWA population, LD is determined not only by recombination frequency, but also by genetic drift, by the mating system of the plant and by the history of selection  approach represents an alternative to biparental linkage mapping for the determination of the genetic basis of traits . Both apMorgante ). The maMorgante .vs 141) and a more densely populated genetic map (384 SNPs (single nucleotide polymorphisms) vs 105 microsatellites) and targeted traits related to anthocyanin accumulation and fruit color.To date only one GWA-based study of variation in eggplant has been performed  but the Norcross, GA, USA), according to the manufacturer’s protocol. The quality of each DNA sample was monitored by electrophoresis through an 0.8% agarose gel and its DNA concentration estimated spectrophotometrically .A core set of 191 accessions . Automatic allele calling was handled by GenCall software (Illumina). Two of the entries were included in duplicate as an internal control. SNP loci in which the minimum allele frequency (MAF) fell below 5%, along with those where >10% of the data were missing, were discarded. Each SNP locus was scored as a binary data point, and the PIC (polymorphism information content) of each was estimated following Anderson et al. [Each accession was genotyped at 384 SNP loci as reported by Barchi et al. ; 339 of n et al. .Past 2.08 software [STRUCTURE v2.1 software [K, the most likely number of populations. Pair-wise kinship coefficients between the accessions were estimated using SPAGeDi software [Genetic similarities between pairs of entries were quantified by the Dice  similarisoftware . STRUCTUsoftware  was usedsoftware  transforsoftware . The diasoftware .2 values against the distance (cM) between adjacent SNP loci, based on the genetic map developed by Barchi et al. [2 (an estimate of LD between SNP loci without any correction); r2s  and r2sv (taking into account both the STRUCTURE output and the kinship matrix). To quantify the reach of LD, an r2 threshold of 0.15 was set [2 values and genetic distance was determined using a locally weighted scatter plot smoothing line [2, r2s and r2sv values [R package LDcorSV[LD decay was quantified by plotting pair-wise ri et al. . The effi et al. : r2 , stem anthocyanin (stean), abaxial leaf lamina anthocyanin (ablan), calyx anthocyanin , corolla color (corcol), adaxial leaf venation anthocyanin (adlvean), abaxial leaf venation anthocyanin (ablvean), peduncle anthocyanin (pedan), fruit color (fcol) and fruit glossiness (fglo). The anthocyanin content of the vegetative part of the plant was scored on a 0–5 scale, with “0” representing no visible anthocyanin pigmentation (completely green tissue), and “5” representing dark violet tissue. corcol was scored as “0” for white, “1” for pink and “2” for violet. fcol was measured using a CR-400 Chroma-meter  to generate three Hunter color coordinates , averaged across three regions of the surface on each fruit; the measurements were reduced to a single variable by calculating the Euclidean distance from white , following Prohens et al. [fglo was scored as “1” for opaque, “2” for intermediate and “3” for bright peel color. The trait data were treated as adjusted entry means (best linear unbiased predictors). Several multivariate linear mixed models were tested using a combination of the F-test (for the fixed component) and the Akaike test (for the random component). The model shown to best fit the data was: pijsb = lj + ys + rbjs + gi + mij + nis + eijs, where pijsb represents the phenotype of the bth replicate of the ith genotype at the jth location in the sth year; lj represents the fixed effect of the jth location, ys the fixed effect of the sth year, rbjs the fixed effect of the bth replicate within the jth location in the sth year, gi the random effect of the ith genotype, mij the random effect of the genotype by location interaction, nis the random effect of the genotype by year interaction and e the residual. Broad-sense heritabilities were calculated from the expressionThe accessions were grown in field both at Montanaso Lombardo  and at Monsampolo del Tronto  in 2010 and again in 2011. In each trial, the material was set out as two randomized complete blocks with six plants per entry per block, and standard horticultural practices were applied. Phenotyping methodology was based on the European Cooperative Programme for Plant Genetic Resources Solanaceae descriptors (ECPGR ) and thes et al. . fglo waσ2g represented the genotypic variance, σ2y the genotype x year interaction, σ2l the genotype x location interaction, σ2e the residual variance, ny the number of years (2) and nl the number of locations (2). Pearson correlation coefficients were calculated between each pair of phenotypic traits. All analyses were carried out by algorithms implemented in R software [where software .Tassel v4.0.25 software [STRUCTURE output, and the mixed linear model , taking into account both the STRUCTURE output and the kinship matrix [QVALUE package implemented in R. The estimation of the overall proportion of true null hypothesis π0 was based on λ range set from 0 to 0.95 by 0.05 and the smoother method was applied [MapChart v2.1 software [http://solgenomics.net/) using the Burrows-Wheeler alignment tool [The GWA analysis was performed using software . Three mp matrix . The mixp matrix –36 to anp matrix , using t applied . q-value applied , all SNP applied , was drasoftware . Syntenysoftware  surroundent tool . AlignmeThe 191 accessions were initially genotyped at 384 SNP loci, of which 338 were retained after quality control. The two replicated accessions gave uniformly consistent allele calls. MAF at most of the SNP loci ranged from 10% to 50%  had ambiguous membership and were thus classified as