Family based association study (FBAS) has the advantages of controlling for population stratification and testing for linkage and association simultaneously. We propose a retrospective multilevel model (rMLM) approach to analyze sibship data by using genotypic information as the dependent variable. Simulated data sets were generated using the simulation of linkage and association (SIMLA) program. We compared rMLM to sib transmission/disequilibrium test (S-TDT), sibling disequilibrium test (SDT), conditional logistic regression (CLR) and generalized estimation equations (GEE) on the measures of power, type I error, estimation bias and standard error. The results indicated that rMLM was a valid test of association in the presence of linkage using sibship data. The advantages of rMLM became more evident when the data contained concordant sibships. Compared to GEE, rMLM had less underestimated odds ratio (OR). Our results support the application of rMLM to detect gene-disease associations using sibship data. However, the risk of increasing type I error rate should be cautioned when there is association without linkage between the disease locus and the genotyped marker. The identification of single-nucleotide polymorphism (SNP) associated with complex diseases is an important goal of current genetic studies. Two important designs are commonly used: one recruits families , and the other uses unrelated individuals (population-based association study) Several statistical methods have been proposed to analyze data from FBAS. Transmission disequilibrium test (TDT) is used to analyze case-parent trios data S-TDT, SDT and CLR all require discordant sibships (DSSs) with at least one affected and one unaffected sibling. Thus the sibships with all siblings affected  would be discarded, leading to a loss of information. Hancock et al. compared generalized estimation equations (GEE) to CLR using simulated family data Multilevel model (MLM) could be a powerful tool for analyzing sibship data, as sibships collected from FBAS are featured by multilevel structure n ascertained sibships and each sibship has at least one affected individual. We use i = 1,2,..,n to denote the ith sibship, j = 1,2,…J to denote the jth individual in each sibship. When J = 2, the sibship becomes a sib pair. The corresponding two-level multilevel logistic model for the probability of being affected conditional on genetic information and other covariates isijD = 1 denotes that the jth individual in the ith sibship is affected. ijG = 1 indicates that the corresponding individual carries the minor allele at the locus under study and β1 is the regression coefficient of ijG for the association between the disease and genetic marker. The intercept term is denoted by β0. The regression coefficients corresponding to environmental or demographic covariates are denoted by γ1,γ2,… and pγ. The βs and γs are always referred to as the “fixed” parameters. The additional random effect, iu, denotes the residual in the second level, which is assumed to be a Gaussian distribution variable with a mean of zero. Its variance, Suppose the data consist of β1 is the odds ratio (OR), an estimate of the genetic relative risk (GRR) when the disease prevalence is low. The Wald test can be used to test the hypothesis of β1 = 0 The exponential of It is also important to notice the difference between MLM and GEE However, in family based studies, it is common practice for the samples to be collected using a proband-ascertained method, by which the families are sampled through an affected member (proband) r” in the superscripts indicates that the corresponding coefficient is from a retrospective model. It is not difficult to show that RMLM uses genotypic information as the dependent variable and disease status as the independent variable. A retrospective two-level logistic model for the probability of carrying the minor allele isThe idea of “retrospective” modeling can be easily applied to GEE r2 = 1, while moderate LD (r2 = 0.26) was simulated between M3 and D. The disease allele frequency (DAF) of D was fixed at 0.20. We specified the minor allele frequencies (MAFs) of M1 and M3 to be 0.20 and 0.32, respectively. Both MAFs of M2 and M4 were specified to be 0.5. For simplicity, we considered a dominant genetic model for all the scenarios. The prevalence of the disease was fixed at 5%.Simulated data sets were generated using the simulation of linkage and association (SIMLA) software (V3.3) Ten scenarios were considered in our simulations. For each setting in each scenario, we simulated 1,000 replicates. In order to generate the sibships which the data sets were comprised of, we simulated three types of pedigrees, denoted by A, B and C, respectively, by using three ascertainment criteria embedded in SIMLA: proband, affected cousin pairs and at least one affected sib pair. The size of sibship was set at 2 in most scenarios, except for scenario 10, in which the sibships from 100 pedigrees (10%) had 3 members. Specified numbers of pedigrees A, B and C were then pooled, as shown by We only considered the single gene disease model in our simulation. The first 8 scenarios were designed to simulate the situations when there were specified hypothesized proportions of CSPs in the data sets. In scenarios 1–4, data sets were simulated with a GRR of the disease locus of either 1.5 or 2. In scenarios 5–8, the GRR was fixed at 1.5, and a continuous environmental factor was also simulated with a relative risk (RR) of 1.5 to examine the performance of each method when there was heterogeneity among families due to some environmental exposure in familial aggregation. We assumed the exposure was a random variable sampled from a Gaussian distribution, with a within-pedigree correlation of 0.5. We considered two special situations in the last two scenarios. Scenario 9 simulated the data sets with dependent sibships by including pedigrees of type B. In scenario 10, 100 pedigrees were designed to have sibships with 3 individuals to reflect the situation when there were various sizes of sibships in the data. Just like scenarios 5–8, an environmental factor correlated within pedigrees was also simulated in each of the last two scenarios.nd-order linearization and PQL approach. A sample code for rMLM modeling can be found in MLwiN  was used to perform MLM and rMLM analysis. Two-level logistic regression models were used to fit the simulated data, with individuals as the first and sibships as the second level units. Although an environmental factor was simulated in scenario 5–10, it was not included in the model to reflect an unknown/un-measurable factor within family. Parameters were estimated using RIGLS with a 2Family procedure was used to implement S-TDT and SDT, the PHReg procedure was used to implement CLR with a robust variance estimate to evaluate the significance GENMOD procedure was used to implement GEE and rGEE.The SAS system  was used for the other analyses. The Basic statistical properties of each method were examined in terms of power, type I error, estimation bias and standard error. For every 1,000 replicates, type I error rate was calculated as the proportion of rejecting the null hypothesis in the model with unlinked and/or un-associated marker . Power was calculated as the proportion of rejecting the null hypothesis in the model with linked and associated marker (M1). We computed the average odds ratio (OR) using For the hypothesis of both linkage and association (M1), S-TDT, SDT and CLR were all valid methods if almost all sib pairs were discordant. Power from the three methods was around 80% or 100% when GRR = 1.5 or 2.0. However, their powers were reduced by the increasing proportion of CSPs. When GRR = 1.5 and the hypothesized proportion of CSPs was 30% , none of S-TDT, SDT and CLR had power greater than 80%. In contrast, rMLM, GEEi, rGEEi and rGEEe had almost the same level of power, which was greater than 90%, almost independent of the proportion of CSPs. The OR estimates of M1 by rMLM, GEEi, rGEEi and rGEEe were lower than the true GRR and those by CLR, while the degree of the underestimate became less with the increasing proportion of CSPs. By comparing the average OR estimates of M1 in Type I error rates were compared with the results of M2, M3 and M4. For M2 and M4, all methods protected the type I error rate at the significant level of 0.05. However, for M3, the type I error rates of both GEEi and rGEEi showed trends of slightly inflating with the increasing proportion of CSPs. The degree of inflation became prominent when GRR = 2.0, as shown by Conclusions derived from scenarios 5–8  are veryResults from GEEi and rGEEi were numerically identical throughout our simulation. They are represented by the same color in The results from scenarios 9–10 are presented in To test for the association using sibship data, traditional methods require data consisting of DSPs or DSSs GEE, rGEE and rMLM all produced negatively biased OR estimates of genetic effect in our simulation, and the degree of bias was greater when the genetic effect was large. There are several issues needed to be clarified on this bias. Firstly, none of the OR estimates resulting from these methods, including CLR, GEE, rGEE, MLM and rMLM, may be reliably interpreted as