Stalk strength is an important trait in maize (Zea mays L.). Strong stalks reduce lodging and maximize harvestable yield. Studies show rind penetrometer resistance (RPR), or the force required to pierce a stalk rind with a spike, is a valid approximation of strength. We measured RPR across 4,692 recombinant inbreds (RILs) comprising the maize nested association mapping (NAM) panel derived from crosses of diverse inbreds to the inbred, B73. An intermated B73×Mo17 family (IBM) of 196 RILs and a panel of 2,453 diverse inbreds from the North Central Regional Plant Introduction Station (NCRPIS) were also evaluated. We measured RPR in three environments. Family-nested QTL were identified by joint-linkage mapping in the NAM panel. We also performed a genome-wide association study (GWAS) and genomic best linear unbiased prediction (GBLUP) in each panel. Broad sense heritability computed on a line means basis was low for RPR. Only 8 of 26 families had a heritability above 0.20. The NCRPIS diversity panel had a heritability of 0.54. Across NAM and IBM families, 18 family-nested QTL and 141 significant GWAS associations were identified for RPR. Numerous weak associations were also found in the NCRPIS diversity panel. However, few were linked to loci involved in phenylpropanoid and cellulose synthesis or vegetative phase transition. Using an identity-by-state (IBS) relationship matrix estimated from 1.6 million single nucleotide polymorphisms (SNPs) and RPR measures from 20% of the NAM panel, genomic prediction by GBLUP explained 64±2% of variation in the remaining RILs. In the NCRPIS diversity panel, an IBS matrix estimated from 681,257 SNPs and RPR measures from 20% of the panel explained 33±3% of variation in the remaining inbreds. These results indicate the high genetic complexity of stalk strength and the potential for genomic prediction to hasten its improvement. Ostrinia nubilalis H. Diatraea grandiosella D. Gibberella zeaeDiplodia zeaeMaize stalk strength impacts grain yield and silage quality due to its relationship with stalk lodging and stover quality. High stalk strength is important in fields plagued by European corn borer, Dissection of stalk strength into its constituent traits suggests the structural composition of the rind, and not the pith or total girth, is the chief determinant of strength Given the numerous mechanisms mediating stalk strength and the continuous variation observed for the trait, several studies were performed to quantitatively dissect its genetic architecture Previous RPR studies laid a foundation for evaluating stalk strength. But, whole genome sequencing of B73 Stalk strength remains a determinant of harvestable yield and forage quality in the use of maize for ruminant animals. Furthermore, new applications in cellulosic ethanol and biopolymer synthesis have caused a surge of interest in stalk strength related traits such as cell wall composition and biosynthesis In this study, we measured the stalk strength (RPR), days to anthesis (DTA), and primary ear height (EHT) of approximately 200 recombinant inbreds (RILs) from each of 25 families composing the maize nested association mapping panel (NAM) The NAM panel, developed by the Maize Diversity Project, was created as previously described NAM families were also grown in Madison, WI at the Arlington Agricultural Research Station (silt-loam soil) in the summer of 2009. In WI fields, 3,453 RILs of the NAM panel were randomized and blocked into 10 maturity groups based on previous flowering data At Muskgrave Research Station in Aurora, NY (silt-loam soil) in the summer of 2010, a set of 2,293 NCRPIS inbreds were measured for RPR. The inbreds were planted in single row plots of 12 plants. The same year, 2,453 inbreds from the NCRPIS diversity panel were measured at South Farm Research Station in Columbia, MO (silt-loam soil). Single row plots of 15 plants were grown. B73, and replicates of the 25 alternate NAM parents, were randomly included as checks in the NY and MO field designs. The 2,293 inbreds measured in both environments were used in GWAS and genomic prediction of the NCRPIS diversity panel .To measure stalk strength, a modified Accuforce Cadet digital force gauge  was assembled with a spike and used to manually pierce stalks as previously described RPR measures were collected near the middle of the stalk internode immediately below the primary ear. Measures were taken from three randomly selected plants per plot. This resulted in the collection of 37,548 RPR measures across NAM families in three environments. Measures taken in the IBM family and the NCRPIS inbred diversity panel amounted to 1,735 and 15,399 observations, respectively. These were taken in two environments. To avoid differential nutrient availability and light capture, the end plants of each plot were not measured. Phenotypic data for DTA and EHT were acquired from the same plots as previously described Three molecular marker sets were used for joint-linkage QTL mapping, GWAS, and GBLUP across the NAM and IBM families, as well as linear mixed model GWAS and GBLUP across the NCRPIS inbred diversity panel. In the first marker set, 1,106 markers were genotyped on an Illumina Golden Gate assay across the RIL families to facilitate joint-linkage QTL mapping A second marker set of 1.6 million SNPs reported in the maize HapMapV1 www.panzea.org.A third marker set of 681,257 SNPs from the NCRPIS inbred diversity panel were genotyped using Genotyping-By-Sequencing (GBS) To partition phenotypic variance into genetic and environmental components for RPR, DTA, and EHT, linear mixed modeling was performed using ASReml v3.0 row ∶ AR1col). All environmental effects and residual correlation structures in each environment’s model were tested by backward selection and retained if they met a likelihood ratio significance of p<0.05. BLUPs for each RIL in the NAM and IBM families were then predicted in each environment.For the RIL families, linear mixed models were first separately fit for each environment including a single fixed effect for the grand mean and multiple random effects. Random effects entering the full model included family and RIL nested within family genotypic effects, as well as the environmental effects of the blocks, rows, and columns of each field design. A separate variance component was fit for RIL nested within each of the NAM and IBM families. An additional family term was constructed to accommodate the replicated parental checks. All random effect terms in the model, including the genotypic effects of family and RIL within family, were modeled with independent G structures. However, a correlated R structure was fit among residuals based on a two-dimensional separable first-order autoregressive spatial structure for rows and columns in each environment  line means for these traits . The unbFor each trait, estimates of broad sense heritability on a line means basis across and within RIL families were calculated from the multi-environment models fitting genotypic effects as a random effect, as previously described The denominator of the broad sense heritability estimator, when computed on a line means basis To map genetic associations underlying the estimated heritable variation, the SAS v9.2 statistics package Next, the previously described stepwise joint-linkage mapping procedure After constructing a family-nested QTL model for RPR, DTA, and EHT from the full dataset, each trait’s model was fit to every other trait for estimation of pleiotropic family-nested QTL. Significance of pleiotropy was determined as previously described By modifying family-nested QTL models for RPR, DTA, and EHT constructed from the full dataset, ten additional models, one for each maize chromosome, were built to account for background genetic variation during joint-linkage-assisted GWAS. In the family-nested QTL models, all terms explaining significant trait variation were fit, with the exception of the family term denoting variation between the NAM and IBM families. Family-nested QTL residing on a model’s designated chromosome were also dropped. Residual trait variance after fitting this model was inferred to represent the joint distribution of error and the missing family-nested QTL of the dropped chromosome.For each trait, residuals from each of the ten chromosome’s models were used in joint-linkage-assisted GWAS of the HapMapV1 SNPs Using the Genome Association and Prediction Integrated Tool (GAPIT) We conducted genomic prediction by GBLUP using the package rrBLUP To perform cross-validation, all NAM RILs (not stratified by family), each NAM and IBM family, and the NCRPIS diversity panel were randomly partitioned into five disjoint subsets. Line means from combinations of one , two (10 folds), three (10 folds), and four (5 folds) subsets were used to calibrate models and predict the remaining line mean values. All prediction accuracies were then averaged across folds. This process was repeated 20 times randomly selecting five disjoint subsets each time to estimate prediction accuracy with respect to the number of lines in the model calibration set.For comparison to GBLUP, prediction of RPR BLUP line means by joint-linkage mapping of family-nested QTL was also performed using PROC GLMSelect in the SAS v9.2 statistics package Prediction accuracy was measured as the coefficient of determination obtained by regressing BLUP or BLUE line means from first stage models against predicted line means obtained by GBLUP or the family-nested QTL models of second stage models for each trait upon cross-validation. This differs from traditional estimates of genomic prediction accuracy as the coefficient of determination between genomic estimated and true breeding values. This metric was not calculable given a lack of true breeding values for RPR in RIL families or the NCRPIS inbred diversity panel.Heritable variation between maize lines was identified for RPR, EHT, and DTA within the NAM, and IBM families, as well as the NCRPIS inbred diversity panel . TransgrBroad sense line means heritability estimates for RPR measures in the surveyed germplasm were low . This waAbout 37% of stalk strength variation in the NAM panel was attributed to environmental variation . This waCorrelations between RPR and DTA, were positive among plots across NAM and IBM families , and EHT , were observed across the NAM and IBM BLUP family means.brown midrib mutants involved in lignin biosynthesis of the phenylpropanoid pathway, a putative 4-coumarate-CoA ligase-like gene (AF466202.2_FG012) potentially involved in the same pathway was located near a linkage marker on chromosome ten at about 69.2 cM with a RMIP of 18. Also, a caffeoyl-CoA O-methyltransferase (GRMZM2G077486) of the phenylpropanoid pathway was flanked by linkage markers on chromosome ten at 38.6 and 40.1 cM possessing RMIPs for RPR of 20 and 11, respectively.The resolution afforded by joint-linkage mapping did not provide gene level characterization of RPR associations. In most instances, robust family-nested marker association persisted an interval of one to three cM before dropping below a RMIP of 10. In these intervals, few genes with known involvement in phenylpropanoid or cellulose synthesis pathways were identified. While no robust associations were found near the brittle stalk 2, glossy1–15, and teopod1, 2 were not identified near associations possessing RMIPs for RPR over 10. Similarly, co-localization of QTL mapped in the previous multi-family RPR study and this family-nested QTL study was not substantial Of the 12 known cellulose synthases in the maize genome, the only synthase whose nearest linkage marker possessed a RMIP over 10 was cellulose synthase-9 (GRMZM2G018241). This gene and marker are located on chromosome two at 82.5 cM and possessed a RMIP of 24. Uncharacterized annotations  with predicted cellulose synthase activity by homology and known transcriptional evidence were also identified on chromosome nine near a linkage marker at about 42.8 cM and chromosome ten at about 38.6 cM on the NAM composite map. Both these linkage markers possessed a RMIP of 20, with the latter also flanked by a marker possessing a RMIP of 10. Cloned loci previously identified for vegetative phase transition and other stalk strength related traits, such as the mutants of To further resolve joint-linkage mapped RPR associations, 141 significant associations were identified by joint-linkage-assisted GWAS in the NAM and IBM families . Family-The effect sizes of GWAS RPR associations across the NAM and IBM families were uniformly small and similar in size and distribution to the significant alleles nested within each family during joint-linkage QTL mapping. No RPR effects with an absolute value greater than 0.05±0.02 KgF were observed for GWAS effect estimates. The most robust association identified across the NAM and IBM families possessed a RMIP of 100. This SNP is located on chromosome three at 176,660,475 bp and was flanked by linkage markers that possessed RMIPs of 10 and 13 during joint-linkage mapping. The nearest annotation is 5,139 bp downstream and encodes a transferase (GRMZM2G165192) responsible for transferring acyl groups other than amino-acyl. No annotations within a 1 cM interval surrounding the association were obvious candidates for stalk strength. The second and third most robust associations were both identified on chromosome eight at 163,943,201 bp and 8,415,595 bp. These possessed RMIP of 94 and 73, respectively. Both were also located near regions of the genome neighboring significant markers identified in joint-linkage analysis. The former is located in an interval wherein two linked markers spaced about 