Detecting epistatic interactions associated with complex and common diseases can help to improve prevention, diagnosis and treatment of these diseases. With the development of genome-wide association studies (GWAS), designing powerful and robust computational method for identifying epistatic interactions associated with common diseases becomes a great challenge to bioinformatics society, because the study of epistatic interactions often deals with the large size of the genotyped data and the huge amount of combinations of all the possible genetic factors. Most existing computational detection methods are based on the classification capacity of SNP sets, which may fail to identify SNP sets that are strongly associated with the diseases and introduce a lot of false positives. In addition, most methods are not suitable for genome-wide scale studies due to their computational complexity.We propose a new Markov Blanket-based method, DASSO-MB (Detection of ASSOciations using Markov Blanket) to detect epistatic interactions in case-control GWAS. Markov blanket of a target variable T can completely shield T from all other variables. Thus, we can guarantee that the SNP set detected by DASSO-MB has a strong association with diseases and contains fewest false positives. Furthermore, DASSO-MB uses a heuristic search strategy by calculating the association between variables to avoid the time-consuming training process as in other machine-learning methods. We apply our algorithm to simulated datasets and a real case-control dataset. We compare DASSO-MB to other commonly-used methods and show that our method significantly outperforms other methods and is capable of finding SNPs strongly associated with diseases.Our study shows that DASSO-MB can identify a minimal set of causal SNPs associated with diseases, which contains less false positives compared to other existing methods. Given the huge size of genomic dataset produced by GWAS, this is critical in saving the potential costs of biological experiments and being an efficient guideline for pathogenesis research. Interacpistasis -4. DetecRecent development of high-throughput technologies has made it possible to produce a huge amount of genotype data and contribute to the analysis of genome-wide association studies (GWAS) -7. Furthet al proposed and developed a multifactor dimensionality reduction (MDR) method [k-way interactions purely by the prediction performance and moreover it employs an exhaustive searching strategy to avoid local optima, which makes it impractical for large-scale datasets. Therefore, when applied to large-scale datasets, MDR requires to use some feature selection methods such as ReliefF [x2 statistic to check each marker or set of markers for significant associations with the disease. Despite their success to some degrees, statistical methods can only be applied to small-scale analysis due to their computational complexity.By far, a number of statistical methods have been proposed to detect epistatic interactions. Among these, the most commonly-used parametric statistical method is logistic regression . Logisti) method -15. MDR  ReliefF  as a fil ReliefF  made eff ReliefF . BEAM iset al. proposed a support vector machine approach for detecting gene-gene interactions based on RFE (recursive feature elimination), RFA (recursive feature addition) and GA  feature selection methods [et al. adopted random forests, which is an ensemble learning technique, to the detection of epistatic interactions in case-control studies [The alternative approaches for statistical methods are machine-learning methods since detecting epistatic interactions is highly related to feature selection problem. Chen  methods . Jiang e studies . They fiIn this paper, we propose a new Markov Blanket-based method, DASSO-MB (Detection of ASSOciations using Markov Blanket) to detect epistatic interactions in case-control studies. The Markov Blanket is a minimal set of variables, which can completely shield the target variable from all other variables based on Markov condition property. Thus we can guarantee that the SNP set detected by DASSO-MB has a strong association with diseases and contains fewest false positives. Furthermore, DASSO-MB performs a heuristic search by calculating the association between variables to avoid the time-consuming training process as in SVMs and Random Forests.We compare DASSO-MB with four other commonly used methods , the minor allele frequencies (MAF) of both disease loci, and the strength of linkage disequilibrium (LD) between the unobserved disease locus and a genotyped locus. LD is a non-random association of alleles at different loci and is quantified by the squared correlation coefficient r2 calculated from allele frequencies [λ) can be determined by the baseline effect α and the genotypic effect θ in Table λ, the disease prevalence and MAF of both disease loci. Then we numerically derive the model parameters θ and α. Based on θ and α, we calculate the conditional probability of each genotype combination given disease status which is necessary for generating data [To generate data, we need to determine three parameters associated with each model: the marginal effect of each disease locus . StepPLR provides both stepwise forward and backward methods for feature selection procedure. We use both methods and set the regularization parameter λ to default value (10-4) for the L2 norm of the coefficients.For stepPLR, we download the R package from CRAN , which is located on chromosome 1 in a region linked to AMD [From the results on simulated data with 100 SNPs, DASSO-MB demonstrates a better performance than four other methods. Notice that a real genome-wide case-control association study may require genotyping of 30,000–1,000,000 common SNPs. In this section, we show that DASSO-MB algorithm can also handle large-scale datasets in real genome-wide case-control studies. We consider an Age-related Macular Degeneration (AMD) dataset, which contains 116,204 SNPs genotyped with 96 cases and 50 controls . AMD . We also remove all SNPs that have more than five missing genotypes. After filtering, there are 91,495 SNPs lying in 22 autosomal chromosomes remained.DASSO-MB detects two associated SNPs. The first one is SNP rs380390, which is already found in  with a sDetecting epistatic interactions associated with complex and common diseases has become an important issue in human genetics and can improve prevention, diagnosis and treatment of those diseases. GWAS provides a huge amount of whole genomic data and therefore an unprecedented opportunity to identify causal genes or SNPs for some complex diseases. Traditional statistical methods, however, are not suitable for dealing with large datasets because of their computational complexity. Machine-learning approaches can be scaled to large datasets, but most existing machine-learning methods do not consider the complexity of genetic mechanisms and only focus on the selection of SNPs sets, which show the best classification capacity. This will introduce many false positives inevitably.In this paper, we use a Markov Blanket-based method, DASSO-MB, to identify epistatic interactions. We compared DASSO-MB with four other methods, BEAM, Support Vector Machine, MDR and stepwise penalized logistic regression over simulated datasets. Our results show that the DASSO-MB algorithm outperforms other methods in terms of the power. It can identify a minimal set of SNPs associated with diseases, which contains less false positives. This is critical in saving the potential costs of biological experiments and being an efficient guideline for pathogenesis research.J over a set of random variables X1,X2…,nX by a directed acyclic graph (DAG) G and encode the Markov condition property: each node is conditionally independent of its non-descendents given its parents [J can be represented asBayesian networks are probabilistic graphical models representing a joint probability distribution  parents . In thisPa(iX) denotes the set of parents of iX in G.where X, Y and Z, if the probability distribution of X conditioned on both Y and Z is equal to the probability distribution of X conditioned only on Y, i.e., P = P(X|Y), X is conditionally independent of Z given Y. This conditional independence is represented asFor three random variables Definition 1 (Faithfulness)A Bayesian network N and a joint probability distribution J are faithful to each other if and only if every conditional independence entailed by the DAG of N and the Markov Condition is also present in J [ent in J .T, MB(T), as a minimal set for which V is the variable set in Bayesian network N. The Markov Blanket of a variable T is a minimal set of variables which can completely shield variable T from all other variables. All other variables are probabilistically independent of the variable T conditioned on the Markov Blanket of variable T. We show an example of the Markov Blanket in Figure MB(T) of the variable T is the set of gray-filled nodes {B, L, M, D, X } and variable S and U are independent of T conditioned on {B, L, M, D, X }.We can define the Markov Blanket of a target variable of Theorem 1.If Bayesian network N is faithful to its corresponding joint probability distribution J, then for every variable T, MB(T) is unique.T is completely determined by the values of variables in MB(T). Therefore, the detection of Markov Blanket has been applied for optimal variable selection problem [MB (T) is the union of direct cause variables (parents), direct effect variables (children), and direct cause variables (spouse) of direct effect variables of T. Thus the Markov Blanket learning method is suitable for detection of epistatic interactions in genome-wide case-control studies, e.g., to identify a minimal set of SNPs which may cause the disease for further experiments.Given the definition of Markov Blanket, the probability distribution of  problem . In addiG2 test is