accurate estimates of GRR in the population. OR is an approximation of RR only when the disease is rare. Secondly, the ascertainment procedure may be inadequately modeled. The sample does not represent the general population but the ascertained one vs 90%, not shown in this article). Given that rMLM provides less biased estimates than GEE and rGEE and is more flexible for modeling complex hierarchical structures, we believe that rMLM has practical value.Our simulations indicated that rMLM, GEE and rGEE all gained more power than CLR with the increasing proportion of CSPs. It may be possible that there are more than 5% of CSPs in the ascertained sample. As an example, the prevalence of total diabetes and prediabetes in China is about 9.7% However, when the markers and the disease locus were under association without linkage (M3), both rMLM and rGEE seemed to have inflated type I error rates, especially when GRR = 2.0. M3 is an extreme example of population stratification. To achieve this level, allele frequency and disease prevalence between sub-populations should be “drastically” different This study has several limitations. Firstly, we only used the dominant genetic model in our simulations. Within MLM framework using MLwiN, we can in theory fit a retrospective multilevel ordinal logistic model for additive genetic model, or a retrospective multilevel multinomial logistic model for co-dominant genetic model. However, some methodological issues need clarification. The coefficients of retrospective ordinal logistic model may not be easy to explain. Equations to convert them to gene's ORs may not be as straightforward as that in retrospective logistic model for dichotomous outcome. Meanwhile, multilevel ordinal logistic model may fail to converge if small proportion presents in some category of the outcome. A possible solution is using the allele instead of the genotype as the outcome in the first level and treating individuals as the second level units. It could “produce” more data for the outcome and may increase the chance of convergence. This model can also account for the correlation between alleles. Secondly, retrospective models may have difficulties in handling the simultaneous effects of several markers. One possible solution for this is to use cumulative polygenetic effects as the outcome. Under the multilevel framework, we also think it is possible to simultaneously treat the SNPs as outcomes by using a multiple responses multilevel model With recent advancements in genotyping technologies, it is possible to genotype thousands, even millions of SNPs simultaneously. We also notice the potential value of rMLM in analyzing disease-SNP set association, which is an important issue in gene-based and pathway-based analysis Text S1Sample Code for fitting a retrospective multilevel model using MLwiN Macro.(DOC)Click here for additional data file.Table S1Measures of power (M1) and type I error (M2–M4) of scenarios 1–4.(DOC)Click here for additional data file.Table S2Measures of parameter estimates  of scenarios 1–4.(DOC)Click here for additional data file.Table S3Measures of power (M1) and type I error (M2–M4) of scenarios 5–8.(DOC)Click here for additional data file.Table S4Measures of parameter estimates  of scenarios 5–8.(DOC)Click here for additional data file.Table S5Measures of power (M1), type I error (M2–M4) and parameter estimate  of scenario 10.(DOC)Click here for additional data file.


Background and Aims. Energy expenditure has been negatively correlated with fat accumulation. However, this association is highly variable. In the present study we applied a genotype by environment interaction method to examine the presence of Genotype x by Total Daily Energy Expenditure and Genotype x by Daily Energy Expenditure interactions in the expression of different body composition traits. Methods and Results. A total of 958 subjects from 294 families of The Portuguese Healthy Family Study were included in the analysis. TDEE and DEE were assessed using a physical activity recall. Body fat percentages were measured with a bioelectrical impedance scale. GxTDEE and GxDEE examinations were performed using SOLAR 4.0 software. All BC traits were significantly heritable, with heritabilities ranging from 21% to 34%. The GxTDEE and GxDEE interaction models fitted the data better than the polygenic model for all traits. For all traits, a significant GxTDEE and GxDEE interaction was due to variance heterogeneity among distinct levels of TDEE and DEE. For WC, GxTDEE was also significant due to the genetic correlation function. Conclusions. TDEE and DEE are environmental constraints associated with the expression of individuals' BC genotypes, leading to variability in the phenotypic expression of BC traits. The hypothesis that the development of many complex traits are the result of the interplay between genetic background and environmental influences has long been postulated  and has This concept has been used to study obesity for several decades , and the FTO rs9939609 polymorphism on body fat accumulation is exacerbated by low levels of PA ;The genetic background of body composition traits is dependent on changes in daily energy expenditure [DEE ].To test for GxTDEE and GxDEE interactions, basic initial hypotheses were formulated regarding the variance/covariance relationship of a BC indicator between family members with different levels of energy expenditure. With regard to GxTDEE and GxDEE interactions, the fundamental null hypothesis is that the expression of a polygenotype  is independent of TDEE and/or DEE levels. It can be shown from first principles that if there are no GxTDEE and/or GxDEE interactions, the same BC indicator measured in subjects with different levels of TDEE and/or DEE will have a genetic correlation of 1.0 and the genetic variance will be homogeneous across all levels of TDEE and/or DEE , 25. On σg2 = exp[αg + γg(EE)], where αg and γg are parameters to be estimated. An additional justification for the exponential function is suggested by the alternative name of this approach, namely, the log-linear model of the variance: lnσg2 = αg + γg(EE). That is, on taking the natural logarithm of the variance modeled as an exponential function, we have the equation of a straight line. In this form, the variance homogeneity null hypothesis obviously holds for a slope-term equal to 0: γg = 0. For the genetic correlation function, we modeled the genetic correlation as an exponential decay function of the pairwise differences in TDEE and/or DEE levels: ρg = exp(−λ|EEi − EEj|), where λ is a parameter to be estimated as a function of the difference in TDEE and/or DEE levels between any two individuals i and j. Here, we also have an elegant reexpression of the interaction null hypothesis, in this case regarding the genetic correlation, in that a genetic correlation equal to 1 is equivalent to λ = 0. This is because for λ = 0, we have ρg = exp(−λ|EEi − EEj|) = e0 = 1. At the same time we employed a similar variance function for the residual environment variance as a function of the TDEE and/or DEE environments because it guards against bias in the detection of additive genetic variance heterogeneity. Allowing for variance heterogeneity  in only the additive genetic variance would lead to a bias in the relevant parameter estimate because it is possible in theory for there to be heterogeneity in the residual environmental variance as well. Thus, allowing for heterogeneity in both the additive genetic variance and residual environmental variance can be said to guard against this bias. Also, since our statistical genetic model assumes from the outset that the genetic and residual environmental effects are uncorrelated we did not posit a corresponding environmental correlation function. Allowing for a residual environmental correlation function on the same environmental variable as that for the genetic correlation function would violate the said assumption.The foregoing requires that we model the variance and correlation as functions of TDEE and/or DEE levels. For the genetic variance function , we modeled the variance using an exponential function to ensure positivity, which is required since any variance is a squared term , 25: σgγg = 0 and λ = 0 are, respectively, distributed as χ12 and are as follows: a chi-square random variable with 1 degree of freedom (d.f.) and ((1/2)χ02 + (1/2)χ12), a 50 : 50 mixture of chi-square random variable with a point-mass at 0, denoted by χ02, and a chi-square with 1 d.f. Prior to examination of these hypotheses, however, we first confirmed if the overall GxTDEE and/or GxDEE interaction models provided a better fit to the data than the standard so-called polygenic model. The LRT for these comparisons can be shown to be distributed as ((1/2)χ22 + (1/2)χ32) . As expected, %FAT was higher in females than in males. Sons and daughters' average BMIs were very similar.The basic descriptive data for TDEE, DEE, and BC traits in fathers, mothers, sons, and daughters are presented in h2) presented in P < 0.001), ranging from 0.21  for %TFAT to 0.34  for WC meaning that the phenotypic expression of BC traits is in part due to moderate-to-strong additive genetic factors, which is a compelling argument to pursue further specific analysis of their