Despite the fundamental role of crossing-over in the pairing and segregation of chromosomes during human meiosis, the rates and placements of events vary markedly among individuals. Characterizing this variation and identifying its determinants are essential steps in our understanding of the human recombination process and its evolution.Using three large sets of European-American pedigrees, we examined variation in five recombination phenotypes that capture distinct aspects of crossing-over patterns. We found that the mean recombination rate in males and females and the historical hotspot usage are significantly heritable and are uncorrelated with one another. We then conducted a genome-wide association study in order to identify loci that influence them. We replicated associations of RNF212 with the mean rate in males and in females as well as the association of Inversion 17q21.31 with the female mean rate. We also replicated the association of PRDM9 with historical hotspot usage, finding that it explains most of the genetic variance in this phenotype. In addition, we identified a set of new candidate regions for further validation.These findings suggest that variation at broad and fine scales is largely separable and that, beyond three known loci, there is no evidence for common variation with large effects on recombination phenotypes. In most sexually-reproducing species, including humans, recombination is crucial to the proper pairing and segregation of homologous chromosomes. Meiotic recombination events result from the formation and repair of double-strand breaks and appear to localize primarily to 1–2 kb «hotspots». At a subset of breaks, the repair leads to a crossover resolution, providing a physical connection between homologous chromosomes that aids in their correct segregation. In the absence of a backup mechanism, at least one crossover is required per chromosome to ensure proper disjunction. Too few crossovers can lead to aneuploidy and, more generally, errors in recombination can compromise genome integrity Given the functional importance of recombination, one might expect the process to be tightly regulated. In some respects it clearly is, as (in most organisms) numerous mechanisms act to ensure the occurrence of at least one crossover per chromosome and events are spaced farther apart and more evenly than expected by chance Even though recombination is subject to many layers of control, which likely buffer the effects of differences among individuals, some of this variation has phenotypic and fitness consequences. In humans, in particular, too little crossing-over or an abnormal placement of events is a leading cause of spontaneous miscarriage and of severe developmental disabilities C. elegans and which appears to play a role in restructing chromosome structure in response to crossing-over, thereby aiding in proper disjunction decreases rates in females. The mean recombination rate in females is also associated with Inversion 17q21.31, again in an Icelandic population Over the past decade, pedigree studies have provided a first glimpse, revealing that in humans, as in other organisms, the mean recombination rate is influenced by genetic variation. Notably, the mean recombination rate in human females was estimated to have a broad-sense heritability of 0.3 based on sib-pairs Studies have also characterized variation in recombination patterns at a finer-scale, in terms of the fraction of crossovers that occur in hotspots detectable in linkage disequilibrium (LD) data  The zinc finger of PRDM9 is predicted to bind a 13-mer motif overrepresented in recombination hotspots relative to coldspots (henceforth «Myers motif») and allelic variants of the finger bind their predicted recognition motifs with the expected affinities in vitro To learn more about variation in human recombination and its genetic determinants, we characterized variation in five aspects of the recombination process, estimated their heritabilities, and performed a genome-wide search for loci associated with differences among individuals at both broad and fine scales.To estimate recombination phenotypes, we used genome-wide genotyping data made available by the Framingham Heart Cohort Study (FHS) and the Autism Genetic Resource Exchange (AGRE) for a large number of pedigrees and focused on autosomes . We considered all nuclear families of two or more children  and applied quality control filters to the data. In total, we were left with 1,154 male and 1,149 female parents (most of whom had two to three offspring) in which we could estimate recombination phenotypes. We inferred the location of crossovers in the offspring by the method of Coop et al. (2008) We also considered genome-wide genotyping data from the Hutterites (HUTT), a founder population of European ancestry, of which we had previously analyzed a much smaller sample (i) The mean rate of recombination, i.e., the genetic map length averaged across children. (ii) The telomere usage, i.e., the fraction of crossovers that occurred in the 20% most telomeric base pairs of each chromosome arm. (iii) The centromere usage, i.e., the fraction of crossovers that occurred in the 20% most centromeric base pairs of each chromosome arm. (iv) The «historical hotspot usage» (defined as in (v) «Myers motif hotspot usage». For a subset of hotspots that are identified from patterns of LD and well-localized, Myers et al. From the crossover calls, we estimated five phenotypes for each parent: Variation in mean recombination rate and historical hotspot usage in the AGRE sample are shown in 2 = 0.23 (p = 0.011) for historical hotspot usage, almost identical to what we had estimated based on a smaller sample of HUTT 2 = 0.25 (p = 0.015) for female mean rate, an estimate consistent with the broad-sense heritability of 0.3 previously obtained from sib-pairs and potentially less confounded by maternal effects 2 = 0.14; p = 0.078). We note that these heritabilities may be substantially under-estimated: while HUTT family sizes tend to be large, parents have a limited number of children, so there remains considerable imprecision in the measurement of recombination phenotypes, notably for historical hotspot usage.To estimate heritabilities of these five phenotypes, we took advantage of the HUTT pedigree structure , which allows us to obtain more precise estimates than would be possible with the equivalent number of nuclear families, and to obtain estimates of the additive genetic variance . We found that two of the five phenotypes were significantly heritable: the estimated narrow sense heritability was hTo investigate the extent to which the genetic basis of variation in recombination rates is sex-specific, we estimated the additive genetic variance components in a combined analysis of male and females of mean rates, standardizing the phenotype within each sex 7 SNPs We sought to identify loci associated with variation in mean rate and historical hotspot usage using the FHS and AGRE population samples. To this end, we included X-linked as well as autosomal markers and imposed additional quality filters on the genotype data. To guard against spurious associations, we controlled for the number of genotyped children  and for cryptic population structure. We considered the two phenotypes as a quantitative trait in males, females and in the two sexes jointly (standardizing the phenotype within each sex). For each of these six tests, we performed a fixed-effects meta-analysis of the association test results from the FHS and AGRE samples for the intersection of 308,869 SNPs surveyed in the two studies −15 for the strongest association; see −3). Thus, the effect of this locus is confirmed in three population samples. In the FHS, it explains 7% of male variance in mean rates, with one allele estimated to add an average of 118 cM to the genetic map. We also replicated the association of RNF212 with female rates, to our knowledge for the first time (p = 2.15×10−4). Of note, the set of SNPs most strongly associated with male rates has no effect on female rates , whereas the set of SNPs associated with female rates show a weaker association in males (p = 1.379×10−9). This pattern suggests that, rather than a single causal SNP with antagonistic effects between sexes, there may be distinct causative SNPs in RNF212. Using the 1000 Genomes and Hapmap panels to impute untyped SNPs does not help to localize the causative allele(s), as the SNPs with the strong associations are seen throughout the gene  with common SNPs in approximately two-thirds of the genome Although variation in RNF212 does not account for the heritability in male and female rates, no other loci meet the cut-off for genome-wide significance. Given the platform used for genotyping FHS and AGRE, we expect that the markers used in this study should be in high pairwise linkage disequilibrium . Substantial LD (r2>0.2) extends out ∼50 kb , falling in the top three most strongly associated regions, two do not . We investigated the source of the discrepancy and concluded that two of the previous associations are likely spurious and due to errors in phenotype estimation  previously reported to be associated with sex-specific mean recombination rate in these same two population samples tion see . In any −8). This finding confirms the strong effect of this locus in two additional population samples. In the HUTT, variation in the zinc finger of PRDM9 alone appears to explain most  of the estimated narrow sense heritability in this trait: after regressing the genotype of PRDM9 for 317 of the 326 parents with typed PRDM9 alleles, h2 = 0.059 (p = 0.06).As our third phenotype, we tested for loci associated with historical hotspot usage in a meta-analysis of the FHS and AGRE data. Since there is no evidence for a marked difference in historical hotspot usage for males and females in these data see also , we only−5 but do not reach genome-wide significance (−6)  , a gene We further examined whether any SNPs strongly associated with either historical hotspot usage or mean rate were also strongly associated with the other phenotype. That was the case for neither RNF212 nor PRDM9. More generally, we found no broader evidence of SNPs strongly associated with one phenotype being enriched for an association with the other phenotype (results not shown). This finding provides further evidence that variation in mean recombination rate and hotspot usage have distinct sources.We considered whether the HUTT show an enrichment of low p-values for the 150 SNPs that were most strongly associated with a recombination phenotype in the meta-analysis of FHS and AGRE. There was no significant enrichment at the 1 or 5% level (results not shown). However, the HUTT sample is small so we only have high power to detect large effect sizes.In addition, we asked whether the top SNPs from the meta-analysis were enriched for genes known to be involved in recombination in model organisms (using a list kindly provided to us by Neil Hunter). While we observed no significant enrichment of our association signals in this set of genes see , we did These results constitute the most comprehensive characterization of variation in human recombination phenotypes to date. They show that mean recombination rates in males and females and historical hotspot usage have significant components of additive genetic variance, and that the two phenotypes are not correlated, suggesting that the genetic map length and fine-scale positioning of events are separately determined For three of the phenotypes, the narrow sense heritabilities were not significantly different from 0: Myers motif usage and centromere and telomere usage  nuclear families of two or more offspring, in which parents and children had been genotyped with genome-wide arrays. We analyzed three population samples of European ancestry, including 732 families in the Framingham Heart Study (FHS) In the AGRE and FHS datasets, all individuals were typed with the Affymetrix GeneChip Mapping 500K Array set, as were most HUTT individuals. A minority of HUTT individuals were typed with two other Affymetrix arrays , and so for the analysis of that population sample, we took the intersection of SNPs on the three arrays. To infer crossovers, we focused on the autosomes, and applied a number of quality control filters to the data, based on the call rate, the Mendelian error rate, measures of identity-by-descent, and tests of Hardy-Weinberg disequilibrium; these steps are detailed in We inferred the location of crossovers in the offspring by the method of Coop et al. (2008)We estimated five recombination phenotypes for each parent, as listed in the main text and detailed in the We conducted a genome-wide association study of mean recombination rate in males and in females as well as of historical hotspot usage in the two sexes. First, we regressed the recombination phenotype on the family size , because we were concerned that the performance of our crossover calling method may depend weakly on the number of offspring in a family. In FHS and AGRE, where there may be population substructure in the phenotype distribution by chance or true population differences in recombination phenotypes, we considered only parents with European ancestry and regressed out ancestry-informative PCs. We then ran a linear regression of the residuals on the genotypes. The association study in the HUTT was conducted by the program GTAM, which tests for an association using an additive model, while accounting for the relatedness in the Hutterite pedigree Materials S1A description of the analyses summarized in the  section, including supplemanty figures and tables.(DOC)Click here for additional data file.Materials S2The table contains the autosomal recombination events detected in FHS, AGRE, and HUTT datasets (first column). Each row is a recombination event. The second and third columns give the sex and chromosome that the recombination event occurred in. The fourth and fifth columns give the positions that bracket the interval in which the recombination event was observed within (positions are mapped to hg18). For the latest version of the data set, please check the websites of G. Coop or M. Przeworski.(XLSX)Click here for additional data file.


