Wolbachia, a widespread symbiont in arthropods, can protect Drosophila and mosquito species against viral infections. We have investigated antiviral protection in 19 Wolbachia strains originating from 16 Drosophila species after transfer into the same genotype of Drosophila simulans. We found that approximately half of the strains protected against two RNA viruses. Given that 40% of terrestrial arthropod species are estimated to harbour Wolbachia, as many as a fifth of all arthropods species may benefit from Wolbachia-mediated protection. The level of protection against two distantly related RNA viruses – DCV and FHV – was strongly genetically correlated, which suggests that there is a single mechanism of protection with broad specificity. Furthermore, Wolbachia is making flies resistant to viruses, as increases in survival can be largely explained by reductions in viral titer. Variation in the level of antiviral protection provided by different Wolbachia strains is strongly genetically correlated to the density of the bacteria strains in host tissues. We found no support for two previously proposed mechanisms of Wolbachia-mediated protection — activation of the immune system and upregulation of the methyltransferase Dnmt2. The large variation in Wolbachia's antiviral properties highlights the need to carefully select Wolbachia strains introduced into mosquito populations to prevent the transmission of arboviruses.In the last decade, bacterial symbionts have been shown to play an important role in protecting hosts against pathogens.  Wolbachia is a bacterial symbiont that is found in many species of insects, and several strains are known to protect the insects against viral infection. We took 19 strains of Wolbachia from different species of Drosophila fruit flies, transferred them into Drosophila simulans, and then infected these flies with two different viruses. We found that about half of the strains slowed the death of flies after viral infection. Given that 40% of terrestrial arthropods may be infected with Wolbachia, this suggests that many species may benefit from this protection. These increases in survival were tightly linked to reductions in the levels of the virus in the insect, suggesting that Wolbachia is reducing the viruses' ability to replicate. Despite the two viruses we used being very different, the level of protection that a Wolbachia strain provided against the two viruses tended to be very similar, suggesting that a single general mechanism underlies the antiviral effects. The extent to which a Wolbachia strain provides protection against viral infection depends largely on the bacterial density— the more Wolbachia, the greater the protection.In recent years it has been discovered that many organisms are infected with bacterial symbionts that protect them against pathogens.  Heritable symbionts are major players in arthropod evolution owing to their high incidence and the diversity of effects they have on their host's phenotype Rickettsia bacterium infecting whiteflies which rapidly spread through US populations by causing sex ratio distortion as well as increased fecundity and survival Spiroplasma bacterium that spread through populations of Drosophila neotestacea, protecting the hosts against a parasitic nematode As secondary symbionts occasionally jump between different host species Wolbachia is a maternally-transmitted alphaproteobacterium that is estimated to infect around 40% of terrestrial arthropods Wolbachia to invade populations by causing embryonic mortality when uninfected females mate with infected males, thus conferring a selective advantage to infected females Wolbachia can also protect Drosophila melanogaster against several RNA viruses Drosophila species Wolbachia has been shown to be associated with a decrease in viral titer Wolbachia increased the survival of the flies but had no effect on viral titer in D. melanogaster infected with Flock House virus (FHV) D. simulans infected with Drosophila C virus (DCV) Wolbachia might also allow its host to tolerate viral infections without affecting the pathogen load. Wolbachia has also been associated with protection against filarial nematodes, Plasmodium parasites and pathogenic bacteria in mosquitoes Wolbachia could potentially be used to control vector-borne diseases such as dengue fever Aedes aegypti, the main vector of dengue virus, Wolbachia was shown to limit the replication of dengue virus as well as chikungunya, yellow fever and West Nile viruses Wolbachia infected mosquitoes were released into the wild, the bacterium spread through the mosquito populations due to the induction of CI Antiviral protection by Drosophila and mosquitoes, different Wolbachia strains are associated with different levels of antiviral protection Wolbachia strains have been characterized for their level of protection, not all studies control the host genetic background, and none have controlled for the confounding effects of the bacterial phylogeny. Nonetheless, several studies found that the Wolbachia strains with the highest density within the host provide the strongest protection against viruses, and tissue tropism may also play a role Wolbachia protects insects against viral infection, how this trait is distributed across the Wolbachia phylogeny, and therefore to what extent it has contributed to the evolutionary success of Wolbachia.In both Wolbachia protects hosts against viruses remain to be elucidated. The protection could be caused by direct interactions between Wolbachia and viruses, competition for shared resources, or indirectly through the regulation of host gene expression Wolbachia infection may up-regulate the host immune system. While this was shown to occur after transinfection of Wolbachia from Drosophila into Ae. aegypti and Anopheles gambiaeD. melanogaster naturally infected with WolbachiaWolbachia to confer antiviral protection in flies Ae. aegypti, Wolbachia has an indirect effect on viral replication through the manipulation of host microRNAs Wolbachia suppresses the expression of AaDnmt2, a methyltransferase gene, by up-regulating the microRNA aae-miR-2940 AaDnmt2 decreases Wolbachia density and increases the titer of Dengue virus, suggesting a causal link between Wolbachia and viral replication. However, Dnmt2, the homolog of AaDnmt2 found in D. melanogaster, was shown to have an antiviral effect against Drosophila C virus The mechanisms by which Wolbachia — the bacterium cannot be cultured outside of insect cells and cannot be genetically manipulated or cloned — we have taken a comparative approach, looking for genetic correlations between levels of antiviral