genetic architecture.Heritability estimates  (ρg) equal to 1 (σg2) homogeneity hypothesis was also rejected under the GxTDEE model   homogeneual to 1 . The onlEE model . This me h2 being significant, but also most importantly showed the importance of both GxTDEE and GxDEE interactions in fat accumulation. To the extent of our knowledge this is the first effort to apply a GxE interaction analysis, using a nuclear family-design study, to test the hypothesis that individual differences in phenotypic expression of BC traits are conditioned by their EE levels; that is, the interindividual variability in different body composition traits is genetically driven and mediated by physical activity exposure.This study, based on a Portuguese sample of families, aimed to quantify the genetic variance of different BC traits as well as to examine the GxTDEE and GxDEE interactions in modulating the manifestation of these traits in family members. Our results not only confirm the importance of genetic factors in governing the expression of these BC traits, with allh2 = 0.34), and its value is comparable to the estimates of 0.38 found in the Linosa study  than in active individuals [OR = 1.095 (CI95% = 1.068–1.123)]. However, in the active group this increase was only 379 g, leading to the conclusion that being active may reduce the genetic predisposition to obesity by 40%. Also, the FTO gene was found, when comparing active to nonactive individuals, to have a diminished influence on BMI  and WC  [GxEE influence on body composition traits has also been studied using DNA analysis , 46. Forviduals) .This issue is highly challenging and important considering that in many countries researchers and policy makers are trying to deal with the obesity epidemic and associated morbidities not only from a health standpoint but also from a financial view given the public burden in costs of obesity related morbidities , 48. ThiWe think that our results add to the efforts in trying to disentangle these matters and help to substantiate the latter arguments by suggesting that the phenotypic expression of BC traits is the result of joint effects of genes, EE levels (environment), and their interactions.Despite the relevance of the present results, some limitations should be acknowledged. Firstly, the sample used may not be representative of the general Portuguese population. Secondly, the method chosen to estimate BC traits, in our case bioelectrical impedance analysis, even though having been previously validated with DXA , is not In conclusion, the present results showed that the genetic expression of BC traits is significantly influenced by energy expenditure levels. Accordingly, physical activity may be considered an environmental variable that promotes interindividual differences in BC traits through genetic mediation. This is valuable information for health practitioners. More efforts should be devoted to not only identify specific loci that control different BC traits but also test if these loci are regulated or not by different PA levels.


In mammalian genetics, many quantitative traits, such as blood pressure, are thought to be influenced by specific genes, but are also affected by environmental factors, making the associated genes difficult to identify and locate from genetic data alone. In particular, the application of classical statistical methods to single nucleotide polymorphism (SNP) data collected in genome-wide association studies has been especially challenging. We propose a coalescent approach to search for SNPs associated with quantitative traits in genome-wide association study (GWAS) data by taking into account the evolutionary history among SNPs.We evaluate the performance of the new method using simulated data, and find that it performs at least as well as existing methods with an increase in performance in the case of population structure. Application of the methodology to a real data set consisting of high-density lipoprotein cholesterol measurements in mice shows the method performs well for empirical data, as well.By combining methods from stochastic processes and phylogenetics, this work provides an innovative avenue for the development of new statistical methodology in the analysis of GWAS data. The goal of quantitative trait mapping based on genome-wide association study (GWAS) data is to find single nucleotide polymorphisms (SNPs) that are associated with a set of quantitative trait (or phenotypic) values under study. Many quantitative traits are thought to have both a genetic basis and an environmental basis, making the associated genes difficult to identify from genetic data alone. The biological complexity of the evolutionary history of genes and the environmental factors acting simultaneously on the trait values makes this a challenging task, even with very large data sets.Quantitative trait mapping has two distinct goals, detection and localization. Detection is achieved if any SNP in a certain region is found to be significant during the association study, while localization addresses how close the detected SNP(s) are to the true causative SNP(s). Localization is usually measured by distance between a significant SNP and the true SNP. Since most data sets will include a large number of SNPs, it is very unlikely that any statistical method will pick up a truly causal SNP, but clearly methods that can provide relatively precise localization will be the most useful.t-test), and those that analyze groups of markers together  and Single Marker Association (SMA) perform an ANOVA on particular groupings of samples to assess the significance of the groupings [Methods of quantitative trait mapping can be broadly classified into two groups: those that model the shared evolutionary history, usually in the form of a phylogenetic tree, and those that do not. Non-tree based methods used in quantitative trait mapping include methods that analyze each marker independently (e.g. the  Mapping  and Sing Mapping ). The t-roupings . Since troupings .local perfect phylogenies, which are phylogenies built on sets of neighboring compatible SNPs identified by the four-gamete test. These methods also require that the SNP data be phased into haplotypes prior to analysis, which is a nontrivial task. The HTreeQA method [By using information contained in the relationships among SNPs, tree-based methods gain power in detection and localization. However, this gain in power comes at the expense of an increased computational cost. In spite of the computational issues, many tree-based methods have recently been proposed for this problem. In the case of discrete trait data, these methods include LATAG, implemented in the software TreeLD , MARGARIA method  avoids tTree-based techniques must assume an underlying model to represent the genealogical history among SNPs along a chromosome. The most common model for evolutionary relatedness within a population is the coalescent process ,10. At ak, and calculates a score for each possible set of k clusters defined by the phylogenetic tree. The score calculated is a penalized likelihood , where the likelihood is a multivariate normal with a different mean in each cluster and an overall shared variance, with zero covariance among observations. The maximum score over all possible sets of k clusters defined by the phylogeny is used to assess the significance of each SNP. This technique produces a test statistic at each location along the genome. Although this clustering technique accounts for the shared evolutionary history among SNPs, QBlossoc has two weaknesses rooted in its assumptions during the score calculation; namely, QBlossoc assumes both independence and a common variance among the quantitative trait values. The method proposed here is a modification of QBlossoc that addresses these two weaknesses.The tree-based methods mentioned above vary in the way that the phylogenetic information is used in the subsequent analysis. One method of particular interest to the present study is QBlossoc . After lOur proposed data analysis technique uses the same near local perfect phylogenies built by , but alsHere, we propose a data analysis method that accounts for the covariance structure present in GWAS data sets, and show that it generally performs similarly to QBlossoc in terms of power of detection and localization, with strong performance in the presence of population structure. Finally, the proposed data analysis method is applied to a GWAS data set containing SNP data for 288 outbred mice . PhenotySince the goal is to search for SNPs associated with a quantitative trait, we will consider both detection and localization. The proposed analysis technique includes calculation of a score at each SNP site and an assessment of significance by performing hypothesis tests via permutation. In order to examine the performance of the methods, we use a novel data simulation technique so that we know the location of the SNP truly associated with the quantitative trait (if one exists). This yields an opportunity to compare the type I error and power of the proposed method with that of QBlossoc. We begin by giving the details of the method of analyzing the data, and then describe the simulation technique.