New high-throughput, population-based methods and next-generation sequencing capabilities hold great promise in the quest for common and rare variant discovery and in the search for ”missing heritability.” However, the optimal analytic strategies for approaching such data are still actively debated, representing the latest rate-limiting step in genetic progress. Since it is likely a majority of common variants of modest effect have been identified through the application of tagSNP-based microarray platforms , alternative approaches robust to detection of low-frequency (1–5% MAF) and rare (<1%) variants are of great importance. Of direct relevance, we have available an accumulated wealth of linkage data collected through traditional genetic methods over several decades, the full value of which has not been exhausted. To that end, we compare results from two different linkage meta-analysis methods—GSMA and MSP—applied to the same set of 13 bipolar disorder and 16 schizophrenia GWLS datasets. Interestingly, we find that the two methods implicate distinct, largely non-overlapping, genomic regions. Furthermore, based on the statistical methods themselves and our contextualization of these results within the larger genetic literatures, our findings suggest, for each disorder, distinct genetic architectures may reside within disparate genomic regions. Thus, comparative linkage meta-analysis (CLMA) may be used to optimize low-frequency and rare variant discovery in the modern genomic era. The genetic architectures of many major neuropsychiatric disorders remain unresolved despite decades of linkage, fine mapping, genomewide linkage (GWLS), candidate gene association and genomewide association studies (GWAS). This lack of resolution is not due to categorical failures of any one of these methods as many independent investigations of each type have produced strong evidence of linkage or genetic association for many neuropsychiatric disorders. Rather, the apparent breakdown lies in the general lack of replication within and across methods. Importantly, although replication is the cornerstone of scientific validation, the lack of replication may be wholly consistent with the underlying genetic architectures of neuropsychiatric disorders. Each genetic method has known strengths and liabilities. Thus, rather than serving as an impediment to progress, contradictory results across studies and methods may offer valuable insights into the genetic architecture of these disorders. Our investigation focuses on bipolar disorder (BP) and schizophrenia (SCZ), which have particular public health significance due to their high heritability and prevalence, frequent treatment resistance and morbidity.Thornton-Wells, et al (2004) The presence of allelic or locus heterogeneity creates heterogeneous disease models because two or more genetic variants  are independently associated with the same trait in the affected population. By contrast, the presence of gene-gene interactions creates a polygenic model because two or more genetic variations interact directly or indirectly, in the individual affected persons, to alter disease risk separate from any independent effect of either variant. Thus, the former refers, implicitly, to a population-level phenomenon while the latter refers to individual-level phenomena. The authors are careful to note that each model may be relevant to different subsets of subjects affected by the same disorder and that these models are not mutually exclusive. Finally, each model will have distinct implications for the nature of the involved variants.inversely proportional to the extent of heterogeneity in the population. Under a model of robust genetic heterogeneity, then, the frequency of any single variant  in the population will necessarily be low . Furthermore, penetrances are expected to be higher for low-frequency variants in order to give rise to a common disease in the population.  The lower the frequencies of each contributing pathogenic variant in the population, the greater the number of variants necessary in the population to mediate risk for a common disease. Thus, a disorder dominated by a heterogeneous model is one in which many relatively rare but more highly-penetrant pathogenic variants mediate risk for the disease in the affected population.The degree of population-level heterogeneity and the extent of individual-level polygenicity each have implications for the expected frequencies and penetrances of the pathogenic or susceptibility variants. The population frequencies of pathogenic variants for a given disease will be directly proportional to the extent of polygenicity required for individual disease expression. Under a common disease model of robust polygenicity, the frequencies of the contributing variants in the population will need to be relatively high in order to fulfill the necessity that each affected individual carries multiple such variants. Furthermore, by virtue of their persistence in the species, common variants are expected to have low disease penetrances. Moreover, we expect that common variants of large effect would have been identified and replicated over previous decades of genetic investigation, including GWAS. Therefore, a disorder dominated by a polygenic model will be one in which several common variants of modest effect contribute to risk for disease in each affected individual.The frequencies of pathogenic variants will, on the other hand, be Genetic association studies, by design, select polymorphic markers within candidate genes or regions and measure the extent of allelic association with disease at those markers within a case-control or family-based design. GWAS, a much larger-scale design, agnostic with regard to candidate genes or regions, uses hundreds of thousands of tag SNPs to identify relatively small regions (tens of thousands of basepairs) likely to harbor susceptibility variants. By using common SNPs, GWAS are optimized for detection of common disease-associated alleles of modest effect.By contrast, linkage studies are family-based studies that measure the cosegregation of trait loci with genetic markers within each family. Genome-wide linkage studies (GWLS), by extension, use a large set (hundreds to thousands) of relatively evenly spaced DNA markers across the genome to detect broad regions (millions of base pairs) likely to harbor disease susceptibility loci, based on the pattern of within-family correlations between marker alleles and disease. Linkage analysis is most robust to the detection of regions harboring loci of large effect or regional clusters of uncommon/rare risk-associated loci Current GWAS are optimally powered to find variants conferring relative risks of >1.1. However, as GWAS are conducted using commercial genotyping arrays designed to tag common variants, these studies are underpowered to identify low frequency risk variants even if these variants confer large (2.0) relative risks To date, there have been 12 published GWAS a priori significance thresholds. Second, the Wellcome Trust Case Control Consortium (WTCCC) GWAS a priori GW significance threshold (p<7E-05). Ferreira et al (2008) Thus far, two independent, primary GWAS in bipolar disorder have each reported one SNP association exceeding genomewide (GW) significance . First, Baum, et al a priori GW significance threshold (p<5E-07). In addition to the combined BP and SCZ meta-analysis by Wang, et al In schizophrenia, one primary GWAS meta-analyses in each disease have identified SNPs  reaching GW significance thresholds in/near a handful of genes , no two meta-analyses in a single disorder have found the same SNP (nor two SNPs within the same gene) to exceed GW significance threshold. Third, two different SNPs within the ANK3 gene  have produced GW significant meta-analytic evidence of association with bipolar disorder and schizophrenia, respectively. Fourth, two SNPs in the CACNA1C gene (rs1006737 and rs7297582) reached GW significance in a combined bipolar and MDD meta-analysis In summary, then, there are several important points regarding extant bipolar and schizophrenia GWAS. First, primary GWAS in each disease have produced very few GW significant SNP findings . Second, while GWAS Thus, while a small number of common variants have shown evidence for genetic association with bipolar disorder and/or schizophrenia, the vast majority of the heritability for these disorders remains unexplained by GWAS studies to date. Therefore, we suggest that extant linkage data may be an untapped and cost-efficient source of valuable information about the regional genomic architecture of low-frequency and rare variants underlying complex disorders.With that said, we are still left with the problem of evaluating and interpreting linkage findings in the context of the unresolved, but certainly complex, genetic architectures of neuropsychiatric disease. Generally speaking, linkage studies present two fundamental statistical barriers to replication: 1) high dimensionality relative to sample size, which may result in a significant number of false positive results and insufficient power, and 2) small effect size, likely due to a disease being caused by multiple mutations in different regions, across or within families  We were interested in identifying differences in results produced by these two methods using the same set of data as we believe that such differences may be especially useful in untangling the genetic architectures of these complex disorders. The primary objectives of our investigation, rather than to complete comprehensive meta-analyses for these disorders, were 1) to compare the meta-analytic findings obtained under two different methods using results from the most recent published GWLS, and 2) to examine the potential implications of convergent and discrepant results for the underlying genetic architectures of bipolar disorder and schizophrenia given other genetic evidence  available for these disorders.Here we look at two meta-analytic methods: Badner and Gershon's multiple scan probability (MSP) method Extrapolating from its methodologic strengths and weaknesses, we expect that MSP will identify relatively strong effect loci that are likely relevant to a smaller number of affected individuals. As such, we expect MSP to implicate regions likely to harbor a genetic architecture most befitting models of genetic heterogeneity. This implication should be strongest for regions in which MSP, alone, finds significant evidence of linkage.GSMA, by contrast, is expected to identify genomic regions that most