commonly used to test independence and conditional independence between two variables for discrete data as an alternative to the X2 test because G2-values are additive and can be applied to more complicated statistical designs [G2 test is that the two variables are independent.The  designs ,30,31. Tijx, is the value of a random variable from N samples with a multinomial distribution. Let i th row, and j th column. If these two variables are independent based on the null hypothesis, the expected value of the random variable ijx is:Assume that we have a contingency table to record and analyze the joint distribution of two variables. The count in a particular cell in a contingency table, ijkx asWe can compute the conditional independence from appropriate marginal distributions in a similar way. For instance, to determine whether the first variable is independent of the second conditioned on the third, we can calculate the expected value of a cell n cells in a contingency table, assume that the observed numbers are denoted by 1O, 2O, …, nO and the corresponding expected numbers by 1E, 2E, …, nE, then, the G2 is given by       For X2) with appropriate degrees of freedom. The degrees of freedom (df) for the G2 test between two variables A and B can be calculated as:which has an asymptotical distribution as chi-square (df = (Cat(A) – 1)×(Cat(B)-1)          (5)df) for the G2 test between A and B conditional on the third variable C can be calculated as:and the degrees of freedom (Cat(X) is the number of categories of the variable X and n is the number of variables in C. Here in (5) and (6) we assume that there are no empty cells in the contingency table. If there are some empty cells in the contingency table, we should reduce the degrees of freedom from (5) or (6) by the number of empty cells.where G2 to test the association and independence between SNPs and disease status.As described next, the proposed DASSO-MB uses G2 score conditioned on MB(T) and is dependent on target variable T , it will be admitted into MB(T). This admission operation is followed by a backward phase to remove false positives by conducting conditional independence tests. If no more variable will be added into MB(T) in the forward phase, we will enter the final backward phase to remove variables that do not belong to MB(T).We use a Markov Blanket-based algorithm, DASSO-MB, to detect gene-gene interactions Figure . Let T dT: KS algorithm [S of MB (T) rather than the remaining set MB (T) - {Y} while conducting the conditional independence tests in the backward phase. Here we let the size of subset S of MB (T) be larger than zero and exclude the empty set because of the joint effect of set of SNPs on the disease status. These two changes can make the detected results more reliable.There are several methods to find the Markov Blanket for the target lgorithm , GS algolgorithm , IAMB [3lgorithm , MMMB [3lgorithm  and HITOlgorithm . DiffereGWAS: genome-wide association studies; DASSO-MB: Detection of ASSOciations using Markov Blanket; SNP: single nucleotide polymorphisms; MDR: multifactor dimensionality reduction; stepPLR: stepwise penalized logistic regression; BEAM: Bayesian epistasis association mapping; MCMC: Markov Chain Monte Carlo; RFE: recursive feature elimination; RFA: recursive feature addition; GA: genetic algorithm; SWSFS: Sliding Window Sequential Forward feature Selection; AMD: Age-related Macular Degeneration; MAF: minor allele frequencies; LD: linkage disequilibrium; HWE: Hardy-Weinberg Equilibrium; DAG: directed acyclic graph.The authors declare that they have no competing interests.   BH designed and implemented the DASSO-MB method. BH and MP participated in testing the existing methods and analyzing experimental results. XWC conceived the study and designed the experiments. All authors helped in drafting the manuscript and approved the final manuscript.


Genome-wide association studies (GWAS) have quickly become the norm in dissecting the genetic basis of complex diseases. Family-based association approaches have the advantages of being robust to possible hidden population structure in samples. Most of these methods were developed with limited markers. Their applicability and performance for GWAS need to be examined. In this report, we evaluated the properties of the family-based association method implemented by ASSOC in the S.A.G.E package using the simulated data sets for the Framingham Heart Study, and found that ASSOC is a highly useful tool for GWAS. Genome-wide association studies (GWAS) are gaining popularity in genetic analysis of complex traits with the development of genotyping technology at the genome level. With genetic information at millions of single-nucleotide polymorphisms (SNPs) and other genetic markers, such studies offer great opportunities and also present challenges in developing appropriate statistical analysis methods. The data distributed by Genetic Analysis Workshop 16 provides a great opportunity to examine the strengths and limitations of current statistical methods for GWAS.Many GWAS have been reported in the literature and many more are being performed. Most of them are population-based association studies and use designs such as case-control studies. Such designs have the advantages that samples are easy to ascertain and that results have relatively high power when analyses are carried out properly. However, it has been shown that population-based approaches, such as case-control studies, can produce spurious associations in the presence of population substructure, especially in large-scale studies at the genomic level ,2. An alASSOC implements a regression method that tests for association between a continuous trait and one or more covariates, including genetic markers from extended family data, and accounts for familial correlations . The proThe FHS simulated data set includes 6,476 subjects with both phenotype and genotype data in 942 pedigrees of up to three generations and 188 singletons. We excluded the singletons from our analysis because they do not have family information. The simulated data contain 200 replicates of the phenotypes. We used the phenotype data from the first replicate. Pedigree files were constructed from the supplied 'triplet_sim' file and merged with phenotype and genotype data. In addition to each of the SNPs, we included subject's age, smoking status, diet, and lipid-lowering drug usage as covariates. We kept all family members in the analysis because ASSOC could account for the familial correlations. We chose to test the association of HDL with all the makers from chromosome 19 in the 50 k panel and 500 k panel because there are two major genes for HDL on chromosome 19. In all, there are 1,639 markers in the 50 k panel and 6,350 markers on 500 k panel on chromosome 19. We assumed an additive model for all the markers. The program was run in a batch mode so that it would test for the association of the SNPs successively in one run. From the simulation model, there are five major genes for HDL. Two were on chromosome 19, and the other three were from chromosomes 8, 9, and 15, respectively. The chromosome locations of the five major genes were given in Table We performed association tests of all 1,639 markers on chromosome 19 with simulated HDL data. Out of 1,639 markers, the tests of 18 markers were significant at the 0.01 level. Because the HDL data were simulated using the markers in the 500 k panel and not the markers in the 50 k panel, and since the markers in the two panels are not close, we assume that the markers in the 50 k panel did not contribute to the HDL phenotype. The significance result reflects false positives. Therefore, our results give an empirical type I error probability of 0.011, which agrees well with the nominal level of 0.01.-6 level. Table We further tested the association of the five SNPs representing the major genes with HDL Table . They wer2 of 0.003 as computed with Haploview [p-values for all the null markers. The observed distribution fits well with the expected uniform distribution and there is no major inflation of type I error. Among the top 50 SNPs ranked by p-values, four SNPs are true findings with polygenic effects.We then tested all 6,350 SNP markers on chromosome 19 in the 500 k panel for association with the simulated HDL data. Among the 15 markers that have polygenic effects on chromosome 19, association tests at six markers were significant at the 0.05 level Table . The marp-values 0.004408 and 0.028563, respectively). None of the major genes was significant with FBAT. Nonetheless, the type I error rate seems well controlled.We also applied FBAT to test the association of HDL with all 6,350 SNPs on chromosome 19. A total of 325 tests are significant at 0.05 level. However, only two polygenes are true positives  based on the common disease, common variants hypothesis .In conclusion, the method implemented in ASSOC provides a valid association test for family-based data and is reasonably powerful approach to be applied in GWAS. However, it should be noted that it is also a rather slow method. In our analysis, it took around 10 minutes to test one marker in our Windows-based workstation with 2.13 GHz CPU. It will take substantial amount of time to perform the test for millions of markers in GWAS. Parallel computing would be the solution.Using the simulated data for the Framingham Heart Study, we found the family-based regression method George et al.  implemenFBAT: Family-based association test; FHS: Framingham Heart Study; GWAS: Genome-wide association studies; SNP: Single-nucleotide polymorphism.The authors declare that they have no competing interests.HX conceived of the study, performed the analysis, and drafted the manuscript. GM participated in the analysis and helped to draft the manuscript. VG participated in the design and coordination of the study. All authors read and approved the final manuscript.


