This provides an alternative to the usual, but conceptually unsatisfying, approach of resorting to univariate tests when explaining and interpreting significant multivariate findings. The method is computationally tractable genome-wide for modest numbers of phenotypes (e.g. 5–10), and can be applied to summary data, without access to raw genotype and phenotype data. We illustrate the methods on both simulated examples, and to a genome-wide association study of blood lipid traits where we identify 18 potential novel genetic associations that were not identified by univariate analyses of the same data.We consider the problem of assessing associations between multiple related outcome variables, and a single explanatory variable of interest. This problem arises in many settings, including genetic association studies, where the explanatory variable is genotype at a genetic variant. We outline a framework for conducting this type of analysis, based on Bayesian model comparison and model averaging for multivariate regressions. This framework unifies several common approaches to this problem, and includes both standard univariate and standard multivariate association tests as special cases. The framework also unifies the problems of  The problem of assessing associations among multiple variables arises in a wide range of settings. Here we are motivated primarily by genetic association studies, which aim to assess associations between genetic variants and one or more phenotypes (observable characteristics) of interest, such as health-related quantitative traits  or disease status. However, many of the issues that arise in this setting also occur elsewhere, and so the statistical framework and results given here have potential for wider application.In genome-wide association studies, published analyses are almost always univariate, considering each phenotype independently, even when multiple phenotypes are available on each individual . Our aims include not only emphasizing the benefits of multivariate association analyses, but particularly to understand The next section (Methods) provides i) further background and motivation; ii) a description of the framework in general terms; iii) detailed consideration of methods for the special case where a multivariate normal distribution can be used for the phenotypes; and iv) a discussion of challenges that may arise in practice when applying these methods. The methods for multivariate normal phenotypes are easily implemented (e.g. in R), and can be applied genome-wide, requiring only summary data, rather than individual genotype data . In Results, we illustrate the methods on both simulated data and on a large meta-analysis of lipid-related traits, identifying several novel putative associations. The Discussion outlines connections between our framework and other work , highlights some of the main limitations and weaknesses, and suggests directions for future work.height and weight on a random sample of (unrelated) genotyped individuals, and we wish to identify genetic variants that are associated with one or both of these phenotypes. In addition, having identified such variants, we wish to assess, for each one, how it is associated with the phenotypes. For example we would like to know whether it is associated with just height, just weight, or both. We refer to the first of these problems as testing for associations, and the second as interpreting the associations.To illustrate some key issues, consider the following simple example. Suppose we have measured both single genetic variant For simplicity, here and throughout this paper, we consider testing and interpreting associations with a Even for a single genetic variant, and just two phenotypes, there are several simple association tests one might consider. These include:weight and height.1. Separate (univariate) tests for association with each of weight controlling for height. .2. A test for association with height controlling for weight. .3. A test for association with height, weight). Although this test can be performed in different ways, many approaches turn out to be equivalent. For example, one can test the global null of no association with either height or weight by either i) MANOVA, treating  as a bivariate normal response and height, weight) as explanatory variables. For reasons discussed in 4. A multivariate test of association with the bivariate phenotype  Conversely, one might naively expect that if both height and weight are associated with genotype then the multivariate test would be preferred. In some cases this is true  Of course, all these issues will be magnified if we consider more than two phenotypes.Even when we understand which tests will be most powerful in which scenarios, we then face a more fundamental problem: in practice, we do not know which association scenario, if any, holds for the variant we are considering, and so it remains unclear which test(s) to perform. A natural reaction to this is to perform several tests. However, while this is a reasonable strategy, it can be surprisingly tricky to interpret the results. For example, if a multivariate test gives a significant result, one does not know whether it is due to an association with testing with model comparison. We define a collection of models, each of which corresponds to a different association scenario  different tests have different power under different association scenarios, but we do not know which scenario we face in advance; and ii) the results of tests involving multiple variables may be difficult to interpret. In this paper we propose a framework that helps overcome both of these challenges. In a nutshell, the idea is to replace The tools we use to implement the model comparison framework are not new, involving ideas and inference procedures from literature on Bayesian regression Consider assessing association between a single predictor variable weight is indirectly associated with height.Simply stated, the aim of a multivariate association analysis is to identify which variables are associated with To formalize this, let 1. C2. C value of The posterior distribution for Because each value of particular coordinate of at least one coordinate of While there are many possible arguments for a Bayesian approach to inference, here we find it particularly convenient that, through the use of BMA, it has the potential to answer questions about aspects of Implementing the above inference approach involves specifying a model The two models that must be specified are those corresponding to the “global null”, in which all variables are in Recall that Now make the following two assumptions:1. The distributions that do not depend on A2. The distribution that does depend on AThen A1–A2 yield a model Thus assumptions A1–A2) leading to (4) may be viewed as desirable in themselves, since they ensure that all the distributions height is unassociated with A1–A2 ensure that the marginal distribution of height will be the same under both Besides simplifying the problem of specifying the many probability distributions We now describe the connection between the support for each partition The support for partition Large values of Now, noting that the null distribution Thus expression (7) establishes a link between the support for each partition U, D, I) vs H0]  =  [Support for YD being associated with g  given YU].is invariant to invertible affine transformations of  and/or  That is, if and are any invertible matrices, and  are any -vectors (matrices) then computed using the transformed phenotypes  and  is the same as using the original phenotypes  .For any fixed and, is monotonically increasing with  (as varies).For fixed , if for each SNPwe use , for some fixed , then  will rank the SNPs in the same way as Property a) above implies that is invariant to choice of coordinate systems for and , and in particular to changing units of measurement (e.g. measuring height in meters vs inches). As a special case, consider the Bayes Factor  (10) for testing whether all the variables are directly associated with . Property a) implies that  is invariant to choice of coordinate system for . Thus, in the settings illustrated in , the result of an association test would be unchanged by rotating the figures.Property b). suggests a certain amount of robustness to choice of . In addition, if we accept  as a reasonable measure of the association information in the data, then b) also provides some level of general reassurance that the priors being used to compute do not overwhelm this information. Some might say that the priors are “uninformative”, or that they “allow the data to speak”Property c) implies that, if the condition on  holds, then ranking SNPs by thevalue from would produce the same rankings as a Bayesian analysis that assumes the stated limiting priors. Thus, this property gives the prior assumptions that implicitly underlie traditional analyses, generalizing the univariate result linking  values and Bayes Factors inIn the special case where  is empty,  is simply the mean-centered genotypes, and so the condition on becomes. This condition, which is the same as the condition incorresponds to assuming that effect sizes of non-null SNPs tend to be larger for rare SNPs . Of course, within the Bayesian framework it is easy to make a different assumption (e.g. that is the same across SNPs) if one prefers. A further connection between our Bayes Factor and the approximate Bayes Factor fromis given in Note S.1.1 in Section S.1 of It is an elementary, although perhaps surprising, result (see  for example) that  is equal to : that is, in a normal regression setting, when testing for association between  andusing a likelihood ratio statistic, it does not matter which way around one does the regression. Thus the above results also link the Bayes Factor with the test statistics from the “reverse” regressions, Proposition 1 above considers properties of the Bayes Factors that arise in the limit Computing the Bayes Factors In practice, the need to specify suitable values for In For modest values of Of course, the number of partitions Even for smaller values of As noted above, The third summary statistic, If some phenotype data are missing, then the elements of both To illustrate some key points, we begin with simple bivariate simulations in which phenotypes We fixed For each dataset we compared the Bayes Factors the potential gain from performing multivariate tests is much higher than any potential loss. Note also that, as expected from previous discussions, the multivariate BFs provide a stronger association signal than the