protection and potential causes such as changes in gene expression. To allow us to do this, we compared the level of protection of 19 Wolbachia strains from a diverse range of Drosophila species that we transferred into a common D. simulans genetic background. We used Drosophila C virus and Flock House virus, which are both RNA viruses with positive-sense single-stranded genomes. Drosophila C virus belongs to the family DicitroviridaeD. melanogaster and D. simulansNodaviridae and was initially isolated from a beetle To overcome the lack of experimental tools available for Wolbachia strains vary considerably in the extent to which they increase the survival of flies after viral infection. There is little specificity, with strong genetic correlations between protection against FHV and DCV, despite these viruses being distantly related. The increases in survival can largely be explained by Wolbachia reducing viral titer. The variation in antiviral protection is largely explained by differences in the density of Wolbachia in host tissues. However, there is no evidence that either activation of the humoral immune response or up-regulation of the methyltransferase gene Dnmt2 play any role in antiviral protection.Using this comparative approach, we show that Wolbachia strains that naturally infect 16 different species of Drosophila . We then followed their survival for 25 days . There was a highly significant interaction for both DCV and FHV . Using this more conservative approach of testing for an interaction of Wolbachia and infection treatment, nine of the 19 Wolbachia strains provided a significant level of antiviral protection, with six protecting against both viruses, one protecting against just FHV and two protecting against just DCV . The genetic correlation between protection to DCV and FHV was high .To examine the extent to which the effects of Wolbachia phylogeny and a strain specific component that is independent of phylogeny. If there is a causal link between the traits, then the strength of their association will be the same for the phylogenetic and strain components. There was no significant difference in the strength of the genetic correlation for the phylogenetic and strain-specific components, consistent with a causal link between the traits. As we have limited power to separate these effects in a single model, we also fitted a model with just the phylogenetic effect. This model again produced a very similar correlation between viruses , and the convergence of parameter estimates was improved.This genetic correlation between viruses could arise either because there is a causal relationship between DCV and FHV protection, or as a consequence of common ancestry (phylogenetic non-independence). We used a phylogenetic mixed model to partition the variance in the two traits into a component that can be explained by correlations across the Wolbachia on viral titers, flies were stabbed with DCV or FHV, and relative viral RNA levels measured at two days post infection (dpi) by reverse transcription-quantitative PCR (RT-qPCR). For both DCV and FHV, viral titer was affected by the Wolbachia-infection status of flies ; DCV: 19,165F = 23.4, P<10−16; FHV: 19,166F = 12.1, P<10−16; Wolbachia strains tended to have similar effects on the two viruses, with a strong positive genetic correlation across the Wolbachia strains between titers of DCV and FHV , or by allowing flies to better cope with infection damage (increasing tolerance). To test whether Wolbachia provides resistance to infection, we compared the survival of flies and viral titers across the 19 Wolbachia strains. Relative to the Wolbachia-free control, seven of the strains were individually associated with significantly reduced DCV titers, and five with reduced FHV titers  than against DCV (2 dpi at end growth phase) and viral titers were reduced from those points on, including at the end of the growth phase.To understand how he flies . For exand 3 dpi . ResistaWolbachia strains (ANOVA on ln(relative density): 18,150F = 115.6, P<10−16; wMelCS, had 114 fold higher density than the lowest density strain, wBor.There was significant variation in the relative density of the different Wolbachia strains tended to live longer after viral infection . This appears to be a specific effect of Wolbachia on survival after viral infection as there is no support for a correlation between Wolbachia density and the survival of the mock-infected flies in this assay . Similar to the survival analysis, bacterial density is negatively genetically correlated with DCV titers . However, there is no support for a correlation between FHV titer and Wolbachia density .Flies infected with high density nfection  and had Wolbachia density and survival after viral infection, we partitioned the variance in these traits into components that are dependent and independent of the Wolbachia phylogeny. The regression coefficient of survival against bacterial density was not significantly different for the phylogenetic and strain components for the two viruses. We are therefore unable to find evidence to suggest that this correlation is an artefact of phylogenetic relatedness, although we would caution that this analysis has very limited statistical power (non-significant phylogenetic component). Given this limited power to partition the variance across the two components, we also fitted a model with phylogenetic component only, and again the correlations between protection and Wolbachia density were similar to the model without the phylogeny .To examine whether there is likely to be a causal relationship between Wolbachia on host gene expression. We first tested the hypothesis that Wolbachia prime the immune system of flies, by measuring the expression of Drosomycin and Diptericin as reporters of Toll and IMD pathway activation respectively. We did not detect a significant genetic correlation between expression of either immune genes and DCV protection ; DCV: 16,122F = 1.56, 0.09; FHV: 16,122F = 0.85, P = 0.63; Dnmt2: gr = 0.12, 95% CI: −0.59,0.90) or FHV-infected flies .We finally investigated if antiviral protection could be explained by an effect of Wolbachia strains in a common host genetic background. This allows us to detect genetic correlations between traits, and infer whether these traits are causally linked.Protective symbionts can be an important component of an organism's defenses against infection, in some cases even being the primary mode of defense Wolbachia is probably the most widespread symbiont in arthropods Wolbachia strains, we showed that, far from being an exception, Wolbachia-mediated protection is a common