For genome-wide association studies in family-based designs, we propose a new, universally applicable approach. The new test statistic exploits all available information about the association, while, by virtue of its design, it maintains the same robustness against population admixture as traditional family-based approaches that are based exclusively on the within-family information. The approach is suitable for the analysis of almost any trait type, e.g. binary, continuous, time-to-onset, multivariate, etc., and combinations of those. We use simulation studies to verify all theoretically derived properties of the approach, estimate its power, and compare it with other standard approaches. We illustrate the practical implications of the new analysis method by an application to a lung-function phenotype, forced expiratory volume in one second (FEV1) in 4 genome-wide association studies. In genome-wide association studies, the multiple testing problem and confounding due to population stratification have been intractable issues. Family-based designs have considered only the transmission of genotypes from founder to nonfounder to prevent sensitivity to the population stratification, which leads to the loss of information. Here we propose a novel analysis approach that combines mutually independent FBAT and screening statistics in a robust way. The proposed method is more powerful than any other, while it preserves the complete robustness of family-based association tests, which only achieves much smaller power level. Furthermore, the proposed method is virtually as powerful as population-based approaches/designs, even in the absence of population stratification. By nature of the proposed method, it is always robust as long as FBAT is valid, and the proposed method achieves the optimal efficiency if our linear model for screening test reasonably explains the observed data in terms of covariance structure and population admixture. We illustrate the practical relevance of the approach by an application in 4 genome-wide association studies. During the analysis phase of genome-wide association studies, one is confronted with numerous statistical challenges. One of them is the decision about the “right” balance between maximization of the statistical power and, at the same time, robustness against confounding. In family-based designs, the possible range of analysis options spans from a traditional family-based association analysis In this communication, we propose a new family-based association test for genome-wide association studies that combines all sources of information about association, the between and the within-family information, into one single test statistic. The new test is robust against population-admixture even though both components, the between and the within-family components, are used to assess the evidence for association. The approach is applicable to all phenotypes or combinations of phenotypes that can be handled in the FBAT-approach, e.g. binary, continuous, time-to-onset, multivariate, etc n family members have been genotyped at m loci with a genome-wide SNP-chip. For each marker locus, a family-based association test is constructed based on the offspring phenotype and the within-family information. The within-family information is defined as the difference between the observed, genetic marker score and the expected, genetic marker score, which is computed conditional upon both the parental genotypes/sufficient statistic ith marker locus by iFBAT. Such an FBAT statistic can be the standard TDT, an FBAT for quantitative/qualitative traits, FBAT-GEE for multivariate traits, etc ith marker, the between-family information can be used to assess the evidence for association at a population-based level by computing a VanSteen-type iT. The screening statistic is computed based on the data for offspring phenotype and the parental genotypes/sufficient statistic. The statistic iT can be a Wald test for the genetic effect size that is estimated based on the conditional mean model iFBATiFBAT statistic is robust against population stratification, the screening statistic iT is susceptible to confounding. For this reason, the VanSteen-type testing strategies have restrictively used the between-family information as weights for p-values of the FBAT-statistic, but never as a component in the test statistic itself.We assume that in a family-based association study, iFBAT and iT are computed. The statistic α*Z is the α quantile of standard normal distribution. ipFBAT and ipT are the p-value of the FBAT-statistics and one sided p-value of the screening statistic where the direction of the one sided screening statistic is defined by the directionality of iFBAT. Based on the statistical independence of iFBAT and iTiZ by combining both Z-statistics in a weighted sum, FBATw and Tw are standardized weights so that the overall family-based association test iZ has a normal distribution with mean 0 and variance 1, i.e. FBATw2+Tw2 = 1. In the literature, this approach of combining two test statistics is known as the Liptak-method iT cannot affect the validity of the overall family-based association test statistic iZ. In the context of a genome-wide association study (GWAS), we are able to achieve this goal by using rank-based p-values for the screening statistic iT instead of their asymptotic p-values.In order to construct a family-based association test that incorporates both the within and the between-family information, the Z-statistics that correspond to the p-values of iT are sorted based on their evidence for association so that Tm)( denotes the screening statistic with the least amount of evidence for association and T(1) the screening statistic with the largest amount of evidence for association. The rank-based p-value, (i – 0.5)/m, is then assigned to the ordered screening test statistics Ti) standard deviation. For quantitative traits in unascertained samples, one can show that optimal power levels are achieved for equal weights, i.e. FBATw = Tw. In general, the equal weighting scheme seems to provide good power levels for any disease mode of inheritance and for different trait types, e.g. binary traits, time-to-onset, etc. The theoretical derivation of optimal weighting schemes for such scenarios is ongoing research and will be published subsequently.The “screening statistics” Furthermore, it is important to note that, instead of the Liptak-method, Fisher's method for combining p-values could have been used as well to construct an overall family-based association test which would have the same robustness properties as the overall-test based on the Liptak-method. However, simulation studies (data not shown) suggest that the highest power levels are consistently achieved with the Liptak method. We therefore omit the approach based on Fisher's method here.ipT in our all simulations. For various scenarios, we verified that the proposed overall family-based association test maintains the α-level.In the first part of the simulation study, the type-1 error of the proposed family-based association test denoted as LIP was assessed in the absence and in the presence of population admixture, and we use the Wald test based on the conditional mean model jth trio, the offspring phenotype jY is simulated from a Normal distribution with mean jaX and variance 1, i.e. N, where the parameter a represents the genetic effect size and the variable jX denotes the offspring genotype. Under the null-hypothesis of no association, the genetic effect size parameter a will be set to 0.For simplicity, we assume in the simulation studies that the random samples are given, i.e. no ascertainment, and that the parental genotypes are known. Assuming Hardy-Weinberg equilibrium, the parental genotypes are generated by drawing from Bernoulli distributions defined by the allele frequencies. The offspring genotypes are obtained by simulated Mendelian transmissions from the parents to the offspring. For the U. Then, the marker allele frequencies for the two subpopulations are independently sampled from the beta distributions (p(1−STF)/STF, (1−p)(1−STF)/STF) for the whole markers in each replicate of the simulated GWAS. A survey reported STF estimates with a median of 0.008 and 90th percentile of 0.028 among Europeans, and the corresponding values are 0.027 and 0.14 among Africans, and 0.043 and 0.12 among Asians STF was assumed to be 0.05, 0.1, 0.2, or 0.3. Each trio was assigned to the one of the 2 subpopulations with 50% probability.For scenarios in which population admixture is present, we assume that the admixture is created by the presence of 2 subpopulations whose phenotypic means differ by 0.2. The allele frequencies for each marker in the two subpopulations are generated by the Balding-Nichols model STF = 0.05, 0.1, 0.2, and 0.3), iZ for a GWAS with 500,000 SNPs. The estimates for the empirical significance levels in FBATw and Tw, for genome-wide significance level 0.05 and iZ is significant at the α-levels of 0.05, 0.01, 10−3, 10−4 and 10−5. The simulation studies are conducted in the absence and in the presence of population admixture. iZ is robust against population stratification and maintains correct type-1 error.In the absence and presence of the population stratification , ,  and . Both regions consist of 10K SNPs and 90K SNPs respectively and if subjects are from the same subpopulation in each genetic region, their assumed allele frequencies of the markers in the corresponding region are equal. For example, the allele frequencies of each marker in the marker region 1 are the same for samples in  and , but they are different for  and . In the simulation study, we generate the parental genotypes based on these allele frequency assumptions and obtain the offspring genotypes based on simulated Mendelian transmissions. Using the Balding-Nichols model we considered STF's of 0.001, 0.005, 0.01 and 0.05 in the simulation studies. The offspring's phenotype was generated under the null hypothesis, but we assumed that each sub-population strata had a different phenotypic mean: 0 for , 0.2 for , 0.4 for  and 0.6 for . Each replicate consists of 2,000 trios with equal number of trios for all 4 possible combinations. The data was analyzed with the proposed overall family-based association test and with standard linear regression after adjusting population admixture with EIGENSTRAT In the next set of simulation studies, we