admixed. PCoAs carried out separately on the EA accessions showed some clustering among the Chinese entries, and among the Indian and SE Asian ones , with the least heritable traits being fglo and corcol, and the most heritable pedan and fcol  were strongly and positively correlated with one another, but only moderately correlated with corcol. The traits fglo and fcol were somewhat inter- correlated, and correlated with the anthocyanin content-related traits, but were uncorrelated with corcol. Both the correlation data and the distribution of each trait are reported in Additional file A summary of the accessions’ phenotypic performance is presented in Table ablan or corcol). The number of associations per trait ranged from four  to 11 (stean), and the total number of SNP loci involved was 20; these loci had a mean MAF of 33.4%. The PVE per association laid between 5% and 24% (mean 10%). In order to match the associations with previously identified QTL, loci linked to one another by <6.8 cM were considered as a unit, and their genomic location was obtained from the Barchi et al. [adlan, stean, calan, adlevean, ablevean, pedan and fcol while E10.3 (three SNPs) included genetic factors for stean, ablevean, adlevean, pedan, fcol and fglo. One of the two other large clusters was on chromosome E02 (one SNP), which was influential for adlan, stean, calan and adlvean, and the other was on E05 (one SNP), with genes/QTL determining stean, adlvean, pedan and fcol , with a MAF of 33.5% and a PVE of 22%; for stean, calan, adlvean, ablvean, pedan and fcol 35442_PstI_L404 (group 10.2), with a MAF of 48.7% and a PVE of 14-24%. For fglo, three highly significantly associated SNPs were detected, namely 3382_PstI_L285, 19601_PstI_L364 and 33571_PstI_L387; these had a MAF of 30% and each had a PVE of 10%.Detailed information regarding the individual genotype/phenotype associations is given in Table adlan, stean, calan and adlvean  corresponds to a segment of T12 in which a gene encoding the anthocyanin synthesis-associated enzyme UDP glucose anthocyanidin 5–0 glucosyltransferase is located , Arabid , barley  and whe . LD was  traits were clustered into 12 groups, scattered over nine chromosomes. The extent of some of the inter-trait correlations suggests that what appeared to be a cluster of QTL is more likely a single pleiotropic locus, although the presence of a set of linked QTL cannot be definitively ruled out. Broad-sense heritabilities were generally >0.5 (the exceptions were fglo (0.38) and corcol (0.42)) with a limited genotype by environment effect, which confirms the proposition that the influence of the growing environment on anthocyanin pigmentation is quite limited [The genetic basis of anthocyanin synthesis and accumulation has been widely explored in the lanaceae–64. In elanaceae, 66, invlanaceae, a QTL a limited , 68.fcol associations, one on chromosome E01 and the other on E05, in correspondence to the association groups E01.2 and E05.1 carrying QTLs for the same trait.The genomic location of eight of the 12 association groups overlapped that of a known QTL, showing how effective GWA can be in identifying the genetic basis of quantitative traits. QTL identified via linkage analysis of bi-parental populations are generally considered to be experiment-specific, unless validated  and haveSolanaceae has been focused on potato, sweet pepper and tomato. In the latter crop, 13 genes (some encoding enzymes and transcription factors) involved in anthocyanin synthesis have been described [stean, adlan,calan and adlvean) and a portion of tomato chromosome T02, where two genes encoding enzymes (flavonone 3-hydroxilase and dihydroflavonol 4-reductase) involved in the anthocyanin production pathway reside. One of these has been identified as the gene underlying the aw (anthocyanin without) QTL, in the presence of which there is a complete absence of anthocyanin throughout plant development [R QTL [adlvean, pedan, stean and fcol) lies in a region syntenic to a portion of T12 which harbors 5GT, a gene involved in the storage of betanidin (a fruit and flower pigment) in the vacuole [ablvean, adlan, adlvean, calan, fcol, fglo, pedan and stean) share synteny with a portion of T10 which carries several genes related to the anthocyanin production pathway, 3GT and the two MYB transcription factors ANT1 and AN2 (a and b loci) [ANT1 regulates the genes encoding chalcone synthase and dihydroflavonol 4-reductase, key enzymes involved in the synthesis of anthocyanin compounds [ANT1 is considered to be the prime candidate for the ag (anthocyanin gainer) QTL responsible for the delayed expression of anthocyanin [AN2a is the likely candidate for QTL I, responsible for tissue-specific anthocyanin expression [AN2b for F, a regulator of anthocyanin expression in the flower [A underlies the accumulation of anthocyanin pigment in the foliage, flower and immature fruit [To date most of the effort invested in the genetic analysis of anthocyanin pigmentation in the escribed . The detescribed , 42, 70,elopment . The samt [R QTL , which p vacuole . E10.2 a b loci) . ANT1 reompounds . ANT1 ispression , 75 and e flower . In sweere fruit .The development of large-scale genotyping capacity has allowed the concept of GWA to become a viable approach for the genetic dissection of quantitative traits. Here, the technique has been applied to uncover the genomic regions harboring genes underlying anthocyanin pigmentation and fruit color traits in eggplant. The GWA mapping approach was effective in validating a number of established QTL and, thanks to the wide diversity captured by the panel of genotypes in study, was able to detect a series of novel marker/trait associations. Synteny with tomato has allowed the ready identification of