consistently harbor one or more loci related to disease across the included GWLS. Importantly, then, GSMA may implicate a region via two different mechanisms, either 1) the same locus is responsible for the region's significance or 2) separate disease-linked, low-frequency loci co-localize to the same region across GWLS samples . If the single locus mechanism pertains, the implicated locus will necessarily be reasonably common and, thus, be more likely to mediate smaller  effects. In this case, significant GSMA findings are most likely to implicate polygenic models. If the multiple loci mechanism pertains, then the convergence of several distinct loci would have been necessary to produce regional significance, and thus, each implicated locus will be of relatively low-frequency in the sampled families and more likely of moderate to larger effect. Under the multiple loci mechanism, significant GSMA findings may be more consistent with heterogeneous models of genetic architecture. Co-localization of MSP and/or GWAS results in a significant GSMA region may then inform the relative likelihood of the two mechanisms see .While full testing of our more specific architectural hypotheses must await sequencing and functional investigations of genes within these regions, examining our results in light of extant genetic literature may provide additional evidence (for or against) these hypotheses. If the two meta-analytic methods are truly implicating regions with distinct architectures, we expect to find: 1) little overlap between GSMA and MSP findings for either disease; 2) relatively more agreement between the regions implicated by GWAS and those implicated by GSMA (as opposed to by MSP), particularly if the GSMA significance derives from the single locus mechanism. That said, there are caveats to the standard interpretation of GWAS that provide for an alternative expectation of agreement between GWAS and MSP findings. As will be elaborated in the Given our comparative objectives, studies included were limited to English-language GWLS of bipolar disorder and schizophrenia catalogued in PubMed and published between 2000 and 2010. Relevant articles were obtained by searching PubMed and from the relevant references cited by authors of previous meta-analyses.  under the null hypothesis and therefore yields an overall p-value that incorporates information from each individual test. When using the MSP method, this value is referred to, simply, as the MSP. Large p-values do not contribute significantly to the sum and inflate the number of degrees of freedom of the chi-square distribution, therefore increasing the MSP. As such, Fisher's method is conservative in that it takes into account evidence both for and against the null hypothesis by design. However, Fisher's method cannot be directly applied to linkage studies, because linkage evidence is often observed for broad regions and not single points Yi in Equation 1. In this study, for the size of the linkage window and p-value threshold, we use values of 30 cM (±15 cM from triggering marker) and 0.01, respectively, following the example of Badner and Gershon (2002) The modification used by MSP allows for the analysis of linkage regions by accounting (correcting) for the effects of crossover, marker spacing, family structure and original linkage methods used. After all original GWLS results are assembled, ‘corrected’ p-values (p*) are derived from each original p-value:Several studies utilize multiple diagnostic models. For example, a study of bipolar disorder may yield one set of linkage scores by counting only patients with bipolar I disorder as affected (narrow model), and another by counting patients with either bipolar I disorder or bipolar II disorder (broad model). This can be dealt with in MSP either by analyzing only the results based on the broadest diagnostic model used in the study (MSP-Single) or by incorporating only the most significant model's p-value and including a penalty for multiple testing (MSP-Best). We elected to complete the MSP analysis using both the MSP-Single and MSP-Best approaches in order to also evaluate and compare the results obtained with each.It is theoretically possible for MSP to find significance because evidence for linkage was present in only one of the included studies. However, even if this is the case, the conservative design of the method allows it to provide more robust statistical evidence of linkage than that provided by the original GWLS. Discrepant linkage evidence between studies does not necessarily invalidate a finding as evidence for linkage can vary considerably depending (among other factors) on the degree of genetic heterogeneity, the proportion of parents homozygous for the susceptibility gene, ethnic stratification within the pedigree sample and ascertainment methods employed The GSMA method for meta-analysis of linkage studies divides each chromosome into segments of fixed length, called ’bins‘. In this study, we use 30 cM bins, following Levinson et al Because GSMA is rank-based, the magnitude of a detected effect is used only to determine its rank, so that if a very large effect is observed only rarely across studies within a particular bin, GSMA will have low power to detect it. This can occur if strong linkage is only found in a region for certain populations or pertains to only one sub-phenotype. Since meta-analyses typically incorporate data from a variety of populations, it is possible to miss regions of importance to only a segment of the affected population when relying solely on GSMA. By design, GSMA will reliably fail to implicate regions in which marker rank is highly variable across In contrast, MSP has higher power to detect such effects, but may fail to detect small signals, even if they occur consistently. For MSP, regions of potential interest are identified based on locations of strong linkage signals from individual studies and not fixed in advance.In our results tables, we report all GSMA bins and MSP windows for which nominally-significant results were obtained on meta-analysis and indicate those results retaining significance after conservative multiple testing corrections. For the GSMA analyses, we applied standard Bonferroni corrections for 120 bins, following the example of Levinson et al (2003) A total of 35 English-language GWLS published between 2000 and 2010 were identified through PubMed literature search. Twenty-nine were included in disease-specific MSP and GSMA analyses, including 13 for bipolar disorder Results in Of the original 4640 Bipolar GWLS marker instances subjected to our meta-analyses, 18 window instances, representing 16 unique windows, yielded at least nominally-significant findings (p<0.05) in one or both MSP meta-analysis . SignifiThe most significant MSP results for both MSP-single and MSP-best (p = 4.61E-08) was found at 5q14.3-q23.3. Two additional windows retained significance under LK-significance criteria for both MSP-Single and MSP-Best: 14q11.2-q13.1 (p = 6.02E-08) and 5p13.3-q13.3 (p = 3.63E-07). Finally, two additional windows met LK-suggestive criteria under both models: 14q12-q22.3 (MSP-Single & MSP-Best p = 1.41E-04) and 6p23-p21.1 . Of the 16 nominally-significant MSP windows, 14 were MSP-only windows. Nine of 14 (64%) significant MSP-only windows contained 13 significant GWAS SNP and/or GWAS meta-analysis associations Of the original 12395 schizophrenia GWLS marker instances subjected to meta-analyses, 22 window instances (representing 16 unique windows) yielded nominally-significant findings (p<0.05) on MSP-Best analysis. Significant MSP results were found on 5 different chromosomes. In contrast to the bipolar results, the schizophrenia MSP-Single results were dramatically weaker than those for MSP-Best and no MSP-Single result approached nominal significance . The mosWhile several bins reached a nominal significance threshold of p<0.05 in each disorder, no bin's significance survived Bonferroni correction for 120 hypothesis tests in either disorder. That said, a pair of adjacent bins in bipolar disorder (10.2 and 10.3) and 2 pairs of adjacent bins in schizophrenia  were implicated by nominally significant GSMA findings. As demonstrated by simulations conducted by Levinson, et al (2003) Six of 120 bins on 4 chromosomes reached nominal significance in the bipolar GSMA analysis, under one or both models. In contrast to the bipolar MSP results, the GSMA-Broad results were consistently (though modestly) more significant than the GSMA-narrow results. The most significant bin under both broad (p = 0.0060) and narrow (p = 0.0099) analyses was bin 3.2, spanning 3p25.3-3p22.1. The second most significant bin under both broad (p = 0.0127) and narrow (p = 0.0172) models was bin 10.2, spanning 10p14-q11.21. Adjacent bin 10.3 (10q11.21-q22.1) was also nominally significant. Of the 5 nominally-significant GSMA bins, 4 (80%) were GSMA-only bins. Four of 4 (100%) significant GSMA-only bins in bipolar analysis contained 10 unique GWAS SNP associations .Seven of the 120 bins reached nominal significance in the schizophrenia analysis. In contrast to the bipolar GSMA results, some GSMA bins produced more significant findings under the GSMA-broad (3 bins) model and others under the GSMA-narrow model (4 bins). The most significant bin under both broad (p = 0.00267) and narrow (p = 0.011058) GSMA models was bin 6.6 at 6q25.3-qter. This is adjacent to another bin significant under both models: 6.5 at 6q23.2-q25.3. Additionally, adjacent bins 3.5 (3q12.3-q22.1) and 3.4 (3p14.1-q12.3) are also both significant under the narrow GSMA model. Of the 7 nominally-significant GSMA bins, 6 (85%) were GSMA-only bins. Only 2 of 6 (33%) GSMA-only bins contained 3 nominally-significant SNP associations all from . AdditioOf the twenty unique genomic regions representing a significant window instance, bin or the overlap thereof , only twSYNE1) Of twenty-two unique genomic regions with significant meta-analytic findings, only one region on chromosome 6 contained partially-overlapping nominally-significant MSP-GSMA results. One MSP window (6q22.31-q24.3) overlapped with a GSMA bin (6q23.2-q25.3), creating one distinct region of MSP-GSMA overlap: 6q23.2-q24.3. Interestingly, no schizophrenia GWAS has implicated this region, but a GWAS in a combined bipolar and major depressive disorder sample implicated a SNP within the non-overlapping portion of this GSMA bin  or of MSP (in schizophrenia) to detect evidence of linkage that withstood multiple testing corrections has several potential explanations. First, there may be no true linkage for these disorders. While theoretically possible, the accumulated evidence for heritability is strong, with heritability estimates of approximately 80–85% rd and 4th position).  