phenomenon, which could potentially have contributed to its evolutionary success.Our results suggest that symbionts may play a role in protecting a substantial proportion of insect species against viral infection. D. simulans. Assuming that Wolbachia is found in 40% of arthropod species D. melanogaster also protect mosquito hosts after artificial transfer. In contrast, the strain wInn, which did not confer protection in this study, was previously found to protect against FHV in its original host D. innubilaWolbachia density have previously been found Wolbachia strain and the host genotype.Among the tested strains, about half were able to confer some level of protection in Wolbachia has previously been shown to protect insects against a remarkably taxonomically diverse array of RNA viruses Wolbachia may have independently evolved different ways of targeting different viruses. Previously it has been observed that strains that protect strongly against one virus tend to protect against other viruses, suggesting the former explanation is true rg = 0.81) of the genetic variation among strains in DCV and FHV protection is common to the two viruses. Furthermore, this pattern appears to be independent of the bacterial phylogeny, indicating that the same genes underlie the level of protection to the two viruses tested. This supports the hypothesis that Wolbachia has a single broad-spectrum mechanism of antiviral protection.Wolbachia-infected flies after viral infection could result from the symbiont increasing either resistance or tolerance to infection Wolbachia in the past Wolbachia may be altering the amount of harm that a given viral titre causes. However, were this to be the case, then it is likely to be a common underlying link, such as both traits relying on Wolbachia density or the same mechanism.The increased survival of Wolbachia infection can lead to higher viral titers or virus-induced mortality Wolbachia strains were associated with an increase in viral titer, although not with increased mortality. This is a tantalizing result, which would suggest care should be taken when introducing Wolbachia into disease vector populations. However, we would caution that this result needs to be investigated in more detail – we measured many traits across many strains, so rare outliers could be an artefact of confounding factors like remaining differences in the genetic background of the strains.In some studies it was shown that Wolbachia plays a key role in determining the level of antiviral protection it provides to its host. This has been previously demonstrated experimentally by manipulating Wolbachia density using antibiotics, and by comparisons of high and low density strains Wolbachia density is causing higher levels of resistance to viruses.The density of Wolbachia density cause between-strain variation in the level of resistance to viruses? Our analysis provides only weak support for other factors being important, as while the genetic correlation (the proportion of genetic variance shared) between Wolbachia density and survival ranges from 0.57–0.76, the upper confidence intervals for all estimates are greater than 0.86. Therefore, while our data suggests other factors are important, the evidence is not strong. Any of these Wolbachia strains may have the intrinsic ability to provide resistance to viruses – they simply need to be present at a sufficiently high density. If true, it is tempting to speculate what this might imply about the underlying mechanism of resistance. It seems more compatible with a mechanism whereby the presence of Wolbachia per se makes cells or the host less hospitable to viruses, such as through competition for resources Wolbachia was expressing specific antiviral factors, then these might be easily gained or lost through evolution, breaking the genetic correlation of resistance and Wolbachia density. It is likely that various mechanisms can lead to variation in bacterial density and thus affect within-host density. For example, it was found recently that a ∼21 kb region encoding eight genes is amplified three to seven times in different wMelPop isolates relative to wMelCS wMelCS and wMel-like strains Wolbachia strains that confer differential protection to viruses will only reveal different ways of varying the bacterial density rather than the actual antiviral mechanisms.Do any factors other than Wolbachia infection may lead to the activation of immune pathways that in turn could limit the multiplication of other parasites. Previous studies in mosquitoes showed that even if Wolbachia can prime the host immune system and increase antiviral resistance, such an effect is absent in D. melanogasterWolbachia-mediated resistance Drosomycin and Diptericin expression level (reporters of Toll and IMD pathways respectively) were uncorrelated to the survival of virus-infected flies. However, other immune pathways and restriction factors could still be involved.One way of rendering the host less hospitable for viruses is through the regulation of host genes. It was argued in the past that Ae. aegypti, the methyltransferase AaDnmt2, whose homolog in Drosophila methylates transfer RNAs and other nucleic acids, has been proposed as a potential candidate to explain the antiviral effect of WolbachiaWolbachia was shown to decrease the expression of AaDnmt2 through the induction of the expression of aae-miR-2940 microRNA. Conversely, the overexpression of AaDnmt2 led to a decrease in Wolbachia density and an increase in the titer of dengue virus. However, it was recently shown that the Drosophila homolog Dnmt2 has an antiviral effect against DCV and Nora virus, the opposite to the pattern seen in mosquito cells infected with dengue virus Wolbachia has no consistent effect on Dnmt2 expression in D. simulans, and variation in Dnmt2 expression does not explain any of the variation in survival after infection. This suggests changes to Dnmt2 expression are not a general explanation of the antiviral effects of Wolbachia. It is possible that a different mechanism of resistance applies to mosquitoes and dengue virus. However, we would argue that the critical experiment to reach this conclusion would be to show that the antiviral effects of Wolbachia on dengue virus require AaDnmt2 or aae-miR-2940, and this experiment has yet to be performed.In the mosquito Wolbachia strains. As such, it has to be taken into account if we are to draw a complete picture of Wolbachia ecology and evolution. For example, protection may favor the rapid sweeps of Wolbachia observed in natural populations wMel and wAu, that induce weak or no CI, can be maintained in natural populations