candidate orthologues for the chromosome E02, E05 and E12 QTLs related to anthocyanin accumulation.http://dx.doi.org/10.6070/H4NG4NK5.The data sets supporting the results of this article are available in the LabArchives repository at the following web address Additional file 1: Table S1: List of the accessions used for the association mapping study. (PDF 426 KB)A) SNP performance. Loci with a MAF <0.05 were excluded from the GWA analysis. B) SNP PIC values across chromosomes. The solid line represents the average genome-wide PIC, and the broken line the variation in PIC value across chromosome E02; note the particularly low informativeness of loci at the distal end of this chromosome. (PDF 233 KB)Additional file 2: Figure S1:A) PCoA of the EA accessions. Those of Chinese origin cluster to the right of the plot, separated from those of S and SE Asian origin. B) PCoA of the WA accessions cluster according to their fruit morphology: group 1 - long, light, curved fruits, group 2 – oblong fruits of intermediate weight, group 3 – round, heavy fruits as defined by Cericola et al. [Additional file 3: Figure S2: The genetic architecture of the components of the germplasm panel. a et al. .  = genotypic variance; Var(m) = genotype by location variance; Var(n) = genotype by year variance; Var(e) = residual variance. (PDF 174 KB)Additional file 4: Figure S3: PVE values. Additional file 5: Figure S4: Pearson’s inter-trait correlations (upper part of the matrix) and regression coefficients (lower part). The histograms included on the diagonal show the distribution of trait values (see also Table


Further methodological development is needed to extend these methods to handle covariates, and to explore more powerful test alternatives.Until very recently, few methods existed to analyze rare-variant association with binary phenotypes in complex pedigrees. We consider a set of recently proposed methods applied to the simulated and real hypertension phenotype as part of the Genetic Analysis Workshop 18. Minimal power of the methods is observed for genes containing variants with weak effects on the phenotype. Application of the methods to the real hypertension phenotype yielded no genes meeting a strict Bonferroni cutoff of significance. Some prior literature connects 3 of the 5 most associated genes ( The advent of next-generation sequencing technology has allowed researchers to actively consider the impact of rare genetic variation on common disease. However, novel statistical methodologies have been needed to leverage the limited evidence provided by any single-nucleotide rare genetic variant (SNV). Two major classes of tests, collapsing and variance components, have been proposed for testing case-control association  for relationships with rare variants in arbitrarily complex pedigrees  as required for our analysis of the Genetic Analysis Workshop 18 (GAW18) data. Two recent papers ,3 proposThe only paper containing methods meeting our criteria for inclusion  is by Zhu and Xiong , who proIn this paper, we will apply the methods of Zhu and Xiong to investigate potential relationships between simulated and real phenotypes and genes, where genes consist of sets of SNVs within the gene. In particular, we are curious about the ability of the methods to maintain type I error and yield reasonable power for simulated phenotypes. Furthermore, through our analysis of the real phenotype, we will explore potential insights into disease etiology for hypertension using the GAW18 data.In the GAW18 data, real phenotype data was available for 855 individuals in pedigrees. We classified each of the 855 individuals as either ever-hypertensive or not-ever-hypertensive based on whether the individual was classified as hypertensive at any of up to 4 measurements (waves) at which phenotypic data was collected. At 849 individuals, the simulated phenotype sample was slightly smaller. When analyzing the simulated phenotype, we again focused on the (similarly defined) hypertension phenotype. In the GAW18 data, there were 200 separate phenotype simulations. Our analysis considers only simulated phenotype #1.SNVs were mapped to genes using a custom implementation of ANNOVAR, where an SNV is assigned to a gene if it is contained within the start-stop position of the gene . To imprcorrP, which summarizes the additional correlation in the samples occurring because of the complex pedigree structure. corr Pis a function of 2 times the kinship matrix. We used 2 approaches to compute the kinship matrix: (a) the theoretical kinship matrix as computed using the kinship2 R package based on stated genetic relatedness of the individuals from GAW18 documentation and (b) the estimated kinship matrix computed by estimating genetic relationships across 732,185 SNVs randomly sampled across the genome using KING [We applied 3 different family-based tests of association considered by Zhu and Xiong . The fol2 Ttest, which is a multivariate test comparing the mean allele counts across t variants  between the cases and controls; it is a multivariate version of the 2-sample t-test. Li and Leal [2 Ttest for case-control data. Zhu and Xiong prove that dividing the 2 Ttest statistic by corr Pproperly accounts for the pedigree structure yielding a t df chi-squared test statistic assuming additive polygenic inheritance.Zhu and Xiong  propose and Leal  consider2 Ttest is that in the presence of rare variants there can be power loss from the large number of rare variants (t) present, and the asymptotic distribution of the statistic may not be valid when many extremely rare variants  are present. Thus, Li and Leal [2 Ttest is then applied to the  collapsed data . Zhu and Xiong show that, similar to the 2 Ttest, adjusting the CMC 2 Tstatistic using corr Pproperly