Θ. At each SNP, the local tree topology is estimated using Blossoc’s approach [The evolutionary history at each SNP site can be represented by a local phylogenetic tree, approach . The braapproach , which yapproach  is basedor model .We modify this method to handle SNP data as follows. First, the same heuristic method as in the Rogers-Swofford method (based on a most parsimonious reconstruction) is applied to the phased 0-1 SNP data at each internal node of the tree. The proportion of SNPs that differ between each node, If ribed in . Notice V(Θ), as shown in the example in Figure For each estimated local phylogeny, the branch lengths are used to estimate the variance-covariance matrix of the tree, k clusters using only the earliest (k−1) edges in the tree. An example of this clustering is shown in Figure k clusters, we define a matrix, D, with elements: The proposed method accounts for only a focused portion of the evolutionary history among observations using a clustering technique. At each SNP site, the tree can be partitioned into i=1,2,…,n and j=1,2,…,k, where n is the number of observations . Then the trait data, Y=, are assumed to follow a multivariate normal distribution along tree Θ: for μ=. However, instead of assuming independence, the variance-covariance matrix of the tree, σ2V=σ2V(Θ), allows for covariance structure to be present among the quantitative trait observations.Here, as in QBlossoc, each cluster has its own mean, denoted Using the distribution in Equation 3, the maximum likelihood estimates of the parameters are straightforward to calculate, Hypothesis testing is carried out using a likelihood framework. In particular, we use a penalized likelihood similar to that proposed by . We defik+1) parameters, including the mean trait value in each cluster and the variance, σ2. The BIC criterion penalizes for k of these parameters. At each SNP, a local tree is scored according to (6), for varying numbers of clusters, k=1,…,kmax, and the resulting tree score is the maximum score over the number of clusters.To calculate LSS, the maximum likelihood is penalized by subtracting a penalty as in the Bayesian Information Criterion (BIC). Calculation of the likelihood involves estimation of  between the maximally-scored locus and the disease locus is calculated.In addition to the tree topology, our method also requires an estimate of the covariance structure in the data. This covariance structure is estimated via estimation of the branch lengths along the topology. By using the clustered tree to consider only the broad-scale phylogenetic relationships among SNPs, our technique can account for the evolutionary history among genes without using all coalescent relationships. Using only broad-scale relationships enables a computationally feasible algorithm that is able to account for the most important aspects of the covariance structure among observations.ms (without selection) [To assess the performance of the proposed likelihood technique, simulated data sets are used. This provides a setting where the presence and location of the SNP truly associated with the quantitative trait is known. In our simulation study, we simulate SNP data for 100 replicate data sets from a diploid population using the program lection) . Each daFor each SNP, quantitative data is simulated along the phylogenetic tree at the disease locus according to a generalized version of the Ornstein-Uhlenbeck (OU) process described by , Yi(t) is the quantitative trait value for the ith lineage at time t, Θ is the target trait value, α is the strength of selection toward the target value, σY is the standard deviation of the process per unit time, and dBi(t) represents a Brownian Motion process for lineage i, so that values of dBi(t) for small time increments, dt, are independent, identically distributed random variables from a normal distribution with mean zero and variance dt. Thus, the OU process is a mean-reverting process with a deterministic component, α(θ−Yi(t))dt, modeling the selection of a trait toward the optimum target value, and a stochastic component, σYdBi(t), providing the “random noise” for the process. Notice that the deterministic portion of this process implies that the selection of the trait toward the target is proportional to the distance between the trait and the target value, Θ. When two observations share a portion of their evolutionary history, they share the trait value, Yi(t), for that portion of time. Along the corresponding phylogenetic tree, observations share an evolutionary history when they evolve along the same lineage.where When this process is applied in the setting of phylogenetics, the stochastic process gives the same value during the time when the evolutionary history is shared for any two observations. However, after two lineages split, their trait values evolve independently from one another. This implies that before a split, two observations are perfectly correlated, while after the split, they evolve in an uncorrelated manner.For this study, a more flexible form of the Ornstein-Uhlenbeck process is used, the Generalized Hansen model . This alXi(t) is the SNP state for the ith observation at time t.The trait is simulated according to this stochastic process with the target trait value determined solely by the SNP state at any time in the evolutionary history at that SNP, where Using the Generalized Hansen Model leaves us with a quantitative trait value for each haplotype that has both a (deterministic) genetic component, determined by the SNP, and a stochastic component. This process imposes an evolutionary history of the quantitative trait which can be portrayed by the phylogenetic tree at the disease locus, and allows the two haplotypes of a diploid individual to evolve independently along the phylogeny at the disease locus. This is intuitive as long as two haplotypes for an individual are unrelated to the trait. In order to simulate data for each individual, or diplotype, based on the haplotypic data, we use an additive model. The trait value for each diplotype is the average trait value across the two copies of the trait for each individual at the disease location.ms: the diploid population size was N0=20,000, the neutral mutation rate for each DNA base pair was μ=2.0×10−10, the rate of recombination per generation per DNA base pair was ν=10−8, and each simulated chromosome was 1,000,000 base pairs long. During simulation of the quantitative trait values, we vary the strength of selection, α, and the standard deviation of the quantitative trait per unit time, σY. The two target trait values we consider are θ1=80 and θ2=100.During the simulation studies, we simulate the SNP using these parameters in kmax=15. The same technique is applied to 200 permutation data sets created by using a permutation of trait values across individuals. The type I error, power, and localization for QBlossoc and LSS are presented in Tables In order to assess the performance of the proposed technique in terms of power and type I error, we begin by analyzing data sets which either include a truly-associated SNP, or do not include an associated SNP. These data sets are simulated using the technique described above. After simulating the data sets for specified parameter values, the local phylogenetic tree at each SNP is estimated using Blossoc, and branch lengths are estimated as described previously. Next, the score in Equation 6 is calculated, using Permutation testing results showed that both QBlossoc and LSS control the type I error around 0.05 . It should be noted that individual SNP computations are easily parallelized in this setting.Although the proposed technique begins to address the limitations of current statistical methodology in the problem of quantitative trait mapping, the technique has several avenues that could be pursued in order to extend the method to more general cases. In the data simulation technique, only codominant trait models have been implemented, but dominant and recessive trait models are straightforward to implement and test. Also, many traits are impacted by both a genetic component and an environmental covariate. By extending the quantitative trait simulation technique, many realistic traits could be simulated with both genetic and environmental covariates.Similarly, LSS is flexible and could be generalized to include environmental covariates as well. Additionally, the current likelihood score requires that genotypic data be phased into haplotypes prior to analysis. Phasing is a nontrivial process which is subject to error. By extending the tree estimation method and likelihood score to be computed on genotypic data, these methods will be more easily applied to real data sets. Advantages of the model include its ability to find different signals than previous statistical methods and its flexibility to be extended to analyze different types of data. Although these extensions are under investigation, the proposed data analysis technique appears to be an impactful modification of the ideas presented in QBlossoc, especially in the presence of population structure.Both authors have no competing interests.Both authors developed the methodology. KLT coded the algorithm, carried out all analyses, and drafted the manuscript. LSK revised the manuscript. Both authors read and approved the final manuscript.