post-hoc analysis wherein the identical set of 6 bins was implicated as in the full analysis, with only one change to the rank order  loci of more modest effect. As most MSP regions were not implicated by GSMA, the susceptibility loci residing in these regions are likely uncommon or rare. And, to the extent that the larger effect sizes necessary for MSP detection implicate higher penetrance loci, substantial individual-level polygenicity would not be necessary for disease expression for loci in these regions. Thus, for the GWLS samples examined, the genetic architecture suggested for both disorders is one dominated by heterogeneous models, via the involvement of many low frequency or rare loci, each relevant to a subset of affected families.A proliferation of recent genetic investigations and reviews suggest that multiple rare allelic and/or structural variants—and therefore an architecture characterized by substantial locus and allelic heterogeneity—may explain a substantial proportion of susceptibility to major neuropsychiatric disorders Interestingly, our MSP-Best analysis consistently produced stronger results than MSP-Single for both disorders. In the case of schizophrenia, in fact, all significant results were found under MSP-Best analysis only. This suggests that the regions implicated by MSP may be more likely to mediate risk for narrower diagnostic models tested across GWLS. For the GSMA analyses, the best-fitting models differed somewhat across disorders. For bipolar disorder, GSMA-Broad produced consistently stronger results than the GSMA-Best model; for schizophrenia, significance was split between GSMA-Broad (4 bins) and GSMA-Best (3 bins). Thus, across disorders, regions implicated by GSMA may be more likely to harbor loci contributing to risk for the broadest phenotypic characteristics. Again, this is consistent with our architectural hypotheses. We generally expect the most clearly defined phenotypes to be the most highly-penetrant and, therefore, more detectable by MSP. On the other hand, loci mediating broader phenotypic characteristics are expected to be less penetrant, perhaps representing common, modifier genes, best detected through GSMA.Short of fine mapping or, ultimately, deep sequencing of regions implicated by each method, further evidence for the architectural implications proposed here may be sought in the extant genetic literature. If differential evidence from MSP and GSMA implicates distinct genetic architectures, we may expect differences in the consistency of candidate gene association evidence within the regions implicated under each method  with, and therefore in relatively close proximity to, the putative common, functional variant. This generally accepted interpretation, however, has at least three caveats that may be relevant when comparing GWAS findings to linkage meta-analysis. First, the correlation between the strength of GWAS association signals and the extent of actual disease association at the risk locus will depend on the allele frequency of the relevant variant, degree of LD with the incorporated marker and the power of the study. Thus, modest GWAS evidence could implicate moderately-common loci and/or moderately-large effect sizes at the actual risk locus. Under these circumstances, we might expect to find regional overlap between GSMA and GWAS findings.There are also at least two situations in which low-frequency or rare loci of relatively large effect may produce significant GWAS signals. The first would be chance oversampling of cases with the same uncommon pathogenic locus . Under such circumstances, considerable inconsistencies between independent GWAS would be expected and overlap with MSP would be possible, but not predictable. The second, and perhaps more likely, situation would be cases in which signals at common SNPs were produced by ‘synthetic’ effects at multiple rare loci. As most recently discussed by Dickson, et al (2010) Given the methodologic distinctions between MSP and GSMA, regions implicated by MSP only suggest the presence of one or more loci that are uncommon or rare in the sampled populations and of relatively large effect. Under standard assumptions of GWAS study design, we would also expect that such loci would not produce positive evidence of association in GWAS studies. In light of the above-noted caveats to standard GWAS interpretation, however, regions implicated by both MSP and GWAS (assuming both findings are true positives), in the absence of positive GSMA findings, have at least two alternative explanations. First, the regions may be implicated by both methods due to independent effects of two distinct types of loci within the region–both rare loci of large effect (+MSP) and other common, loci of modest effect (+GWAS). Second, the regions may be implicated by both methods non-independently—that is, a single locus or proximal cluster of loci that are uncommon to rare and of relatively large effect are creating both linkage and association signals  and contributions from rare variants Given the two alternative mechanisms by which GSMA bin significance can arise see , the speGSMA-only regions without co-localized GWAS evidence may be more likely to harbor low-frequency loci of ‘moderate’ effect  In addition to the possible architectural causes, less frequent GSMA-GWAS overlap in schizophrenia may also result from the missing marker data for many of our included GWLS, ethnic differences between samples, or low power of the schizophrenia GWAS to date.The regional colocalization of GSMA and MSP evidence suggests either the presence of an admixture of locus types  or of loci that are relatively common and relatively large in effect.ANK3 gene suggests that this gene is very likely among the contributors to the linkage signals. Though the convergence of MSP, GSMA and GWAS data may suggest the presence of a single, common locus of relatively large effect size, there is also evidence to support an alternate architecture at this locus.Though the two MSP windows that overlapped with significant GSMA bins were not among the bipolar windows meeting LK-significance or -suggestive criterion, their significance under both MSP models (broad and narrow), their overlap with two adjacent GSMA bins and the presence of GWAS SNP association evidence therein provides a strong complement of evidence for the localization of at least one strongly disease-linked variant. Moreover, the fact that a bipolar GWAS ANK3 markers (rs9804190 and rs1094336) across three independent samples and found strong evidence supporting ANK3 as a bipolar susceptibility locus with true, independent allelic heterogeneity; their data did not support an interacting model at these two alleles. Given our significant MSP findings in this region, and the fact that linkage is robust to allelic heterogeneity, the low GWAS odds ratio (OR) estimates for the ANK3 gene most likely derive from the fact that genotyped tag SNPs in GWAS studies are not the actual functional variants mediating disease risk and are likely not in complete LD with the true variant(s). Additionally, the population-based design of GWAS will produce low OR estimates if disease in only a small portion of the sampled population is mediated by this locus, even if the functional variant were genotyped. Hence, the ORs produced by GWAS are unlikely to represent the true effect sizes of the functional variant(s) which are only approximated, in both location and effect, by the tagSNPs genotyped in GWAS First, at least three different SNP markers (rs9804190 One significant MSP window (6q22.31-q24.3) overlapped with a significant GSMA bin (6q23.2-q25.3), creating one distinct region of MSP-GSMA overlap: 6q23.2-q24.3. Although neither the MSP window nor the GSMA bin reached LK evidence criteria, the likelihood that the GSMA results represent false positives are diminished by the fact that bin 6.6, adjacent to the overlapping bin 6.5, was also significant. Together, these findings provide a strong complement of evidence for the localization of at least one variant strongly-linked to schizophrenia. Further characterization of the true functional variant and follow-up family and population-based studies will clarify the best architectural model befitting this linked region.Our meta-analyses produced nominal evidence of linkage for bipolar disorder and schizophrenia in several genomic regions. While only windows in the bipolar MSP analysis produced evidence meeting the stringent LK-significance (3 windows) or LK-suggestive (5 windows) criteria, several other aspects of our results lend weight to our nominally-significant regions. First, we expect our results to be conservative given the likely neutralizing effects of missing data in both GSMA and MSP analyses, as suggested by comparison of full to RED bipolar analysis results in both GSMA and MSP. Second, in both bipolar disorder and schizophrenia, adjacent pairs of bins were implicated by GSMA. As noted by previous authors Our most interesting finding is that our analysis of an identical set of marker results implicated almost entirely distinct genomic regions under the two methods. As MSP is most robust to the identification of relatively rare loci of strong effect, we expect that the regions implicated by positive findings in MSP only are most likely to harbor a genetic architecture most befitting models of genetic heterogeneity. As GSMA is most robust to the detection of genomic bins that most consistently harbor disease-related locus(i) across GWLS, we expect that the regions implicated by positive findings on GSMA only will be more likely to contain loci befitting polygenic, interacting models. Furthermore, we found a greater number of significant MSP windows than GSMA bins, suggesting that a greater number of genomic regions are likely to mediate heterogeneous architectural models while fewer are likely to mediate polygenic risk architecture.Despite strong heritability, further large scale linkage studies are unlikely to be completed given the costs of ascertaining large numbers of families and the failure of results to converge convincingly to date. Discussion abounds in the literature as to the most appropriate direction for current and upcoming genetic investigations. Some have advocated larger GWAS  in order to map the common variants with very small effect sizes. Advocates on the other end of the variant frequency spectrum propose the use of whole genome sequencing as the ultimate, model-free method to identify rare, highly-penetrant, functional variants. Approaches in between the extremes include: candidate gene and regulatory region sequencing, population-based approaches to linkage analysis using IBD sharing Our analysis represents a pilot investigation to explore the use of complementary meta-analysis to illuminate genetic architecture in complex neuropsychiatric disorders. As suggested by the present results, this approach may help to prioritize regions for further analysis, depending upon the objectives of the investigators. While the identification of loci contributing modestly to population-level risk may be of greater epidemiologic relevance , the identification of disease-associated rare variants, which are much more likely to be functional, will be more helpful in elucidating underlying pathophysiological mechanisms. For these reasons, we would encourage research collaboratives and consortia with access to large numbers of full GWLS results to conduct comparative linkage meta-analyses on their own troves of linkage data.File S1Supporting Information (text).