Wolbachia and the broad spectrum of viruses affected by the protection, it is likely that Wolbachia-mediated protection has substantially contributed to the evolution of arthropods. By protecting against infection, symbiont-based immunity may in turn influence the evolution of the host immune system. Although the mechanisms remain to be elucidated, protection is tightly linked to the bacterial density. Therefore, variation in the selective pressure exerted by viruses could partly explain why Wolbachia strains vary so much in density, and why some are found in somatic tissues whereas other are restricted to the germ cells Wolbachia strains that could be introduced into mosquito populations to limit the spread of arboviruses. However, for successful introduction, the choice of a strain should not only be based on the level of protection but also consider costs on host fitness and strength of CI that will affect the invasive potential of Wolbachia.Together with previous studies, our results show that antiviral protection is very common among Wolbachia strains used in this study and their original host line are listed in Error! Reference source not found. To control for host genetic effects, all Wolbachia strains were transferred into the D. simulans STCP genetic background. This line was previously obtained through six generations of brother-sister crossing D. simulans were generated by six generations of backcrossing Wolbachia-infected females to STCP males, and the remaining five were transferred by microinjection (The origin of the 19 njection Table 1.Wolbachia infection status of the STCP lines was checked by PCR using the diagnostic primers wsp81F and wsp691R Wolbachia-infected mothers (data not shown). Three fly stocks, transinfected with the strains wBai, wBic and wBor, showed imperfect vertical transmission . For those three strains, the presence of Wolbachia was checked by PCR one generation before each experiment and only offspring from infected mothers were used in the experiments. Additionally, in qPCR assays (see below), flies of those three strains that were used in the experiments were first isolated individually, their Wolbachia infection status was confirmed and only Wolbachia-infected individuals were kept and pooled in groups of 4–6 flies.Two generations before the beginning of the experiments, the For all the experiments, flies were maintained on a cornmeal diet  at a constant temperature of 25°C with a 12-hour light/dark cycle at 70% relative humidity.Wolbachia strains was inferred from the partial sequences of the eight genes 16S rRNA, aspC, atpD, ftsZ, sucB, groEL, coxA and fbpA previously used in Multilocus Sequence Typing studies et al. (2006). Accession numbers and the origins of the sequences are described in th run, a UPGMA tree was used. The UPGMA starting tree was compared to the eight other trees and showed a good convergence with seven of them based on the tree comparison tool implemented in ClonalFrame v1.2 The phylogeny of the 19 Drosophila line 2 cells (DL2). For each infection assay, one viral aliquot was defrosted on the day of infection and diluted in Ringer's solution 8 TCID50/mL for DCV and 3.38×108 TCID50/mL for FHV.Viruses were produced and titrated as in 2, flies were either infected with DCV, FHV, or mock-infected with Ringer's solution Austerlitz Insect Pins) bent ∼0.25 mm from the end , dipped into viral or Ringer's solution as in For each fly line, 3–6 day-old female flies were collected. After being anaesthetized with COWolbachia strain were assigned to two of the three treatments. The same was done for the Wolbachia-free flies, except that the number of replicates was doubled to increase statistical power. The stabbing order of the fly lines as well as the sequence of treatments were randomized each day. Mortality that occurred on the day following infection was attributed to stabbing injuries and was discarded from the analyses.The survival assay was replicated on six consecutive days. On each day two vials of flies from each Wolbachia density, DCV and FHV titers as well as the expression of the three host genes Drosomycin, Diptericin and Dnmt2 were measured by qPCR on a BioRad iQ5 thermocycler using primers, probes and cycle conditions listed in Wolbachia density was measured on pools of 10 virus-free 3–6 day-old female flies (n = 10 pools) from which DNA was extracted using the Gentra Puregene kit (Qiagen). For viral titers and host gene expression, 3–6 day-old flies were first infected with DCV or FHV, as described above, and, 2 days after infection, 10 flies were pooled (n = 10 pools per virus), homogenized in TRIzol Reagent (Ambion) and frozen at −80°C. Total RNA was extracted using the Direct-zol-96 RNA kit (Zymo Research) by following the manufacturer's instructions, including a 15 min DNase I digestion step.The Wolbachia density were measured relative to the endogenous control gene actin 5C  with random primers. Host gene expression and the actin 5C  using thEF1α100E .In addition to the single timepoint analysis of viral titers, variation of titers was measured in another infection experiment for Wolbachia-infected fly dying at a given time-point divided by the probability of a Wolbachia-free fly dying. The infection treatment , the Wolbachia infection status (the 19 strains and no Wolbachia) were treated as fixed effects, and the replicate vial as a random effect. The overall significance of multilevel factors or their interactions was tested using likelihood ratio tests to compare models with or without these terms. Flies that were alive at the end of the experiment were treated as censored data. Variation in Wolbachia density and viral titers was analysed using linear models on ln-transformed data to reach the assumptions of normality and homoscedasticity. Differences in viral titer with the Wolbachia-free control were assessed using Dunnett's tests in order to correct for multiple comparisons.Survival data were analyzed with a Cox's proportional hazards mixed-effect model using the coxme package in R twiy is the response of the thi biological replicate for Wolbachia strain w, for which we have measured trait t. tβ is the intercept term for trait t with a level for each trait, and it can be interpreted as the mean trait value across the Wolbachia strains. The Wolbachia strain random effect, s:twu, is the deviation from the expected value for trait t in strain w. Random effects were assumed to be from multivariate normal distributions with zero mean vectors (illustrated for a model with three traits):2s:t1σ is the genetic variance for trait 1t, and s:t1,t2σ is the genetic covariance between trait 1t