Salmonella propagation by apparently healthy chicken and subsequent food security concerns could be decreased by the selection and use of chicken lines more resistant to carrier-state. In the present study we applied the first steps of the genomic selection methodology to assess the interest of including genetic markers for the genetic evaluation of hen lines infected with Salmonella Enteritidis.Salmonella carrier-state at two different ages. A total of 600 animals were typed with 1536 SNP markers and artificially infected with S. Enteritidis. Phenotypes were collected four weeks  or five weeks (adults) later. Two types of variance component analyses, including or not including SNP data, were performed and compared. All variance components were estimated by Bayesian methods and Gibbs sampling.We studied commercial laying hen lines divergently selected for resistance to The comparison of both genetic analyses shows that SNP are efficient in capturing genetic variation, although none of them captures a large affect on the traits studied. Average accuracies do not change between analyses, showing that using SNP data does not really increase information.Salmonella carrier-state resistance in laying hens is promising, although a denser SNP coverage of the genome on a higher number of animals is needed to assess its feasibility and efficiency compared to classical pedigree evaluation.These preliminary results show that genomic selection for  Salmonella carrier-state has a rather weak heritability [Salmonella, once infected. The use of chicken more resistant to Salmonella carrier-state could be a way to decrease the propagation of Salmonella in poultry stocks, which could have a direct impact on food safety. The feasibility of selection for an improved resistance to carrier state has been demonstrated by a divergent selection experiment from a laying hen commercial line [Salmonella Enteritidis..Like most disease resistance related traits, resistance to tability ; in additability . Resistaial line . In the ial line  to assesCaeca). Two hundreds and eight hens were inoculated at the peak of lay The presence/absence of Salmonella in spleen (AdultSpleen), liver (AdultLiver) and caeca (AdultCaeca) and the global contamination rate Adult0-1 (0 for no organ contaminated/ 1 for one or more organ contaminated) were considered for further analyses.The S. Enteritidis (SE) nalidixic acid and streptomycin resistant PT 4 strain 1009 was used for all challenges. Chicks and adult hen resistance was assessed as described previously . Three hSNP marker genotypes were obtained by the Illumina Golden Gate technology on a BeadExpress station ; 194 markers were chosen to specifically cover three previously identified QTL regions on chromosomes 1, 2 and 5 ,7, whileA. Approach COMVC (combined variance components): two random effects, one with covariance matrix A (thus based on pedigree) and the other using a combined pedigree-genomic relationship matrix H[A only (PEDBLUP), or including the pedigree-genomic relationship matrix H (COMBLUP) as well. To obtain only one EBV a new relationship matrix was created weighting each matrix by its associated variance component [r was computed in both cases from the diagonal elements (PEV) of the inverse of the mixed model equations, as http://nce.ads.uga.edu/~ignacy/newprograms.html, with the modifications included to account for genomic relationship matrices [For each of the 5 traits, two preliminary analyses were performed. Approach PEDVC (pedigree-variance components): regular estimation of genetic parameters using the usual pedigree-based relationship matrix  matrix H. After v matrix H estimateomponent . The thematrices .-6), but they were retained in the analysis, because a selected population is not expected to behave in Hardy-Weinberg equilibrium [From 1536 original SNP, only 831 turned out to be polymorphic; the rest were discarded from statistical analyses. A set of 141 SNP were not in Hardy-Weinberg equilibrium (p<10ilibrium .Table Table S. Enteritidis, which is the first step toward genomic selection.Overall, the use of SNP does not change the picture of genetic evaluation. Genetic parameters and theoretical accuracies are similar. This is probably partly due to an insufficient SNP density and to a lack of phenotypic data. A denser SNP coverage and more phenotypic data are thus needed to perform a more efficient evaluation of the interest of including SNP markers for the genetic evaluation of hens infected with The authors declare they have no competing interest.AL performed the genetic evaluations. FC and CB acquired phenotypic and genotypic data. AL and FC drafted the manuscript.


Important knowledge about the determinants of complex human phenotypes can be obtained from the estimation of heritability, the fraction of phenotypic variation in a population that is determined by genetic factors. Here, we make use of extensive phenotype data in Iceland, long-range phased genotypes, and a population-wide genealogical database to examine the heritability of 11 quantitative and 12 dichotomous phenotypes in a sample of 38,167 individuals. Most previous estimates of heritability are derived from family-based approaches such as twin studies, which may be biased upwards by epistatic interactions or shared environment. Our estimates of heritability, based on both closely and distantly related pairs of individuals, are significantly lower than those from previous studies. We examine phenotypic correlations across a range of relationships, from siblings to first cousins, and find that the excess phenotypic correlation in these related individuals is predominantly due to shared environment as opposed to dominance or epistasis. We also develop a new method to jointly estimate narrow-sense heritability and the heritability explained by genotyped SNPs. Unlike existing methods, this approach permits the use of information from both closely and distantly related pairs of individuals, thereby reducing the variance of estimates of heritability explained by genotyped SNPs while preventing upward bias. Our results show that common SNPs explain a larger proportion of the heritability than previously thought, with SNPs present on Illumina 300K genotyping arrays explaining more than half of the heritability for the 23 phenotypes examined in this study. Much of the remaining heritability is likely to be due to rare alleles that are not captured by standard genotyping arrays. Phenotype is a function of a genome and its environment. Heritability is the fraction of variation in a phenotype determined by genetic factors in a population. Current methods to estimate heritability rely on the phenotypic correlations of closely related individuals and are potentially upwardly biased, due to the impact of epistasis and shared environment. We develop new methods to estimate heritability over both closely and distantly related individuals. By examining the phenotypic correlation among different types of related individuals such as siblings, half-siblings, and first cousins, we show that shared environment is the primary determinant of inflated estimates of heritability. For a large number of phenotypes, it is not known how much of the heritability is explained by SNPs included on current genotyping platforms. Existing methods to estimate this component of heritability are biased in the presence of related individuals. We develop a method that permits the inclusion of both closely and distantly related individuals when estimating heritability explained by genotyped SNPs and use it to make estimates for 23 medically relevant phenotypes. These estimates can be used to increase our understanding of the distribution and frequency of functionally relevant variants and thereby inform the design of future studies. Although genome-wide association studies (GWAS) have resulted in the discovery of thousands of novel associations of loci to hundreds of phenotypes The narrow-sense heritability of a phenotype  We further introduce a new variance components method that provides simultaneous estimates of For most of the 23 phenotypes examined here, our results show that Below, we provide an overview of the approaches we used to estimate various components of heritability. The details of these approaches are provided in the Methods section.We used a linear mixed model approach to estimate components of heritability. In this approach, each phenotype is modeled using a multivariate normal distribution. Each of the components of heritability that we estimated corresponds to a different model of the phenotypic covariance.Narrow-sense heritability  is the sum of additive, dominant, and epistatic components of heritability. The additive, dominant, environmental (ADE) model can be used to obtain joint estimates of dominance and additive components of heritability, using two covariance matrices based on IBD2 (two copies shared IBD) and IBD Broad-sense heritability . However, fine-scale estimation of KIBD in population samples is dependent on information about the chromosomal phase of alleles, which requires long-range phasing of the data KIBDIdeally, estimates of narrow-sense heritability of a particular phenotype would be based on a genetic relationship matrix constructed from causal variants, representing the true genetic contribution to the phenotype 2, age, sex, and geographic region were included as covariates to prevent confounding. These estimates range from 0.099 for recombination rate to 0.691 for height. The only quantitative trait yielding an estimate not significantly different from 0 was sex-ratio of offspring. For each of the eight quantitative phenotypes with published estimates of IBD-based estimates of Previous studies, based on either genealogical or direct estimates of IBD sharing, have been limited to closely related individuals (first-cousins or closer), and may therefore be upwardly biased due to the impact of shared environment, dominance, or epistatic interactions 2. One suggested solution to this problem is the use of KIBS, the genome-wide proportion of alleles shared identical-by-state (IBS) at all genotyped loci, as a substitute for KIBDKIBS provides a poor estimate of KIBD for distantly related pairs of individuals). Taking advantage of long-range phase based estimates of KIBD, we sought to evaluate the use of KIBS for the estimation of h2. For this purpose, we computed KIBS as defined in 2, the KIBS matrix captures information from two distinct sources, depending on the degree of relationship between pairs of individuals. For large values of IBS it estimates genetic covariance over all SNPs in the genome. For low values of IBS it estimates genetic covariance over just those SNPs on the genotyping platform KIBS therefore tend to lie between the true value, In most cases, researchers do not have access to long-range phased genotypes with which to estimate h2, but setting values of KIBS less than or equal to a threshold t (KIBS>t) to 0, for t = 0.00, 0.025 and 0.05. This threshold defines the separation between closely and distantly related individuals. We evaluated this approach using both simulations and real data sets and observed a significant downward bias of narrow-sense heritability estimated from tresholded IBS . Extensive testing of this model was performed to demonstrate that it estimates the appropriate quantities (see Methods), and estimates