univariate BFs even when only one phenotype is associated with Next we performed some conventional “power” simulations in scenarios involving Independence: phenotypes were independent, one phenotype associated with One variable directly associated, rest unassociated: One variable directly associated, rest indirectly associated: Multivariate 1: a more complex scenario in which 2 variables are directly associated with Multivariate 2: two variables are directly associated and the rest are unassociated. (Variables are correlated at varying levels.)Latent factor: a single latent factor is simulated that is associated with The code used to simulated each scenario is given in For each scenario we simulated 10,000 “alternative” data sets with a genotypic association and 10,000 null datasets with no genotypic association . Each dataset had In addition to the three BFs considered in the previous section  was the one with TC, TG and HDL directly associated, and LDL indirectly associated. There followed a long tail of models assigned modest weights; no other individual model had weight We next applied our framework genome-wide to attempt to identify novel associations. For computational convenience we took a two-stage approach, which first identified approximately This analysis identified 18 novel independent associations (SNPs more than 0.5Mb apart) with stronger evidence for association in this analysis than the weakest of the 95 associations reported in One of these associations involves a non-synonymous SNP in ANXA9, which codes for the Annexin-A9 protein. The annexins are a family of calcium-dependent phospholipid-binding proteins, and studies in cows have associated variation in or near ANXA9 with milk-fat yield NROB2  regulates metabolic pathways, including hepatic bile acid, lipid, and glucose homeostasis STAB1  codes for the protein stabilin-1 which acts as a scavenger receptor for acetylated low density lipoprotein and oxidized LDL VEGFA codes for the protein “Vascular endothelial growth factor A”, and variants near VEGFA have been implicated in a range of clinical conditions, including diabetic retinopathy AKR1C4 codes for the enzyme Aldo-keto reductase family 1 member C4, and plays a major role in bile acid biosynthesis VIM codes for Vimentin, which assists in the transport of LDL cholesterol from a lysosome to the site of esterification ERLIN1 codes for the protein Erlin-1, which is a member of the prohibitin family of proteins that define lipid-raft-like domains of the endoplasmic reticulum DGAT2 encodes one of two enzymes which catalyzes the final reaction in the synthesis of triglycerides, and has been implicated as a major target for the action of niacin in regulating lipids Thus, although we can not be sure that all the associations in testing for and interpreting associations. Our applications to both real and simulated data suggest that the potential gains in power from multivariate association analyses outweigh the losses in power that can result in specific situations where univariate analyses are most powerful. In addition we emphasized that the settings in which multivariate analyses have increased power can be counter-intuitive: in particular they have power advantages when only one of the phenotypes is associated with genotype, a setting that might naively have been expected to favor the univariate analysis.We have introduced a framework for association analysis of multiple related phenotypes. This framework unifies such analyses in two ways: it includes standard univariate and standard multivariate tests, as well as many other types of test one might consider, as special cases; and it unifies the problems of measured variables provide effectively no additional information for assessing the global null (as in 1c for example). Of course, we do not know a priori which of the three categories each variable falls into, and so we try all possibilities, weighting each analysis by how well it explains the observed data. In essence the method conducts an exhaustive search for subsets of variables that are highly associated with exactly which subset of variables are associated with Although our framework makes extensive use of Bayesian statistics, we emphasize also its intuitive appeal. In particular, it captures three intuitive principles illustrated in scenarios 1a-c above: i) variables that are unassociated with ed with  ; ii) varresponse ; and iiiThe field of multivariate statistics is so vast that there are inevitably numerous close connections between our work here and previous work. Here we highlight connections with two particular subfields of multivariate analysis: Directed Acyclic Graphical models (DAGs), and Seemingly Unrelated Regressions (SUR).Our framework has close connections with Bayesian Directed Acyclic Graphical (DAG) models, particularly for Gaussian data. The main different from typical application of DAGs is that here we focus narrowly on the relationship between one variable Similarly, the model Note that under each model a single explanatory variable, variable selection in the SUR model is effectively the same as the problem we consider here. However, despite this formal relationship, the aforementioned papers have a very different focus from ours, and – perhaps partly as a result – make use of methods and priors that differ in several details from those presented here. For example, none of them encompasses the concept that some response coordinates may be indirectly associated with an explanatory variable; that is, effectively they consider only our categories Our work also has close connections with work on Bayesian variable selection in Seemingly Unrelated Regressions (SURs). Seemingly Unrelated Regressions were introduced by Ys with multiple Xs, would unnecessarily constrain the permitted relationships among variables. For example, it would not allow both Given these connections it is natural to consider extending our framework to simultaneously assess associations with multiple SNPs/covariates. The connection with DAGs might suggest building a single DAG  relating the We have tried to make our framework as simple and “clean” as possible. Inevitably, when applying it to real data, complications arise, and the veneer of cleanliness starts to be chipped away. For example, in our analysis of the Global Lipids data, the most common partition  seems likely to reflect the phenotype measurement protocol rather than interesting biology. Here we attempt to anticipate issues that may arise when applying the framework in practice; in some cases we have partial answers or suggestions for how to approach these issues, but in many cases further work may be required.Perhaps the biggest limitation of our work is that, although the conceptual framework (Section “A unified framework”) is quite general, we provided a practical implementation only for the special case of multivariate normal phenotypes. Furthermore, implementing the framework for other phenotype distributions may prove challenging. One possible approach would be to define Another limitation of our work, is that the effect of genotype is assumed to affect only the mean, and not the variances or covariances, of the phenotypes. This assumption also underlies most univariate analysis approaches to genetic association studies, but it is conceivable that some genetic variants (or other variable) could affect phenotype (co)variances instead of, or in addition to, the mean. This represents another potential avenue for future methods development.A slightly easier, although still potentially tricky, issue, is how to deal with phenotypes that are approximately, but not exactly, multivariate normal. [The methods here actually require only that the likelihood for As shown in Corollary 1 above, the Bayes Factor height and weight two possible natural parameterizations would be i) log(height) and log(weight), or ii) log(height) and log(BMI) where height but not weight, whereas ii) would not. One might choose between parameterizations based on this consideration. It would also be possible to consider both parameterizations: because i) and ii) are simply affine transformations of one another the BFs computed from i) and ii) effectively both involve the same null hypothesis in the denominator, and so are directly comparable with one another. This idea was used in As a result, before computing Another issue related to choice of coordinate system is the possible use of principal components analysis (PCA) on the phenotypes We have used the terms “directly associated” and “indirectly associated” to refer to variables obeying certain conditional independencies with genotype In addition to these interpretational challenges, another difficulty that arises in practice is that data will often be relatively uninformative about which of the three categories is possible to obtain data that strongly favor a variable being in In contrast to the difficulty of being confident that a variable is in either Finally, a related objection to our framework is that models involving “indirect” associations correspond to very precise conditional independence assumptions that are almost certain to be contravened in any real system. Putting positive weight on these “impossible” models seems counter-intuitive. Similar arguments are sometimes advanced against the use of “point” null hypotheses in settings where the null hypothesis is very unlikely to hold precisely . One response to this criticism is that these models should be viewed as capturing “approximate” conditional independences that exist in the data. However, we admit that, conceptually, it might be more satisfying to attempt to quantify the extent of the conditional dependence, rather than testing whether or not it is equal to 0, as we effectively do here.Given these difficulties, the reader might be forgiven for wondering whether the distinction between direct associations  from The Bayes Factors depend on the matrix of phenotype correlations, In our genome scan, to reduce computation, we first used simple multivariate and univariate tests to identify a set of “promising” SNPs on which to perform a full Bayesian association analysis. Specifically, for each SNP Next, for all 8 065 promising SNPs, we computed Bayes Factors for all partitions The first of these comes from the fact that We took an “Empirical Bayes” approach to obtain joint prior probabilities for the partition We then estimated the prior probability of each combination, http://www.snp-nexus.org/www.ensembl.org.The associations reported in Supplementary Information S1(PDF)Click here for additional data file.