and 2t. twie is a residual capturing the between-vial variation for each trait . Residuals were assumed to be normally distributed and a separate variance was estimated for each trait with the following variance-covariance structure (illustrated for a model with three traits):Genetic correlations between traits were estimated by fitting a series of multi-response mixed models using a Bayesian approach in the R package MCMCglmm Wolbachia density, viral titer and gene expression , the p:twu, which is the deviation from the expected value for trait t in strain w due to the phylogeny, i.e. the component of the between-strain variation that is explained by the phylogeny s:twu is the variation that is not accounted for by the phylogeny under a Brownian model of evolution tβ can be interpreted as the trait value in the Wolbachia strain at the root of the phylogeny. For the phylogenetic effect, p:twu, the following variance-covariance structure was assumed (illustrated for a model with three traits):A is a matrix with elements jka standing for the proportion of time that strain j and k have had shared ancestry since the root of the phylogeny. 2p:t1σ is the variance of the phylogenetic effect for trait 1t, and p:t1,t2σ is the covariance of phylogenetic effects between trait 1t and 2t. Under a Brownian model of evolution, the phylogenetic covariance between two Wolbachia strains is inversely proportional to the time since they diverged from their common ancestor. The phylogenetic effects themselves were poorly estimated and are therefore not reported. We also fitted these phylogenetic models without the strain effect as this improved model convergence and statistical power to test for genetic correlations.Genetic correlations between two traits can arise either because the traits are causally related or because of phylogenetic non-independence. To explore these explanations we also fitted a phylogenetic mixed model, which included an additional random effect, 10) were used for the fixed effects and are virtually non-informative in this context. We used several prior probability distributions for the Vp and Vs covariance matrices to ensure our results were robust to the prior selected. Results presented were obtained using parameter expanded priors, but we also fitted models with inverse-Wishart and flat priors that gave equivalent results. We also repeated the analyses after removing outliers so that the distribution of the residuals was normal. In all cases our conclusions were unaffected by these changes. Finally, models were run after removing strains wBai, wBic and wBor, since those strains showed unstable Wolbachia infection status. Estimates of genetic correlations as well as their statistical significance were very similar to models that include these 3 strains, and are therefore not reported. The models were run for 13,000,000 iterations with a burn-in of 3,000,000. We checked for convergence by visually examining the trace of the posterior sample and ensuring the autocorrelation between successive samples in the MCMC chain was <0.1. Credible intervals (CI) were estimated from the posterior distribution of parameter estimates as the 95% highest posterior density intervals.Independent normal priors with zero mean and large variance . Survival is expressed as the negative natural log of the hazard ratio compared to Wolbachia-free flies, as estimated from a Cox's mixed-effect model. Error bars are standard errors. Symbols above the bars give the significance relative to the Wolbachia-free controls .(TIF)Click here for additional data file.Figure S2Time-course of viral titers. (A) DCV and (B) FHV titers in Wolbachia-free flies (black), wAu- (blue), wSh- (red) and wAna-infected flies (light blue). Points represent the mean value of 2 replicates. Error bars are standard errors. Significance was tested using polynomial regressions with backward model selection to remove non-significant terms. For DCV, the selected model was: log2(meantiter) = μ+strain+day+day2+day3+strain×day+strain×day2. For FHV, the selected model was: log2(meantiter) = μ+strain+day+day2+strain×day+strain×day2. Comparisons with the Wolbachia-free flies showed that only wAu-infected flies significantly reduced viral titres, with the strain-by-day interaction  and the quadratic strain-by-day interaction being significant , indicating a slower accumulation of DCV and FHV compared to the controls.(TIF)Click here for additional data file.Figure S3Immune gene and Dnmt2 expression levels after viral infection. (A–B) Expression of Drosomycin after (A) DCV and (B) FHV infection. (C–D) Expression of Diptericin after (C) DCV and (D) FHV infection. (E–F) Expression of Dnmt2 after (E) DCV and (F) FHV infection. Expression levels relative to the fly gene Actin 5c were normalised based on the qPCR plate effect . Symbols above the bars give the significance relative to the Wolbachia-free controls based on a Dunnett's test .(TIF)Click here for additional data file.Table S1Cox's proportional hazards mixed-effect model on virus- and Ringer-infected flies. The strain-by-treatment interaction can be interpreted as the protective effect corrected for the between-strain variation in Ringer-infected flies.(DOC)Click here for additional data file.Table S2MLST genes used to build the Wolbachia phylogeny.(DOC)Click here for additional data file.Table S3Primers and probes used in this study.(DOC)Click here for additional data file.


We as the Epidemiologic Architecture for Genes Linked to Environment study genotyped candidate gene and GWAS-identified index variants in NHANES as part of the larger Population Architecture using Genomics and Epidemiology I study for collaborative genetic association studies. To enable basic quality control such as estimation of genetic ancestry to control for population stratification in NHANES san genome-wide data, we outline here strategies that use limited genetic data to identify the markers optimal for characterizing genetic ancestry. From among 411 and 295 autosomal SNPs available in NHANES III and NHANES 1999–2002, we demonstrate that markers with ancestry information can be identified to estimate global ancestry. Despite limited resolution, global genetic ancestry is highly correlated with self-identified race for the majority of participants, although less so for ethnicity. Overall, the strategies outlined here for a large epidemiologic study can be applied to other datasets accessible for genotype–phenotype studies but are sans genome-wide data.Population stratification or confounding by genetic ancestry is a potential cause of false associations in genetic association