(DOCX)Click here for additional data file.Table S1Included Bipolar Disorder Genome-wide Linkage Scan Characteristics.(DOCX)Click here for additional data file.Table S2Included Schizophrenia Genome-wide Linkage Scan Characteristics.(DOCX)Click here for additional data file.Table S3Average and Range of GSMA Bin Ranks for Significant MSP-Only Windows.(DOCX)Click here for additional data file.Table S4Average and Range of MSP Window Ranks for Significant GSMA-Only Bins.(DOCX)Click here for additional data file.Table S5Reduced Analysis Results for Bipolar Disorder.(DOCX)Click here for additional data file.


Traditional quantitative genetics assumes that an individual's phenotype is determined by both genetic and environmental factors. For many animals, part of the environment is social and provided by parents and other interacting partners. When expression of genes in social partners affects trait expression in a focal individual, indirect genetic effects occur. In this study, we explore the effects of indirect genetic effects on the magnitude and range of phenotypic values in a focal individual in a multi-member model analyzing three possible classes of interactions between individuals. We show that social interactions may not only cause indirect genetic effects but can also modify direct genetic effects. Furthermore, we demonstrate that both direct and indirect genetic effects substantially alter the range of phenotypic values, particularly when a focal trait can influence its own expression via interactions with traits in other individuals. We derive a function predicting the relative importance of direct versus indirect genetic effects. Our model reveals that both direct and indirect genetic effects can depend to a large extent on both group size and interaction strength, altering group mean phenotype and variance. This may lead to scenarios where between group variation is much higher than within group variation despite similar underlying genetic properties, potentially affecting the level of selection. Our analysis highlights key properties of indirect genetic effects with important consequences for trait evolution, the level of selection and potentially speciation. Complex social interactions are widespread among animals and are of considerable interest to both behavioural ecologists Standard quantitative genetics theory assumes that the phenotype, or trait values of an individual, are affected by its genes and the environment. Environmental effects are usually considered to have no genetic basis, and therefore be non-heritable. However, every individual living in a social environment is affected by the social behaviours of conspecifics, which is partly given by their genotypes. The environment provided by conspecifics is often the most important component of the environment experienced by individuals, frequently having profound effects on trait expression and fitness The influence of the genotypes of other individuals on the phenotype of a focal individual is referred to as indirect genetic effect (IGE) The idea that the phenotype of an individual is affected not only by the genes it carries, but also by the genes of other individuals was proposed already by Hamilton However, social interactions among individuals are ubiquitous and IGEs are not limited to interactions among relatives Drosophila melanogaster, the genotypic composition of social groups (single versus mixed genotypes) was shown to affect expression of clock genes, genes for pheromonal profile on the cuticle and mating frequency There have been very few studies of IGEs within social groups Unlike effects of the physical environment, social influences have both an environmental and genetic component. Because of this genetic (heritable) component, social influences are subject to selection and can evolve, while the environmental component may also act as a selection factor. By affecting the strength of selective pressure and changing the expected genotype-phenotype relationship, IGEs can change the speed and direction of evolution Models of IGEs are traditionally formulated in two different ways: the trait-based approach developed by Moore Here, we provide a detailed analysis of IGEs and their dependence on key parameters: the strength of interaction between individuals, group size and population genotypic characteristics. Unlike Moore We begin by generalizing Moore et al. 's model ions see .The first term represents direct genetic effects (DGE), with matrix The second term represents associative effects To investigate the dependence of the focal individual's phenotype on the genotypes of its social partners, it is necessary to separate the focal individual's genes from those of its conspecifics and rewrite The first term of The second term In As stated above, some interactions may contain a feedback loop that occurs when one trait affects the same trait in a social partner or when it alters the expression of a different trait in the focal individual via interactions with social partners The first, simplest class involves situations, in which a trait in a focal individual influences some other trait in its social partners, however, these affected traits do not alter the expression of any trait in the focal individual . A commoIt is easily seen whether or not a situation belongs to this class - only unaltered traits may affect other traits, otherwise feedback occurs. Formally, the condition The mean phenotype is given byTo obtain the relationship between an individual's phenotype and the group mean phenotype, we have to express an individual's genotype as its deviation from the mean genotypeThe first term corresponds to the mean phenotype, while the second term represents an individual's deviation from the mean phenotype. Note that an individual's deviation from the mean phenotype is linearly dependent only on the strength of the interaction and the deviation from mean genotype but not on the number of individuals.Phenotypic (within group) variance for each trait can be written asThe second class comprises situations, in which a trait in a focal individual (trait X) affects a different trait in its social partners (e.g. trait Y), which in turn influences a trait Z, different from both X and Y in the focal individual. This scenario describes two partial interactions: trait X affecting trait Y and trait Y affecting trait Z. However, no trait affects itself by any set of partial interactions see . In otheFor this class of interaction, From The within group phenotypic variance of each trait is given byThe last class contains situations, in which a particular trait affects its own expression by interacting with other individuals. Both types of interactions described in Moore et al. Such feedback introduces a possibility of increasing trait values to infinity, as depicted in Note that both direct and indirect genetic effects may reach extreme values under the above conditions as the effects of Individual and mean phenotypes, as well as variances are defined as in the case of feedback at the level of the individual . This phenomenon is akin to In our analysis, we distinguish between three classes of interactions that fully describe all possible ways in which IGEs can manifest. In the simplest class of interaction where no feedback occurs, IGEs depend linearly on group size and the strength of interactions. The stronger the interaction or the more individuals are in the group, the stronger the IGEs. However, this assumes that interaction strength does not depend on group size itself, which is not necessarily true. For example, the effect of interactions among particular individuals may be less intense in larger groups The second class comprises of situations, where a feedback loop exists to the same individual, but not to the same trait. An example of such a situation is cooperation based on kin recognition, when the presence of a specific trait increases cooperation  impacts on group stability Our study highlights the importance of IGEs for trait evolution and shows the mechanisms by which IGEs manifest. Scenarios where IGEs and group properties become more important for trait evolution than DGEs and the potential for the occurrence of extreme phenotypes further suggests that IGEs may need to be considered for their role in speciation but certainly when quantifying community interactions Z in We begin by generalizing Moore et al. 's model We can rewrite We analysed the role of interaction strength and number of individuals for both direct and indirect genetic effects in our model. Unlike previous frameworks, our model was developed with agent based modelling in mind. Equations were derived for individuals, therefore can be directly used in agent based models for calculations of an individual's phenotype, when genotypes are known.To illustrate the interaction strength effect on intragroup and intergroup phenotypic variance, we simulated ividuals , 6 and 7We assume that each individual is haploid and has three genes and three traits. Groups were created by assigning each gene for each individual a random value sampled from a standard normal distribution. Then, the mean genotype of the whole population was calculated and subtracted from the genotype of each individual, thus the population mean genetic value of each gene was set to 0.Matrix tion see . We calcAppendix S1(PDF)Click here for additional data file.