1.7 cM apart possessed a combined RMIP of 62. The latter neighbors a linked marker with a RMIP of 14 in joint-linkage mapping. In both instances, no obvious candidates for stalk strength related pathways or developmental processes were apparent. The nearest respective annotations were a glycosyl-transferase (GRMZM2G002023) 4,605 bp downstream and an O-glycosyl hydrolyzing enzyme (AC234160.1_FG003) 3,349 bp downstream.brown midrib, brittle stalk, or teopod loci or near enzymes with known involvement in phenylpropanoid and cellulose synthesis pathways or vegetative phase transition. Comparisons between significant RPR associations identified in the RIL families and those enriched in the NCRPIS inbred diversity panel revealed little discernible commonality.In addition to joint-linkage-assisted GWAS across the NAM and IBM families, sequential single marker GWAS was also performed across the NCRPIS diversity panel regressing BLUP line means for RPR against SNPs. . To accoGiven the highly polygenic architecture of RPR, genomic prediction was performed to determine the ability of all genotyped diversity to explain variation in BLUP line means for RPR, DTA, and EHT across all NAM families possessing a broad sense line means heritability over 0.05 . An IBS Fitting a family-nested QTL model with an included family term, constructed by joint-linkage mapping of calibration sets subsampled from each of the heritable NAM families, wielded lower prediction accuracies than GBLUP . ConstruAn IBS relationship matrix constructed for the RILs of the IBM family was less predictive of variation in BLUP line means for RPR, DTA, and EHT than that obtained across all NAM families when fit by GBLUP . Cross-vIn addition to RIL families, the accuracy of GBLUP at predicting BLUP line mean variation in RPR, DTA, and EHT was assessed in the NCRPIS inbred diversity panel . This waIn a final assessment of genomic prediction accuracy, BLUE line means of RPR, DTA, and EHT between families and inbreds across environments were predicted by GBLUP . CorrelaIn this study, we inferred the genetic architecture and genomic prediction accuracy of RPR as a proxy for maize stalk strength. In total, over 50,000 plants were measured for RPR across NAM and IBM families, and the NCRPIS diversity panel. These measures were collected in addition to DTA and EHT within three environments for NAM and IBM families, and two environments for the NCRPIS inbred diversity panel.Transgressive segregation for RPR was observed in many NAM and IBM families . This fiDespite the increased genetic variation in RPR among RILs relative to their parental values, estimates of broad sense heritability calculated on a line means basis were low in all families . This coHowever, it is most likely the reduction in heritability resulted from the decreased replication of measures taken on each inbred in this study relative to the former multi-family RPR study Of the heritable RPR variation that was observed in this study, approximately 60±4% was explained by variation between families. With a shared B73 founder, all SNPs differing between families also segregated within at least a fraction of the families depending on an allele’s frequency among founders. Variation between RIL families may then be attributed to mutation and ancestral recombination occurring between the non-B73 progenitor of each family; whereas, variation within families may be attributed largely to recent recombination. Differences in variance within and between families are likely due in part to the reduced functional diversity segregating within a single family relative to across families. But, given the random genetic effects used to model RPR, another reason for increased variance estimates between families, is an increased number of observations available to estimate between family variance. This increase in observations between families relative to within them reduced the error and the shrinkage of random effects modeling between family variance.To resolve family-nested QTL explaining RPR variation, BLUP line means for RPR were used in bootstrapped joint-linkage mapping of the RIL families. After accounting for RPR variation between families, variation in families was mapped to family-nested molecular markers. This identified 78 family-nested markers with a RMIP over 10 . Given tWhile the identified number of family-nested QTL is highly dependent on the mapping resolution and method employed, the number entering into a single model for RPR in our approach was 18±2 before the permutation-based threshold for model entry was reached. Of these family-nested QTL, only about half were significant within a given NAM or IBM family. A single family-nested QTL model explained 81±3% of the variation across RPR BLUP line means. Supporting the presence of repulsion phase linkages of RPR loci in NAM parents, positive and negative allele effects relative to the common parent, B73, were observed within all families. The allele series present in all family-nested QTL may be attributed to the genetic background specificity of the effects and differing linkage patterns among nearby loci whose cumulative effect is explained by the family-nested QTL. Further highlighting the highly polygenic genetic architecture of RPR, all family-nested QTL effects were small and none explained over 2.7% of the BLUP variation in RPR across RILs after accounting for the between family variation. Although covariation was observed for DTA, EHT, and RPR among line and family means, and several loci for these traits co-localized, no significant mutually pleiotropic family-nested QTL were identified. This supports previous studies indicating ear height is a poor proxy for stalk strength during selection After joint-linkage mapping, RPR variation between BLUP line means of the RIL families was further resolved by joint-linkage-assisted GWAS. This analysis revealed the segregation of 141 significant non-nested associations across families, after accounting for variation between families . FurtherIn addition to joint-linkage-assisted GWAS, a sequential single marker linear mixed model GWAS of RPR BLUP line mean variation was performed in the NCRPIS diversity panel . HoweverEven in sizeable populations, such as the NCRPIS diversity panel, only the most common and largest additive effect alleles not severely confounded with population structure will significantly associate with a trait during a single marker mixed model GWAS. If the functional diversity of stalk strength is correlated with fitness and follows the Fisher-Orr model However, it remains to be determined if these studies should focus on candidate genes based on known molecular homology. GWAS associations identified as significant in the NAM and IBM families as well as the top 100 associations with a false discovery rate just over 10% in the NCRPIS diversity panel did not co-localize with genes involved in phenylpropanoid and cellulose synthesis, or vegetative phase transition. This lack of co-localization with genes in pathways known to influence many constituent traits of stalk strength may be due to their conservation in natural variation. This may result as a consequence of negative fitness effects. Nonetheless, given the low heritability of RPR, and high levels of diversity observed, it is likely the numerous anatomical and compositional factors influencing RPR greatly complicate mapping of causal loci. While little pleiotropy was observed between stalk strength and ear height or days to anthesis, interactions among other constituent traits may greatly influence stalk strength, and may do so in a non-additive manner. Future mapping efforts should decompose stalk strength into its constituent traits to reduce latent complexities limiting power and aid mapping of their potentially simpler genetic architectures.Given the high degree of complexity in stalk strength genetic architecture inferred while mapping RPR, genomic prediction was performed using GBLUP to model relatedness based on an IBS relationship matrix. This method revealed substantial variation in BLUP and BLUE line means for RPR, DTA, and EHT was predictable using a fraction of RILs randomly selected from each NAM family . While BAs a comparison to GBLUP, the expected prediction accuracy of family-nested QTL models constructed by joint-linkage mapping subsets of the full data set was also assessed across the BLUP line mean variation for RPR. The variation explained in NAM by family-nested QTL models, 81% , and thaIn the NCRPIS diversity panel, GBLUP was also performed to assess expected prediction accuracies. This was accomplished with an IBS relationship matrix estimated from 681,257 SNPs. While significant prediction accuracies were attained, they remained lower than those observed in the NAM panel. The increased genetic diversity and reduced marker density in the NCRPIS panel relative to the NAM and IBM families may be attributed to this lower prediction accuracy. The potential complexity of the underlying genetic architecture for each trait increases as the diversity in the population increases, the marker density and size of the calibration set limit the degree that GBLUP is both informed of, and able to explain this complexity. Also, given the highly structured nature of the NCRPIS panel and the prevalence of rare alleles, the genetic architecture explaining variation in the surveyed traits may have evolved by differing mechanisms within each subpopulation of the diversity panel. This may introduce genetic background specificity and non-additivity into modeling the global population and is a potential reason for the more limited prediction accuracy of GBLUP in the NCRPIS diversity panel relative to the NAM panel.While the expected RPR prediction accuracy of a given calibration set size is informative, variation in prediction accuracies was present at all the calibration set sizes in both NAM and NCRPIS diversity panels. Variations in accuracy were especially high within the family-nested QTL models in the NAM panel. This suggests the exact set of lines chosen to calibrate a model may have a larger influence on prediction accuracy when family-nested QTL or other marker effects are selected than when a GBLUP model is assumed and all effects are included but shrunken to the mean. In GBLUP, RPR prediction accuracies did not significantly differ if lines included in a calibration set were randomly selected across families, or were stratified by family. Given the large fraction of BLUP line mean variation in RPR explained by between family variation, family stratified sampling should ensure this variation is better modeled. However, a randomly selected 20% of the NAM panel appeared to sufficiently sample most families to accurately capture between family RPR variation. Previous studies have revealed the gains to be had from strategically sampling the phenotypic/genotypic space when developing calibration sets for genomic prediction Stalk strength and its constituent traits will continue to play an important role in the selection of maize varieties maximizing grain harvestability and silage desirability. This study presents a comprehensive look at the genetic architecture of stalk strength and an assessment of its prediction accuracy. Future efforts detailing the genetic architecture of the anatomical, compositional, and phase change traits underlying stalk strength may reveal simpler architectures and better leverage our existing biological knowledge to understand the genetics of stalk strength. Understanding the genetic architecture of these traits and employing crop modeling to realize how they interact to influence stalk strength is a logical path to better inform plant breeding decisions. Breeding efforts in low heritability traits like stalk strength must incorporate a present, but inherently limited, understanding of genetic architecture and an ability to predict breeding values into a unified selection framework. These efforts will improve prediction of a population’s response to frequency-dependent selection on alleles, haplotypes, and genotypes. Given the availability of inexpensive sequence data, this is increasingly becoming an achievable goal in the optimization of crop improvement.Figure S1DTA and EHT transgressive segregation within the RIL families and NCRPIS diversity panel.(TIF)Click here for additional data file.Figure S2RPR, DTA, and EHT correlations within the RIL families and NCRPIS diversity panel.(TIF)Click here for additional data file.Figure S3RPR, DTA, and EHT associations within and across the RIL families and NCRPIS diversity panel.(TIF)Click here for additional data file.Figure S4GBLUP of DTA and EHT BLUP line means across the RIL families and NCRPIS diversity panel.(TIF)Click here for additional data file.Figure S5Family-nested QTL-based prediction of RPR BLUP line means across the RIL families.(TIF)Click here for additional data file.Figure S6GBLUP of RPR, DTA, and EHT BLUE line means across the RIL families and NCRPIS diversity panel.(TIF)Click here for additional data file.Table S1RPR, DTA, and EHT BLUP and BLUE line means across the RIL families.(TXT)Click here for additional data file.Table S2RPR, DTA, and EHT BLUP and BLUE line means across the NCRPIS diversity panel.(TXT)Click here for additional data file.Table S3RPR, DTA, and EHT family-nested QTL associations within the RIL families.(TXT)Click here for additional data file.Table S4RPR joint-linkage-assisted GWAS results across the RIL families.(TXT)Click here for additional data file.Table S5RPR linear mixed model GWAS results across the NCRPIS diversity panel.(TXT)Click here for additional data file.