accounts for the pedigree structure. In our implementation of CMC, we used 2 MAF cutoffs: 5% and 0.5%.Of course, the downside to the and Leal  proposedp value from all single-marker tests within the gene. Zhu and Xiong compute a single-marker p value using either a Pearson p value using corrP. To generate a gene-based p value, we follow Zhu and Xiong and use the minimum p value across all variant sites within the gene. However, because we do not correct for multiple testing, we expect the type I error rate to be inflated using this approach.For comparison, Zhu and Xiong also consider taking the minimum Our analysis consisted of 2 main parts: using the simulated phenotype and using the real phenotype to investigate potential genotype-phenotype relationships in the sample. The results section is structured accordingly.We started by applying each of the tests described above to all 6625 genes, in particular, testing for association between the genotypes of the SNVs in each gene with the simulated hypertension phenotype. Table p values from the tests using the real and estimated kinship matrices are highly correlated , with the estimated kinship matrices providing lower p values on average. Thus, we will use the estimated kinship matrix for all subsequent analyses. Because of the inability of p values from T2 and CMC5% was 0.55 (Spearman = 0.54); between T2 and CMC0.5% 0.8 (Spearman = 0.80); and 0.67 between CMC5% and CMC0.5% (Spearman = 0.67).As expected, EPHA4, had a p <0.05 for all 3 approaches, which controlled the type I error rate . Of the remaining genes identified as significant by at least 1 of these 3 methods, most (6 of 10) had p values less than 0.10 for 1 of the other 2 methods, and all 10 had p values less than 0.18 for at least 1 of the other 2 methods.Table p values were below a Bonferroni-corrected alpha value of 0.05/6625 = 7.5 × 10−6 for the 6625 genes. The minimum p value for any gene with CMC5% was 1 × 10−4. For T2 there were 5 genes with p values less than 1 × 10−4 , with 1 of these (MYBPHL) being the only gene for CMC0.5%% with a p value less than 1 × 10−4.When we applied the 3 remaining tests to the real hypertension phenotype on the entire sample of 855 individuals using the estimated kinship matrix, no minimum Few methods currently allow for the analysis of binary phenotypes with rare variants in complex pedigrees. We have applied 4 of the published methods to both real and simulated phenotypes. While the methods appeared to control the type I error rate for smaller genes (less than 200 SNVs), they performed poorly (low power) when the variance in blood pressure was small. Although this finding is based on the simulation model for GAW18 data, power to detect causal genes may still be a significant hurdle in real analyses.We considered the use of both the theoretical and estimated kinship matrices. We found that use of the theoretical kinship matrix proved slightly overconservative, while using the estimated kinship matrix provided empirical type I error rates in line with the nominal levels. Even though the precise reasons for the overconservative nature of the theoretical kinship are unknown, we surmise that cryptic relatedness and population stratification between pedigrees, which are not reflected in the theoretical kinship matrix, will be controlled through use of the estimated kinship matrix. Because these issues may be present in any data set, we recommend estimating kinship matrices in practical applications of family-based tests of association for rare-variant data.2, CMC5%, and CMC0.5%), each test will be most powerful for particular genetic architectures. In particular, for truly causal genes the proportions of causal rare or common variants versus noncausal rare and common variants will determine which method is best. Because the "best" method here will be a product of the simulation strategy taken, we do not wish to extrapolate this simulated genetic architecture to suggest the use of one approach over the others.Even though minor differences in power existed across the 3 tests considered here  [ST6GALNAC2 is associated with susceptibility to IgAN, which is commonly associated with hypertension  cholesterol [TRAT1 and DHX8 have little exposure in the literature related to hypertension or related outcomes. We note, however, that none of these genes reached a conservative (Bonferroni-corrected) significance threshold, nor did we replicate SNVs known to be associated with hypertension in large genome-wide association studies.In applying the 3 tests to the real phenotype, we found modest evidence of a relationship between a handful of genes and hypertension. These genes are featured in a modest amount of prior literature, suggesting their potential association with blood pressure, cardiovascular development, and renal function. In particular, egnancy)  and maliegnancy) . ST6GALNsee Ref. ). MYBPHLlesterol . TRAT1 aIn addition to the lack of power from small sample size and, potentially, the choice of analysis methods, we note that our approach did not consider covariates because the methods considered in this paper do not provide obvious approaches to control covariates. As noted in the introduction, there is a dearth of methods available for the analysis of data like that in GAW18, and we know of few methods currently available that work for analysis of rare variants with binary traits on complex pedigrees, allowing for control of covariates and for which software is publicly available. With increased interest in family-based designs for the analysis of rare-variant data, further methodological development is needed in this area.The application of methods for the analysis of rare-variant data collected on complex pedigrees for relationship with a binary