of To enable unbiased calculation of 2>0. Our results are concordant with the previous estimates of 2 ratio of 0.53  and found that only height, with a value of 0.58 was significantly different  can upwardly bias estimates of KIBD and KIBD2, where the latter represents the fraction of the genome with both chromosomes shared IBD for each pair of individuals KIBD was performed (see Methods) H2. The only class of relationship with significant IBD2 is siblings who share an expected ¼ of their genome IBD2. This analysis will therefore focus overwhelmingly on the difference between siblings and other classes of relationship. Siblings are also subject to epistatic interactions and shared environment and so this analysis will be influenced by all three factors . We note that this analysis will not detect shared environment effects that decay exactly in proportion to genome-wide IBD.First, we estimated additive and dominance-like effects simultaneously under an ADE  model with variance components 2, they do not distinguish between the possible sources of inflation. The fact that the narrow sense heritability estimate We initially examined a subset of 11 quantitative and dichotomous traits, viewed as likely candidates for environmental effects, in a subset of 15,000 genotyped individuals using the ADE framework. The results for these phenotypes are shown in ects see . While tIn order to address this issue, we performed a pedigree-based analysis, making use of genealogical information KIBD2 due to dominance and would have larger estimates of KIBD2. Again, this is not what is observed. Finally, if If the heritability estimate of two copy IBD when fit jointly with IBD (Our results show that IBDK), suggests that first cousins have shared environmental factors stronger than either of these other classes of relationship. Although we condition on age a strong non-linear effect of age on phenotype, or a cohort effect, could produce this elevated correlation amongst first cousin phenotypes.Two additional results from We have made use of long-range phased genotype data and genealogical information from an Icelandic cohort to shed light on the problem of missing heritability, and the relative contributions of common and rare sequence variants and environmental factors to complex human phenotypes.First, we examined IBD based estimation of narrow-sense heritability2. The estimated value of Second, we developed a new method to estimate Finally, we investigated the impact of shared environment, dominance, and epistasis on estimates of A standard way to quantify the contribution of environmental effects is to fit an ACE model Interestingly, our estimate of the heritability of height (0.69) is lower than previous estimates (0.8) 2, this fraction is larger than previous estimates We conclude that, for quantitative traits, more than half of This research was approved by the Data Protection Commission of Iceland and the National Bioethics Committee of Iceland. The appropriate informed consent was obtained for all sample donors.We analyzed 38,167 individuals from the deCODE data set genotyped on the Illumina 300K chip. Owing to the sensitive nature of genotype data, access to these data can only be granted at the headquarters of deCODE Genetics in Iceland. The details of the genotyping, quality control, IBD estimation and genealogy are described elsewhere The deCODE Genetics genealogy database, containing all contemporary Icelanders and most of their ancestors going back to the year 1650, was used to determine the genealogical relationships between individuals A description of the phenotypes is given in We used a linear mixed model approach to estimate the components of heritability in our data sets. In this approach, each phenotype Y is modeled from a multivariate normal distribution KIBS>t and KIBS respectively. To jointly estimate KIBD and KIBS. The intuition for this approach is that the large elements of genetic covariance matrix KIBS are good estimates of the pair-wise IBD of individuals. Indeed, this is why KIBS only provide information about SNPs in LD with those on the genotyping platform. This is why the KIBS applied to unrelated individuals in the approach of Yang et al. estimates KIBS into two components, one provides estimates of the phenotypic variance explained by SNPs on the genotyping platform, and the other provides an estimate of the remaining phenotypic variance. The total narrow-sense heritability is the sum of the parameters for KIBS>t and KIBS, and the heritability explained by genotyped SNPs is the parameter for KIBS.For a normalized phenotype with mean 0 and variance 1, to estimate KIBD2 is a combination of shared environment, dominance, and epistatic effects. The parameter for KIBD is the narrow-sense heritability. Under the assumption of no shared environment or epistatic effects, the sum of these estimates is the broad-sense heritability. In all cases we adjusted for age, gender, and region of Iceland as fixed effects. We use REML including a constant vector instead of ML to prevent bias in heritability estimation To estimate KIBS matrix is estimated as defined in KIBS>t is the KIBS matrix with all entries less than t set to zero, with the exception of the diagonal, which is not changed.The KIBD matrix is the fraction of the genome shared IBD between individuals i and j. Pair-wise IBD estimates were estimated as described in KIBD2 matrix is defined similarly, but pair-wise IBD2 estimates (both chromosomes IBD) are used in place of pair-wise IBD estimates. That is, a pair of individuals is IBD2 at a particular SNP if they are IBD on both haplotypes. Entry,  is set to 1.0. We note that none of the kinship matrices defined here, and hence none of the resulting heritability estimates rely on the genealogy, but are based on direct estimates from the genetic data.Entry  of the ean zero  and the ean zero . Entry , KIBS>t+KIBS does not provide a good estimate of since KIBS>t will be influenced by genotyped variants. However, KIBS>t as an estimate for the true heritability depends on the relatedness structure of the data set. In data sets with families, such as the cohort examined here, or the FHS data set When the relatedness of individuals in the data set is moderate (e.g. K = 0.125), the joint model 1 and C2 by selecting a causal variant every 500 SNPs along the even chromosomes for C1 and repeating the process along the odd chromosomes for C2. We chose effect sizes 1α and 2α for C1 and C2 respectively and set the sub-phenotypes for an individual by summing the product of their genotypes  times the corresponding effect sizes. We then added random noise 1ε and 2ε to each sub-phenotype and summed together the two sub-phenotypes to generate a final phenotype for each individual. The even chromosomes correspond to the observed genotypes in a GWAS and the odd chromosomes correspond to SNPs not in LD with the genotyped SNPs. For any choice of 1α and 2α, and variances of 1ε and 2ε we can compute the heritability of the phenotype due to all SNPs We performed a similar set of experiments to those described above, but this time used real genotype data with simulated phenotypes in order to verify that issues due to LD, IBD estimation, population structure, or other similar confounders did not affect our results. We selected 8000 individuals randomly from the complete data set and generated two sub-phenotypes for each individual. We generated two sets of causal variants CKIBD, KIBS, KIBS>t, and KIBS>t+KIBS. The results are shown in KIBS, which always lies between KIBS by examining the estimate of We recomputed the relationship matrices K using only the even chromosomes. For each simulated phenotype we estimated heritability using enotypes . We obseFor a given class of relatives, (e.g. siblings), for each phenotype we computed the correlation between the phenotype across all pairs of that class. The heritability estimate was then generated by dividing the correlation by the fraction of the genome expected to be shared IBD (e.g. 0.5 for siblings). It is not possible to place standard errors on the heritability estimate of the phenotypes due to the complex relatedness structure of the individuals in each class. One pair of siblings for example, might be the grandfather and granduncle of another pair of siblings. However, it is possible to compute an empirical mean and standard deviation across traits.To compare the classes of relatives we computed the empirical mean and standard deviation of the differences of the heritability estimates across traits. The standard error of the difference is the standard deviation estimate divided by the square root of the number of phenotypes (17 in this case). We applied a Wald test to determine the p-value KIBD2+KIBD and the likelihood of the narrow-sense heritability estimated from KIBD.To determine the significance of the combined effects of shared environment, dominance, and epistatic interaction we constructed a one degree of freedom likelihood ratio test. We computed the likelihood of the ADE model fit with covariance matrices The heritability estimates in cale see  using thFigure S1Average heritability estimates of type 2 diabetes, coronary artery disease, and hypertension in pregnancy for six classes of relationship. The differences in heritability estimate between classes of relationship are consistent with a shared-environment only effect on phenotypic correlation, but not with a dominance only or epistasis only effect on phenotypic correlation.(PDF)Click here for additional data file.Table S1Definition of subscripted parameters.(DOCX)Click here for additional data file.Table S22h) for 12 dichotomous traits on the liability scale.Narrow-sense heritability ((DOCX)Click here for additional data file.Table S3t = 0.05.Heritability estimates over simulated data for a range of relatedness structures. Model refers to the relatedness structure of the data. 0.5 represents 700 pairs of individuals with 50% of their genome IBD. 0.5,0.25 represents 350 pairs with 50% IBD and 350 pairs with 2.5% IBD. 0.125,0.025 represents 350 pairs with 12.5% IBD and 350 pairs with 2.5% IBD. We used a threshold (DOCX)Click here for additional data file.Table S4Heritability estimates from data simulated over even and odd chromosomes of 8,000 individuals from the decode cohort.(DOCX)Click here for additional data file.Table S5Heritability estimates from data simulated over even and odd chromosomes of 8,000 individuals from the decode cohort.(DOCX)Click here for additional data file.Table S6Narrow-sense heritability estimated from thresholding IBS ((DOCX)Click here for additional data file.Table S72h) for 12 dichotomous traits on the observed scale. Narrow-sense heritability ((DOCX)Click here for additional data file.Table S8sib represents sib-pairs, avuncular represents uncle/aunt-niece/nephew, and grandparent represents grandparent-grandchild. We note that the significance values are more a measure of power than of model.Differences in heritability estimates between pairs of classes of relationships. If there is no effect of shared environment, dominance, or epistatic interaction then (DOCX)Click here for additional data file.Table S9IBS based estimates ((DOCX)Click here for additional data file.Text S1Using extended genealogy to estimate components of heritability for 23 quantitative and dichotomous traits.(DOCX)Click here for additional data file.