To test this hypothesis we performed a genome-wide association study comparing the allele frequency of 572,352 single nucleotide polymorphisms (SNPs) in 1,413 monozygotic (MZ) and 5,451 dizygotic (DZ) twins with 3,720 healthy singletons. Twins and singletons have been genotyped using the same platform. SNPs showing association with being a twin at P-value < 1 × 10-5 were selected for replication analysis in 1,492 twins  and 1,880 singletons from Finland. No SNPs reached genome-wide significance  in the main analysis combining MZ and DZ twins. In a secondary analysis including only DZ twins two SNPs (rs2033541 close to ADAMTSL1 and rs4149283 close to ABCA1) were genome-wide significant after meta-analysis with the Finnish population. The estimated proportion of variance on the liability scale explained by all SNPs was 0.08  when MZ and DZ were considered together and smaller for MZ  compared to DZ  when analyzed separately. In conclusion, twins and singletons can be used in genetic studies together with general population samples without introducing large bias. Further research is needed to explore genetic variances associated with DZ twinning.Twin registries around the globe have collected DNA samples from large numbers of monozygotic and dizygotic twins. The twin sample collections are frequently used as controls in disease-specific studies together with non-twins. This approach is unbiased under the hypothesis that twins and singletons are comparable in terms of allele frequencies; i.e. there are no genetic variants associated with being a twin  Twin brothers and sisters have been extensively studied in Genetic Epidemiology with the aim of disentangling the genetic architecture of multiple biological and behavioral traits. Traditionally, this has been done by mean of quantitative genetic modeling, in which observed and expected variance/covariance structures are estimated and compared utilizing phenotypic twin data .The possibility of using these twin data for such scientific purposes has driven the establishment of multiple large twin cohort studies and registries around the globe ,3. These registries have traditionally focused on collecting phenotypic data longitudinally on large numbers of participants. However, because of the recent advances in genotyping methods, many twin registries collect DNA from the participating twins. Given the population based nature of most twin cohorts, analyzing this genomic material would allow studying not only the genetic architecture of the collected phenotypes, but also the identical by descent (IBD) sharing of alleles , MZ disc-5 in a sample of twins and singletons from Finland. We first performed a genome-wide association (GWA) study comparing twins participating in the TwinGene study with healthy singletons enrolled as controls in a large study on schizophrenia susceptibility. Second, we attempted to replicate SNPs showing association with being a twin at P-value < 1 × 10Since most twin studies jointly used MZ and DZ in GWAS, we focused on this combined outcome in our primary analysis. In secondary analysis DZ twins were studied separately. This stratified analysis was justified by two reasons. First, some twin materials may consist of purely MZ or DZ twins and second, if genetic variants predisposing to multiple ovulations exist, their detection would be improved by including only DZ twins given the differences in the biological origins of MZ and DZ twins .The Swedish Twin Registry is a population-based national register currently including close to 200,000 Swedish twins born from 1886 to 2008  in MZ and 0.09  in DZ twins. When MZ and DZ twins were analyzed together, the estimated proportion was 0.08 .We conducted this analysis to test the hypothesis that twins have similar genetic architecture as singletons. If this is the case, biological twinness does not confound GWAS, and as consequence, genetic data derived from twins can be used in such studies without introducing large bias. On the other hand, if genetic variants associated with biological twinness exist, they can bias GWAS in two ways. First, if the twins are used as healthy controls in disease-specific GWAS, spurious association can be detected. Second, if the GWAS is conducted only on twins or in combined samples where twins and non-twins are analyzed together (for example to investigate a continuous phenotype) spurious association can be detected if the genetic variants associated with biological twinness are also associated with the phenotype of interest.In the present study we did not find common genetic variants that were associated with being a twin. In a secondary analysis of DZ twins versus non-twins, we identified two SNPs that were genome-wide significant in the stage 1 and when meta-analysed with the Finnish samples. Given our sample size, we have 80% power to detect genetic variants with an effect size of 1.22 and 1.25 and an allele frequency of 0.50 and 0.20, respectively. Therefore, rarer variants or variants with smaller effect size might have been missed in this study. To evaluate the potential for discovery of SNPs associated with twinness, we estimated the proportion of variance on liability scale explained by all common SNPs available in our genotyping array. A high proportion of variance would indicate that common SNPs play a large role and thus, that many associated SNPs might be discovered with larger samples. We observed a small proportion of variance explained (0.06 for MZ and 0.09 for DZ twins) indicating that there is, relatively speaking, a limited potential for discovery of many genetic variants associated with biological twinness http://www.twinsuk.ac.uk/publications.html#2010). GWA studies have also been performed only using samples of related individuals. For example, a GWAS for association with height and body mass index has been conducted in a sub-sample of the Australian Twin Registry including 11,536 individuals composed of Australian twins, family members, and unrelated individuals [Twins samples have already been used in several GWA studies, together with other singletons samples or independently. A genotyped sample of individuals from the UK twin registry has been part of a large number of GWA meta-analysis . In 2010ividuals . The autividuals . Genome-Although practically identical procedures and platforms were used, the twins and singletons were genotyped in different laboratories and at different time-points. This might have introduced systematic bias by increasing the risk to detect spurious association and by inflating the estimates of the proportion of variance explained by all common SNPs. However, these are issues only if positive findings are observed. Because our main analysis on twins compared to non-twins revealed no significant locus and the estimated “chip-heritability” was low, we consider the effect of this potential bias negligible. It is important to highlight that the aim of this study was not to identify new genetic variants predisposing to twinning, for example, by influencing the probability of blastocyst fragmentation, multiple ovulation or mere survival of more than one concomitant fetus. We recognize that to pursue this aim a better approach would be to investigate the genetic architecture of parents of MZ and DZ twins. Other studies with larger sample size are needed to investigate these hypotheses. Nevertheless, we identified two loci, ADAMTSL1 and ABCB1, likely to be associated with DZ twinness. ABCA1 is involved in cholesterol transport and SNP markers on the same loci have been found previously associated with HDL-levels in several large GWAS -33. Furt-5 in the main analysis. Finns are considered an outlier population on the European genetic landscape [http://www.euengage.org/press.html) and results have been reasonably comparable to those observed in other European populations. In addition, it should be acknowledged that, while we know that both Predict-CVD study sample and the wave 5 and 6 of the Swedish schizophrenia study do not include pairs of relatives, it is uncertain whether any of the participants to these studies could be a member of a twin pair. Notwithstanding, while this may potentially introduce an error in our analyses, it may be safely neglected as twins would represent ~2% of the participants in these population-based samples. We used a Finnish population to replicate SNPs with a p-value < 1 × 10andscape , other pIn conclusion, we did not find evidence for large genetic differences between twins and singletons, supporting the practice to use twins together with singletons in genetic studies without introducing bias.Figure S1Plot of the first 3 MDCs from the Finnish samples (Panel A.) and Swedish samples (Panel B).(JPG)Click here for additional data file.Figure S2The plot is centered on rs2033541 (purple diamonds).The R2 values are from the CEU HapMap2 samples. The CEU HapMap2 recombination rates are indicated in blue on the right y axes. The figures were created with LocusZoom (http://csg.sph.umich.edu/locuszoom/). Mb, megabases. (PDF)Click here for additional data file.Figure S3The plot is centered on rs4149283 (purple diamonds).The R2 values are from the CEU HapMap2 samples. The CEU HapMap2 recombination rates are indicated in blue on the right y axes. The figures were created with LocusZoom (http://csg.sph.umich.edu/locuszoom/). Mb, megabases.(PDF)Click here for additional data file.