assess the effects of the local population stratification on the overall family-based association test. We generate local population stratification under the following assumptions: there are two subpopulations, a, is given as a function of the heritability, h2, the minor allele frequency Dpı and the phenotypic variance, σ2, by: a = σh/[2p(1−p)(1−h2) ]0.5. In the simulation study, we assume heritabilities of h2 = 0.001, 0.005, 0.01 and 0.015 for 2,000, 2,500 and 3,000 trios. The allele frequency of the disease locus, Dpı, is 0.3 and the phenotypic variance is 1. We compare the achieved power levels of the proposed overall family-based association test, iZ, with the weighting approach by Ionita-Laza et al Y on the genotype X. Bonferroni correction is used to adjust for multiple testing in the population-based analysis, FBAT, QTDT and the proposed method. The results in α-level of 0.001 for the all genetic models. The results confirm that the Liptak's method combining iT and iFBAT has similar power to the population-based method, and the choice of equal weights performs well. The simulation results in STF = 0.001, 0.005, 0.01, and 0.05, and the additive mode of inheritance at the disease locus with values for the heritability of h2 = 0.005, 0.01 and 0.015. The disease allele frequency Dpı in the ancestral population is assumed to be 0.3. The phenotypic data is simulated so that their phenotypic means for two subpopulations are 0 and 0.2 respectively. Each individual/trio is assigned to either subpopulation with probability 0.5. The parental genotypes are used to estimate the ancestry for EIGENSTRAT as before. Various methods have been suggested to adjust the population stratification in a population-based designs and we compare the proposed methods with the EIGENSTRAT approach iT of our approach, i.e. principal component analysis based on the parental genotypes and the offspring's phenotype is integrated into the generalized Armitage test for iTiZ is considerably more powerful than population-based analysis adjusted with EIGENSTRAT. QTDT is slightly more powerful than FBAT, but it is much less powerful than LIP as is in ipT is calculated from the conditional mean model For the analysis of quantitative traits, ipT, and the genome-wide significance level was obtained with Bonferroni correction. When we let n and infn be the total number of individuals and the number of informative trios respectively, infn: (2n−infn) are used for the weights of iZ because some of parental phenotypes are available.For the assessment of the severity of pulmonary diseases, the lung volume of air that a subject can blow out within one second after taking a deep breath is an important endo-phenotype. It is referred to as the forced expiratory volume in one second (FEV1). FEV1 is an important measure for lung function and we apply the proposed method to a family-based GWAS of FEV1. The proposed method is applied to 550K GWAS Framingham Heart Study (FHS) data set for FEV1, and then we confirm whether the selected SNPs are replicated in the British 1958 Birth Cohort (BBC), another population sample, as well as two samples of asthmatics in the the Childhood Asthma management program (CAMP) −7 and our results show that only the first ranked SNP, rs805294, is significant at the genome-wide level 0.2 with Bonferroni correction. For rs805294, we also checked the significance in other data sets, BBC, CAMP −8 and 1.081×10−7 respectively, and they become 4.625×10−9 and 3.554×10−8 if the p-values from one-tailed tests are used for BBC, CAMP and ACG with the same direction of FHS. If the p-value from the Affymetrix gene chip in BBC is combined with the other studies, then they are 3.787×10−8 (Liptak's method) and 1.890×10−7 (Fisher's method) for two-tailed tests, and 1.098×10−8 (Liptak's method) and 6.236×10−8 (Fisher's method) for one-tailed tests. As a result we can conclude that rs805294 is significantly associated with FEV1 at a genome-wide scale and the gene, LY6G6C, associated with rs805293 will be investigated in further studies.Genome-wide association studies have become one of the most important tools for the identification of new disease loci in the human genome. However, even though advances in genotyping technology have enabled a new generation of genetic association studies that provide robust and replicable findings, population stratification/genetic heterogeneity and the multiple testing problems continue to be the major issues in the statistical analysis that have to be resolved in each study. While family-based association tests provide analysis results that are completely robust against confounding due to population-substructures, the analysis approach is not optimal in terms of statistical power. Numerous approaches have been suggested to minimize this disadvantage of family-based association tests but the previous approaches had to compromise either in terms of robustness or in terms of efficiency.STF. Rank-based p-value directly rescales the statistics based on their ranks, which always generates the uniformly distributed p-value and provides validity even for varying STF due to local population stratification etc.In this communication, we develop an approach that efficiently utilizes all available data, while maintaining complete robustness against confounding due to population substructure. The proposed methods combines the p-values of the family-based tests (the within-component) with the rank-based p-values for population-based analysis (the between component) to achieve optimal power levels. The use of rank-based p-values for the population-based component is similar in spirit to the genomic control approach. In principle, the genomic control functions as rescaling the variance inflated due to population stratification under the assumption of the constant Although our simulations are limited to independent unascertained samples and quantitative traits, the proposed work can be easily extended to ascertained samples, large pedigree, or different trait types, etc. By replacing the parental genotypes with the sufficient statistics by Rabinowitz&Laird Text S1The validity of the proposed method.(0.04 MB DOC)Click here for additional data file.


The number of genome-wide association studies (GWAS) is growing rapidly leading to the discovery and replication of many new disease loci. Combining results from multiple GWAS datasets may potentially strengthen previous conclusions and suggest new disease loci, pathways or pleiotropic genes. However, no database or centralized resource currently exists that contains anywhere near the full scope of GWAS results.We collected available results from 118 GWAS articles into a database of 56,411 significant SNP-phenotype associations and accompanying information, making this database freely available here. In doing so, we met and describe here a number of challenges to creating an open access database of GWAS results. Through preliminary analyses and characterization of available GWAS, we demonstrate the potential to gain new insights by querying a database across GWAS.APOE, LPL). At the same time we identified novel, highly suggestive loci for a variety of traits that did not meet genome-wide significant thresholds in prior analyses, in some cases with strong support from the primary medical genetics literature , suggesting these genes merit further study. Additional adjustment for linkage disequilibrium within most regions with a high density of GWAS associations did not materially alter our findings. Having a centralized database with standardized gene annotation also allowed us to examine the representation of functional gene categories (gene ontologies) containing one or more associations among top GWAS results. Genes relating to cell adhesion functions were highly over-represented among significant associations (p < 4.6 × 10-14), a finding which was not perturbed by a sensitivity analysis.Using a genomic bin-based density analysis to search for highly associated regions of the genome, positive control loci  were detected with high sensitivity. Likewise, an analysis of highly repeated SNPs across GWAS identified replicated loci (e.g., We provide access to a full gene-annotated GWAS database which could be used for further querying, analyses or integration with other genomic information. We make a number of general observations. Of reported associated SNPs, 40% lie within the boundaries of a RefSeq gene and 68% are within 60 kb of one, indicating a bias toward gene-centricity in the findings. We found considerable heterogeneity in information available from GWAS suggesting the wider community could benefit from standardization and centralization of results reporting. Analytic and computational approaches that further probe the results of individual studies or combine results from multiple GWAS datasets may strengthen previous conclusions, suggest novel loci or pathways [The number of genome-wide association studies (GWAS) is growing nearly exponentially, heralding an era of unprecedented discovery. Numerous novel genetic loci underlying disease susceptibility have been discovered using the unbiased GWAS approach, and many of these associations hold up to rigorous standards for replication . Journalpathways , contribpathways . A key v). The overall objective of this study was to create an open access, centralized database of significant published GWAS results, and to provide basic informatics standardization of these results in the format of the current genome build with updated gene annotations. We furthermore sought to characterize and analyze this initial GWAS database to assess data availability, data quality and annotations across all phenotypes, and to identify key genomic characteristics of GWAS associations and opportunities and obstacles to further analysis of this potentially vast genetic data space. With this objective, we collected and analyzed GWAS results compiled from a series of 118 GWAS studies published through March 1, 2008, all of which tested trait associations with > 50,000 markers, identifying genomic characteristics of associated loci in GWAS, facilitating new analyses and highlighting limitations in available data sources , scanning the citations within each article and through direct searches of journal websites where GWAS were previously published. For citation information for all included articles and data sources [see Additional