Meiotic recombination causes a shuffling of homologous chromosomes as they are passed from parents to children. Finding the genomic locations where these crossovers occur is important for genetic association studies, understanding population genetic variation, and predicting disease-causing structural rearrangements. There have been several reports that recombination hotspot usage differs between human populations. But while fine-scale genetic maps exist for European and African populations, none have been constructed for Asians.Here we present the first Asian genetic map with resolution high enough to reveal hotspot usage. We constructed this map by applying a hidden Markov model to genotype data for over 500,000 single nucleotide polymorphism markers from Korean and Mongolian pedigrees which include 980 meioses. We identified 32,922 crossovers with a precision rate of 99%, 97% sensitivity, and a median resolution of 105,949 bp. For direct comparison of genetic maps between ethnic groups, we also constructed a map for CEPH families using identical methods. We found high levels of concordance with known hotspots, with approximately 72% of recombination occurring in these regions. We investigated the hypothesized contribution of recombination problems to age-related aneuploidy. Our large sample size allowed us to detect a weak but significant negative effect of maternal age on recombination rate.We have constructed the first fine-scale Asian genetic map. This fills an important gap in the understanding of recombination pattern variation and will be a valuable resource for future research in population genetics. Our map will improve the accuracy of linkage studies and inform the design of genome-wide association studies in the Asian population. Homologous recombination during meiosis results from the resolution of programmed DNA double-strand breaks by crossover between non-sister chromatids. Recombination is concentrated into hotspots roughly 2 kb in length scattered throughout the genome. RecombiPRDM9 and local patterns of recombination[PRDM9 alleles, including novel SNPs predicted to affect DNA binding . At all ages, there is considerable variation in the recombination rate phenotype, and the linear model accounts for this variation poorly. We did not find a significant effect following a similar analysis for paternal age. We further tested for significant reductions on each chromosome between women younger and older than 30 , but this may be an artefact of multiple testing on 23 chromosomes. These chromosomes are also different to those identified as candidates previously[It is known that reduced recombination on chromosome 21 is associated with Down syndrome. There i Figure . Chromoseviously. This maGiven that the effects of age on recombination are small, they may be susceptible to discrepancies in methodology. In the study by Kong et al., ages weWe have constructed the first high-resolution genetic map for Asians. Our map will be a useful resource for future population genetics research, improve the accuracy of linkage studies, help to predict disease-causing structural rearrangements and inform the design of genome-wide association studies in the Asian population. In general, Asian recombination patterns were similar to those in Europeans. A higher proportion of Asian and European recombination was mapped to hotspot regions than in previous studies. These results validate the application of combined genetic maps to Asians. Our data show that maternal age has a weak, negative effect on recombination rate, and there are no strong chromosome-specific effects.We used nuclear family genotype data to find Asian recombination patterns. By directly observing recent recombination events, this approach avoids the problem of coalescent methods finding recombination receding many generations into the past. Several deterministic programs using parent-sibling tracing methods have been described in the literature,8,16,18,A and B. For any genomic locus in a parent, two possible modes of transmission are possible: both children may receive the same allele, or each child may receive a different allele. These paternal and maternal transmission states combine to yield four possible states. Where the transmission state differs at adjacent genomic loci, we can infer that a crossover occurred between them during a paternal or maternal meiosis. We model the sequence of states along the markers on a chromosome as a Markov process. Observed genotypes at a given locus in all four family members may be consistent with a subset of these states. For example, if the father, mother and child genotypes are AA, AB, AA and AB respectively at some SNP, then we can infer that the mother is transmitting different alleles to the two children, but can make no inference regarding paternal transmission. Homozygous loci are uninformative because they are consistent with all four states. A hidden Markov model was constructed with a state space consisting of the four transmission states, and transition weights between these states corresponding roughly to previously reported genome-wide recombination rates[′ and 3′ directions as far as more than one state remains possible. This non-probabilistic, strict delimitation of boundaries protects the algorithm from sensitivity to changes in state transition or emission probabilities. The SNPs marking the prediction interval were mapped to NCBI build 36 physical position. Alternative hidden Markov models were used to find maternal recombinations on the X chromosome  triples in three families where checks found mathematical inconsistency. We were able to rescue data for three children in one such family where they formed a consistent trio. This left 9 children in three families where recombinations could not be distinguished consistently. These were removed from the analysis.http://genome.ucsc.edu/cgi-bin/hgLiftOver) was used to perform this transfer, during which 6 hotspots were partially deleted.This study used genotype data from Mongolian pedigrees, generated by the Illumina Human 610-Quad Beadchip yielding 569,132 markers. The data was originally collected for association studies in the GENDISCAN project. This was approved by the Institutional Review Boards of Seoul National University, approval number H-0307-105-002. Mendelian errors were filtered using PedCheck and double recombination errors were filtered using Merlin. Markers with a low call rate (<99%), high error rate (>1%) or low minor allele frequency (<0.01) were excluded as described previously. We alsoThe authors declare that they have no competing interests.JSS conceived of this study. JSS and JHS managed the GENDISCAN project and the Healthy Twin Study respectively. TB constructed the hidden Markov model, analysed the data and drafted the manuscript. YSJ helped the analysis. All authors participated in manuscript writing. All authors read and approved the final manuscript.Supplementary Notes. Details on X chromosome hidden Markov models, concordance analysis, alternative simulations, algorithm comparison and Mongolian exome sequencing results.Click here for fileList of Crossover Prediction Intervals. The complete unordered list of recombination events detected in Mongolian and Korean families. The first column is the sex of the individual in which recombination was observed, the second column is the chromosome on which it was located, and the third and fourth mark the physical position of the start and end point of the range in which the algorithm determined the recombination could have occurred. Positions are given in terms of NCBI build 36.Click here for fileGenetic Maps. Archive containing combined genetic maps for all chromosomes. The SNP list text files contain the rs numbers of all of the SNPs shared by the Mongolian and Korean cohorts, ordered by physical position. The map files give the genetic distance between each of these markers in order in centimorgans. All observed Asian recombination events are mixed to form this map.Click here for filehttp:////python.org). Quartet Analysis Algorithm. Archive containing a script to be opened using Python  is available to run on new datasets. Given the identities of the father, mother and two children in a family quartet, and genotype data in PLINK format, it returns a list of recombination prediction intervals. For instructions and input file requirements, please see the file README.txt. This package also includes example input files (*.syn) generated during simulations.Click here for file