Genome wide association studies (GWAS), mostly in Europeans have identified several common variants as associated with key lipid traits. Replication of these genetic effects in South Asian populations is important since it would suggest wider relevance for these findings. Given the rising prevalence of metabolic disorders and heart disease in the Indian sub-continent, these studies could be of future clinical relevance.We studied seven common variants associated with a variety of lipid traits in previous GWASs. The study sample comprised of 3178 sib-pairs recruited as participants for the Indian Migration Study (IMS). Associations with various lipid parameters and quantitative traits were analyzed using the Fulker genetic association model.-7. We identified particularly strong association signals at rs662799 in APOA5 , rs10503669 in LPL  and rs780094 in GCKR  loci in relation to triglycerides. In addition, the GCKR variant was also associated with total cholesterol . We also replicated the association of rs562338 in APOB (p=0.03) and rs4775041 in LIPC (p=0.007) with LDL-cholesterol and HDL-cholesterol respectively.We replicated five of the 7 main effect associations with p-values ranging from 0.03 to 1.97x10We report associations of five loci with various lipid traits with the effect size consistent with the same reported in Europeans. These results indicate an overlap of genetic effects pertaining to lipid traits across the European and Indian populations. Cholesterol and triglycerides are major plasma lipids and key heritable risk factors for cardiovascular disease ,2. Commo9. The average population differentiation within 19 Indian sub populations was identified to be 3 fold greater than that observed in a study of 23 European population groups 2) 2)  and X11,For stratified analysis dietary fat intake was defined by a binary variable which grouped individuals as low and high fat intake after defining the median as the cut-off point. Fat intake was assessed by an interviewer-administered semi-quantitative food frequency questionnaire (FFQ). Gene-Environment  interaction effects were tested while including Gene-Environment interaction terms within the fixed effects component of Fulker’s association model.2) was calculated using the z2 statistic of Zaykin et al. [2 statistic under the null hypothesis that the two populations have the same average pair-wise LD. Permutation tests were performed using the cvpermute command in MATA in STATA v11.2 .We used genotype data available from phase-3 of HapMap-CEPH (Centre d'Etude du Polymorphisme Humain) and GIH (Gujarati Indians in Houston) populations to compare the linkage disequilibrium between the two population groups. The overall difference in pair wise LD  range of 7-21% and a sample size of 3178 sib pairs; we had over ≥80% power to detect associations which explained ≥0.003% of variation in the studied lipid traits. Sample size calculations were performed using the Genetic Power Calculator  at statiE/C-I/C-IV gene cluster; CETP: Cholesteryl ester transfer protein gene; LDLR: Low density lipoprotein receptor gene; GCKR: Glucokinase (hexokinase 4) regulator gene; LPL: Lipoprotein lipase gene; SNP: Single nucleotide polymorphism; GWAS: Genome wide association study.LD: Linkage Disequilibrium; SNP: Single nucleotide polymorphism; APOA5: Apolipoprotein A-V gene; APOB: Apolipoprotein B gene; APOE/CI/C4: Apolipoprotein The authors declare that they have no competing interests.SE, GDS, FD, DP, YB-S, KSR, GRC, SK and IMSG contributed to the conception and design of the study. SR, KKV, VG, CJS, SP, SNM, SK, NJT, GDS, FD, YB-S, SE and GRC contributed to the analysis and interpretation of data. SR, FD, SE, GRC and GDS were responsible for drafting the article. SR, VG, FD, SE, GRC, YB-S, DP, VG, SK, LB and NJT contributed to critical revision of the paper. All authors have read the manuscript and gave their final approval for this version of the manuscript to be published.


Unified Mixed Model (UMM) on data of a low-density genome-wide association study for growth and wood property traits carried out in a Eucalyptus globulus population (n = 303) with 7,680 Diversity Array Technology (DArT) markers. Model comparisons were based on the degree of deviation from the uniform distribution and estimates of the mean square differences between the observed and expected p-values of all significant marker-trait associations detected. Our analysis revealed the presence of population and family structure. There was not a single best model for all traits. Striking differences in detection power and accuracy were observed among the different models especially when population structure was not accounted for. The UMM method was the best and produced superior results when compared to GLM for all traits. Following stringent correction for false discoveries, 18 marker-trait associations were detected, 16 for tree diameter growth and two for lignin monomer composition (S∶G ratio), a key wood property trait. The two DArT markers associated with S∶G ratio on chromosome 10, physically map within 1 Mbp of the ferulate 5-hydroxylase (F5H) gene, providing a putative independent validation of this marker-trait association. This study details the merit of collectively integrate population structure and relatedness in association analyses in undomesticated, highly heterozygous forest trees, and provides additional insights into the nature of complex quantitative traits in Eucalyptus.The promise of association genetics to identify genes or genomic regions controlling complex traits has generated a flurry of interest. Such phenotype-genotype associations could be useful to accelerate tree breeding cycles, increase precision and selection intensity for late expressing, low heritability traits. However, the prospects of association genetics in highly heterozygous undomesticated forest trees can be severely impacted by the presence of cryptic population and pedigree structure. To investigate how to better account for this, we compared the GLM and five combinations of the  Understanding genotype-phenotype relationships and discovering genes or genomic segments with roles in the control of complex traits are challenges of major biological and economic importance. Deciphering this connection is considered to be geneticists' ultimate goal to determine the genetic underpinnings of biological processes while enhancing directional selection strategies in improvement programs. The combined advances in molecular markers development, functional genomics, and analytical methods, made it possible to gain insights into the architecture of complex traits by identifying underlying genes and genomic segments involved in their control  Unified Mixed-Model’ (UMM) UMM model as fixed or random effects, respectively et al. Glycine maxHordeum vulgareBrassica rapaTriticum aestivumHowever, in such wild populations genetic structure, such as the presence of provenance or racial effects and/or intra-racial spatial relatedness between trees may affect association genetics results UMMQ (population structure) and/or K (family structure) matrices in the UMM is expected to unnecessarily remove parts from the error term's variation and degrees of freedom to the population and/or family effects. This results in changes in the mean square error term which ultimately affects the statistical power of the association tests.To date, a number of association genetics studies have been reported for forest trees using either structured or unstructured populations. Various analytical methods have been applied to detect associations, including classical general linear model (GLM) with and without family structure Pinus taedaPinus contortaPinus taedaEucalyptusa priori choice of genes that are allegedly involved in trait control, genome-wide studies are unbiased in this respect, and therefore tend to better converge to the true genetic architecture of the complex traits investigated.Due to the lack of accessible genome-wide genotyping systems and given the generally low extent of linkage disequilibrium in forest trees, all these association studies were carried out based on the targeted analysis of polymorphisms in candidate genes. Only more recently genome-wide genotyping approaches have been applied in EucalyptusEucalyptus species Eucalyptus grandis reference genome, showed that they preferentially target the gene space with 77% of them positioned at <1 kbp from the nearest gene model. Moreover, they display a largely homogeneous distribution across the genome, thereby providing gene-targeted genotyping and good coverage for genome-wide applications in association genetics and Genomic Selection (GS) Recently, a high throughput Diversity Array Technology (DArT) marker platform was developed for species of Eucalyptus globulus core and intergrade populations were genotyped with the 7,680 DArT marker array. In the present study, our main objectives were: (1) to test the efficacy of including the Q and/or K matrices in the association genetics analyses for complex traits for growth and wood properties and (2) to evaluate and compare the efficacy of different association mapping models to avoid declaring false marker-trait associations based on the degree of deviation between the observed and expected p-values of marker-trait associations. Additionally, despite of the relatively limited size association mapping population we had access to, our study also contributes to the understanding of the genetic architecture of economically important traits in Eucalyptus globulus.As part of the Biotech MERCOSUR project Eucalyptus globulus Argentinian trial belongs to the Instituto Nacional de Tecnología Agropecuaria (INTA) and no specific permits were required to carry out the study. The three Eucalyptus globulus Uruguayan trials belong to Mundial Forestación. All the available data from these three trials were provided by the company director Rogerio de Aguiar de Moraes under the agreement of the Biotech MERCOSUR project. Eucalyptus globulus is an exotic tree species in Argentina and Uruguay and is not protected or endangered.The Eucalyptus globulus (Labill.) individuals growing at four separate trial sites was used in this study  as described previously eH =  iP is the frequency of the ith allele at the DArT marker locus. Because DArT markers are dominant, the allele frequencies were estimated making the frequency of ‘0’ genotypes equivalent to iP2, assuming Hardy-Weinberg Equilibrium.A subset of 2,364 DArT markers was selected for the analysis based on quality parameters out of the 7,680 included on the genotyping array. The selected DArT markers had Call Rate (percentage of samples that could be scored as ‘0’ or ‘1’) greater than 80%, Reproducibility (reproducibility of scoring between replicated samples) greater than 97% and were polymorphic with frequencies of samples scored as ‘0’ or ‘1’ ranging between 0.95 and 0.05. Level of polymorphism for each marker was calculated by the expected heterozigosity: K) with 10 independent runs for each K, each run starting with a burn-in period of 50,000 steps followed by 100,000 Markov Chain Monte Carlo iterations. The most probable value of K was selected according to the ΔK method et al. 2) implemented in the program TASSEL version 3.0.137 2 values were calculated separately for unlinked loci and for loci on the same chromosome. The 95th percentile of the square root transforming of r2 distribution was taken as a population-specific critical value of r2Genotypic data for a subset of 400 randomly taken DArT markers from the total of 2,364, were used to determine both population structure and pair-wise kinship coefficients among the 303 individuals, using the model-based Bayesian clustering algorithm implemented by STRUCTURE Unified Mixed-Model y, α, v, u, and e are vectors of adjusted phenotypic observations, DArT effects (fixed), population effects (fixed), kinship effects (random), and residual effects, respectively, and S, Q, Z are incidence matrices relating y to α, v, and u, respectively. Several models were tested including GLM without population and family structures (GLM), and UMM with different combinations of population and family structures . Additionally, as recommended by Price et al.Q matrix was substituted by the principal coordinate's analysis' (PCA) P matrix resulting in two additional models (P and P+K). We removed the last column of the Q matrix to eliminate linear dependence between columns; however, all the columns  were used in the P matrix to represent the population structure because it does not result in linear dependency. All analyses were conducted using TASSEL version 3.0.137 p<0.05 level, and were further corrected for multiple testing using the false discovery rate (FDR) method for multiple comparisons p<0.05. The FDR thresholds were calculated using the QVALUE package http://www.r-project.org/).The association mapping tests were carried out using two steps. In the first, data were standardized within each site and trait by subtracting each individual measurement from the mean trait value at that site and dividing the adjusted measurement by the site's standard deviation. The effect of large-scale environmental variation within each site was removed by exporting residuals from an analysis where replicate and incomplete block  was included as fixed or random effects, respectively. In the second step, these residuals were used as adjusted phenotype and single-marker associations were determined using the p-values of all DArT markers following the method described in Stich et al.p-values, suggesting that the type I error of the tested model could be substantially higher than the nominal α-level Model comparisons were based on the degree of deviation from uniform distribution and estimates of the mean square differences (MSD) between the observed and expected p>0.27). However, wood chemical traits were highly inter-correlated  and significantly different from zero (p<0.05), while PILO was only weakly positive correlated with DBH (0.16 p = 0. 