file One-hundred-eighteen GWAS articles published before March 1, 2008 and their associated supplemental information was collected. The articles were identified through Pubmed searches  the SNP had an identifiable ID or verifiable genomic position, 2) a statistical p-value for association was reported, 3) the p-value was less than or equal to 0.001  if the association was from a raw, unadjusted scan, 4) the p-value was less than or equal to 0.05 if the association was derived from replication, fine mapping or re-sequencing efforts, or if it was identified as belonging to a locus or region that was specifically identified as an We independently verified the quality of the extracted GWAS results database in a blinded fashion. Three independent reviewers extracted information from the same 2 GWAS articles in parallel to ensure they applied our inclusion criteria in the same manner. Twelve of the 118 GWAS articles were randomly selected. These articles were assigned 4 each to 3 reviewers. Each reviewer independently generated information from the GWAS article according to the guidelines above and then compared their results to the original extracted results.Information from the GWAS papers spanned at least 3 human genome Builds and 12 dbSNP builds, resulting in SNP positions and SNPids that have shifted in some cases. Additionally, some papers gave only genome coordinates without SNPids or supplied only commercial chip IDs. Thus, in order to maximize the analysis of available GWAS results in the current genome build context and retrieve current SNP annotation it was necessary to apply multiple strategies to update SNP coordinates and SNPids. For some markers old genome coordinates were translated into current coordinates using the UCSC Genome Browser LiftOver conversion tool in order to discover missing SNPids. When only commercial chip IDs were given these were translated into rsIDs using the most appropriate annotation files from the corresponding company. For some associations we were unable to establish SNP identification based on the information provided in the original report. Although this was only the case for a handful of associations, it does suggest more vigilance is required by journals in order to standardize the reporting of genetic variants .To facilitate retrieval of current SNP annotation information we wrote a Perl program, GRASP . Current coordinates were retrieved from the dbSNP table "b128_SNPChrPosOnRef_36_2". Alias SNP IDs were retrieved from the "RsMerge128Arch" table and used to find current coordinates when necessary. SNPs that mapped to multiple genome locations were noted and further gene annotation was not included for these. The GRASP program integrated UCSC human genome browser annotation tracks for RefSeq genes and UCSC Known genes, yielding standardized annotations for overlapping and nearby genes for all GWAS SNP associations [see Additional file The main GWAS database contains 56,411 unique SNP-phenotype entries [see Additional file -3, or which were significant in replication or further analysis at p = 0.05.  of GWAS articles, fewer than 40 SNP-specific association results were made publicly available, and in many studies results for very few loci and SNPs were disclosed (25 studies reported results for 10 or fewer SNPs). In thirty-one (26%) articles, the authors disclosed the complete set of associations, and in the remaining articles (n = 34), they disclosed only a moderate number of top-ranked associations (defined as ≥ 40 associations for ≥ 4 distinct loci). There was also substantial heterogeneity in the format and type of results data available from GWAS studies. In many studies, information regarding SNP strand, alleles and direction of effect, sample sizes passing quality control for individual SNPs, and genetic model were unavailable, thus precluding or limiting the conduct of formal meta-analyses. Despite the heterogeneity and limited data availability, we extracted a minimal redundancy database of 56,411 statistically significant SNP-phenotype associations across all studies by use of custom computer programming to facilitate further analysis. Briefly, the criteria for inclusion was the most significant mention per SNP per study, and only included SNPs with unadjusted genome-wide p-values for association ≤ 1 × 10Currently available GWAS results span 3 builds of the human genome 34–36) and at least 12 builds of dbSNP (118–129). Since SNPids are being modified and merged over time, and the relative positions of SNPs often shift between human genome builds, there are substantial informatics challenges to GWAS meta-data accumulation, analysis and viewing. Using current dbSNP information, including mapping of alias SNPids, we migrated all reported SNPs from GWAS associations in Additional file –36 and a2) in the same regions for the HapMap CEU samples. Both analyses identified many previous strongly replicated loci within regions of the genome showing the highest density of previous associations (Table P < 5 × 10-8), clearly highlighting both the density and magnitude of association signals at many replicated loci. Figure -8 ≤ P ≤ 1 × 10-4, making apparent a number of clusters that approach the genome-wide significant threshold (P < 5 × 10-8). Across the genome, the 99th percentile cutpoint based on density of associations included bins with 13 or more GWAS associations within less than or equal to 100 kb. The MHC class II loci contained the densest bins. There are numerous phenotypes associated with the MHC loci, consistent with significant pleiotropy of this region, but there is also evidence for pleiotropy for a previously replicated Alzheimer's disease locus , which displays a signal for Crohn's disease, and a second replicated Alzheimer's locus (DAPK1), which shows evidence for Type II diabetes and related traits across multiple studies.Using our standardized GWAS results database [see Additional file ns Table . In FiguSLC16A7, also known as MCT2), a ubiquitously expressed transporter that imports and exports lactate and pyruvate. Other clusters of interest include: a complement related factor, CSMD1, mainly for association with HIV-1 viral load; and associations with Crohn's disease and Type I diabetes at OAS1, an enzyme that degrades viral RNA and has previously been associated with Type I diabetes, multiple sclerosis and SARS infection. Accounting for LD in the density analysis changed the rankings of the top regions  was associated 11 times across GWAS, including association with Alzheimer's disease, lipid-related traits and coronary artery disease (CAD). Some replicated loci contained multiple SNPs with repeated associations, which may be due to LD and differences in representation on arrays  which showed association with BMI-related traits and hypertension and is located in a cluster of GABA receptor subunits, notable for the role of GABA signaling in sympathetic vasomotor tone; RAPGEF1 , an exchange factor involved in cell signaling, was associated with BMI-related traits; PIGU (rs2889849), a subunit of glycosylphosphatidylinositol transamidase, was associated with lipid- and BMI-related traits; and SPAG16 (rs10498015), a sperm-associated protein, was associated with height, weight and lipid-traits , 52,554 unique SNPs were observed, and the bulk of these SNPs were associated with a single phenotype once n = 49,313). Examining the most redundant SNPs across GWAS associations revealed a set of known, replicated loci, validating this approach (Table 13. ExamiP < 4.6 × 10-14) across the meta-dataset, as were genes related to signal transduction (P < 9.7 × 10-11), transport activity (P < 1.1 × 10-9), and protein phosphorylation (P < 2.4 × 10-7) (Table P < 2.4 × 10-9) [see Additional file Using our standardized RefSeq gene annotations of GWAS associations, we identified all protein-coding genes containing one or more association among top GWAS results n = 5,966). We explored whether genes with specific types of biological function are over-represented across significant GWAS results using GOminer, software originally designed for microarray analysis [6. We expP < 4.6 × 10-14 for all diseases). We make the compiled results fully available in supplemental files, [see Additional file In our evaluation of a comprehensive GWAS results database across diverse phenotypes, we confirm the potential benefit of open access to GWAS results data by a series of observations. After re-annotation of all reported results, we determined that more than two-thirds of associations are in or within reasonably limited physical and genetic distance from a protein-coding gene, with a significant minority of associations more distant from a protein-coding gene. While intentionally hypothesis generating, the results of our analyses  suggest novel candidate genetic loci that require further replication, but we also noted GWAS associations of interest in at least one locus with previous evidence for association. A gene encoding 2',5' oligoadenylate synthetase 1 (OAS1) is stimulated by interferon, plays an important role in innate immunity and was previously shown to be genetically associated with Type I Diabetes [in silico analysis of GWAS results. During the review of this article, published and unpublished studies came to our attention, which provide some additional validation for results we present. We noted in Table RAPGEF1 and PIGU across multiple GWAS and suggested these as potential novel candidate genes for further study and replication. Recently a genome-scan for melanoma, reported the most significant association, which was replicated, was found in PIGU (p < 1.0 × 10-15) [2 0.57). This genomic region (20q11.22) also ranked relatively high in our bin-based analysis  as a previously, unreplicated region that contained a high density of GWAS associations for diverse diseases. In an analysis of 222 candidate genes for association with diabetes and related traits, extending previously published GWAS analyses, Gaulton and colleagues [RAPGEF1 SNP (rs4740283) as the most statistically significant associated SNP with Type II Diabetes among all SNPs and genes they analyzed. This SNP is nearby and in complete LD  with a RAPGEF1 SNP, rs7034356, we reported here in Table PIGU and RAPGEF1, as well as some as yet unpublished, but replicated GWAS results for other genes we highlight strongly suggest that the availability and analysis of GWAS results across diverse traits