phenotype suggests the potential for modest power for large variant effects with a sample of 855 individuals, but minimal power for variants and genes with weaker effects. Application of the methods to a real phenotype found modest evidence of association between the hypertension phenotype and five genes, three of which have limited prior association with hypertension-related phenotypes. Further methodological work is needed to develop more powerful methods allowing for control of covariates in the analysis of complex pedigrees and for use on larger genes.The authors declare that they have no competing interests.All authors participated in design of the overall study; AL and AB carried out various aspects of data preprocessing, including gene mapping and building preliminary data analysis files; BG estimated the kinship matrices; CA, AH, and NT ran statistical tests, analyzed data, and conducted literature review. NT drafted the final manuscript. All authors read and approved the final manuscript.


Many statistical methods have been developed to test, using next-generation sequencing data, for rare variants that are associated with a trait. However, many of these methods make assumptions that rare variants are in linkage equilibrium in a gene. In this report, we studied whether transmitted or untransmitted haplotypes carry an excess of rare variants using the whole genome sequencing data of 15 large Mexican American pedigrees provided by the Genetic Analysis Workshop 18. We observed that an excess of rare variants are carried on either transmitted or nontransmitted haplotypes from parents to offspring. Further analyses suggest that such nonrandom associations among rare variants can be attributed to population admixture and single-nucleotide variant calling errors. Our results have significant implications for rare variant association studies, especially those conducted in admixed populations.Next-generation sequencing technologies have been designed to discover rare and  Next-generation sequencing technologies have become a major tool for identifying disease-associated rare variants . Many stp values <0.001; and (c) observed Mendelian errors.The GAW18 data includes 464 Mexican American individuals from 16 large pedigrees with half genome sequence data available. Our goal is to study the LD among rare variants using the sequencing data by comparing the number of rare variants on transmitted and untransmitted haplotypes. In our analysis, we excluded all the single-nucleotide polymorphisms (SNPs) with a minor allele frequency (MAF) >0.01. We also excluded these SNPs with (a)a missing genotyping rate >5%; (b) Hardy-Weinberg equilibrium (HWE) test GAW18 also provides hypertension data. We used the hypertension status provided by GAW18, which is based on blood pressure measurements at 4 study exams in the past 20 years. An individual is defined as hypertensive if the individual's systolic blood pressure (SBP)>140, or diastolic blood pressure (DBP)>90, or on antihypertensive medications at one of 4 exams and as normotensive otherwise. If an individual has missing values for all 4 exams, the individual's hypertension status is considered as missing.m be the number of trios regardless of an offspring's disease status in the data and L be the number of rare variants in a gene or a genomic region. We denote m12 to be the total number of transmitted minor alleles and m21 to be the total number of nontransmitted minor alleles across the L variants in m trios. In this way, m12 is equal to the total number of rare variants falling in transmitted haplotypes, and m21 is the total number of rare variants in nontransmitted haplotypes, respectively. If rare variants are randomly distributed in haplotypes , we would expect m12 =m21. We can use the TDT statistic T follows a chi square distribution with 1 degree of freedom (DF). When only the trios with affected offspring are included, this test will test the association between rare variants and disease status.We first selected family trios of "mother, father, and child" from each of the 16 large pedigrees. Among the 16 pedigrees, 1 pedigree does not include any trio who has sequencing data available. Thus, the family trios were all from 15 pedigrees. Similar to the traditional transmission disequilibrium test (TDT), we examine the transmission of a rare variant allele. Because our analysis focuses on those variants with a MAF≤1%, we expect no more than 1 parent to be heterozygous. If both parents are heterozygous for a variant, this variant is excluded from our analysis. Thus, any minor transmitted alleles to an offspring from a parent must fall on the same haplotype because of no recombination. We examine all the rare variants in a gene or a region simultaneously instead of examining 1 variant at a time. Let http://www.ensembl.org). As a result, we had 38,091 genes and regions. The average number of SNPs in a gene or a region was 92.We applied the proposed methods to the GAW18 sequence data. After quality control, there are 2,749,275 rare SNPs remaining for association analysis. We identified 5 trios with affected offspring and 36 trios with unaffected offspring. Because the number of affected offspring trios is small, we only analyzed the unaffected offspring trios. Because some of the trios were selected from the same pedigrees, we analyzed 15 independent unaffected offspring trios. This was done by randomly selecting 1 family trio if multiple family trios were available for a pedigree. We grouped SNPs into genes or regions according to the Ensembl software  for all the genes or regions across the genome and we observed a substantial inflation of the test statistic, suggesting rare variants are not randomly distributed on transmitted and nontransmitted