05).Pearson correlations were also calculated between the residuals from the measured traits using the CORR procedure in SAS E-value≤1e−3) against the Eucalyptus grandis genome database , was carried out. To assess the putative identities of these DArT markers, BLASTX searches were performed against the GenBank non-redundant protein database (http://blast.ncbi.nlm.nih.gov/Blast.cgi) with an E-value cut-off≤1e-10. Annotation and mapping routines were run with Blast2GO http://www.geneontology.org/), and an enzyme classification number (EC number). Secondly, the Geneious pro 6.0.3 software (Biomatters http://www.geneious.com/) was used to assemble redundant DArT marker probe sequences, using the default parameter of 80% identity in a word length of 14 nucleotides. Thirdly, the genomic position the DArT marker probes as determined by aligning their sequences to the Eucalyptus grandis reference genome (version 1.1) Eucalyptus grandis genome version 1.1 available in Phytozome, .Based on the sequence information of the trait-associated DArT markers the following analyses were carried. Firstly, a sequence BLASTN search , with an average of 0.33 and most of them having eH values greater than 0.40  varied from 0.012 to 0.032. The number of pair-wise estimates r2 above the baseline 0.025 varied from 3.63% to 9.23%. However, a second-degree loess curve that fitted the r2 estimates did not reach the 95th percentile baseline for any linkage group (2 marker pairs) LD decays rapidly below a centimorgan, a recombination fraction found to correspond, on average, to 513 kbp Eucalyptus species at the single gene level showed that LD decays rapidly within a few hundred base pairs bona fide LD based genome-wide association study (GWAS).In the selected sample of 303 trees, pair-wise rge group , indicatE. globulus spp. pseudoglobulus (Naudin ex Maiden). Genetic group 3 included 101 trees (33%) belonging to the Furneaux Group of Islands, and North-Eastern and South-Eastern Tasmanian races, the Chilean provenance in the Argentinian trial and the Portuguese land race. This clear racial genetic grouping is in line with the results reported in similar native population studies of E. globulus using microsatellite markers et al. E. globulus spp. pseudoglobulus, whereas in Jones et al. E. globulus spp. globulus (such as Otways) and E. globulus spp. bicostata, than to E. globulus spp. pseudoglobulus. The resulting patterns from the STRUCTURE program suggest that the inclusion of the Q or P matrices in the analyses is expected to affect the association test's statistical power (see below). In spite of the unambiguous clustering, consistent with the geographically and taxonomically distinct subpopulations, the overall FST value was only 0.095±0.01 indicating a moderate genetic differentiation between the three E. globulus genetic groups. The estimate is similar to Steane et al. E. globulus and integrated races.The genetic structure obtained by STRUCTURE and PCA was similar . The firp-values for differences of the least square means  had the highest density (lowest Pilodyn) of the three At the phenotypic level, visual inspection of the box plots based on the residual trait values in each of the three subgroups defined by STRUCTURE , and there means  showed sK matrix in the association genetics analyses. We knew a priori that some of the trees were related, because they belonged to the same open-pollinated family, the average relationship coefficient for these trees was 0.232 , whereas the average for the unrelated pairs of trees was 0.032 . Mean relationship within genetic groups was 0.076, 0.069 and 0.083 for genetic groups 1, 2, and 3, respectively. As expected, the relationship among trees from the same genetic group was greater than those from different genetic groups. This was particularly true between groups 2 and 3 (0.011). The most frequent class of genetic relationship was for values between 0.00 – 0.05 (75.6%), followed by values between 0.05 – 0.10 (12.7%) (P<0.0001), confirming the presence of isolation-by-distance as the probable cause of the family structure found and once again justifying the inclusion of the K matrix in the association genetics analyses.The pair-wise relatedness among the 303 trees resulted in the identification of an array of variable relationships , indicat (12.7%) . Given tp-values was highest for the GLM model (Q or P), the models that included a population structure performed consistently better than those that did not for all traits (E. globulus population being studied. The MSD of the Q model (and P model) ranged from 0.000469 (0.000069) for Extractives to 0.006154 (0.001328) for PILO, and was considerably lower than the value found for the GLM model (P or Q) dramatically increases the statistical power. Moreover, the GLM model produced a number of apparent false positive or spurious associations across all traits  with respect to the Q and P models (from 1.18% to 6.98%) in the six traits tested (Q and/or K matrices). Yu et al. In the present study, we have incorporated the kinship relationship among trees. Accounting for family structure is expected to remove most of the variance associated with close relatedness that would not have been explained by the D values  and showp-values , whereass tested . This fip-values were similar and have similar MSD distributions (p<0.05) marker-trait associations for all studied traits  and by Stich et al. Arabidopsis thaliana.As expected, the complete Q+K ibutions . Furtherd traits . These fp-values . This resulted in 962 positive associations before multiple testing corrections at the significance level of 2) in the selected models was always modest, accounting for 4.02% to 13.76% . Recent studies in Eucalyptus have reported low numbers of QTLs for growth and wood quality traits, whose effects rarely accounted for more than 5% of the observed variance E. globulus, Bundock et al. et al. E. nitens, Thumma et al. 2 varying from 2.8% to 7.3% and averaging 5%. Gion et al. E. urophylla and E. grandis. In conclusion, most QTLs had effects below 5% and only 13 of them had effects above 15%. However, for growth traits the R2 values varied from 4.1% to 42.2% and from 5.0% to 37.0% for wood traits. In four-year-old progenies of two interspecific backcross families of E. urophylla and E. grandis, Kullan et al. 2 varied from 4.6% to 8.0% averaging 5.9% for DBH, and from 3.1% to 12.2% averaging 5.9% for wood density.The amount of phenotypic variation explained by each marker . However, it is interesting to note that the magnitude of these 18 associations did not change across the six models , except for marker ePt-638303 for DBH which was not significantly associated when using the K and Q+K models. Such consistency of results, notwithstanding the slight differences in R2 estimates across models, is a promising indication that the associations are indeed real  under a fixed model (Eq. 1) were 21 and 24 times larger than those estimated under the random model (Bayesian LASSO) for DBH and S∶G ratio, respectively. Furthermore, the proportion of the genetic variance explained by the markers (2 ip (1-ip) ip is the frequency of one allele at that locus and We compared the results of estimating markers effects simultaneously as random effects or fixed effects using Eq. 1. DArT markers effects were fitted as random using Bayesian least absolute shrinkage and selection operator (LASSO) in the BLR package for R, version 2.12.2 . ResultsE-value threshold of <1.e-10, eight DArT marker sequences, all associated with DBH, had significant BLASTX matches  associated with S∶G ratio in our population was also mapped to a QTL by Freeman et al. et al. et al. et al. E. grandis (640 Mbp) and E. globulus (545 Mbp) genomes is largely due to the sum of many small insertions/deletions widely distributed across the genome (Josquin Tibbits unpublished). It is therefore reasonable to speculate that this 1 Mbp difference between the marker and the gene could in fact be much smaller in the E. globulus genome. As tentative as it may be, this putative co-localization provides an appealing indirect biological validation of the association we found for S∶G ratio in our study.Comparison of genomic position of the associations found with previous QTL mapping studies were carried out, although to date, few have been the QTL detection reports in E. globuluset al.Eucalyptus breeding populations with 780 and 920 individuals respectively, several hundred DArT markers associated with DBH were found spread out across all 11 chromosomes. When fitted in genomic selection models, the 200 associated DArT markers of largest effect captured over 80% of the heritability for diameter growth (DBH), although the individual effects of these markers rarely surpassed 1%. Assuming that this is the most likely genetic architecture of this growth trait in Eucalyptus, and therefore that the whole genome takes part in controlling this complex trait, comparative QTL position analyses for such multifactorial traits become too uncertain to be of any use.Additional comparisons between the associations found in our study and QTLs mapped for diameter growth in previous reports are only possible at the coarse linkage group level. For example, as in our study, QTLs for diameter growth were also detected on linkage groups 3, 5, 7 and 10, in a recent multi-pedigree p-values between the different models, when a considerable trait by model interaction was observed. Assessing the impact of different population structures and analytical models on the power and accuracy of association genetics in other Eucalyptus populations and forest tree species in general will be important to validate our results. On other hand, had phenotype prediction by a Genomic Selection approach been the goal, the converse would be true. GS estimates all marker effects simultaneously, precluding the prior search for significant associations by rigorous significance tests, but rather retaining all markers or subsets of them as predictors of performance, while focusing exclusively on selection efficiency. In such a context, most likely the several hundred associations we had found prior to stringent correction for false discoveries would be retained in a predictive model, a subject we are currently investigating, in line with recent findings in EucalyptusThe results of this study highlight the importance of taking into account all relevant sources of variation and assessing the relative value of using different analytical models in association mapping studies in forest trees. The approach taken in our analysis was especially rigorous to avoid declaring false marker-trait associations, generally considered more detrimental than false negatives in genome-wide associations studies. In particular, it was important to account for possible genetic structure in the data, both from regional genetic groups (races and provenances) and within population kinship relationships (cryptic family presence). It was also essential to use more stringent significant threshold levels in the tests, such as 1 or 5%, and to look at the mean squared differences between observed vs. expected Eucalyptus to date. Moreover, given the size limitation of our mapping panel we recognize that we had limited power to detect many smaller effects, and that the marker-trait associations found, despite the high statistical stringency used to declare them, will require independent validation. This is likely the current status of most association mapping studies previously reported in Eucalyptus that used even smaller population sizes, varying from 86 to 323 and averaging 186  values for the 2,643 DArT markers genotyped in the E. globulus mapping population (average eH = 0.33).(DOCX)Click here for additional data file.Figure S22 for pairs of DArT markers across the genome , against genetic distance (in cM) in the 303 Linkage Disequilibrium (LD) decay as measured by rE. globulus trees. The second-degree Loess fitting curve illustrates the LD decay based on the nonlinear regression of r2 on genetic distance while the horizontal line indicate the baseline r2 values based on the 95th percentile of the r2 values distribution.(DOCX)Click here for additional data file.Figure S3Boxplots of growth and wood properties variation in the studied sub-populations. See text for traits' abbreviation.(DOCX)Click here for additional data file.Figure S4Distribution of pair-wise relatedness coefficients among the 303 E. globulus trees. Values greater than 0.5 are not shown and account for only 0.08% of the distribution.(DOCX)Click here for additional data file.Table S1Significances for the differences of the least square means based on subpopulations estimated by the STRUCTURE software. See text for traits' abbreviation.(DOCX)Click here for additional data file.