studies. Estimation of and adjustment for genetic ancestry has become common practice thanks in part to the availability of ancestry informative markers on genome-wide association study (GWAS) arrays. While array data is now widespread, these data are not ubiquitous as several large epidemiologic and clinic-based studies lack genome-wide data. One such large epidemiologic-based study lacking genome-wide data accessible to investigators is the National Health and Nutrition Examination Surveys (NHANES), population-based cross-sectional surveys of Americans linked to demographic, health, and lifestyle data conducted by the Centers for Disease Control and Prevention. DNA samples ( In case-control studies, spurious associations can occur when genetic ancestry is associated with both the disease as well as the genetic marker . A classPopulation stratification can be addressed at both the study design and data analysis levels. When designing a genetic association study, investigators should take care to collect at least self-identified race/ethnicity data , which in = 14,998) and allowed for candidate gene analyses with limited genotyping  conducted by the National Center for Health Statistics (NCHS), Centers for Disease Control and Prevention CDC; . NHANES notyping . Extensinotyping .We as the Epidemiologic Architecture for Genes Linked to Environment (EAGLE) study, a study site of the Population Architecture using Genomics and Epidemiology (PAGE) I study  accessedn = 7,159) and NHANES 1999–2002 . EAGLE also accessed NHANES 2007–2008  but only one nuclear marker has been genotyped in this dataset  in which DNA was collected in phase 2 . The analysis described here is limited to participants of three self-reported races/ethnicities: non-Hispanic white (NHW), non-Hispanic black (NHB), and Mexican American (MEX). The sample sizes for these three race/ethnicities were 2,630 (NHW), 2,108 (NHB), and 2,073 (MEX) for NHANES III and 4,003 (NHW), 1,350 (NHB), and 1,877 (MEX) for NHANES 1999–2002. And additional 348 (NHANES III) and 609 (NHANES 1999–2002) samples were available from participants who self-identified as “other” and “other Hispanic” but not included in this present study.Supplementary Table S1). The EAGLE study either accessed existing genetic data in NHANES  in at least one NHANES subpopulation, and genotype call rates were at least 90%. We pruned the data so that the pairwise 2r of these markers across all comparisons within a 250 kb window was equal or less than 0.80. More stringent r2 thresholds of 0.50 and 0.10 yielded 361 and 266 SNPs in NHANES III, respectively, and 269 and 226 in NHANES 1999–2002, respectively, underscoring the overall SNP selection process of the EAGLE study.All data were subjected to basic quality control metrics including concordance of blinded duplicates supplied by CDC and checks of Hardy Weinberg Equilibrium stratified by self-reported race/ethnicity. All SNPs included in this analysis were in Hardy–Weinberg Equilibrium  were calculated stratified by self-identified race/ethnicity and were binned into three groups: monomorphic and rare (<5% MAF), MAF 5–25%, and MAF > 25%. MAF distributions were then compared between NHANES III and NHANES 1999–2002 for each self-identified race/ethnicity. Distributions were also compared across the three major racial/ethnic groups within each survey. Statistically significant differences in MAF were identified using chi-square tests (2x3 and 3x3 tables). Population differentiation was measured by the fixation index (FST), which was calculated using the formula developed by Weir and Cockerham .K = 3 and used the population info flag for only the unrelated HapMap 3 samples  representing the continental ancestries.Processing of genotype files into the input format for STRUCTURE and principal component analysis (PCA) analysis was performed with the genetic analysis, translation, and organization software PLATO . To esti-10), we anchored HapMap 3 samples into discrete clusters and allowed the NHANES samples to partition themselves iteratively. Each dataset was run with a round of 10,000 burn cycles followed by 50,000 reps. Eigenvectors were generated by the princomp function and plotted with the GGPlot2 package . The distribution of minor MAFs, however, differed significantly between NHANES for both non-Hispanic whites  and Mexican Americans  owing to fewer rare and monomorphic variants available in NHANES 1999–2002  compared with NHANES III . Likewise, the distribution of MAFs differed significantly across the three self-identified racial/ethnic groups for both NHANES III  and NHANES 1999–2002 .For both NHANES III and 1999–2002, the majority of markers available in any self-identified group are common  revealed that a portion of the observed marker allelic variability is explained by population structure.To measure how informative the markers available in NHANES III and 1999–2002 are for estimating genetic ancestry, we calculated pairwise fixation index (FST) between racial/ethnic groups in HapMap 3, NHANES III, and NHANES 1999–2002 . FST is a measure of population differentiation based on the variance of allele frequencies in a subpopulation compared with the total population . As expeFigure 1). In contrast, the ASN HapMap population consistently presented higher FST values in NHANES III than 1999–2002 with the CEU population (0.20 vs. 0.11) and the YRI population (0.22 vs. 0.17). The lower FST detected in the CEU-ASN and YRI-ASN comparisons by the NHANES 1999–2002 markers suggests that our estimates of admixture and population structure are likely to be underestimates. We also note significantly lower mean FSTs between African and European descent ancestral groups in NHANES (NHW × NHB) compared with the HapMap 3 populations . This latter finding reflects European admixture found in African American populations resulting in a reduction of allelic diversity between the two groups.To estimate the effectiveness and equivalence of our AIMs in the two surveys to estimate ancestry, we compared the FST values measured across HapMap populations. The mean pairwise FST between CEU and YRI was consistently 0.12 when using either the NHANES III or the NHANES 1999–2002 markers, suggesting they are both equally effective at measuring the population structure across these two groups  and NHANES 1999–2002 (2). However, based on our FST results of these markers in HapMap 3, this result is likely a result of a lack of Asian AIMs available in the NHANES 1999–2002 population.Table 2; Supplementary Figures S1–S4). Overall, we found nearly all of the self-reported non-Hispanic whites in NHANES (>97.5%) clustered consistently