Populus requires 1) an appropriate mapping population, 2) high-quality phenotypic data and 3) informative genotypic data. With the goal of reducing the recalcitrance of lignocellulosic biomass for economic production of biofuels and understanding basic mechanisms of cell wall formation in Populus we established 4 clonally replicated common gardens experiments each with 1100 native P. trichocarpa genotypes collected from along the northwest coast of the U.S. and Canada. A high-throughput phenotyping pipeline was developed to measure cell wall chemistry, pretreatment response and enzymatic sugar release. Initially 18 genotypes were resequenced to an average 30X depth in order to design a SNP array to test for statistical association using MMAX and PCA methods of testing among ca. 2500 candidate genes. Genetic structure and linkage disequilibrium (LD) was assessed using SSR and SNP markers. Outlying genotypes were excluded from the analyses and estimates of LD were used to design the bead array. Candidate genes were selected based on QTL intervals, expression profiling within developing xylem and expert opinion. MMAX and PCA results revealed similar significant associations for all measured phenotypes and several SNPs within the candidate gene set explain a relatively high degree of the phenotypic variance. As a result, resequencing has continued in order to conduct GWAS in Populus; the complete set of 1100 genotypes will be complete in 2012.Genome-wide association studies (GWAS) have been used to identify regions of the genome related to various phenotypes in humans, corn, rice and cattle. Successful application of this approach to bioenergy crops such as


Recent breakthroughs in next-generation sequencing technologies allow cost-effective methods for measuring a growing list of cellular properties, including DNA sequence and structural variation. Next-generation sequencing has the potential to revolutionize complex trait genetics by directly measuring common and rare genetic variants within a genome-wide context. Because for a given gene both rare and common causal variants can coexist and have independent effects on a trait, strategies that model the effects of both common and rare variants could enhance the power of identifying disease-associated genes. To date, little work has been done on integrating signals from common and rare variants into powerful statistics for finding disease genes in genome-wide association studies. In this analysis of the Genetic Analysis Workshop 17 data, we evaluate various strategies for association of rare, common, or a combination of both rare and common variants on quantitative phenotypes in unrelated individuals. We show that the analysis of common variants only using classical approaches can achieve higher power to detect causal genes than recently proposed rare variant methods and that strategies that combine association signals derived independently in rare and common variants can slightly increase the power compared to strategies that focus on the effect of either the rare variants or the common variants. Genome-wide association analysis of common DNA variants  has been successful in finding common variants associated with complex diseases and phenotypes. However, most of these associated variants have small effect size, and thus the proportion of heritability explained is usually modest. An increasingly popular suggestion to address this issue is to shift attention from searching for common variants of small effect to searching for rare variants with larger effects . HoweverMost rare variant methods test for a relationship between the disease state or a quantitative trait and the number of mutations in a gene. The statistical test is usually performed by collapsing genotypes across variants that have low frequency, with or without weighting, followed by a univariate test on the aggregate variable. A challenge to overcome in the analysis of rare and common variants jointly is that methods for common variants are suboptimal for the analysis of rare variants, and, conversely, methods proposed for the analysis of rare variants focus essentially on accumulation of rare variants within a given functional unit and are not designed to capture the effect of common variants . Nevertheless a few methods have been proposed to identify regions that hold both common and rare variants. A haplotype-based approach is one solution when only common variants are available , and somIn this study, we compare several strategies for analyzing sequence data in the context of an exome-wide association study in which a large number of genes, each of which contains either rare and/or common causal and noncausal variants, have been sequenced in unrelated individuals. We split all genes into subgroups according to the MAF of the SNPs and analyze each subgroup independently using different methods. First, we compare the power and type I error rate of three recently proposed collapsing methods ,5 when sFLT4, HIF1A, VEGFA, and VEGFC) and hence had only rare causal variants. The other five genes  were all part of group 2. With the exception of H1F3A, all genes had at least one causal SNP with a MAF > 1%. Two of them, KDR and FLT1, also had one causal variant with a MAF > 5%.In this study we considered the first 100 replicates of quantitative phenotype Q1 in 697 unrelated individuals in the Genetic Analysis Workshop 17 (GAW17) data set [We analyzed only the genes of groups 1 and 2 which contain rare variants. Group 1 was analyzed using rare variant methods only. Group 2 was analyzed using the same rare variant methods, then with common variant approaches, and finally with the new combined tests that we defined.T are collapsed without weighting the markers; (2) the weighted (WE) approach proposed by Madsen and Browning [Topt that maximizes the score and optionally allows for weighting. The significance level of these three scores is estimated empirically using permutation of the phenotype value. These tests were conducted using the VT Test software (http://genetics.bwh.harvard.edu/vt/dokuwiki/start). The principles of these tests are described in more detail in the GAW17 background papers on collapsing methods [We use three rare variant methods that collapse variants from the same gene based on the MAF to build a score. These tests have been recently extended to the analysis of quantitative phenotypes by Price et al. . The thrBrowning , in whicBrowning , which i methods .G. First, we conducted a classic genome-wide analysis of Q1 for all available SNPs that have a MAF over a given threshold T using a linear regression under an additive model; we used the minimum p-value Pmin.G of each gene as the summary statistic. Second, we allowed for simultaneous effects of multiple variants by using the LASSO (least absolute shrinkage and selection operator) algorithm [pC. The LASSO method is described in more detail in the GAW17 background papers on machine learning methods [T. The p-value Plasso.G of the “best (minimum pC) model” identified by the LASSO method was used as the summary statistic for this approach.We compared two approaches to summarize single-SNP associations for each gene lgorithm  to identlgorithm  of Mallo methods . In our Pmin.G and Plasso.G for the number of markers in the gene, we can consider these two p-values as an association test for the gene. We refer to these two approaches later as CVpmin and CVlasso. Note that our correction of Plasso.G involves multiplication by the total number of SNPs in gene G. This is likely conservative because the number of degrees of freedom of a LASSO fit is equal to the number of nonzero coefficients of the fit [After correcting  the fit , which iG to estimate the association with the phenotype and hence are already using information from common SNPs. Thus for the combined test we aggregate the association signal from rare variants derived with the FT approach and the association signal from common variants derived using either CVpmin or CVlasso in the set of SNPs excluded by the FT approach. We used Fisher’s method to combine p-values from rare and common variant tests. Fisher’s method is a classical tool for meta-analysis of multiple tests. The principle is to form a single test U from a set of np-values ip obtained from n independent. U is defined as:Although the VT and WE approaches focus on the aggregation of rare variants, they use all available SNPs from gene n tests, U has a chi-square distribution with 2n degrees of freedom.Under the null hypothesis of no association of any of the pmin and CVlasso for the two thresholds. We then applied the combined test to group 2. Because we defined two statistics to summarize results from the common variant approaches and used two thresholds for the FT test, we applied four combined approaches. For all the tests we conducted, the final p-values were corrected for multiple testing using a Bonferroni correction.We first compared type I error rate of the three rare variant approaches and the power to detect the four causal genes of group 1 and the five causal genes of group 2. We used two different MAF thresholds (1% and 5%) for the FT test. We also compared in group 2 the power and type I error rate of the common variant association tests CVp-values. The technique of genomic control consists in measuring the inflation factor λ of the distribution of a test statistic, which reflects the difference between the observed distribution and an expected distribution, and dividing all observed values of the tests by this factor. In large-scale analysis, in which most tests are expected to be distributed under the null hypothesis of no association, the inflation factor is usually derived as the ratio between the observed median of the observed test statistic and the expected median under the null hypothesis. The mean of the statistic or of its null distribution can be used instead of the median [p-value as the observed statistic. The inflation factor λ was derived as the ratio of the mean of the observed chi-square statistic over the mean of the expected chi-square statistic under the null hypothesis of no association.The first analyses we conducted were subject to a substantial inflation of type I error. We used genomic control  to corree median . In thisThe first group of genes included 1,732 genes having only SNPs with MAF < 5%. The mean number of SNPs per gene was 3.155 (SD = 4.116), and the mean frequency of SNPs in this group was 0.006 (SD = 0.009). The second group included 1,142 genes having both rare and common variants (at least one SNP with MAF < 5% and at least one SNP with MAF ≥ 5%). The mean number of SNPs per gene was 16.336 (SD = 20.173), and their frequency on average was 0.035 (SD = 0.088). Group 3 included 331 genes having only variants with MAF ≥ 5%. There was a mean of 1.106 (SD = 0.387) SNPs per gene, and the frequency was 0.186 (SD = 0.124) on average.T of 5%. All these tests were highly inflated with a mean inflation factor λ across the 100 replicates of 2.26 (SD = 