haplotypes. We examined where these significant genes were located in the genome using the Manhattan plot  and identified 170 of the 175 variants as present in the 1000 Genomes Project database. Among these 170 variants, 154 variants are present only in African samples; the other 16 variants are present in Africans and in other ethnic populations in the 1000 Genomes Project database. Similar results were observed for the KIF1B gene. Thus, our result suggests that the excess of rare variants in haplotypes, or the LD among the rare variants, is caused by population admixture with African ancestry populations.Figure t Figure . We obsede novo variants, in whole sequencing data. But genotype calling errors are unable to explain the excess of rare variants carried by a few haplotypes in this data. When association tests for rare variants are conducted in admixed populations such as African Americans and Mexican Americans, the LD among rare variants created by population admixture can generate false-positive findings. Our results also suggest that even the TDT may not overcome this problem if multiple rare variants are analyzed together.It has been suggested that rare variants are likely independent in general . HoweverIn summary, our analysis indicates that substantial LD among rare variants can be created by population admixture and by genotype calling errors. Novel statistical approaches for rare variant association analysis are required to account for the LD among the rare variants because of either population admixture or genotype calling errors. Family data have been suggested as having many statistical advantages in detecting rare disease variants ,10 and mThere is no competing interest among the authors.XZ designed the overall study, TF conducted statistical analyses, TF and XZ drafted the manuscript. All authors read and approved the final manuscript. We thank the 2 anonymous reviewers and Dr. Heather Cordell for their constructive comments, which lead to the substantial improvement of the manuscript.


Maternal-fetal genotype incompatibility (MFGI) is increasingly reported to influence human diseases, especially pregnancy-related complications. In practice, it is challenging to identify the ideal incompatibility model for analysis, since the true MFGI mechanism is generally unknown. The underlying MFGI mechanism for different genetic variants can vary, and to use a single incompatibility model for all circumstances would cause power loss in testing MFGI.In this article, we propose a practical 2-step procedure that incorporates a model selection strategy based on an entropy measurement to select the most appropriate MFGI model represented by data and test the significance of the MFGI effect using the chosen model within the generalized linear regression framework.Our simulation studies show that the proposed two-step procedure controls the type I error rate and increase the testing power under various scenarios. In a real data application, our analysis reveals genes having an MFGI effect, which may not be detected with a non-model selection counterpart. Current advances in high-throughput biotechnology have popularized genome-wide association studies (GWAS) to detect genetic variants that increase the risk of complex diseases. Over the past decade, thousands of single nucleotide polymorphisms (SNPs) have been reported to be associated with various human diseases. Despite the numerous successes of GWAS, the majority of heritability for many complex diseases remains unexplained -5. Recen% for preterm delivery in first pregnancy and 27% for preterm delivery in any pregnancy [The underlying genetic architecture can be especially complicated for diseases developed during human pregnancy, since both maternal and fetal genomes are involved. In general, the fetus inherits one copy of the genome from each of its parents, and the two copies are not identical. Previous family-based or twin studies indicated that the heritability for obstetric diseases is high. For example, it is reported in an earlier twins study that heritability was 17regnancy  and heriregnancy , pretermregnancy ,10, smalregnancy , pre-eclregnancy -14, and regnancy . The incEvidence support the important role of interaction between maternal and fetal genes, more than maternal genes alone for the etiology of pregnancy complications, are accumulating -19. In o% missing, the dyad sampling data, methods based on logistic regression models were proposed [Study designs in which data are collected from parent-offspring triads or mother-offspring dyads are the most commonly used to investigate the marginal and joint effects of maternal and fetal genes. Most currently available statistical approaches for analyzing this type of data fall in the framework of generalized linear regression models. Maternal fetal genotype tests based on the log-linear modeling for child-parent triads have been developed ,27-29. Tproposed ,23,25.Gic denotes the MFGI effect, it is problematic to decide when to code the variable as 1 or 0. Parimi et al. [Although it has been widely hypothesized that mismatches between maternal and fetal genotypes can cause incompatibility, the underlying biological mechanism remains unclear. Therefore, it is challenging to appropriately model incompatibility and code the corresponding variable accordingly. That is, suppose a variable i et al.  evaluateIn this study, we developed a 2-step statistical strategy for testing MFGI effects in designs that collect data from the mother and offspring that can increase the testing power under a wide range of scenarios. We propose to select the MFGI model based on an entropy measurement via a permutation procedure; then we test the MFGI effect using the selected incompatibility model