FUT3) gene is responsible for the expression of the Lea and Leb blood group antigens. The individuals, who not synthesize these antigens have the phenotype Lewis negative, due to the presence of some single nucleotide polymorphisms (SNPs), such as 59T>G, 508G>A and 1067T>A, whose distribution is different in various ethnic groups. Our aim was to verify the frequencies of these SNPs in an admixed population of Belém-Pará-Brazil.The Lewis , 17.3% (508G>A) and 5.3% (1067T>A).The discrepancies between blood and salivary Lewis phenotypes are related to the relatively high frequencies of 59T>G and the null allele 508G>A. Whereas 38.6% of the individuals were Lewis negative based on blood, only 17.24% also tested negative when their saliva were analyzed.ST values reveal distinct frequencies of the FUT3 SNPs between the present sample and its representative ancestral populations. These observations will help to evaluate the Lewis antigens impact as susceptibility markers, in genetic association studies to certain diseases.We have found a marked consistency between the phenotypes and genotypes of the Lewis blood group system. Furthermore, our obtained F The Lewis antigens were discovered in the erythrocytes, although they are synthesized in the epithelium and then incorporated through the membrane of the erythrocytes from the plasma a and Lewisb are the principal antigens of this system a antigen and a reduction in salivary ABH substances. The Le(a−b+) phenotype, which is found in individuals with the Se gene, results from the association between the Lea specificity and the Led (type H-1) antigen determinant, resulting in the Leb type antigen, a product of the epistatic interaction between the secretor and Lewis loci Le) gene which codify non-functional transferases, and are labeled le. In this case, the individuals, whether secretors or not, do not express the Lea or Leb antigens.The Lewis antigens are biochemically related to the ABH antigens, being produced from the same precursor substances. The Lewisle) contain single nucleotide polymorphism (SNP), many of which inactivate the enzyme 59/508le, which have been detected in Asian (24%) and African (19%) populations, while the 202/314le (17%) and 59/1067le (4%) were found mainly in European populations The silent variant of the Lewis gene (The frequency of the different Lewis phenotypes varies significantly among different ethnic groups. The Le(a-b+) phenotype is the most common overall, but varies from 75% in Europeans to 61% in Africans, and 42% in Asians b in their secretions et al.,Some individuals present changes in the expression of the Lewis antigens  when affected by certain diseases and/or physiological conditions, especially in the erythrocytes, due to their secondary acquisition by these cells. In this case, some individuals that are Le(a−b−) in their blood present LeUnderstanding the complexity of the polymorphisms of the Lewis system is especially important for defining the function of these antigens as markers for the differentiation of the normal condition and pathological alterations observed in human tissue. As the expression of the Lewis antigens in the blood does not always allow the identification of the true phenotype, the present study investigated the frequency of the 59T>G, 508G>A, and 1067T>A SNPs, and their effects on the expression of the phenotypes of these antigens in the population of Belém a city of Pará state in the northern Brazil.et al.,This study analyzed samples of blood and saliva from 150 unrelated and randomly-selected individuals  from the admixed population of Belém in the northeast Brazilian Amazon region. The major groups involving in the admixture process of the Belém population were mainly Portuguese (47%), Africans (23%) and Native Indians (30%). These estimated proportions of ethnic admixture are based on a previous study of Guerreiro In the attempt to control the population heterogeneity and for operational convenience, the sample collection is randomly stratified by the 8 administrative districts that comprise the city of Belém. According to the proportion of the population of each district the individuals have been randomly-selected from the spontaneous demand in the Central Laboratory, which is reference laboratory for clinical analysis in the state of Pará.The study was approved by the Ethics in Research Committee of the Tropical Medicine Nucleus of the Federal University of Pará, and all the study subjects agreed in writing to participate in the study after reading an informed consent form.a, and anti-Leb antibodies (Fresenius Hemocare Brasil Ltda).A 5 ml sample of peripheral blood was obtained from each participant and stored in a tube containing heparin. The phenotypes of the ABO and Lewis systems were determined by the conventional direct hemagglutination technique, using the monoclonal anti-A, anti-B, anti-H, anti-Leet al.,a (1∶500), and anti-Leb(1∶1000) antibodies from Fresenius Hemocare Brazil.The ABH and Lewis secretor status of the subjects was determined by DOT-ELISA assay, based on the technique described by Pflug FUT3 gene was genotyped for the identification of the 59T>G and 508G>A mutations using the sn3-sn4 and sn8-sn9 primers, respectively  by digestion with Mspl. To detect the 508G>A SNP, the sn8-sn9 primer set was used to amplify a fragment of 206 bps and induce a cleavage site for PvuII, which resulted in the production of two fragments, of 104 bps and 102 bps.The ectively . In ordeHindIII in the mutant allele, generating fragments of 85 and 64 bps. The PCRs were based on 1 µL of genomic DNA, 5 pmol of each primer, 1.25 mM of dNTP, 2 mM of MgCl2, 0.5 unit of Taq polymerase in 2.5 µl of buffer . A negative control (amplification with no DNA sample) was included in all runs. The products were analyzed by electrophoresis in 2% agar gel colored with ethidium bromide. Markers of standard DNA with molecular weights of 50 bps and 100 bps from Fermentas Life Science were used in all procedures.To detect the 1067T>A SNP, an initial amplification was conducted using the P1 primers , which pet al. The distribution of frequencies and proportions was processed using the Bioestat 5.0 program of Ayres The analysis of the blood of the 150 subjects returned the following phenotype frequencies for the Lewis system: 57% (85/150) presented the Le(a−b+) phenotype and 4% (7/150) were Le(a+b+), while 39% (58/150) presented phenotype Le(a−b−). In the latter group, 82.76% (48/58) of the individuals expressed the Lewis antigens in the saliva, and were this classified as nongenuine Lewis-negative. The remaining 10 subjects presented no antigens in the saliva, and were classified as genuine Lewis-negative.FUT3 gene. Overall, seven different haplotypes were inferred for the 150 subjects, in which the alleles with the isolated 59Le or 59/508le SNP were the most common. By contrast, alleles with the isolated 508le and 1067le SNPs or the 59/1067le and 59/508/1067le combinations were the rarest. The genotype and haplotype frequencies observed for the Lewis gene (FUT3) are shown in Three very common SNPs –59T>G, 508G>A, and 1067 T>A – were analyzed in the 59Le or 59/508le SNP, in six and four cases, respectively. The distribution of the Lewis genotypes according to the ABO and Lewis blood group phenotypes are presented in The 59T>G polymorphism had an overall frequency of 47.66%, being detected in 121 individuals, of which, 22 were homozygous and 99 heterozygous. The 508G>A SNP was much rarer, with a frequency of 17.33%, being detected in 44 individuals, of which eight were homozygous, included one sample which presented the isolated 508G>A SNP. The 1067T>A SNP was found only in the heterozygous form, at a frequency of 5.3%, with the isolated from being recorded in six individuals, and the combined form, with FUT3 genotype frequencies indicated that the study population was not in Hardy-Weinberg equilibrium . The analysis of linkage disequilibrium between the pairs of combined sites also indicated a highly significant deviation  between the combinations of alleles at sites 59 T>G and 508 G>A.The rates of heterozygosity recorded for the SNPs at positions 59T>G, 508G>A, and 1067T>A were 66%, 24%, and 11%, respectively. Analysis of the FUT3) gene, the different genotypic and phenotypic configurations were grouped in the following categories  in blood and saliva) –10 individuals with the genuine Le(a−b−) blood phenotype, which all presented the a and/or Leb antigens in saliva) – included 48 individuals that had the 59T>G SNP in homozygote (n = 14) or heterozygote (n = 14). In some cases (n = 20), this SNP was combined with the 508G>A and/or 1067T>A null alleles in the heterozygous condition. In this group, 10 individuals secreted only the Lea substance in saliva, so that they were ABH non-secretors, while 