may be useful in predicting and supporting functional loci for further biological study.The preceding examples, and others in Tables Diabetes , multiplDiabetes , SARS [1Diabetes  and hepaDiabetes . Here weP < 7.1 × 10-20). This expands on an earlier report on the over-representation of cell adhesion genes in significant addiction-related GWAS results [Creation of a standardized results database allowed us to conduct a functional gene category analysis. The over-representation of cell adhesion genes was strongest among weight- and BMI-associated traits ( results . The fin results . Current results , and notin silico comparisons across multiple GWAS for related phenotypes, for example to find SNPs associated with both LDL cholesterol and CAD [a priori evidence for association for use in the analysis of new trait scans [a priori linkage, or functional evidence such as prior gene expression GWAS. Our results (Figure Consistent, widespread standards of reporting and annotation of full disclosure results may facilitate hypothesis-generation and extend discovery that is already occurring from GWAS and their follow-up studies. While GWAS have resulted in the discovery of new and strongly replicated genetic associations relevant to human disease, there continues to be a substantial challenge to discovering meaningful genotype-phenotype associations among a surfeit of data. The typical staged approach to GWAS discovery consists of ranking statistical associations and replication testing in large follow-up sample cohorts; while some "true" associations are found positioned relatively low on the initial p-value ranked list . A recen and CAD . As moreit scans ,26,27. Ws Figure  suggest A growing number of GWAS investigative teams including the Diabetes Genetic Initiative , the WelA previous working group paper suggested criteria for establishing and evaluating GWAS reports and replication, and their report highlights the types of information that would be central to a GWAS data standard . The cenWe provide a comprehensive open access database of available GWAS results, along with general observations and first analyses. We observed substantial heterogeneity in the amount and type of information currently reported in GWAS articles. After substantial data collection and informatics integration efforts, our first pass analysis across GWAS indicates there may be substantial benefits to centralizing and opening access to GWAS results. We found support for potential pleiotropy of known, replicated loci, as well as the suggestion of new, interesting candidate genes and functional categories that require further validation and study. The creation of an open access resource for GWAS results should encourage and facilitate new genetic and genomic analysis, and provides a potential resource for easier participation in results sharing among interested researchers.The authors declare that they have no competing interests.The project was designed and implemented by ADJ, with significant input from CO. Both ADJ and CO wrote and edited the manuscript.The pre-publication history for this paper can be accessed here:Summary information on the 118 GWAS studies included in this study. Information on GWAS including genotyping arrays, phenotype descriptions, discovery and replication samples, analytic strategies, data availability, URLs, publication date and contact information. Data fields are described in detail in Additional file Click here for file56,411 GWAS genotype-phenotype associations and annotation. The database of significant GWAS associations and additional gene and SNP annotations used in this paper. Data fields are described in detail in Additional file Click here for fileSupplemental text. Supplemental text for the paper providing detailed descriptions of how data fields were ascertained for Additional files Click here for fileMicrosoft Access 2007 database of 56,411 GWAS genotype-phenotype associations and annotation. The database of significant GWAS associations and additional gene and SNP annotations used in this paper. Data fields are similar to Additional file Click here for fileGOminer gene ontology analysis results for GWAS in disease sub-categories. GO categories significantly enriched among significant disease groupings of GWAS results. Studies included in disease groups are identified in Additional file Click here for fileFormatted files for more than 400 GWAS analyses that can be used to upload and browse results in UCSC Genome Browser using Genome Graphs. This archive file contains Genome Graph files for all GWAS associations contained in Additional files  at regional, chromosomal and whole genome levels. A file "README.txt" describes file naming conventions. The file "JohnsonODonnell_ALLgwas_graph.txt" contains a single Genome Graph file containing all associations.Click here for file


Compared to the conventional linkage mapping, linkage disequilibrium (LD)-mapping, using the nonrandom associations of loci in haplotypes, is a powerful high-resolution mapping tool for complex quantitative traits. The recent advances in the development of unbiased association mapping approaches for plant population with their successful applications in dissecting a number of simple to complex traits in many crop species demonstrate a flourish of the approach as a “powerful gene tagging” tool for crops in the plant genomics era of 21st century. The goal of this review is to provide nonexpert readers of crop breeding community with (1) the basic concept, merits, and simple description of existing methodologies for an association mapping with the recent improvements for plant populations, and (2) the details of some of pioneer and recent studies on association mapping in various crop species to demonstrate the feasibility, success, problems, and future perspectives of the efforts in plants. This should be helpful for interested readers of international plant research community as a guideline for the basic understanding, choosing the appropriate methods, and its application. The level of the genetic diversity is pivotal for world food securityand survival of human civilization on earth. Historically, humans exploitedplant species for their livelihoods that resulted in domestication of many ofthem as improved cultivars to produce food for the better supply of the humandiet . Presentgenetic ×environmental (G × E) interactions [The narrow genetic base of modern crop cultivars is the serious obstacleto sustain and improve crop productivity due to rapid vulnerability ofgenetically uniform cultivars by potentially new biotic and abiotic stresses. Howeverractions , 6. Thesractions , 6. ThisIn this review, we provide a brief description for the concept ofgenetic mapping; then, as a flourish of the crop genomics era, we thoroughlyreview one of the powerful genetic mapping tools for crops, linkagedisequilibrium (LD)-based association study, as a high-resolution, broaderallele coverage, and cost effective gene tagging approach in plant germplasmresources. This provides an opportunity to widely dissect and exploit existingnatural variations for crop improvement.Themain goal of genetic mapping is to detect neutrally inherited markers in closeproximity to the genetic causatives or genes controlling the complexquantitative traits. Genetic mapping can be done mostly in two ways : (1)usiF2, back cross (BC), double haploid(DH), recombinant inbred line (RIL), and near isogenic line (NIL) populations,derived from the genetic hybridization of two parental genotypes with analternative trait of interest, need to be developed. Secondly, theseexperimental populations including a large number of progenies or lines aremeasured for the segregation of a trait of interest in the differentenvironmental conditions. Thirdly, a set of polymorphic DNA markers,differentiating the parental genotypes and segregating in a mapping population,need to be identified and genotyped. For that, usual practice is that, first,the parental genotypes are screened, and if markers are polymorphic over theparents, then, all individuals of a mapping population are genotyped with thesepolymorphic molecular markers. Once genotypic data of a mapping population isready, marker data is used to construct the framework linkage maps,representing the order (position) and linkage (a relative genetic distance incM) of used molecular markers along the linkage groups or segments ofparticular chromosomes. This is accomplished through assessing of recombinationrates between the marker loci. Consequently, these markers ordered along thelinkage map are statistically correlated with phenotypic characteristics ofindividuals of a mapping population, and QTL regions affecting a trait ofinterest, along with closely positioned marker tags to that QTL, areidentified.Sothat such a linkage analysis can be done –8, firstOnecan imagine these linkage marker maps as a “road map,” marker tags as thelabels directing to specific places, and QTLs to a community/neighborhood (withspecific function) on the map . The preTheselimitations, however, can be reduced with the use of “association mapping” .TurningTheadvantages of population-based association study, utilizing a sample ofindividuals from the germplasm collections or a natural population, overtraditional QTL-mapping in biparental crosses primarily are due to (1)availability of broader genetic variations with wider background formarker-trait correlations , (2)likelihood for a higher resolution mapping because of the utilization ofmajority recombination events from a large number of meiosis throughout thegermplasm development history, (3) possibility of exploiting historicallymeasured trait data for association, and (4) no need for the development ofexpensive and tedious biparental populations that makes approach timesaving andcost-effective –19.Althoughthe overall approach of population-based association mapping in plants variesbased on the methodology chosen (see below sections), assuming structuredpopulation samples, the performance of association mapping includes thefollowing steps see : (1) selGeneticlinkage generally refers to coinheritance of different loci within a geneticdistance on the chromosome. There are two terms used in population genetics,linkage equilibrium (LE), and linkage disequilibrium (LD) to describe linkagerelationships (co-occurrence) of alleles at different loci in a population. LEis a random association of alleles at