with the reference samples of European ancestry . At a stricter threshold of >90% European ancestry, at least 90% of self-reported non-Hispanic whites were concordant with genetic ancestry in NHANES III and 1999–2002.We next identified outliers of genetic ancestry compared with self-identified race/ethnicity (Table 3). In comparison with the European Americans, we observed less concordance between self-reported race/ethnicity and a single ancestral population among non-Hispanic blacks. At the strictest threshold (90%), only 44% of self-reported non-Hispanic blacks were concordant with African continental ancestry. However, analogous to diminished FSTs between African Americans and European Americans, these results are expected given recent admixture events between the two groups  clustered with reference samples from West Africa as expected . Self-reported Mexican Americans from NHANES III clustered more with the Asian continental ancestry cluster than self-reported Mexican Americans from NHANES 1999–2002. This difference may reflect the larger proportion of markers with higher pairwise FSTs between Asian and European groups available in NHANES III  compared with NHANES 1999–2002 . A comparison of the principal components analysis (PCA) of the Mexican Americans in NHANES III and 1999–2002 reveals that of the three groups, self-reported Mexican Americans are the most similar to the European genetic cluster . However, the Asian admixture is more pronounced in our analysis of the Mexican Americans in NHANES III than NHANES 1999–2002, consistent with our results from the STRUCTURE analysis.Overall, the proportion of the membership of Mexican Americans in the European, African, and Asian clusters was found to be 0.44, 0.07, and 0.49 in NHANES III and 0.98, 0.01, and 0.01 in NHANES 1999–2002, respectively  in Hyattsville, MD or send SAS code to the RDC remotely using the Analytic Data Research by Email (ANDRE) portal . During The present study has several strengths and limitations. Major strengths of NHANES include sample size and the racial/ethnic diversity. However, as already mentioned, NHANES III and 1999–2002 have limited genetic data which greatly limits the resolution of genetic ancestry that can be estimated for each dataset as well as for each individual participant. Only global ancestry could be estimated as opposed to local ancestry, and the resolution of the global estimates are dependent on the availability of AIMs. Furthermore, as already noted, we do not have sufficient AIMS to reliably estimate global ancestry among self-identified Mexican Americans, particularly in NHANES 1999–2002. Also, the genetic data available does not completely overlap between NHANES, making comparisons difficult between surveys.Recommendations on how to properly estimate genetic ancestry and adjust for population stratification in studies involving Hispanic populations are evolving now that large genetic datasets are available for these populations . It has Despite the major weaknesses of NHANES, we demonstrate that global genetic ancestry can be estimated in the largest self-identified groups and that the majority of self-identified labels (non-Hispanic whites and non-Hispanic blacks) are concordant with these estimates. Overall, NHANES remains useful for specific genotype-phenotype studies, and the data and approaches described here can be applied to control for gross population stratification despite the lack of genome-wide data.The listed authors provided substantial contributions to the conception or design of the work , the acquisition , analysis , or interpretation of the data  for the work; drafted the work (MO) or revised it critically for important intellectual context ; gave final approval of the version to be published ; and agreed to be accountable for all aspects of the work in ensuring that questions related to accuracy or integrity of any part of the work are appropriately investigated and resolved .The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Arabidopsis transcription data.This paper proposes an inegrative two-stage genome-wide search for pairwise epistasis on expression quantitative trait loci (eQTL). The traits are clustered into multi-trait complexes that account for correlations between them that may result from common epistasis effects. The search is done by first screening for epistatic regions and then using dense markers within the identified regions, resulting in substantial reduction in the number of tests for epistasis. The FDR is controlled using a hierarchical procedure that accounts for the search structure. Each combination of trait and marker-pair is tested using a model that accounts for both statistical and functional interpretations of epistasis and considers orthogonal effects, such that their contributions to heritability can be estimated individually. We examine the impact of using multi-trait complexes rather than single traits, and of using a hierarchical search for epistasis rather than skipping the initial screen for epistatic regions. We apply the proposed algorithm on Both epistasis detection power and heritability contributed by epistasis increased when using multi-trait complexes rather than single traits. Epistatic effects common to the eQTLs included in the complexes have higher chance of being identified by analysis of multi-trait complexes, particularly when epistatic effects on individual traits are small. Compared to direct testing for all potential epistatic effects, the hierarchical search was substantially more powerful in detecting epistasis, while controlling the FDR at the desired level. Association in functional roles within genomic regions was observed, supporting an initial screen for epistatic QTLs. Epistasis, or interaction between genes, is a fundamental phenomenon that is believed to play an important role in diverse fields of biology, including quantitative genetics and genomics of complex diseases, gene regulatory networks and biochemical pathways and sex evolution, as well as genome and proteome evolution. Despite the growing interest in searching for epistatic interactions, there is no consensus as to the best strategy for their detection within a genome-wide scan A more recent approach takes into account the strong correlations between neighboring markers in the new generation of ultra-dense genetic maps, enabling a dramatic reduction in the number of tests to be performed. Such an approach is also adopted by A widely used approach for reducing the dimension of gene expression data is identifying groups of genes that share similar expression profiles. For instance, instead of analyzing