In the area of genetic epidemiology, genetic risk predictive modeling is becoming an important area of translational success. As an increasing number of genetic variants are successfully discovered, the use of multiple genetic variants in constructing a genetic risk score (GRS) for modeling has been widely applied using a variety of approaches. Previously, we compared the performance of a simple, additive GRS with weighted GRS approaches, but our initial simulation experiment assumed very simple models without many of the complications found in real genetic studies. In particular, interactions between variants and linkage disequilibrium (LD) (indirect mapping) remain important and challenging problems for GRS modeling. In the present study, we applied two simulation strategies to mimic various types of epistasis to evaluate their impact on the performance of the GRS models. We simulated a range of models demonstrating statistical interaction and linkage disequilibrium. Three genetic risk models were compared in terms of power, type I error, C-statistic and AIC, including a simple count GRS (SC-GRS), an odds ratio weighted GRS (OR-GRS) and an explained variance weighted GRS (EV-GRS). Simulation factors of interest included allele frequencies, effect sizes, strengths of interaction, degrees of LD and heritability. We extensively examined the extent to how these interactions could influence the performance of genetic risk models. Our results show that the weighted methods outperform simple count method in general even if interaction or LD is present, with well controlled type I error. In recent years, Genome-Wide Association Studies (GWAS) and candidate gene studies have identified a large number of genetic variants with varying effect size that are associated with complex diseases , an odds ratio weighted (OR-) and an explained variance weighted (EV-) genetic risk score method. We employed two simulation strategies to represent (1) epistasis (gene-gene interaction effects on the phenotype) and (2) linkage disequilibrium. The effect sizes and allele frequencies were considered as important factors to evaluate the role of weights in the GRS construction. We also addressed the relationship among effect size, allele frequency, interaction effect, heritability and the predictive power for the GRS models. The main goal of this study was to explore the relationship between the degree of interaction and the performance of genetic risk scores in model prediction in a wide range of scenarios, which may in turn help guide the application of GRS in risk prediction.In the present study, GRS models were evaluated for single nucleotide polymorphism (SNP) data only. However, it could be easily generalized to other genetic variants or risk factors. It should be noted that we choose SNPs in the GRS construction based on either the previous knowledge of the disease predisposition or the data at hand. Several promising approaches, such as random forests , but together interact to predict disease. This “statistical interaction” was simulated assuming that the multiple loci genotypes jointly contribute to an underlying (unobserved) continuous trait by varying their interaction term under a linear regression model. The disease occurs if this continuous trait exceeds a certain threshold.Gi at SNP i was generated independently under Hardy-Weinberg Equilibrium (HWE). The genotype value was coded as 0, 1, and 2, representing the number of risk alleles. Minor allele frequencies (MAF) of the SNPs were set to 0.4 and 0.05, which resemble common and relatively rare variants. Continuous phenotypes Y were then generated conditional on genotypes, according to0 = 20 and σ2 = 10. Binary affection status D was assigned to 1 (case) if phenotype Y > median(Y) and D was 0 (control) otherwise, where the threshold median(Y) was only chosen in order to achieve prevalence P(D) = 0.5 and balanced case and control data. Under this linear model, β =  was ranged to reflect different effect sizes (ES) among SNPs. SNPs 1 and 2 have main effects only, while SNPs 3 and 4 have interactions where β34 reflects the strength of interactions  and interaction. All common variants, all rare variants, common plus rare variants were simulated with both same and different effect sizes among these SNPs, and three settings of interactions  were considered, which led to 18 combinations in total. For each combination, 100 replicates were generated with 250 cases and 250 controls. In preliminary studies we simulated datasets with sample sizes of 1000. The results showed similar patterns and thus the additional details were not included.a = 0, 1, 2, the heritability can be expressed as:P(Ga) is the genotype frequency of locus A, P(D) is the disease prevalence and P(D|Ga) is the penetrance. Penetrance was defined as the probability of disease conditional on a particular genotype combination at the disease risk locus/loci. Similarly, the total heritability due to the two loci A and B, with genotypes a, b = 0, 1, 2 respectively, is:P(Gab) is the frequency of genotype combinations of a and b, and P(D|Gab) is the corresponding penetrance. The heritability due to the marginal effect of locus A is defined as:Heritability in the broad sense is defined as the proportion of the phenotypic variance that could be attributed to variance of genotypic values, and in the narrow sense it is due to the additive genetic effect  and interaction effects . Low heritability  was chosen to reflect detectable effect sizes in the realistic genetic association studies and to ensure the reasonable power to discriminate the difference of performance  was investigated. We assumed two loci were correlated regardless of disease outcome. To mimic linkage disequilibrium, simulations were performed by designing the genotype combination frequencies of two or more loci, and in turn contributing to disease in an additive but relatively independent fashion under a probabilistic model. We simulated a true disease risk model involving two independent “deleterious” SNPs (SNPs 1 and 2). Two scenarios were considered with SNP 3 was dependent (strong LD model) and independent (weak LD model) of SNP 2 respectively. SNPs 1 and 2 were generated as multinomial under HWE, and then SNP 3 was generated according to Supplemental Table S4. In Scenario 1, for each level of SNP 2 values, the genotype frequencies of SNP 3 varied. We defined that SNPs 2 and 3 were in strong LD (correlated). In Scenario 2, the genotype frequencies of SNP 3 were fixed and irrelevant to the genotype of SNP 2. In this case, we defined SNPs 2 and 3 were in weak/no LD (non-correlated). GRS approaches were compared when only “deleterious” SNPs were included (true model), or when all three SNPs were included . In the case of weak/no LD, including the third SNP could also be thought of as including a false positive locus.k was the baseline penetrance and θ was the specified relative risk (RR) of having a disease between different genotypes for each SNP.Rather than the linear model in simulation one, a direct probabilistic model was used here to generate the disease status. To simplify, an additive genetic mode was determined. Let the alleles from SNP 1 be denoted “A” and “a”, and let those from SNP 2 be denoted “B” and “b”. Then, SNP 1 has three genotypes as “AA”, “Aa” and “aa”, whereas SNP 2 has three genotypes as “BB”, “Bb” and “bb” correspondingly, thus leading to nine genotypes combinations. Table k was fixed at 0.1. Balanced  case-control data was simulated with a total sample size of 400. 100 replicates were simulated as training data to calculate external weights for OR- and EV-GRS approaches, and then another 100 replicates were generated as test data to evaluate the performance of GRS methods.As presented in Supplemental Table S5, MAFs ranged from 0.4 to 0.05 to represent common and relatively rare variants. Four scenarios were included, one where both SNPs 1 and 2 were common or rare, one where SNP 1 was common and SNP 2 was rare, and vice versa. Relative risks (RRs) considered in our model were either 1.25 or 1.75 to simulate different effect sizes between SNPs 1 and 2, and 1.5 to simulate models where both SNPs had the same effect sizes. Baseline penetrance P-value <0.05 across the number of simulated replicates  to evaluate the performance of each of the GRS. Power or type I error rate was calculated as the number of times the model is statistically significant at P-value for the likelihood ratio test was recorded for each replicate, and then the number of times across the 100 replicates that the P-value was less than 0.05 was calculated as the type I error. Under the true disease risk model (involving any causative SNP), the C-statistic, AIC and P-value for the likelihood ratio test were recorded. The power was calculated as the proportion of times a true model was correctly identified  across 100 replicates. For each model, the C-statistic and AIC were averaged across all replicates. All results were statistically evaluated for differences under a generalized linear model, and Tukey's method was used to adjust for pair-wise contrasts between methods, which has been described previously , the www.r-project.org). For all the remaining data simulations and analyses were applied using SAS 9.2 (www.sas.com).In simulation one, data generation was performed on R platform , as shown in Supplemental Tables S6, S7. EV- is slightly better than OR-GRS, with no significant difference. In respect to AIC, there is no significant difference.In summary, the weighted approaches outperform the SC-GRS across all scenarios in terms of power and C-statistic . There are no statistically significant differences in terms of type I error among these methods and the cut-off value 0.05. While SC-GRS has the lowest type I error, EV- is still preferable than OR-GRS .Table The primary goal of our study was to explore how interaction and correlation could impact the risk prediction and to further determine the usefulness of genetic risk score as a predictive model that allows for gene-gene interaction, assuming sample sizes and genetic effect sizes likely to be encountered in real genetic studies. Since in real data the underlying disease mechanism is often unknown and is likely to vary across diseases, we try to employ relatively comprehensive simulation strategies to resemble potential complicated sources of interaction. Based on a wide range of simulation experiments, we observed that the weighted methods generally outperform the simple count method.H2G3G4 increases from 0.2 to 0.9% when ES4 increases from 0.2 to 0.5 (models 1–4). In the case of MAF3 = MAF4 = 0.05 and ES4 = 0.8, H2G3G4 increases from 0.4 to 0.7% when ES3 increases from 0.2 to 0.8 (models 10–7). The increase of heritability is more rapid for common variants. In respect to the MAF and heritability, in the case of ES3 = ES4 = 0.5 and MAF3 = 0.4, H2G3G4 increases from 0.9 to 1.5% when MAF4 increases from 0.05 to 0.4 (models 31–19). In the case of ES3 = 0.2, ES4 = 0.8 and MAF4 = 0.05, H2G3G4 increases from 0.4 to 0.5% when MAF3 increases