0.29), 2.75 (SD = 0.36), 2.73 (SD = 0.36), 2.23 (SD = 0.26), and 2.29 (SD = 0.48) for the FT5%, WE, VT, CVpmin,5%, and CVlasso,5% tests, respectively (those tests that depend on a threshold are indicated with the subscript T percentage) , we first measured the type I error rate of each of the rare variant tests and of the two common variant tests using a threshold ) Figure . We usede Figure . Using t1% and FT5% tests for the genes from group 1. After Bonferroni correction to correct for multiple testing, none of these tests were able to capture any of the four causal genes from group 1. The top ranks and p-values of the causal genes among the 1,732 tested genes of this group for replicate 1 were VEGFC for the FT1% test , FT5% test , and VT test  and VEGFA for the WE test . Thus an inspection of the top genes will capture only a small fraction of causal genes yet will result in many false positives.Table (pmin+FT) for the combined test of CVpmin and FT and Comb(lasso+FT) for the combined test of CVlasso and FT). We considered the two thresholds of 1% and 5%. Power and type I error rate of all these tests are presented in Table pmin had a power equal to 0.20 whatever threshold was used, and CVlasso had a power of 0.094 and 0.158 for T = 1% and T = 5%, respectively. Using the combined tests always slightly increased the power to detect the five causal genes of this group compared to the power of the tests considered alone. The highest power (0.23) was observed for the combined approach that used CVpmin,1% and FT1%. It is perhaps surprising that CVpmin exhibited greater power than CVlasso, but note that the LASSO-based procedure was not forced to include in its minimum pC the single SNP with minimum p-value according to the genetic model used. Alternative approaches to stepwise SNP selection in the common variants context are worthy of investigation.The second group of genes was analyzed first using the rare variant methods only, then using the common variant tests only, and finally using the combined test , supporting our strategy, which is based on the combined analysis of both rare and common variants.Genome-wide analysis of sequence data will be a major challenge in complex trait associations over the next several years . Before p-values from rare and common variant analyses. This approach does not take into account potential linkage disequilibrium between rare and common variants; however, the type I error rate of the combined test was not inflated in these data. Other strategies based on permutation analysis can be defined to compute p-values of the combined test when linkage disequilibrium is expected.In this study we used Fisher’s method to combine We compared two thresholds of 1% and 5% for the FT test, the common variant test, and the combined tests. We observed a higher power to detect causal genes when a threshold of 1% was used for the combined test; this seems to indicate that classical approaches, such as linear regression, should be preferred to collapsing approaches when the number of heterozygotes and homozygotes for the rare allele is large enough. Hence the choice of the threshold may depend on the sample size. In this study we analyzed 697 samples, and the minor allele of a SNP with a MAF of at most 1% would be found in a maximum of 14 subjects. Analyzing SNPs with a lower MAF in these data was unreasonable. However, SNPs with a MAF < 1% can be analyzed using regression if the sample size is large enough.We did not use additional functional information of nonsynonymous SNPs, as proposed by Price et al.  using, fFLT1 and KDR were always in the top 10 of all rare variant tests, including the WE and VT tests. Hence, if the focus of the study is not association testing but rather a screening approach to pick up a set of interesting genes, then these rare variant tests would give results similar to the combined test in these data.We used genomic control to correct for inflation of type I error rate. Other types of correction or adjustment for population stratification that we conducted (results not shown) were unsuccessful in correcting the type I error. Whether a similar effect will be seen in real data is unclear. Although this correction leads to low power of the rare variant tests, the two causal genes Our analysis of the GAW17 data set is far from exhaustive. Multiple correlated phenotypes generated to represent phenomena of epistasis and gene-environment interaction are present in this simulated data set. Extension of the combined common and rare variant testing procedure to accommodate information on correlated phenotypes and environmental exposures would be of interest.p-value from the common SNPs and the fixed threshold test of rare SNPs while using a MAF of 1% to separate the rare from the common variants. Nevertheless, considering the low power of the rare variant methods in these data and the strong correction that was applied to all tests to correct the inflation of the type I error rate, the small increase in power that we observed in these data needs to be considered with caution, and more research in this domain is clearly warranted.The analysis of these simulated data shows that classical approaches, such as linear regression testing common variants, were able to capture more of the association signal between causal genes and the trait of interest than the rare variant tests alone, which was null in all situations we considered. However, combining the association signal from rare and common variants within each gene using Fisher’s method can slightly increase the power to detect the causal genes. The highest power was observed when we combined the minimum The authors declare that they have no competing interests.HA conceived of the study, performed statistical analysis and drafted the manuscript. WQ participated in the design of the study and performed statistical analysis. BP participated in the design of the study and helped draft the manuscript. NZ participated in the design of the study. MHC participated in the design of the study and helped to draft manuscript. VC participated in the design of the study, performed statistical analysis and helped to draft the manuscript. All authors read and approved the final manuscript.


In this study we directly compared a number of multivariate GWAS methods using simulated data. We focused on six methods that are implemented in the software packages PLINK, SNPTEST, MultiPhen, BIMBAM, PCHAT and TATES, and also compared them to standard univariate GWAS, analysis of the first principal component of the traits, and meta-analysis of univariate results. We simulated data (N = 1000) for three quantitative traits and one bi-allelic quantitative trait locus (QTL), and varied the number of traits associated with the QTL (explained variance 0.1%), minor allele frequency of the QTL, residual correlation between the traits, and the sign of the correlation induced by the QTL relative to the residual correlation. We compared the power of the methods using empirically fixed significance thresholds (α = 0.05). Our results showed that the multivariate methods implemented in PLINK, SNPTEST, MultiPhen and BIMBAM performed best for the majority of the tested scenarios, with a notable increase in power for scenarios with an opposite sign of genetic and residual correlation. All multivariate analyses resulted in a higher power than univariate analyses, even when only one of the traits was associated with the QTL. Hence, use of multivariate GWAS methods can be recommended, even when genetic correlations between traits are weak.Joint association analysis of multiple traits in a genome-wide association study (GWAS),  This is often followed by an informal comparison of evidence for association at particular loci across the studied traits  have been very successful in the identification of common genetic variants associated with complex traits. Usually, information on a set of related traits is collected in populations sampled for GWAS. These traits are typically analyzed separately, its e.g. . Howevere.g. A number of methods for simultaneous analysis of multiple traits in population-based GWAS have been published e.g. . AlthougWe compared the power of the methods under empirically fixed type I errors to one another and to standard univariate (UV) analysis, univariate analysis of the first principal component of the traits (UV-PCA), and meta-analysis of univariate results (UV-MA). In UV-PCA, the first principal component of a standard principal component analysis is extracted and used in a univariate analysis. In UV-MA, p-values obtained in standard UV GWAS analyses are combined in a meta-analysis approach. Our goal was to provide researchers with insights that will guide the application of the methods to real data.We simulated genotype and phenotype data for 1,000 individuals. Simulations were performed in R.q and major allele frequency p. Genotypes were generated by sampling two alleles independently from a binomial distribution as 0 or 1, using two trials and a probability of success of each trial equal to q. The genotype is the sum of the two alleles, which can be 0, 1 or 2. Because alleles were sampled independently, genotypes were in Hardy Weinberg equilibrium.Genotype data were simulated for one bi-allelic quantitative trait locus (QTL) with minor allele frequency j  were simulated. The trait-specific QTL heritabilities , MAF of the QTL q, and residual correlation between the traits excluding the QTL effect (rEjj) were controlled.Phenotype simulation was based on work by Saint-Pierre and colleagues j, was determined from h2j and q using the following formula First, the effect of the QTL on the individual traits, aj with the number of effect (minor) alleles. The residual component Secondly, the traits were constructed by adding up the trait-specific effect of the QTL and a residual component. Here, the trait-specific effect of the QTL was assumed to be additive and obtained by multiplying a2j and rEjj is the residual correlation between the traits excluding the QTL effect. The correlated residuals were generated using the function mvrnorm from the R package MASS. Third, all traits were centered and scaled to have zero mean and unit variance.where https://genepi.qimr.edu.au/staff/manuelF/multivariate/main.html) was: plink.multivariate —noweb —file geno —mqfam —mult-pheno pheno.phen —out output. We applied an additive model. MV-PLINK produces an F-statistic and a p-value per genetic variant analyzed. This p-value of multivariate association was extracted from the output. Note that the canonical correlation analysis (CCA) applied by MV-PLINK is similar to multivariate analysis of variance (MANOVA) as CCA is applied to a single genetic variant at a time.The command used for association testing with MV-PLINK https://mathgen.stats.ox.ac.uk/genetics_software/snptest/snptest.html#multiple_phenotype_tests) was: snptest -data geno.gen pheno.sample -o output -bayesian 1 -method expected -mpheno T1 T2 T3 -prior_qt_mean_b 0 -prior_qt_V_b 0.02 -prior_mqt_c 4 -prior_mqt_Q 6.The command used to perform additive association testing with MV-SNPTEST 10 Bayes Factor (BF) per genetic variant, which was extracted for the purpose of this study.An inverse Wishart prior [IW] was set on the error covariance matrix ∑ and a matrix normal prior [N] on the vector of parameters, according to recommendations of the authors. Method ‘expected’ was applied, which results in the use of expected genotype counts (∼dosages) in the analyses. The output file contains a loghttp://cran.r-project.org/web/packages/MultiPhen/MultiPhen.pdf) for the R software (http://www.r-project.org/) MultiPhen is an R package available from CRAN  the sample is split in a training set, which is used to construct the optimal linear combination of traits from a heritability point of view, and a test set, which is used for association testing between genotype and the optimal linear combination of traits. In this way, use of the same data for both estimation of the optimal linear combination of traits and association testing is avoided. In addition, so called ‘bagging’ is performed, in which bootstrap samples are drawn from the training sample and the optimal linear combination of traits is averaged across bootstrap samples. The null distribution of the test statistic is obtained in the same way, using permutation of the data. We applied the additive model and set input parameters to values recommended by the authors: 50 subsets and bagging subsets for the determination of the distribution of the PCHAT test statistic under the null hypothesis; 200 and 50 subsets and bagging subsets, respectively, for testing the association of a genetic variant with the trait; 150 individuals for the subsets; and 1000 simulations for determination of the distribution of the test statistic under the null hypothesis. The option “both” was used for the analysis, resulting in a permutation experiment to determine the null distribution of the test statistic, after which the association test is performed using the standard deviation and degrees of freedom obtained in the permutation test. PCHAT produces 11 output files. In one of them, the association result is expressed as a p-value, which was extracted for this study.In PCHAT http://ctglab.nl/software) requires a correlation matrix of the traits and univariate association results as input. Full, symmetrical correlation matrices were generated using the corr option in R. UV analyses for the traits were performed by fitting linear models using the lm function in R. TATES was run in R using the freely available script specifying three traits and one genetic variant. The output contains the TATES trait-based p-value corrected for the correlations between the traits, which was extracted for this study.TATES http://www.sph.umich.edu/csg/abecasis/Metal/), using univariate results per trait as input files and the analysis scheme ‘scheme samplesize’, which uses p-value and direction of effect as input for the MA and weighs according to sample size. PCA was performed in R using the princomp command. UV-PCA was executed using the first principal component (PC) in a univariate analysis as described above.UV analyses were performed as described under ‘TATES’. Resulting p-values were extracted for the purpose of this study. UV-MA was performed with METAL 10 BF for each replicate per method per scenario. Significance thresholds were set in such a way that 5% of the 10,000 replicates per method yielded a significant result . This was done by sorting the 10,000 association measures in ascending  or descending order (Bayes Factors) and defining the empirical significance threshold as the mean of the 500th and 501st association measure.For each simulation scenario (see below) 1,000 datasets were simulated. Empirical significance thresholds for all methods were derived based on permutation of the traits generated in these simulation datasets, resulting in the null distribution of the test statistic. We generated 10 permuted datasets per simulation dataset, resulting in a total of 10,000 permuted replicates per scenario. These replicates were analyzed with the multivariate methods, resulting in a p-value or logi.e. which trait resulted in the smallest p-value. These 10,000 p-values were sorted in ascending order and the mean of the 500th and 501st p-value was set as the threshold.UV analysis results in one p-value per trait. We adjusted the significance thresholds for three UV association tests, ensuring that alpha was fixed at 5% for all traits combined. For each null model, we first determined which trait was most strongly associated with the QTL per replicate, 10 BF was larger than the empirical significance thresholds, ensuring an equal type I error rate of 5% for all methods.The power is defined as the percentage of 1,000 replicates for which the extracted p-value was smaller or logjj, h2j, rG and q) as shown in Simulations were focused on three main scenarios in which one, two or three out of the three traits were associated with the QTL. Within these main scenarios, data sets were generated for a given combination of parameter values . The QTL was fixed to explain 0.1% of the trait variances. By varying the sign of a1, we created a QTL induced correlation (rG) between trait 1 and traits 2 and 3 which was either positive or negative, enabling us to study the influence of a negative genetic correlation.We simulated positive residual correlations between the traits and studied scenarios with a relatively high and low residual correlation  are comparable to the results presented in Results for simulation scenarios with different heritabilities for the three traits  was recorded. For TATES and UV-MA, run time also included the time used for UV association analyses of the three traits. MV-BIMBAM was the fastest method using 9 seconds, while PCHAT needed 437 minutes and 15 seconds. Run times for MV-PLINK, MV-SNPTEST, MultiPhen, TATES, UV-PCA and UV-MA were 23 seconds, 1 minute and 10 seconds, 3 minutes and 18 seconds, 23 seconds, 23 seconds and 19 seconds, respectively.In this study, we used simulated data to compare the performance of six multivariate genome-wide association methods  and standard univariate analysis, univariate PCA, and meta-analysis of univariate analyses. Our results showed that there is not a single method that performed best under all simulation scenarios. However, all six multivariate methods resulted in a higher power than UV analysis, even when only one of the traits was associated with the QTL. UV-MA only outperformed all methods when all traits were associated with the QTL and the genetic correlation was positive.et al. for bivariate analyses and is due to the differences in the penalty for multiple testing Use of multivariate GWAS can be recommended even when genetic correlations between traits are expected to be weak. Indeed, even when only one of the traits was associated with the QTL and thus in the absence of genetic correlation and pleiotropy, MV analyses resulted in higher power than UV analyses. This was described before by Liu i.e. the relative amount of shared genetics, and sign of genetic correlation, i.e. difference in sign of QTL effect, on power varied across the different methods. For MV-PLINK, MV-SNPTEST, MultiPhen and MV-BIMBAM, higher power was observed with increasing residual correlation in case of a single QTL trait and when two or all three traits were associated with the QTL with a negative genetic correlation. The latter is due to the resulting opposite sign of genetic and residual correlation. Indeed, we observed a similar increase in power when simulating a positive genetic correlation and negative residual correlation (data not shown). This effect has been described before for these and other methods The influence of the strength of residual correlation, 10 BF i.e. 5 divided by 3) in case of uncorrelated traits, which is in line with a Bonferroni correction for three independent tests. As expected, for correlated traits the adjusted threshold was less stringent and somewhere between 1.7 and 5%. We found that significance thresholds for UV-MA were highly dependent on trait correlations with increased stringency with increase in correlation. Trait correlations result in longer tails for the test statistic distribution, and therefore a more stringent threshold must be applied to keep the type I error at 5%. Thus, use of the UV-MA can potentially lead to a high number of false-positive findings if traits are highly correlated and the significance threshold is not appropriately adjusted.We would like to emphasize that all methods were compared based on empirically derived significance levels, adjusting each method to an exact 5% type I error rate. Null simulations illustrated that for MV-PLINK, MV-SNPTEST, MultiPhen, MV-BIMBAM, TATES and UV-PCA these empirical significance levels were all close to the nominal level of 0.05 for p-values or between 0.01-1 for loget al. and van der Sluis et al., which showed that both methods result in the same power when restricting the analysis to normally distributed traits Some of the methods included in our study have been compared to one another before. MV-PLINK and MultiPhen were compared by O'Reilly In addition to power (and type I errors), there are other characteristics that are important to take into account when deciding upon the appropriate multivariate GWAS analysis. MV-PLINK output results contain trait loadings, which indicate how much each trait contributed to the multivariate association result e.g. number of (bagging) subsets) for PCHAT were not varied. Also, we did not study the effect of missing data. This was explored by Klei et al. for PCHAT who concluded that dropping individuals with missing data had a substantial diminishing effect on power of the test et al. Our simulations are not exhaustive. Data were simulated for three traits according to an additive model, and analyzed accordingly. We did not simulate and analyze other, non-additive genetic models and/or (higher-order) interactions, nor did we study scenarios with more than three traits. In addition, priors for MV-SNPTEST and MV-BIMBAM and input parameters Click here for additional data file.Table S2Power of the multivariate GWA methods for scenarios with all three traits associated with the QTL with an explained variance fixed at 0.1% for trait 1, 0.2% for trait 2 and 0.05% for trait 3.(XLSX)Click here for additional data file.Table S3Power of the multivariate GWA methods for scenarios with one out of three traits associated with the QTL with an explained variance fixed at 0.1%.(XLSX)Click here for additional data file.Table S4Power of the multivariate GWA methods for scenarios with two out of three traits associated with the QTL with an explained variance fixed at 0.1%.(XLSX)Click here for additional data file.Table S5Power of the multivariate GWA methods for scenarios with all three traits associated with the QTL with an explained variance fixed at 0.1%.(XLSX)Click here for additional data file.