38 individuals were ABH and Lewis secretors.Non-genuine Lewis-negative (characterized by Le(a−b−) in blood but with expression of the Le59Le/59Le). Then, the proportion of individuals which are heterozygous for the 59/508le and/or 59/1067le haplotypes is significantly higher for the non-genuine Lewis-negative individuals . On the other hand, the proportion of individuals that are heterozygous for the isolated 59 T>G SNP is significantly higher in the group with the Lewis-positive phenotype .Of the Lewis-positive individuals, 75% (69/92) presented heterozygous genotypes (Le/_), while the other 25% were homozygous for the Le allele (Le/Le). In the case of the non-genuine Lewis-negative individuals, 70.83% (34/48) were heterozygous (Le/−) and 29.17% (14/48) were homozygous for the 59T>G SNP  alleles in the group non-genuine Lewis-negative phenotype is approximately double that found in those with the Lewis-positive phenotype, with the opposite pattern being observed for the mutant On the other hand, in the non-genuine Lewis-negative individuals, non-O blood group phenotypes (in particular A1) were most common, with 54.17% (26/48) of the cases, whereas in the Lewis-positive individuals, non-O phenotypes were present in 38.04% (35/92) of the individuals (p = 0.05 for Fisher’s test). All these differences between positive and non-genuine Lewis-negative individuals can be visualized and conferred in ST values  presented the Lewis antigen in their saliva, contradicting the negative result from the blood samples.In the present study, 92 of the 150 study subjects had Lewis-positive phenotypes, which were identified by the presence of at least one FUT3 gene resulted in the identification of three principal SNPs, at positions 59T>G, 508G>A, and 1067T>A, which are known to account for 90% of the Lewis-negative phenotypes in Europeans, confirming the presence of the corresponding genotype combination, as predicted by existing knowledge of the effects of the isolated SNPs or haplotypes. However, the haplotypes corresponding to the Lewis genotypes cannot be determined reliably in all cases.The molecular analyses of the 59Le SNP, and the other with SNPs at positions 59T>G and 508G>A (59/508le). This distribution of alleles is effectively ambiguous, because heterozygous individuals that were either 59Le/Le or 59/508Le/le were recorded in both positive and negative Lewis blood groups. In addition, when null alleles, that is, 59/508le, 59/1067le, 1067le, 508le, and 59/508/1067le, were homozygous, the individuals presented the genuine Lewis-negative phenotype, which determines the absence of the expression of Lewis antigens in both the blood and the saliva, confirming the inactivating effect of these SNPs located in the catalytic domain Based on the available data In the present study, the 59T>G SNP, either homo- or heterozygous and isolated or in combination with other null mutations, was recorded in all individuals with Lewis antigens in the saliva, but with negative results for the blood samples. Given this, the pattern of blood-saliva discrepancies in the characterization of the Lewis phenotypes is consistent with that observed in previous studies, in which the non-genuine Lewis-negative trait was related to the presence of this type of mutation in the trans-membranous region 59Le allele does not act on the glycolipids, due to its differentiated activity in relation to the acceptor substrates, that is, glycolipids versus glycoproteins a and Leb factors in the plasma and, thus, an Le(a−b−) blood phenotype. Experimental molecular studies have shown that the isolated 59T>G SNP presents a reduction of approximately 50% in the levels of the FUT3 enzyme, which is probably a result of the reduction in its potential for retention in the Golgi complex, although it is normally present in conjunction with the 508G>A and 1067T>A SNPs In addition, studies in enzymatic kinetics have shown that the enzyme produced by the a antigens in the intestinal mucosa, in particular, that the quantity of Lea in the samples of Le/Le individuals was approximately twice that of the Le/le heterozygotes, indicating a regulatory effect of the Lewis gene a antigens in the saliva varying considerably, but randomly between the heterozygotes and homozygotes, invariably being reduced.One other aspect that has been analyzed in previous studies is the correlation between the amount of Lewis enzyme and the level of expression of the Leet al.,It seems likely that a set of genetic and epigenetic factors interact to limit the activity of the FUT3 enzyme, which may then synthesize quantities of antigens that are undetectable in serological tests, resulting in the apparent expression of the Lewis-negative phenotype. In addition, this data also provides the different proportions between the inactive alleles, which compose the heterozygote frequencies of Lewis-positive and non-genuine Lewis-negative individuals, illustrating the known genetic dosage effect, which has been demonstrated in a previous study by Nishihara b epitopes in comparison with group O individuals, which can interfere with the power of recognition of some Lewis antibodies, resulting in positive individuals which are characterized as being negative One interesting result of the present study was the predominance of non-O blood groups in non-genuine Lewis-negative individuals. This may be explained by the fact that the biosynthetic routes of the ABH and Lewis antigens are related, and cause competition between the A/B glycosyltransferases and the Lewis fucosyltransferases for the common type 1 H precursor. This leads to a reduction in the number of LeFUT3 genotype and/or blood group A1 are the most likely to express the non-genuine Lewis-negative phenotype, indicating that the negatively modulating effect of the 59T>G SNP may be accentuated under certain circumstances, either pathological  or physiological conditions, such as pregnancy, which may cause a reduction in the circulatory concentration of active Lewis glycolipids, resulting in the incompatible expression of Lewis antigens in the blood Given this, individuals that have the heterozygous FUT3 gene. In the present study, by contrast, the isolated form of the 59Le allele was present at a relatively high frequency, which indicates the possibility that other combinations of 59T>G may exist, involving mutations that were not investigated in this population. An even more likely explanation may be the ethnic composition of the sample and the dynamics of the population, considering the possible contribution of its Amerindian component to the frequency of the 59Le allele, although this group has not been studied in detail. The differences in the frequencies of the FUT3 SNPs observed between the present sample and its representative ancestral populations (According to the distribution of frequencies recorded in previous studies ulations  may be tST values reflect the distinct frequencies of the FUT3 SNPs between Belém and its ancestral populations Overall, the results of the present study indicated a marked consistency between the phenotypes and genotypes of the Lewis blood group system. The molecular analyses conducted in the present study helped to elucidate the serological discrepancies in phenotypes through the identification of the different mutant alleles and their respective frequencies, especially those related to the individuals classified as non-genuine Lewis-negative. In addition, our obtained F


Biological functions typically involve complex interacting molecular networks, with numerous feedback and regulation loops. How the properties of the system are affected when one, or several of its parts are modified is a question of fundamental interest, with numerous implications for the way we study and understand biological processes and treat diseases. This question can be rephrased in terms of relating genotypes to phenotypes: to what extent does the effect of a genetic variation at one locus depend on genetic variation at all other loci? Systematic quantitative measurements of epistasis – the deviation from additivity in the effect of alleles at different loci – on a given quantitative trait remain a major challenge. Here, we take a complementary approach of studying theoretically the effect of varying multiple parameters in a validated model of molecular signal transduction. To connect with the genotype/phenotype mapping we interpret parameters of the model as different loci with discrete choices of these parameters as alleles, which allows us to systematically examine the dependence of the signaling output – a quantitative trait – on the set of possible allelic combinations. We show quite generally that quantitative traits behave approximately additively (weak epistasis) when alleles correspond to