from 0.05 to 0.4 (models 10–16). It is consistent with the assumption that both effect size and MAF are essential to drive the heritability and the impact of effect size seems more obvious. We also observed a clear pattern of heritability and power. The power of SC-GRS has improved from 26 to 75 and that of weighted GRS from 26 to 85, as the total heritability increases from 0.5 to 1.7% (models 1–4). Therefore, it becomes easy to identify the risk model when the heritability is high.In simulation one, as expected, we observed a clear and intuitive relationship among effect size, MAF, heritability and power for all methods. For instance, in the case of MAF3 = MAF4 = 0.4 and ES3 = 0.2, A–C). Similarly, common variants have MAF = 0.4 and rare variants have MAF = 0.05. In panel (A), ES1 was fixed at 0.1 if two loci were common, whereas ES1 was 0.3 if two loci were rare. When ES2 increases from 0 to 0.5, the total heritability and marginal heritability due to SNP 2 increase more rapidly for common than rare variants. In panels (B–C), effect sizes for two loci were fixed at 0.5 and SNP 1 was considered as common and rare respectively. The total and marginal heritability due to SNP 2 increase as MAF2 increases from 0 to 0.5, and decline as risk allele frequency (RAF) 2 increases from 0.5 to 1. This relationship pattern further illustrates the validity of explained variance genetic risk score. Both the log scale of effect size and the square root of minor allele frequency are appropriate to explain the genetic variance due to SNP (that is heritability), and thus it is reasonable to incorporate both ES and MAF to construct the weight. Secondly, we investigated the relationship between interaction effect and heritability, and the results were shown in panels (D–F). Both marginal effect sizes were set to 0.1 for panel (D) (common variants) and 0.4 for panel (E) (rare variants). In panel (F), SNP 1 was common and SNP 2 was rare, but they were set as the same effect size 0.2. We considered both positive (β12 > 0) and negative interaction effect (β12 < 0). For positive interaction, when interaction effect increases, the total, marginal and interaction heritability increase consistently (panels D–F). Furthermore, as the interaction effect increases, the marginal heritability due to rare variant is more sensitive than that due to common variant (panel F). However, it is relatively complicated to account for negative interaction effect. The pattern depends on both marginal and interaction effect sizes. It also explains the complicated pattern for Figures To further demonstrate the relationship between the potential important factors and heritability, we utilized two-locus model to calculate the heritability due to total, marginal and interaction, according to formulas 13–15 respectively. Figure To further address the role of allele frequency in the heritability, we applied one-locus model to calculate the heritability (formula 12). Effect size was fixed at 0.5 and risk allele frequency ranged from 0 to 1. Explained variance weight was obtained using formula 8, where the effect size was equivalent to log odds ratio in the logistic regression model. In Figure It should be noted that the performance of all three GRS models do not significantly differ for the models with rare variants with the same effect sizes, regardless of the strength or presence of interaction Figure . Referri34) and that of SNPs 5 and 6 (β56). Similarly, model 38 involved three-way interactions, where SNPs 3, 4, and 5 were interacted to cause disease by specifying β345. The power improvement of the weighted GRS approaches were exaggerated compared with the SC-GRS. The details of results were presented in Supplemental Table S3. It seems that the impact of simulated effects may be amplified by the number of SNPs and the degree of interaction. Based on our empirical evidences, we expect these results could be generalized to larger models, but the extrapolations should be interpreted cautiously. Future studies should further evaluate the performance of these GRS methods for larger, and increasingly complex models.Understanding that current simulations may include a limited number of SNPs and low level interaction, as a follow up we also considered more complicated scenarios with six disease-causing SNPs. As shown in Supplemental Table S2, model 37 involved two two-way interactions, by varying the interaction term of SNPs 3 and 4  will definitely be an important future direction. It is believed that to account for interaction or more complex architectures appropriately, the refinement and extension of risk models becomes an important priority in the human genetics.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.


Genome-wide association study (GWAS) aims to discover genetic factors underlying phenotypic traits. The large number of genetic factors poses both computational and statistical challenges. Various computational approaches have been developed for large scale GWAS. In this chapter, we will discuss several widely used computational approaches in GWAS. The following topics will be covered: (1) An introduction to the background of GWAS. (2) The existing computational approaches that are widely used in GWAS. This will cover single-locus, epistasis detection, and machine learning methods that have been recently developed in biology, statistic, and computer science communities. This part will be the main focus of this chapter. (3) The limitations of current approaches and future directions. The background of Genome-wide association study (GWAS).The existing computational approaches that are widely used in GWAS. This will cover single-locus, epistasis detection, and machine learning methods.The limitations of current approaches and future directions.PLOS Computational Biology.This article is part of the “Translational Bioinformatics” collection for With the advancement of genotyping technology, genome-wide high-density single nucleotide polymorphisms (SNPs) of human and other organisms are now available Genome-wide association study is an inter-discipline problem of biology, statistics and computer science single-nucleotide polymorphism (SNPs), i.e., a variation of a single nucleotide in the DNA sequence. In most cases, there are two possible nucleotides for a variant. We denote the more frequent one as “0”, and the less frequent one as “1”. For bases on autosomal chromosomes, there are two parallel nucleotides, which leads to three possible combinations, “00”, “01” and “11”. These genotype combinations are known as “major homozygous site”, “heterozygous site” and “minor heterozygous site” respectively. These genetic variations contribute to the phenotypic differences among the individuals. (A phenotype is the composite of an organism's observable characteristics or traits.) Genome-wide association study (GWAS) aims to find strong associations between SNPs and phenotypes across a set of individuals.A human genome contains over 3 billion DNA base pairs. There are four possible nucleotides at each base in the DNA: adenine (A), guanine (G), thymine (T), and cytosine (C). In some locations in the genome, a genetic variation may be found which involves two or more nucleotides across different individuals. These genetic variations are known as More formally, let Scalability Most GWAS datasets consist of a large number of SNPs. Therefore the algorithms for GWAS need to be highly scalable. For example, for a typical human GWAS, the dataset may contain up to millions SNPs and involve thousands of individuals. Inefficient methods may consume a large amount of computational resources and time to find highly associated SNPs.Missing markers Even with the current dense genotyping technique, many genetic variants are still not genotyped. Current methods usually assume genetic linkage to enhance the power. Imputation, which tries to impute the unknown markers by using existing SNPs databases, is another popular approach to handle missing markers. The well known related projects include the International HapMap project Complex traits One approach in GWAS is to test the association between the trait and each marker in a genome, which is successful in detecting a single gene related disease. However, this approach may have problems in finding markers associated with complex traits. This is because that complex traits are affected by multiple genes, and each gene may only have a weak association with the phenotype. Such markers with low marginal effects are hard to detect by the single-locus methods.In the remainder of the chapter, we will first discuss the single-locus methods. We will then study epistasis detection (multi-locus) approaches which are designed for association studies of complex traits. For epistasis detection, we will mainly focus on exact two-locus association mapping methods.As the rapid development of high-throughput genotyping technology, millions of SNPs are now available for genome-wide association studies. Single-locus association test is a traditional way for association studies. Specifically, for each SNP, a statistical test is performed to evaluate the association between the SNP and the phenotype. A variety of tests can be applied depending on the data types. The phenotype involved in a study can be case-control (binary), quantitative (continuous), or categorical. We categorize the statistical tests based on what kind of phenotypes they can be applied on.Let In a case-control study, the phenotype can be represented as a binary variable with 0 representing controls and 1 representing cases.A contingency table records the frequencies of different events. Many tests can be used to assess the significance of the association between a single SNP and a binary phenotype. The test statistics are usually based on the contingency table. The null hypothesis is that there is no association between the rows and columns of the contingency table.Pearson's The value of the test statistic isG-test is an approximation of the log-likelihood ratio. The test statistic isThe null hypothesis is that the observed frequencies result from random sampling from a distribution with the given expected frequencies. The distribution of G is approximately that of When the sample size is small, the Fisher exact test is useful to determine the significance of the association. The p-value of the test is the probability of the contingency table given the fixed margins. The probability of obtaining such values in For complex traits, contributions to disease risk from SNPs are widely considered to be roughly additive. In other words, the heterozygous alleles will have an intermediate risk between two homozygous alleles. Cochran-Armitage test can be used in this case There is no overall winner of the introduced tests. Cochran-Armitage test may not be the best if the risks are deviated from the additive model. Meanwhile, In addition to case-control phenotypes, many complex traits are quantitative. This type of study is also often referred to as the quantitative trait locus (QTL) analysis. The standard tools for testing