different loci and equals the product of allele frequencies within haplotypes,meaning that at random combination of alleles at each locus its haplotypes  frequencyhas equal value in a population. In contrast, LD is a nonrandom association ofalleles at different loci, describing the condition with nonequal (increased orreduced) frequency of the haplotypes in a population at random combination ofalleles at different loci. LD is not the same as linkage, although tightlinkage may generate high levels of LD between alleles. Usually, there issignificant LD between more distant sites or sites located in differentchromosomes, caused by some specific genetic factors , 22–24 tD) was developed by Lewtonin in 1964. The simplifiedexplanation of the commonly used LD measure, D or D′ (standardized version ofD), is the difference between the observed gametic frequencies of haplotypesand the expected gametic haplotype frequencies under linkage equilibrium (D = PAB − PAPB = PABPab − PAbPaB)[D, a various different measures of LD , and δ) have been developed to quantify LD [The concept of LD was first described by Jennings in 1917, and itsquantification ( PAbPaB). Besidesntify LD , 27–29. ntify LD , 25, 26 ntify LD , 31, andD′ and r2 is the most commonly used measuresof LD [D′ is informative for the comparisons of different allelefrequencies across loci and strongly inflated in a small sample size and low-allelefrequencies; therefore, intermediate values of D′ is dangerous for comparativeanalyses of different LD studies and should be verified with the r2 before using for quantification of the extent of LD [r2,the square of the correlation coefficient between the two loci have morereliable sampling properties than D′ with the cases of low allele frequencies[r2 is affected by both mutation and recombination while D′ is affected by more mutational histories  [r2 that is also an indicative of marker-traitcorrelations [r2 value varies from 0 to 1, and itwill be equal to 1 when only two haplotypes are present. The r2 valueof equal to 0.1 (10%) or above considered the significant threshold for therough estimates of LD to reveal association between pairs of loci [Choosing the appropriate LD measures really depends onthe objective of the study, and one performs better than other in particularsituations and cases; however, esof LD , 26. D′ es used) , 26, 31.elations , 26, 32. of loci .It is noteworthy to briefly mention here that theestimation of above described GLD (commonly used in association mapping)between different loci ordered within gametes assumes that a targetedpopulation or sampled germplasm is randomly mating and under HWE. Nevertheless,many natural populations violate HWE due to different genetic eventsoccurred in history of a population, and are under Hardy-Weinberg disequilibrium(HWD). A concept of “zygotic disequilibrium (ZLD)” was introduced for such anonequilibrium population  that meaLD can be calculated using available haplotypingalgorithms . One of r2, and p-value as well as D′) that helps to visualize theblock of loci (red blocks) in significant LD. The large red blocks ofhaplotypes along the diagonal of the triangle plot indicate the high level ofLD between the loci in the blocks, meaning that there has been a limited or norecombination since LD block formations. There is freely available specificcomputer software, “graphical overview of linkage disequilibrium” (GOLD) [Graphicaldisplay of pairwise LD between two loci is very useful to estimate the LDpatterns measured using a large number of molecular markers. Pairwise LD can bedepicted as a color-code triangle plot  based on” (GOLD) ,to depi” (GOLD) , 40 and ” (GOLD)  have als” (GOLD) . LD blocr2 values  usually plotted against the genetic (cM) or weighted (bp)distance referred to as a “LD decay plot” (r2) decreases below 0.1 or half strength of D′ (D′ = 0.5) basedon curve of nonlinear logarithmic trend line are also used as a cutoff point. The decrease of the LD within the genetic distance indicates that theportion of LD is conserved with linkage and proportional to recombination [Toestimate the size of these LD blocks, the ay plot” . One cane, e.g., , 43, 44)bination , 25.There are many genetic and demographic factors thatplay a role in the shaping of the haplotypic LD blocks in a genome , 25, 26.LD conserved with linkage is very useful forassociation mapping. However, more often there is a significant LD betweenpairs of loci located far from each other or even in different chromosomes thatmight cause spurious correlations in association mapping. These long stretchedLD or LD between unlinked loci indicate the existence of other LD generatingfactors than linkage itself in a genome , 22, 23.Thepopulation structure (existences of distinctly clustered subdivisions in apopulation) and population admixture are the main factors to create such an LDbetween unlinked loci. This primarily happens due to the occurrence of distinctallele frequencies with different ancestry in an admixed or structuredpopulation. Theoretically, relatedness generates LD between linked loci, yet itmight also generate LD between unlinked loci pairs when predominant parentsexist in germplasm groups. There is evidence that relatedness caused LD betweenlinked and unlinked loci in an equal proportion in maize germplasm . ThehigKnowing these factors that are increasing ordecreasing LD in a genome, obvious question one might ask is whether increased ordecreased level of LD is favored in association mapping? Very extensive level ofLD (means LD persists within a long distance), theoretically, reduces a numberof markers needed for association mapping, but makes resolution lower (coarsemapping). In contrast, less extensive level of LD (means that LD quickly decayswithin a short distance) requires many markers to tag a gene of interest, butin high resolution (fine mapping). Hence, choosing a population with low orhigh level of LD depends on the objective of association mapping study.Furthermore, increased LD level due to LD between unlinked loci is not salutaryin association mapping since it tends to cause spurious marker-traitassociations. LD generated by selection, population structure, relatedness, andgenetic drift might be theoretically useful for association mapping in specific situations and population groups that reduces number of markers neededfor association mapping , 22, butD′ and p-values) [r2 isalso very sensitive and has a large variance with rare alleles [Thereare other factors affecting LD referred to as a whole “ascertainment bias” thatare associated with an assayed sample and data characteristics. Some of thesefactors leading to inaccurate estimate of LD were well reviewed by Gupta et al.. One of -values) , 48–50.  alleles , 51. Hen alleles , 44, 51) alleles ), and .Thequantification methodology of LD, perfectly suitable for biallelic codominanttype of markers  and nowlargely extended to multiallelic simple sequence repeats-SSRs), has been welldeveloped and used in human, animal, and plant populations .Coulda dominant marker data be used for LD quantification? There are some reportswhere LD level of natural forest tree populations has been measured usingdominant markers (AFLPs) and commonly used statistical approach .There Recently,Li et al.  investigLD quantification and LD-based association mapping have been a research objective in plantsbeginning with the model organism as Arabidopsis, and now extended to crops asmaize, barley, durum wheat, spring wheat, rice, sorghum, sugarcane, sugar beet,soybean, and grape, as well as in forest tree species, and forage grasses.FRI gene in a 20 global sample of A. thaliana, highly selfing model plantspecies. They determined that LD decays within a 1 cM distance or 250 kb.Later, investigation of the same authors [RPM1 in aglobally-derived set of 96 Arabidopsis accessions revealed that a genome-wideLD extended up to 50–250 kb. LD blocksextended up to 50–100 cM in localMichigan Arabidopsis populations. These long-stretched LDs in local Arabidopsispopulation were explained as a genetic bottleneck or founder effect throughintroduction A. thaliana into North America in recent past (200 years ago). In contrast,in other study that targeted the region surrounding another disease resistancegene rps5, Tian et al. [CLAVATA 2 region ofArabidopsis [MORE AXILLARYGROWTH 2 (MAX2) and MORE AXILLARYGROWTH 3 (MAX3) in a panel of 96 accessions from a restricted geographicrange in Central Europe. In their genome-widesurvey of 1347 fragments of 600-bp lengths, Plagnol et al. [Nordborg et al.  sequence authors  with marn et al.  reportedbidopsis . Recentlbidopsis  reportedl et al.  reportedZea mays L.), a highly outcrossing crop species, very rapidgenome-wide LD decay was determined. Tenaillon et al. [r2 = 0.2and extended up to 1000 bp (~1 kb) in a group of US inbred lines. Later,Remington et al. [r2 = 0.1except sugary1 (su1) loci, where LD remained significant (r2 = 0.3 − 0.4)for 10 kb distance. This was explained by strong selective episodes in su1 gene. In the same study, Remingtonet al. [In maize  extended up to 3 kb. Jung et al. [adh1 locus. Stich et al. [P < .5) LD blocksize of 26 cM for flint group, or 41 cM for dent group with nonuniformdistribution of LD among 10 chromosomes. They showed a very long stretched LDblocks up to 105 cM in chromosome 2 and up to 103 cM in chromosome 7 in flintand dent groups, respectively. Obtaining of different result from earlierstudies [phenylalanineammonia lyase (PAL) gene with ther2 > 0.2 in a survey of 32 European maize inbred lines.Long stretches of LD for maizealso were reported. Thornsberry et al.  measuredg et al. reportedh et al.  examinedstudies  was explstudies examinedstudies  reportedTriticum durum Desf.), Maccaferri et al. [D′ = 0.67 and 0.43,respectively. In hexaploid wheat (Triticumaestivum L), almostcompletely self-pollinating species, strong LD was determined to occuron average within <1 and ~5 cM for region on chromosome 2D and centromericregion 5A that was surveyed with 36 SSR markers in a 95 cultivars of winterwheat [In the selfing tetraploidwheat , aselfing species, Garris et al. [Xa5 using 21 SSRs ina survey of 114 rice accessions. They determined the strong LD within 100 kbwith r2 = 0.1. Agrama and Eizenga [Oryza staiva, and its wild relatives using 176 SSR markers. Although it was not specificallyindicated, LD decay plot suggests a long range LD declining ~50 cM with D′ = 0.5in the “International” and “US” rice collections. Interestingly, LD persistedover an average of 225 cM distance with significant D′ > 0.5 in a wildaccessions. In contrast, many other studies reported a less extent of LD inwild and landrace (broad-based) germplasm and high extent of LD in cultivar(narrow-based) germplasm resources in plants [O. rufipogon decays within 5 kb, while it declines at 50 kb in O. sativa ssp. indica accessions. Mather et al. [japonica (>500 kb), followed by tropical japonica (~150 kb) and indica (~75 kb) that was revealed by using unlinked SNPs. LD extends over a shorterdistance in O. rufipogon (≪40 kb) than in any of the O. sativa groups assayed in their study [In rice , wherethe extent of LD varied from 10 cM to 50 cM range depending on assayed set of agermplasm [Ha) in threedifferent gene pools and reported a long stretched LD extended up to at least212 kb in inbred barley and 98 kb in landrace barley germplasm. In contrast tothese long range LDs observed in barley germplasm, Morrell et al. [LD also has been extensively quantified another highly self-pollinatedcrop, barley  [Glycine max) [Beta vulgaris L) [Sorghum bicolor) [Vitis vinifera L) [Populus trichocarpa) [Poplus termula) [Pinus taeda)[Pseudostugamenziensii) [Picea abies) [Zea mays L) [Lolium perenne) [Gossypiumhirsutum L) [G.hirsutum variety germplasm demonstrated that a genome-wideaverages of LD extended up to genetic distance of 25 cM with r2 > 0.1.Likewise, our another companion study using 95 core set microsatellite markersin a total of 286 “exotic” G. hirsutum revealedthat a genome-wide averages of LD decays within the genetic distance at <10 cM in the landrace stocks germplasm and >30 cM in photoperiodic varietygermplasm, providing evidence of the potential for association mapping ofagronomically important traits in cotton .Furthermore, genome-wide LDhas been quantified for many other plant species that extended up to 10 cM insugar cane (ine max) , 80, 3 cgaris L) , 50 cM ibicolor) , 5–10 cMifera L) , 16–34 khocarpa) , <500 bptermula) ,2000 bps taeda), 1000 bpziensii) , 100–200a abies) , 200-1,  mays L) , 88, andperenne) –91. Alsosutum L) . Survey Importantinformation and implication for association mapping gained from above studiesare that: (1) LD more quickly declines in outcrossing plant species than highlyself-pollinating plants, enabling high resolution mapping of a trait ofinterest in outbreeder plant germplasm. At the same time, LD rapidly declinesin crop variety groups (even in selfing species) compared to populationsderived from biparental crosses, which provides an advantage of discovery morepolymorphisms in the variety germplasms than biparental populations ofself-pollinated crops ; (2) theThereare many types of different methodologies that have been developed and initially arewidely used for association mapping studies in human (comprehensively reviewedby Schulze and McMahon ), yet peTheclassical methodology and design of association mapping is “case and control” approach that identifies the causativegene tags in the comparison of allele frequencies in a sample of unrelatedaffected (referred to as “cases”) individuals and a sample of uninfected orhealthy individuals (referred to as “controls”) , 94. ThiToefficiently eliminate the confounding effects coming from population structureand stratification, Spielman et al.  developeNonetheless,initial TDT approach had issues with the use of multiallelic markers, multiplemarkers, missing parental information, extended (larger) pedigrees, and complexquantitative traits . ToaddrFurther,there were many studies to extend the TDT approaches to QTL and covariates .One of Althoughfamily-based association mapping methodology is effective to controlconfounding effects of a sample and remove spurious associations, it is lesspowerful design  and haveMethodslike “genomic control,” which simply rescale p-values without changing the ranking of loci are not likely to be useful in genome-wide scans where theexistence of true positives is not in doubt.”“Q) in association mapping (by a logisticregression) to correct the false associations. Population structure and sharedcoancestry coefficients between individuals of subdivisions of a population canbe effectively estimated with STRUCTURE program using several models for linked and unlinked markers [K) inassociation mapping referred to as “mixture model” was proposed by severalother studies [Tobetter deal with highly structured populations, Pritchard et al. , 62deve markers . Similar studies , 132. HoQ-matrix) and level ofpairwise relatedness coefficients—“kinship” (K-matrix) in the analysis. Toperform MLM: (1) Q-matrix is generated using STRUCTURE, (2) the pairwise relatedness coefficients betweenindividuals of a mapping population (K-matrix) [SpaGedi software [Q- and K-matrices are used in association mapping to control spuriousassociations. Although computationally intensive, MLM approach found to beeffective in removing the confounding effects of the population in associationmapping [Hence,recently, Yu et al.  develope-matrix)  measuredsoftware , and (3)mapping .Q + K MLM model than any of theother tests that used K- or Q-matrix alone. However, they also noted that (1) Kmatrix would alone be good enough if a kinship estimated as a proportion ofshared haplotypes for each pair of individuals (as denoted K*); (2) thereplacement of Q-matrix  [P-matrix  [LaterZhao et al.  extensivnalysis)  with P-mnalysis)  performenalysis) , thussunalysis) .STRUCTURE [Thereare other types of mixed models for association mapping that have its ownadvantages to control population confounding effects and tag a geneticcausative of a trait of interest. One of such mixed models utilizes a samplewith pedigree information to measure a pedigree-based relatedness andincorporates it directly in QTL-mapping and association mapping , 138.ThTRUCTURE .However,as stated by Malosetti et al.  and otheTheother mixed model approach combines QTL and LD analyses of distinct studies. Inthat, QTLs or candidate genes with already annotated biological function(s) areused as a priori information inassociation mapping , 141. Thp-value) associations (control for Type I error) such as a permutation test [The power of association mapping is the probability ofdetecting the true associations within the mapping population size that reallydepends on (1) the extent and evolution of the LD in a population, (2) thecomplexity and mode of gene action of the trait of interest, (3) sample sizeand experimental design. The power can be increased utilizing the better data and increasingthe sample size. In QTL mapping studies, there are specific statisticalapproaches to estimate the false-positive level of the obtained strong in association mappingbecause of possibility of getting unreliable values due to (1) overestimationof effects (selection bias), (2) association coming from neglecting confoundingeffects of a sample, (3) poor experimental design, and (4) instability ofgenetic effects across different environments [Bayes factors guiding toproperly design the experiments with given power to detect reliable effects. Todetect the reliable effects in association mapping, experiments should bedesigned at least with the Bayes factor of 20 that may require much larger sample sizes. Bayes factor provides stronger evidence than conventional p-values[Bayes factor value(say B = 20) reached with larger sample than the original experimental design,then, the original results indicate a very weak evidence to provide the realeffects [Bayes factorcan be calculated using R function of ld.design from ldDesign package [A statistical approach within the Bayesian framework is usedtest the reliability of obtained significance  with earlywood microfibril angle trait [To date association mapping has also been extended to longlifespan plant species, forest tree populations , where ale trait , and polle trait  werereple trait , 88, 161CRY2 with flowering time were reported [PHYC withflowering and growth response in Arabidopsis. Later Zhao et al. [PHYC),but challenged the power of these associations detected by using “standardlinear methods without correcting population structure.” They put it as “Clearly, none of these polymorphisms wouldhave been picked up in a genome-wide scan” while noting the use ofdifferent sample and trait measurements in the original studies. They alsoreported one of the significant flowering time associated polymorphisms in CLF gene in their genome-wide analysisusing MLM [FRI gene) and pathogen resistance  associated polymorphisms were also reported [SPS1, MAX2, and MAX3)associated with branching architecture in a survey of 36 genes involved inbranch development that were genotyped in a panel of 96 Arabidopsis accessionsfrom Central Europe.Association mapping oftraits in Arabidopsis also has been reported and overall suitability of theapproach well documented. Associations of reported , 146. Bareported reportedo et al.  revisitesing MLM . Flowerireported .Recentlreported  reportedChoosing the appropriate association mapping depends on (1)the extent and evolution of the linkage disequilibrium in a population, (2) thelevel of population structure and stratification, (3) availability of pedigreeinformation, (4) complexity of the trait of interest under study, and (5)availability of the genomic information and resources. Based on reportedstudies, GC is favored approach when population structure is suspected, butfailed to be detected ; howeverThus the association mapping methodology, initially developedby the human geneticists, has found its successive application in plantgermplasm resources, in particular after recent improvements in minimization ofspurious associations. The examples of association mapping studies performed invarious plant germplasm resources including model plant Arabidopsis and extendedto various crop germplasm largely demonstrate the flourish of crop genomics erawith the utilization of powerful LD-based association mapping tool. This isalso a good indicative of the potential utilization of this technology with theother crops and plant species in the future. Currently, a number of suchstudies are, perhaps, in progress in many laboratories worldwide. Thenear-future completion of genome sequencing projects of crop species, poweredwith more cost-effective sequencing technologies, will certainly create a basisfor application of whole genome-association studies , account