small changes of parameters; epistasis appears as a result of large differences between alleles. When epistasis is relatively strong, it is concentrated in a sparse subset of loci and in low order (e.g. pair-wise) interactions. We find that focusing on interaction between loci that exhibit strong additive effects is an efficient way of identifying most of the epistasis. Our model study defines a theoretical framework for interpretation of experimental data and provides statistical predictions for the structure of genetic interaction expected for moderately complex biological circuits. Heritable phenotypic properties are often defined by complex pathways and therefore dependent on multiple polymorphisms affecting different genes. Mapping phenotypic consequences of such genetic variation is central to our understanding of disease susceptibility and is fundamental to understanding evolutionary dynamics. How does the effect of multiple genetic polymorphisms occurring together relate to the effect of same polymorphisms in isolation? It is often assumed that individual effects add without interference, yet interactions between polymorphisms have been observed in numerous contexts. The extent to which interactions shape phenotype distributions depends on the nature of interaction intrinsic to the biological system and on the distribution of polymorphisms in the population. Here we approach the systems aspect of the problem by using quantitative modeling of a moderately complex bio-molecular pathway - invertebrate phototransduction - to provide a statistical characterization of non-additive effects of multiple parameter changes. We find that interaction is associated with small subsets of polymorphisms and demonstrate that focusing the study on the set of strong additive polymorphisms accounts also for a significant fraction of total interaction: a finding relevant to the genome-wide-association analysis. Fisher generic behavior. Previous work, for example, has used metabolic flux analysis combined with the quantitative genetics approach Molecular genetics and systems biology have taught us that cells and organisms function as interacting molecular networks Present work is based on the idea that alleles at different genetic loci can be represented by discrete values of different parameters of a mathematical model describing the behavior of a molecular network. This enables a systematic exploration of the “genotype” to “phenotype” mapping represented by the model and a quantitative characterization of the strength of epistasis that may be expected for different allele sets. As a representative example we shall consider invertebrate phototransduction It is useful to set the problem of epistasis into the context of the general problem of understanding parameter dependence of quantitative traits as described by systems biology models. In most cases this dependence is characterized through the sensitivity analysis The strength of phenotypic variation induced by an allele emerges as a key parameter that characterizes the genetic landscape of the trait Our theoretical analysis is based on a quantitative model of invertebrate phototransduction odule B” , which lFollowing the success of the model in representing mutant phenotypes we assume that systematic study of phenotypes corresponding to sets of discrete parameter values can provide insight into the expected extent of physiological epistasis. Let How different the phenotypes are expected to be depends quantitatively on the difference between the parameter values that define the alleles at each locus. This difference is characterized here by a positive parameter The performance of the photoreceptor cells can be used to define some simple traits. For example, reliability of the response to one photon, defined as the probability that one photon elicits a QB is a possible characterization of the response of the system. This probability, a number between zero and one, defines a “quantitative trait” Following Pumir et al Active metarhodopsin in turn activates G-proteins according to:The activated G-protein deactivates by reacting with PLC and becomes inactivated, before returning to its resting state, Activation of and leads to the production of activator molecules which in turn opens As a result of the opening of where Opening and closure of channels, as well as several steps in the cascade are modulated by the positive, The kinetic coefficients of the model have been determined by imposing that the statistical properties of the response of the receptor to a single photon are correctly predicted by the model. The equations that define the model involve a number of coefficients, which quantify the activation and deactivation rates, as well as the various feedbacks that play a crucial role in the process. Reference values of all parameters are as given in Table 1 in The stochastic version of kinetic equations was simulated via Gillespie algorithm as described in The advantage of our model system is that it allows us to determine numerically the full mapping between the genotype and phenotype. To this end, we begin by representing a vertex on a 16-dimensional hypercube by using for each allele a variable physiological epistasis. The representation (11) is the most compact parameterization of arbitrary functions that can be defined over the Here, the first term is the constant component of The representation of the phenotype function via Eq.11 provides  a simple measure of the distribution of epistatic interaction among different orders: we define an “epistatic power spectrum” as the average variance of all total variance contributed by where If one focuses on a particular locus, say locus These definitions will allow us to demonstrate that, independent of particular alleles, some loci are more likely to exhibit background dependence or epistasis than the other.To identify the extent of “physiological epistasis” in the phototransduction model we computed the properties of the single photon response The mean variation of the The total variance due to We find extensive variability in the strength of epistasis even between terms of the same order  use linear regression between quantitative traits and genetic polymorphisms to identify loci that contribute additively to the phenotype We have used a quantitative model of signal transduction to develop a computational approach to study the nature of interaction between multiple parameters representing key components and reactions of the pathway on the molecular level. Our approach relies on the quite general assumption that these bio-chemical parameters are defined by the structure and expression level of proteins and hence are encoded genetically. Thus we assume that a genetic polymorphism corresponds to a parametric polymorphism. Our interpretation of parameters as loci and of discrete values that they take as alleles is an abstraction in the sense that we do not connect model parameters with specific genetic sequences. Instead we have formulated and focused on questions that are independent of the specific connection between parameters and sequences.As expected we find that epistasis is weak for parameter alleles quantitatively similar to each other. Less obviously, we find that the strength of epistasis decays exponentially with the order of interaction even when alleles correspond to large changes in system parameters. Epistasis involves only a small fraction of possible subsets of loci and is dominated by pairwise interactions. Yet the number of interactions is sufficiently large that the total contribution can be substantial even if individual terms are small. Our findings with regard to weak alleles are clearly general and can be rigorously ascertained via their connection with the Taylor expansion. The generality of the conclusions for strong alleles , provides a very general way of characterizing the extent of epistasis. It would be interesting to develop mathematical ideas that could provide a classification of dynamical systems, such as bio-chemical networks modeled here, and generate bounds on the strength of “parametric entanglement” as characterized by the epistatic spectra introduced here.Epistatic interactions involving more than two loci are a manifestation of nonlinearities occurring in a genotypic space involving combinations of alleles with large phenotypic effects. Such nonlinearities are clearly observed experimentally in the binding affinity of transcription factors; see Finally, we stress the conclusion that a significant fraction of epistasis can be found by focusing on the loci identified by their additive contribution: this notion has immediate practical implications in the context of GWA studies.Text S1Supplementary materials.(1.76 MB PDF)Click here for additional data file.