within the logistic regression framework.n independent mother-offspring pairs . Let Gm and Go denote the maternal and fetal genotypes of a particular SNP, respectively. Under the commonly used additive genetic model, Gm/o = 0,1, or 2 if the mother/offspring has 0, 1, or 2 copies of the minor allele. Let Y = T denote the vector of the phenotype, where yi is the dichotomous disease outcome of the ith family unit in the sample, in which yi = 1 or 0 corresponds to the affected or unaffected individuals.Consider a study that enrolls case and control mother-offspring pairs from a target population. Collected data include genotypes of mothers and offspring, disease phenotype (phenotype of mother or child) of interest, and other covariates with a total of M1,M2,M3, and M4. It is possible that any of the mismatched maternal-fetal genotype combination leads to incompatibility or that only a specific mismatched genotype combination or a certain collection of these genotype combinations is associated with the risk of disease.Therefore, in the absence of evidence from molecular genetics analysis, it is challenging to determine which incompatibility model fits the biological mechanism. Here, we consider 11 biologically-plausible incompatibility models,i = 1,2,⋯,d are the possible values of X and their corresponding probabilities; b is the base of the logarithm and is commonly assumed to be 2 in the information theory. We propose the following 2-step procedure to test MFGI effects: Step 1: Select the MFGI model Let p and 1 - p be proportions of cases and controls, respectively, in a given data set. Entropy of the disease outcome can be computed where This entropy serves as a measure of the uncertainty of disease outcome in the initial data set.M1 =  are considered “high risk” and other combinations are considered “low risk”. The high and low risk labels split the initial data set into 2 subsets. Entropy of disease outcome within each subset, H (D|risk = high) and H (D|risk =low), can be calculated using Equation (2). The conditional entropy of disease status, given a particular MFGI model, is then defined as Under each of the 11 plausible MFGI models listed in Table This conditional entropy measures the remaining amount of uncertainty of disease outcome given the MFGI model. The difference between this conditional entropy and the original entropy is the information gain , which reflects the amount of information that a certain MFGI model provides (Equation (4)). To adjust for the uncertainty of disease status due to sampling, the information gain ratio was used (Equation (5)) as the criterion to select the optimal model to code the MFGI effect. As shown in Table Ri,i = 1,2,⋯,11} for each model and identify the model with the maximum information gain ratio Rmax = max {R1,R2,⋯,R11} as a candidate model;1. Obtain the information gain ratio {b = 1,2,⋯,B, permute the disease label and obtain the maximum information gain ratio 2. For 3. Calculate the empirical p-value of selecting the model by chance τ (say τ = 0.0001), we can conclude that the candidate model was not selected by chance and will be used as the analysis model in the next step of testing. Otherwise, Model 11 will be used as the analysis model. Step 2: Test the MFGI effect Once an optimal incompatibility model is selected, it will be used to code the incompatibility effect in a logistic regression model to assess the significance of the incompatibility effect, that is, If the obtained empirical P-value is less than a pre-defined cutoff Gm and Go represent the maternal and offspring additive variables, respectively, which are coded as 0, 1, or 2 corresponding to aa, Aa, and AA, respectively, where A is the risk allele; and Gic is the variable of MFGI. The value of Gic depends on the selection result from Step 1. For example, if Model 1 is selected as the analysis model, then Gic = 1 for mother-offspring pairs with genotype combination  and Gic = 0 otherwise. Testing the MFGI effect corresponds to testing the null hypothesis H0:βic = 0. The likelihood ratio test was applied for this purpose.where N = 1,000,000 families (parents and a child) were generated in a population assuming symmetric mating and Mendelian transmission of alleles. Parental genotypes were generated by multinomial distribution with a pre-specified genotype frequency. Either the Hardy-Weinberg equilibrium  or the Hardy-Weinberg disequilibrium  for homozygous carriers, heterozygotes, and noncarriers of the minor allele, respectively) was assumed. Fetal genotypes were simulated based on parents’ genotypes following Mendelian inheritance. Paternal data were then dropped to mimic the maternal-fetal study design. Binary phenotypes were simulated based on a quantitative liability variable Z=T, where zi denotes the liability variable of the ith subject. A threshold was determined to ensure that disease prevalence remained at 5%. Mother-offspring pairs with the underlying quantitative liability that exceeded the threshold were “diagnosed” as affected and others as unaffected. Simulated data were treated as a population. Then samples with the size n were randomly taken for subsequent analysis.To demonstrate that the proposed approach is valid in controlling the type I error rate and that it is statistically powerful, we conducted a series of simulations under the null and alternative hypotheses. Genotypes of The underlying quantitative liability trait was simulated through the following regression model (Equation (7)), αs are defined the same way as βs in Equation (6). Without loss of generality, we set the overall mean α = 0 and σ2 = 1. Performance of our proposed two-step approach  was compared with that of its non-model selection counterpart . Quantitative data were generated