the association between a single marker and a continuous outcome are analysis of variance (ANOVA) and linear regression.The F-test in one-way analysis of variance is used to assess whether the expected values of a quantitative variable within several pre-defined groups differ from each other.For each SNP The total sum of squares (SST) can be divided into two parts, the between-group sum of squares (SSB) and the within-group sum of squares (SSW):In the linear regression model, a least-squares regression line is fit between the phenotype values and the genotype values We have the sums of squares as follows:To achieve least squares, the estimator of In a typical GWAS, the test needs to be performed many times. We should pay attention to a statistical issue known as the multiple testing problem. In the remainder of this section, we will discuss the multiple testing problem and how to effectively control error rate in GWAS.Type 1 error rate, is the possibility that a null hypothesis is rejected when it is actually true. In other words, it is the chance of observing a positive (significant) result even if it is not. If a test is performed multiple times, the overall Type 1 Error rate will increase. This is called the multiple testing problem.Let Because of the multiple testing problem, the test result may not be that significant even if its p-value is less than a significant level For the single-locus test, we denote the p-value for a association test of a SNP Many methods can be used to control FWER. Bonferroni correction is a commonly used method, in which p-values need to be enlarged to account for the number of comparisons being performed. Permutation test In Bonferroni correction, the p-value of a test is multiplied by the number of tests in the multiple comparison.In the permutation test, data are reshuffled. For each permutation, p-values for all the tests are re-calculated, and the minimal p-value is retained. After Let False discovery rate (FDR) controls the expected proportion of type 1 error among all significant hypotheses. It is less conservative than the family-wise error rate. For example, if 100 observed results are claimed to be significant, and the FDR is 0.1, then 10 of results are expected to be false discoveries.One way to control the FDR is as follows The vast number of SNPs has posed great computational challenge to genome-wide association study. In order to understand the underlying biological mechanisms of complex phenotype, one needs to consider the joint effect of multiple SNPs simultaneously. Although the idea of studying the association between phenotype and multiple SNPs is straightforward, the implementation is nontrivial. For a study with total In this section, we will focus on the recently developed exact method for two-locus epistasis detection. Different from the single-locus approach, the goal of two-locus epistasis detection is to identify interacting SNP-pairs that have strong association with the phenotype. FastANOVA FastANOVA utilizes an upper bound of the two-locus ANOVA test to prune the search space. The upper bound is expressed as the sum of two terms. The first term is based on the single-SNP ANOVA test. The second term is based on the genotype of the SNP-pair and is independent of permutations. This property allows to index SNP-pairs in a 2D array based on the genotype relationship between SNPs. Since the number of entries in the 2D array is bound by the number of individuals in the study, many SNP-pairs share a common entry. Moreover, it can be shown that all SNP-pairs indexed by the same entry have exactly the same upper bound. Therefore, we can compute the upper bound for a group of SNP-pairs together. Another important property is that the indexing structure only needs to be built once and can be reused for all permutated data. Utilizing the upper bound and the indexing structure, FastANOVA only needs to perform the ANOVA test on a small number of candidate SNP-pairs without the risk of missing any significant pair. We discuss the algorithm in further detail in the following.Let For any SNP The basic idea of ANOVA test is to partition the total sum of squared deviations Let Let Let Theorem 1(Upper bound of)The notations in the bound can be found in We now discuss how to apply the upper bound in Theorem 1 in detail. The set of all SNP-pairs is partitioned into non-overlapping groups such that the upper bound can be readily applied to each group. For every Note that If there are To efficiently retrieve the candidates, the SNP-pairs Suppose that there are 32 individuals, and the genotype of For any SNP For multiple tests, permutation procedure is often used in genetic analysis for controlling family-wise error rate. For genome-wide association study, permutation is less commonly used because it often entails prohibitively long computation times. Our FastANOVA algorithm makes permutation procedure feasible in genome-wide association study.Let As our initial attempt to develop scalable algorithms for genome-wide association study, FastANOVA is specifically designed for the ANOVA test on quantitative phenotypes. Another category of phenotypes is generated in case-control study, where the phenotypes are binary variables representing disease/non-disease individuals. Chi-square test is one of the most commonly used statistics in binary phenotype association study. We can extend the principles in FastANOVA for efficient two-locus chi-square test. The general idea of FastChi is similar to that of FastANOVA, i.e., re-formulating the chi-square test statistic to establish an upper bound of two-locus chi-square test, and indexing the SNP-pairs according to their genotypes in order to effectively prune the search space and reuse redundant computations. Here we briefly introduce the FastChi algorithm.For SNP Theorem 2(Upper bound of )straight line in the 2-D space of For given phenotype Suppose that there are 32 individuals, Similar to FastANOVA, in FastChi, we can index the SNP-pairs in Both FastANOVA and FastChi rework the formula of ANOVA test and Chi-square test to estimate an upper bound of the test value for SNP pairs. These upper bounds are used to identify candidate SNP pairs that may have strong epistatic effect. Repetitive computation in a permutation test is also identified and performed once those results are stored for use by all permutations. These two strategies lead to substantial speedup, especially for large permutation test, without compromising the accuracy of the test. These approaches guarantee to find the optimal solutions. However, a common drawback of these methods is that they are designed for specific tests, i.e., chi-square test and ANOVA test. The upper bounds used in these methods do not work for other statistical tests, which are also routinely used by researchers. In addition, new statistics for epistasis detection are continually emerging in the literature. Therefore, it is desirable to develop a general model that supports a variety of statistical tests.The COE algorithm takes the advantage of convex optimization. It can be shown that a wide range of statistical tests, such as chi-square test, likelihood ratio test , and entropy-based tests are all convex functions of observed frequencies in contingency tables. Since the maximum value of a convex function is attained at the vertices of its convex domain, by constraining on the observed frequencies in the contingency tables, we can determine the domain of the convex function and get its maximum value. This maximum value is used as the upper bound on the test statistics to filter out insignificant SNP-pairs. COE is applicable to all tests that are convex.The methods we have discussed so far provide promising alternatives for GWAS. However, there are two major drawbacks that limit their applicability. First, they are designed for relatively small sample size and only consider homozygous markers  Divide the set of factors into 10 equal subsets.Select a set of Create a contingency table for these Compute the case-control ratio in each combination. Label them as “high-risk if it is greater than a certain threshold, and otherwise, it is marked as “low-risk”.Use the labels to classify individuals. Compute the misclassification rate.Repeat previous steps for all combinations of Choose the model whose average misclassification rate is minimized and cross-validation consistency is maximized as the “best” model.MDR designs a constructive induction method that combines two or more SNPs before testing for association. The power of the MDR approach is that it can be combined with other methodologies including the ones described in this chapter.Logistic regression is a statistical method for predicting binary and categorical outcome. It is widely used in GWAS Let The potential of genome-wide association study for the identification of genetic variants that underlying phenotypic variations is well recognized. The availability of large SNP data generated by high-throughput genotyping methods poses great computational and statistical challenges. In this chapter, we have discussed serval computational approaches to detect associations between genetic markers and the phenotypes. For further readings, the readers are encouraged to refer to Question 1: The table below contains binary genotype and case-control phenotype data from ten individuals. Give the contingency table and use Question 2: Assuming that we have the following SNP and phenotype data, is the SNP significantly associated with the phenotype? Here, we represent each SNP site as the number of minor alleles on that locus, so 0 and 2 are for major and minor homozygous sites, respectively, and 1 is for the heterozygous sites. We also assume that minor alleles contribute to the phenotype and the effect is additive. In other words, the effect from a minor homozygous site should be twice as large as that from a heterozygous site. You may use any test methods introduced in the chapter. How about permutation tests?Question 3: Categorize the following methods in the table. The methods are Question 4: Why is it important to study multiple-locus association? What are the challenges?Answers to the Exercises can be found in Cantor RM, Lange K, Sinsheimer JS (2008) Prioritizing GWAS results: a review of statistical methods and recommendations for their application. Nat Rev Genet 9(11): 855–867.Cordell HJ (2009) Detecting gene-gene interactions that underlie human diseases. Nat Rev Genet 10(6): 392–404.Manolio TA, Collins FS, Cox NJ, Goldstein DB, Hindorff LA, et al. (2009) Finding the missing heritability of complex diseases. Nature 461(7265): 747–753.Moore JH, Williams SM (2009) Epistasis and its implications for personal genetics. Am J Hum Genet 85(3): 309–320.Phillips PC (2010) Epistasis - the essential role of gene interactions in the structure and evolution of genetic systems. Am J Hum Genet 86(1): 6–22.Wang K, Li M, Hakonarson H (2010) Analysing biological pathways in genome-wide association studies. Nat Rev Genet 11: 843–854.Text S1Answers to Exercises(PDF)Click here for additional data file.