A whole genome association study of mother-to-child transmission of HIV in Malawi. Genome Medicine 2010, 2:17.A correction to: Bonnie R Joubert, Ethan M Lange, Nora Franceschini, Victor Mwapasa, Kari E North, Steven R Meshnick andthe NIAID Center for HIV/AIDS Vaccine Immunology.  We wish to report some corrections to our study , none ofA total of 246 infants  passed laboratory quality control. Statistical quality control removed 15 individuals for low genotyping, resulting in a total of 231 individuals . Of the 655,352 SNPs tested, 68,297 failed statistical quality control due to HWE P < 0.001 in the controls (N = 431), low genotyping rate , or for MAF < 0.01 , where some overlap of SNPs across exclusion criteria existed. Results were presented for 587,055 SNPs.Additional data files A Word document giving effect estimates for top SNPs of interest, by mode of transmission. The data provided represent the genome-wide association analysis by mode of HIV transmission.Click here for fileA Word document giving effect estimates for SNPs near or within genes associated with HIV/AIDS. The data provided represent the genome-wide association analysis for specific regions that have previously demonstrated association with HIV/AIDS, described in the Introduction section.Click here for file


Identifying genetic variants associated with complex human diseases is a great challenge in genome-wide association studies (GWAS). Single nucleotide polymorphisms (SNPs) arising from genetic background are often dependent. The existing methods, i.e., local index of significance (LIS) and pooled local index of significance (PLIS), were both proposed for modeling SNP dependence and assumed that the whole chromosome follows a hidden Markov model (HMM). However, the fact that SNP data are often collected from separate heterogeneous regions of a single chromosome encourages different chromosomal regions to follow different HMMs. In this research, we developed a data-driven penalized criterion combined with a dynamic programming algorithm to find change points that divide the whole chromosome into more homogeneous regions. Furthermore, we extended PLIS to analyze the dependent tests obtained from multiple chromosomes with different regions for GWAS.The simulation results show that our new criterion can improve the performance of the model selection procedure and that our region-specific PLIS (RSPLIS) method is better than PLIS at detecting disease-associated SNPs when there are multiple change points along a chromosome. Our method has been used to analyze the Daly study, and compared with PLIS, RSPLIS yielded results that more accurately detected disease-associated SNPs.The genomic rankings based on our method differ from the rankings based on PLIS. Specifically, for the detection of genetic variants with weak effect sizes, the RSPLIS method was able to rank them more efficiently and with greater power. At the present time, genome-wide association studies (GWAS) have become a very popular tool for identifying novel genetic variants for complex traits. GWAS typically tests hundreds of thousands of markers simultaneously, making it necessary to improve the power of large-scale multiple testing. Fortunately, the false discovery rate (FDR) for controlling such procedures, which was introduced in a seminal paper, is one Fortunately, Wei and Li pointed out that genomic dependency information could significantly improve the efficiency of analysis of large-scale genomic data,13. We aTherefore, the above methods are all based on the strong assumption that each chromosome follows a HMM or HMRFM. However, there are usually various LD patterns or haplotype blocks in the data, which result in heterogenity of dependencies among SNPs and variations in the disease risk rates of casual alleles in the different blocks. Hence, we suggest that the different blocks of each chromosome should follow different HMMs. Wei et al. have staIn addition, the existing methods,15 assumIn this paper, we first focus on the problem of how to infer simultaneously the number of components in a normal mixture distribution as well as the change points of each chromosome. We put forward a data-driven penalized criterion for model selection in HMM, and propose a sliding window-based improved version of the dimension jump method to estimα and has the smallest false non-discovery rate (FNR) among all valid FDR procedures by combining the testing results from different chromosomes. In this section, we extend the chromosome-specific PLIS to the analysis of different chromosomes with multiple regions. In what following, we formulate our statistical model and elaborate the theoretical foundations of our method.First, Sun and Cai developewc and mc denote the change point set and the number of components for chromosome c. Suppose the case-control genotype data are available from the Lcr SNPs in the r-th region of chromosome c, c=1,…,C, r=1,…,Rc. We let θrl(c)=1 indicate that SNP l from region r of chromosome c is disease-associated and θrl(c)=0 otherwise. For each SNP, we first obtain a p-value by conducting a χ2-test to assess the association between the allele frequencies and the disease status, then we convert the p-value into a z-value Zrl(c) using the transformations proposed in Wei et al.27], we pλc is unknown and needs to be calibrated and estimated from the data themselves. Slope heuristics)However, our method could be improved in several ways. In the present paper, we conducted large-scale multiple testing under a special form of dependence (HMM) for the hypotheses. Because complex LD structure(s) are usually stored in SNP data, the Markov chain may not be the most appropriate model for SNP dependence. Therefore, general forms of dependence such as the Markov random field should be considered in future, where the whole network is divided into a region-specific Markov random field network; this would improve the screening efficiency in GWAS.Besides, the question of how to select an ideal candidate change point set is one issue that needs further consideration. Clearly, better prior knowledge can help us find the change point set to reduce the space of competing models in the model selection procedure. Thus, a better algorithm needs to be developed by using prior information to obtain the candidate change point set.c-th chromosome, the computational complexity for three procedures is O(Lmin2Lc),O(Lc log(Lc)) respectively, where Lc denotes the number of SNPs on the c-th chromosome,T=50 in our Algorithm 2, and mmax is usually chosen between four and six[Lmin) as well as the maximum value of the number of change points (Kmax) in large-scale GWAS. Based on our simulation studies, with the setting, Lmin=300, Kmax=5, T=50, and mmax=6, it took about 40 min for our RSPLIS procedure to analyze 8000 SNPs from two chromosomes. We expect that the running time for large-scale GWAS is still acceptable because we can use parallel computing for each chromosome.The computational complexity and feasibility of our RSPLIS approach for analyzing GWAS data that contain tens of thousands of SNPs merit further discussion. The RSPLIS method is made up of three independent procedures: a procedure for getting the candidate change point set, the adaptive criterion-based model selection procedure with HMM parameter estimations, and the pooled FDR control procedure for all the chromosomes with multiple regions, where the second procedure is the most time consuming. Fortunately, our method runs the second procedure chromosome-by-chromosome, which facilitates parallel computing. For each chromosome, say, the  and six. In addiIn this paper, we first modeled the observed dependent SNP data via region-specific multiple HMMs divided by change points, where we developed a novel data-driven penalized criterion combined with the DP algorithm to find change points. Second, we proposed a RSPLIS method to conduct the dependent tests from multiple chromosomes with different regions for GWAS. Finally, we have shown the numerical performances of the RSPLIS procedure using both simulated studies and analysis of a real data set.http://math.nenu.edu.cn/faculty/wszhu/softwares/RSPLIS.html. This site contains the program files and code introduction.Matlab and R code for RSPLIS can be accessed at The authors declare that they have no competing interests.Designed the experiments: JX, WZ; Performed the experiments: JX; Wrote the paper: JX, WZ and JG. All authors contributed to the analysis, read, and approved the final manuscript.The derivation of the dynamic program algorithm and the proof of theorem1. Additional fileClick here for file