using a particular MFGI model listed in Table h2 = 0.05,0.10,0.15). The effect size of incompatibility was computed as described by Parimi et al.: let q is the proportion of incompatible maternal-fetal genotypes in the simulated population. For a given heritability level h2, we can calculate the incompatibility effect through the equation where We illustrated the proposed method via an application to a sub-analysis of a broader candidate gene study that investigates the role of genetic factors on the risk of complications of pregnancy. Details of this sub-study have been previously published in a genetic association study . Briefly% of preterm births [%) in either the mother sample or the offspring sample. Also, when searching across SNP markers, samples that did not follow Mendelian inheritance were excluded from the analysis. Our analysis included 742 SNPs in 190 candidate genes for 721 mother-offspring pairs (case-control ratio = 136:585). Maternal age which has been previously shown to be statistically significant [τ = 0.05 was used in the model selection step because we try to find as many true positives as possible, although the chance that we make the type I error may be slightly inflated when maternal and/or fetal main effects co-exist with the MFGI effect.pPROM occurs in 3%–4.5% of pregnancies in the United States and is responsible for about 30m births . Althougm births ,10,36,37nificant  was inclτ used in the model selection step. According to our simulations, the empirical type I error rate exceeds the nominal level slightly under scenarios II and III, where either maternal or fetal main effect was simulated, when a loose cutoff value of τ = 0.05 was used, the obtained empirical type I error rate is around 0.06 (detailed data not shown here). As the cutoff value gets more stringent, the obtained empirical type I error rates approaches to the nominal level. Table τ = 0.0001, which are controlled at the nominal level. The subsequent power estimates were also based on τ = 0.0001. As shown in Table To assess the type I error rate, we simulated the phenotype under the null hypothesis of no MFGI effect. Specifically, data were generated under Scenarios I-III with sample sizes of 500 and 1000. Empirical type I error rates were estimated as the proportion of simulations with P-value less than 0.05 across 11,000 replicates. Overall, the test size was well controlled at the nominal level (0.05) for both approaches under all scenarios we considered. The estimates of type I error rate for the model selection approach relies on the cutoff value Table In comparison, SNPs identified in genes MMP14, TNFRSF1A, AQP2, CRHR1, and GJA4 had OR greater than 1, indicating that a high risk of pPROM is possible with the mother-offspring pairs who have certain genotype incompatibility combinations defined by the corresponding selected incompatibility models. For example, SNP rs2236302 in the exon 5 region of gene MMP14, mother-offspring pairs who have the genotype combination  are at higher risk of developing pPROM: 33 of the 104 mothers in the defined “high risk” group developed pPROM whereas only 99 of 611 mothers in the “low-risk” group developed pPROM . The confidence interval of the OR for SNP rs5743627 in gene IL10 covers 1, indicating that the MFGI effect is not marginally significant. As we are aware of, this is the first analysis that have been done which specifically investigates the genotype incompatibility effect between maternal and fetal gene that underlying pPROM. We believe that our analysis results are helpful for generating hypotheses for future studies or wet lab validations.The importance of maternal-fetal genotype incompatibility in human diseases, particularly in obstetrical complications, was first discussed in the 1990s  and has A commonly used approach is to code the incompatibility effect whenever there is a disagreement between maternal and fetal genotypes . HoweverIntuitively, our approach will boost the statistical power by adding a MFGI model selection step. The power gain results from the fact that the true underlying incompatibility model can be selected most of the time with enough samples. We conducted extensive simulation studies, considering the effect of heritability, assumption about HWE, sample size and different disease gene functions. The results indicate that the proposed 2-step strategy works well when the underlying truth is unknown compared with the full model approach. Our approach controls the type I error rate at the nominal level and achieves higher power than the full model approach without performing incompatibility model selection. Our approach does not pose strong assumptions, and its performance is quite consistent under settings such as HWE or HWD, with or without maternal and/or fetal main effects.We applied the 2-step approach to study maternal-fetal genotype incompatibility effects associated with pPROM and identified several interesting SNPs. Our findings provide clues about the biological mechanism through which MFGI in these genes may have an adverse or protective effect on pPROM. Our results can be used to generate hypotheses for future biological validations to study pathogenesis of pPROM.Overall, this method can be applied to study the maternal-fetal genotype incompatibility component of obstetrical complications, such as preeclampsia and other human diseases in which maternal and fetal genetic factors interact and increase the risk of disease.The authors declare that they have no competing interests.SL developed the model, performed the statistical analysis, and drafted the manuscript; YC conceived the idea, participated in the model design and manuscript writing. RR collected the data. All authors read and approved the final manuscript.