The focus in dairy cattle breeding is gradually shifting from production to functional traits and genetic parameters of calving traits are estimated more frequently. However, across countries, various statistical models are used to estimate these parameters. This study evaluates different models for calving ease and stillbirth in United Kingdom Holstein-Friesian cattle.Data from first and later parity records were used. Genetic parameters for calving ease, stillbirth and gestation length were estimated using the restricted maximum likelihood method, considering different models i.e. sire , animal, univariate and bivariate models. Gestation length was fitted as a correlated indicator trait and, for all three traits, genetic correlations between first and later parities were estimated. Potential bias in estimates was avoided by acknowledging a possible environmental direct-maternal covariance. The total heritable variance was estimated for each trait to discuss its theoretical importance and practical value. Prediction error variances and accuracies were calculated to compare the models.On average, direct and maternal heritabilities for calving traits were low, except for direct gestation length. Calving ease in first parity had a significant and negative direct-maternal genetic correlation. Gestation length was maternally correlated to stillbirth in first parity and directly correlated to calving ease in later parities. Multi-trait models had a slightly greater predictive ability than univariate models, especially for the lowly heritable traits. The computation time needed for sire  models was much smaller than for animal models with only small differences in accuracy. The sire  model was robust when additional genetic components were estimated, while the equivalent animal model had difficulties reaching convergence.For the evaluation of calving traits, multi-trait models show a slight advantage over univariate models. Extended sire models  are more practical and robust than animal models. Estimated genetic parameters for calving traits of UK Holstein cattle are consistent with literature. Calculating an aggregate estimated breeding value including direct and maternal values should encourage breeders to consider both direct and maternal effects in selection decisions. Calving is a key event on a dairy cattle farm and successful calvings are important to financial success of the farm. Calving complications lead to an increase in veterinary and labour costs and a decrease in revenue  -3. FurthIn recent years, dairy cattle breeders have shown an increasing interest in selection for functional traits  and gradCalving ease (CE) and stillbirth (SB) are phenotypes that are generally scored on categorical or binary scales which make them sensitive to subjectivity, especially CE . FurtherOverall, statistical models can account for direct and maternal effects in two ways i.e. animal models that fit calf and dam effects directly and S-MGS models that fit direct and maternal effects through the sire of the calf and dam, respectively . Each ofThis genetic covariance is however suggested to be sensitive to estimation bias -14. ThusHowever, given the high standard errors of the estimated maternal variances and direct-maternal covariances, it appears that statistical models used to analyse calving traits can still benefit from optimization. Previous studies on the estimation of genetic parameters for calving traits have been comparing models. However, in most cases, studies limit themselves to single comparisons, such as univariate versus multi trait models within either a sire or animal model framework ,24. The GL was added to the multi-trait model to study any benefits of this indicator trait to the predictive ability of the model. Specific attention was given to the potential bias of the sensitive genetic correlation between direct and maternal effects and, lastly, a ‘total heritable variance’ for calving traits was estimated, combining direct and maternal variance components. This parameter was recently reported for the analysis of traits affected by indirect genetic effects  and is snd and 3rd parity and had values for each of the three traits (prior to edits on SB data described earlier). Furthermore, the thresholds for the minimum size of herd-year and sire contemporary groups were increased to 7 and 5 records, respectively. Finally, the final later parity dataset consisted of 54 744 records, originating from 2 108 herds, 1 918 sires and 5 886 maternal grandsires, with an accompanying pedigree of ~ 290 000 individuals and 4 generations deep.Data on calving in Holstein Friesian cattle was provided by two milk recording organisations (MRO) in the UK i.e. the Cattle Information Service (CIS) and National Milk Records (NMR). GL was calculated from insemination and calving dates and restricted to 265–295 days. Only records on single born calves were used. Datasets from first and later parity records contained 43 135 and 330 753 records respectively, spanning the years 1995 to 2009. This data was checked for inconsistencies in parity, breed, calving date and age at calving. Incorrect records were discarded, as were contemporary groups with fewer than two records . Age at calving was restricted to 18–48 months for heifers and 30–70 months for cows. To avoid herds where farmers unrealistically recorded the same CE score for most or all contemporary groups of calvings, the standard deviation of CE score within herd-year was calculated. Herd-year classes with standard deviations of zero were deleted when this was considered statistically improbable  given the herd size and CE score distribution. Sex of stillborn calves was not recorded by one of the data sources. As sex has been shown to have a considerable effect on SB [CE was scored on a categorical scale, which ascends in calving difficulty and differs between data sources. Scores were therefore harmonised and transformed into values on the underlying normal distribution  within data source and parity prior to analysis. Detailed information on the recording system and transformation of CE scores is reported in Eaglen et al. . SB was i for CE, SB and GL is modelled byIn this study, models will follow Willham’s model  where thi, the direct additive effect  is expressed at the start of life while, if i is a female, the maternal additive effect of i  is expressed whenever she calves. ED,i and EM,j are the direct environmental effect, property of calf I, and maternal environmental effect, property of dam j, respectively.Thus, during the life of In all cases, optional fixed effects and potential interaction effects were tested for significance in SAS V9.1 (P < 0.05)  and thenFurthermore, the limitations of analysing categorical traits, such as CE and SB, with linear models are well known. Multiple model assumptions are violated due to the fact that values of categorical data are bounded within certain limits e.g. 0 to 1 or 1 to 4. Therefore, generalized linear mixed models (GLMM) such as threshold models can be more appropriate for the analysis of categorical traits since scores are transformed by the model into values on an underlying continuous liability scale. This study aimed to evaluate statistical models with the ultimate goal of implementation in national genetic evaluations of CE, SB and GL. Although threshold models are implemented in routine national genetic evaluations in France and the USA ,30, in tTo study the difference between animal and S-MGS models, first parity data were analysed by linear univariate models. Direct and maternal genetic effects were incorporated by fitting genetic effects for calf and dam for the animal model and sire and maternal grandsire for the S-MGS model:y is a vector representing the observations for CE, SB or GL; X, Zd,Zm and Zhy are known incidence matrices for non-genetic, and direct and maternal genetic and herd-year effects, respectively; b is a vector of non-genetic effects, ad is a vector of the random direct additive-genetic effects of the calf (sire), am is a vector of the random maternal additive- genetic effects of the dam , hhy is a vector of random herd-year effects and e is a vector of residuals. Vectors ad and am were assumed to follow a multivariate normal distribution, with MVN where, G0 was a 2 × 2 direct-maternal (S-MGS) variance-covariance matrix,⊗ is the Kronecker product of matrices, and A was the relationship matrix. e was assumed to be MVN, where I denotes the identity matrix and σe2 the residual variance. Non-genetic effects in the models included sex of the calf, herd, sire breed (only for GL), year and month of calving, the interaction of year and month of calving; age of the dam (months) treated as a covariate and the interaction of herd and year of calving treated as a random factor. S-MGS models yield sire and maternal grandsire (co)variances  which were subsequently transformed algebraically into direct and maternal (co)variances  according toIn Equation 2, Bivariate animal models were fitted pairwise among CE, SB and GL, separately for first and later parity data:Zpepepe). The covariance matrix of the genetic terms equalled, G = G0 ⊗ A where G0 was a 4 × 4 symmetrical direct-maternal variance-covariance matrixIn this model, vectors and incidence matrices correspond to those in the univariate animal model (Equation 2) and subscripts 1 and 2 denote traits. Non-genetic effects for later parities were the same as for univariate first-parity models, with the addition of a interaction between age of dam and parity treated as a fixed factor, and a random permanent environmental effect , and MVN, where Re and Rpe denote the residual and permanent environmental 2 × 2 variance covariance matrices and σe2and σpe2 were the residual variance and permanent environmental variance.Residuals, nd and 3rd parities combined) treated as correlated traits. The model equalled equation 4, with yi a vector representing the observations for each trait in first (y1) and later parities (y2). Random genetic effects were fitted for the sire and maternal grandsire. The fixed and random non-genetic effects were the same as in the univariate animal model. Estimates of sire and maternal grandsire variances were transformed into direct and maternal effects according to equation 3.To study the genetic correlation between calving traits in first and later parities, bivariate S-MGS models were fitted with first and later parities (2hd2 and hm2) were estimated by:Direct and maternal heritabilities ) can cause bias in the estimated genetic parameters. Although it is possible to fit a correlation structure in the residual to avoid this problem, computational complexity is then substantially increased. Therefore, in this study, we chose to avoid this potential bias by removing from the data all individuals that appeared as both calf and dam. Residuals of these specific records would otherwise be correlated [A negative direct-maternal relationship would be worrying for the dairy cattle industry since it suggests that selecting a sire that is genetically superior for ease of birth may later cause a problem when its daughters calve. Koch  showed trrelated . Then toAd,i) and its maternal breeding value , which is referred to as the TBViAdditive genetic variances are estimated to evaluate the genetic differences between animals that can be used to generate a response to a chosen selection strategy. Equation 8 demonstrates that in the case of maternally affected traits, there are two additive genetic variances that can respond to selection. Analogous to the additive direct genetic variance, the additive maternal genetic variance is equivalent to the variance of maternal breeding values of individuals in the population, under random mating. The presence of two genetic variances responding to selection raises the question of a ‘total’ additive variance. According to Bijma et al. , the totfrom which the total heritable variance follows as:σTBV2 represents the total genetic variance available for response to selection, with response predicted by R = ιρMσTBV2 where ι is the selection intensity and ρM is the accuracy of selection [σTBV2 as described by Bijma et al. [In this context, the election . This iselection , Meyer [election  and Kochelection , which relection . Given ta et al. .Table 2)σAd2 , in Table d2 Table . The PEVTable Both direct and maternal heritabilities for SB were low, irrespectively of parity, with the direct heritability ranging from 1.8% to 2.0% (not significant in first parity) and the maternal heritability ranging from 2.0% to 3.2%. These estimates agree with values from the literature, which range from 1.6% to 10% for direct heritability and from 2.0% to 13% for maternal heritability -34,36,37The estimated genetic direct-maternal correlations for CE and GL presented in Table 2Due to very low heritabilities and very high standard errors, the estimated direct-maternal genetic correlation of SB, obtained by the different models, were not informative. Studies estimating this covariance in large datasets (> 400 000) report correlations close to zero ,23,38, aTable vice versa. Genetic correlations between GL and SB in later parities were not significant  were non-significant, except for the genetic correlation between direct SB and maternal CE in first parity, which was high and positive. This specific relationship is difficult to estimate at the animal level and the high estimate may be due to the inaccuracy of the SB variance components. In general, studies in the literature report non-significant genetic correlations between the genetic direct effects and the genetic maternal effects between traits [All relationships between direct effects of one trait and maternal effects of the other trait , the estimates of i as described by Bijma et al. [i and σTBV2 show the importance of considering maternal effects and their interrelationship with direct effects, practically, an index value that is not the simple sum and represents the total impact of an individual would be useful to farmers. This would be in addition to the separate direct and maternal EBV that are already provided.When a farmer makes a selection decision based on a maternally affected trait, population mean performances change in response to both its direct and maternal breeding value. The TBVa et al.  is suggea et al. ,48 showsIn this section, animal models are compared to S-MGS models, and univariate models to bivariate models. Furthermore, the benefit in treating first and later-parity calvings as correlated traits in a bivariate between-parity model is discussed. A potential bias due to an environmental direct-maternal covariance is also evaluated. All models that are discussed are linear models. Several studies have explored the advantages of threshold models over linear models for the analysis of calving traits ,50 givenTable Table Table One of the important points when using GL as an indicator trait for the analyses of calving traits is its potential non-linear relationship with CE and SB. The relationship of GL with both SB and CE was clearly non-linear on a phenotypic scale (Figure Table Calving traits in first and later parities were highly correlated, which results in a considerably greater predictive ability of PTA for all traits when later parity information is added as a correlated trait to the model Table . AccuracσTBV2 indicate that the total additive genetic variance in a calving trait may be lower than the additive direct variance when the genetic direct-maternal covariance is highly negative and the additive maternal variance is small.Heritabilities for CE, SB and GL in UK Holstein cattle were in the range of previously reported genetic parameters for these traits. Both the direct and maternal genetic variances were considerably lower in cows than in heifers. Direct and maternal effects of CE were negatively correlated but this was established only in first parity. CE and SB were genetically highly correlated traits for both direct and maternal components, especially in first parity. GL showed a moderate relationship with CE and SB, which differed between parities but implies that genetically longer gestations are associated with reduced calving performance. The three traits all had high and positive genetic correlations between parities but parities were not demonstrated as being genetically distinct for any trait with the data available. Different between-parity genetic correlations estimated for direct GL and maternal GL emphasize that these are separate traits and thus should be treated as such. Estimates of Results from this study further demonstrated that estimating genetic parameters for calving traits is complex. Developing a statistical model for a maternally affected trait requires a careful balance between sufficient predictive ability and computational practicality, which in turn are affected by the size of the dataset, potential biases in data recording, the trait in question, computational facilities and the amount of time in hand. However, in general, PTA estimates for calving traits benefitted from multi-trait models. Furthermore, estimates were only slightly less accurate when a S-MGS model was fitted instead of an animal model. With the current computing facilities, S-MGS models exceeded animal models in terms of practicality, as their robustness allowed the analysis of more data and the inclusion of more traits e.g. information from later parities. In the genetic evaluation of calving traits genetic correlations between traits and between parities need to be estimated and the direct-maternal genetic correlation must be considered with caution.The authors declare that they have no competing interests.SAE, JAW, EW and MPC conceived and designed the study. SAE, JAW and EW designed the models and SAE analysed the data. SAE, JAW, EW and MPC interpreted the results, and SAE, JAW, EW and MPC wrote the paper. All authors read and approved the final manuscript.Herd year variances, permanent environmental variances and prediction error variances. The estimated herd-year and permanent environmental variances from first and later parity univariate and bivariate models plus the prediction error variances of average first parity PTA from 25 young sires born between 1999 and 2006 and 25 older sires born between1990 and 1998.Click here for file


For nearly a century, twin and adoption studies have yielded substantial estimates of heritability for cognitive abilities, although it has proved difficult for genomewide-association studies to identify the genetic variants that account for this heritability . However, a new approach, genomewide complex-trait analysis (GCTA), forgoes the identification of individual variants to estimate the total heritability captured by common DNA markers on genotyping arrays. In the same sample of 3,154 pairs of 12-year-old twins, we directly compared twin-study heritability estimates for cognitive abilities  with GCTA estimates captured by 1.7 million DNA markers. We found that DNA markers tagged by the array accounted for .66 of the estimated heritability, reaffirming that cognitive abilities are heritable. Larger sample sizes alone will be sufficient to identify many of the genetic variants that influence cognitive abilities. Cognitive abilities predict educational attainment, income, health, and longevity, and thus contribute importantly to the intellectual capital of knowledge-based societies . Since tAlthough the consensus concerning heritability of cognitive abilities is not unanimous , twin anFew discoveries would have greater impact than identifying some of the genes responsible for the heritability of cognitive abilities. The first attempts to find genes associated with cognitive abilities focused on genes involved in brain function . Howevermissing-heritability problem , can be used to estimate genetic variance accounted for by all the SNPs that have been genotyped in any sample, not just samples consisting of special family members such as twins or adoptees  are inherited independently , but Mendel did not know that genes can be on the same chromosome, in which case they are not inherited independently (linkage disequilibrium). This violation of Mendel’s second law is complicated by the fact that during meiosis, on average each pair of chromosomes—one from the mother and one from the father—crosses over (recombines) once; in the population, genes on the same chromosome are separated by this process of recombination to the extent that they are not close together on the chromosome. GCTA provides a lower-limit estimate of heritability because it misses genetic influence due to causal variants that are not highly correlated with the common SNPs on genotyping arrays.A difference between GCTA estimates and twin-study estimates of heritability is that GCTA estimates only additive genetic effects, whereas the twin method captures nonadditive as well as additive genetic effects. Additive genetic effects are caused by the independent effects of alleles, which add up in their effect on a trait; nonadditive genetic effects are those that interact. Because GCTA adds up the effect of each SNP, it does not include gene-gene interaction effects; the twin method captures nonadditive as well as additive genetic effects because the DNA sequence of identical twins is virtually identical and thus they share all genetic effects, including nonadditive ones . We investigated verbal and nonverbal cognitive abilities and language ability, in addition to general cognitive ability and the anchor variables of height and weight.This Method section is brief because descriptions of the sample and measures have been published previously . The samDetails of the measures are described in Genotyping on the Affymetrix 6.0 GeneChip and subsequent quality control were carried out as part of the Wellcome Trust Case Control Consortium 2 project  for 3,15Twin-based heritability estimates for the same sample, shown in the second column of This is the first study in which GCTA estimates of heritability for diverse cognitive abilities were compared directly with twin-based estimates using the same measures at the same age in the same sample. The Affymetrix 6.0 DNA array yielded GCTA estimates that accounted on average for .66 of the twin heritability estimates for language, verbal, nonverbal, and general cognitive abilities. Note that the GCTA estimates accounted for a greater proportion of the twin heritability estimates in the case of cognitive abilities than in the case of height (.44) and weight (.50).Among the cognitive scores, general cognitive ability had the highest GCTA estimate (.35) and the highest ratio (.76) between its GCTA estimate and its twin heritability estimate (.46). Although the GCTA estimates did not differ significantly among the cognitive abilities because of their large confidence intervals see , previouWhy might these common SNPs tag general cognitive ability more than height and weight? Common SNPs are likely to be common because they are old, having spread through the population over many generations, but there seems no obvious reason why the evolutionary architecture for general cognitive ability should differ from height in this way. However, there is one major genetic difference between cognitive and physical traits: Assortative mating (nonrandom mating) is at least twice as great for general cognitive ability (correlation between spouses: ~.45) as for height and weight ~.20; . The effThe strongest test of the effect of assortative mating would involve a different application of GCTA: Rather than using GCTA to estimate genetic similarity between pairs of unrelated individuals, researchers could use GCTA to estimate genetic similarity between spouses. This GCTA index of assortative mating could then be related to traits to assess the contribution of assortative mating. In the present case, the prediction is that the GCTA index of assortative mating will be associated more strongly with cognitive than with physical traits and more strongly with verbal than with nonverbal abilities. However, we were unable to test this hypothesis in the present sample because we did not have DNA from the parents of the twins.These results suggest that research using current DNA arrays with their common SNPs could identify genes that account for about two thirds of the heritability of cognitive abilities simply by including larger samples. But why is the cup only two-thirds full? Accounting for the rest of the missing heritability is likely to require other DNA variants not well tagged by the common SNPs on current DNA arrays . AlthougAlthough GCTA requires very large samples genotyped on very large numbers of DNA markers, it is a welcome addition to the armamentarium of quantitative genetics because it is such a different approach—based on DNA markers in the population, rather than on family relationships—and can be used in any large sample of unrelated individuals rather than requiring special family members, such as twins. GCTA can be used to confirm any findings that have emerged from quantitative genetic research. For example, the heritability of general cognitive ability increases from childhood through adulthood ; GCTA esGCTA can be extended to multivariate analyses that address the genetic covariance between traits. The first multivariate GCTA analysis yielded a genetic correlation of .62 in a 50-year longitudinal study of general cognitive ability from childhood to old age . This coIn summary, GCTA estimates confirmed about two thirds of twin-study estimates of heritability for cognitive abilities, using the same measures at the same age in the same sample. This finding implies that, with sufficiently large sample sizes, many genes associated with cognitive abilities can be identified using the common SNPs on current DNA arrays. Whole-genome sequencing might help to close the rest of the missing-heritability gap by identifying rare DNA variants that contribute to the heritability of cognitive abilities, although other possibilities remain, including the possibility that twin and adoption studies have overestimated heritability. GCTA might also mark the beginning of the end of the nature-nurture controversy because it is much more difficult to dispute DNA-based evidence for genetic influence than it is to question the results of twin and adoption studies. Nonetheless, the ultimate goal is to find the specific DNA sequences responsible for the widespread influence of genetics on individual differences in behavior—nucleotides G, C, T, and A, rather than GCTA.