each individual gene expression trait for the purpose of eQTL mapping, treating principal components of the individual gene expression as traits has been shown to improve the performance of eQTL analysis We propose an inegrative two-stage approach for searching for pairwise epistasis, which pursues the potential power benefits of both initial screening and the use multi-trait complexes. In the first stage, clusters of traits are constructed, and the first principal component of each cluster is regarded as a single (complex) trait in eQTL analysis. Here the clusters are formed using the Weighted Gene Co-Expression Network Analysis (WGCNA) algorithm, a clustering-based framework for building gene expression networks The proposed framework allows flexibility in choosing the modeling approach of epistasis. In this paper we use the Natural and Orthogonal Interactions (NOIA) model An important issue when testing a large amount of hypotheses is the control of type I error across all tests. We suggest controlling the False Discovery Rate (FDR), i.e. the expected proportion of false epistatic effects discoveries, among all discovered epistatic effects. The initial screen for epistasis followed by a higher resolution scan within the selected regions implies that the tests performed within the two steps are organized in a hierarchical manner. The hierarchical FDR controlling procedure offered by We evaluate the performance of the proposed two-stage algorithm by examining the contribution of using multi-trait complexes rather than single traits, and of using a hierarchical search for epistasis, rather than skipping the initial screen for epistatic regions. We first do so by implementing the proposed hierarchical testing on single traits and on trait complexes, and implementing the modeling of epistasis with and without an initial screen for potential epistatic regions. We compare these alternatives by several performance measures including the contribution of the epistatic effect to the traits’ heritability, the detection power of the procedure and the level of FDR control. The data is simulated under several configurations of number of individual QTL effects and size of epistatic effect. In addition, we compare the proposed algorithm to an alternative QTL detection method that is based on the popular Bayesian interval mapping approach and applies a Markov chain Monte Carlo (MCMC) algorithm for evaluating the posterior of genetic architecture G, the vector of expected phenotypic values of the two possible alleles, to E, the vector of genetic effects, by G = S E, where S is a genetic-effect design matrix. Due to the absence of heterozygotes in RIL populations, the dominance effect is eliminated from the model of Consider a locus A and a quantitative trait affected by this locus. A11G and A22G, and a is the additive effect of locus A.such that R is a reference point that is interpreted as the mean over the phenotypic values A and B, with genetic-effect design matrices AS and BS, respectively, the two-locus vector of genetic effects, ABE, can be expressed by the matrix productExtending the model for two loci Where A two-locus statistical model of the effects on for RIL populations may be defined as follows. A genome-wide statistical formulation for the link in (2) can be defined as follows Let n observed expression values and Unlike the hierarchical approach, flat partitioning techniques such as k-means and its variants produce independent clusters of genes. We prefer to avoid assuming such independence due to the potential networking relations between genes. In additions, these techniques typically require pre-specifications of the number of clusters, which is an impractical challenge when searching for traits connected by common epistatic effects.If the hypotheses can be arranged in a form of a tree, a hierarchical procedure to control the FDR across the tree of hypotheses is suggested Several types of hierarchical FDR criteria can be defined. A general FDR bound is given by Since the interest in this work is in all identified epistatic effects, whether by framework or by secondary markers, This work presents an algorithm based on a two-stage procedure for detecting epistatic interactions between pairs of markers across the genome. In the first step, multi-trait complexes are identified by the WGCNA clustering algorithm  obtained in the preceding dimension-reduction step. In the second step, only the combinations of meta-traits and framework marker pairs showing epistasis (regardless of the main effects) are further explored. Now the scan is performed with higher resolution, using “secondary”, more densely positioned markers found near the corresponding framework markers. The NOIA model is employed individually on each tested combination in each step, in order to test for epistasis. Due to the orthogonality property, each identified effect is independent of the rest of the effects in the model, such that the heritability of an effect, namely the contribution of the effect to the total gene expression variance, can be obtained.The full algorithm is formally described as follows. Identification of multi-trait complexes - using WGCNA clustering.Identification of epistasis - using the two-step hierarchical testing procedure:Let For each rejected hypothesis, the hypotheses within its family are tested for the combinations of the corresponding meta-trait with all corresponding pairs of secondary markers.Consider a single trait with phenotypic trait values Let BF = 3 based on the findings of The procedure in Arabidopsis map (see Section 2.5) at twelve regions around framework markers in three chromosomes. Epistatic effects were “implanted” on the actual markers at absolute levels ranging from 0.19 to 0.21, in accordance with effects observed for single traits included in trait-complexes that were found to have epistatic effects. These levels also allowed flexibility in power between single-trait analysis and meta-trait analysis. All possible main effect and epistasis combinations were examined in the simulation . Gene expression intensities were simulated according to a four-cluster structure, each cluster containing fifteen traits. Two of the four clusters contained traits with epistasis attributed to pairs of markers emerging from the partial Arabidopsis map. For a cluster simulated with epistasis, 13 (86%) of its traits had either inter-chromosomal or intra-chromosomal epistatic effects. The two remaining non-epistatic traits represented error generated by non-specific cluster identification. All effects were signified by NOIA model coefficients, where the interaction coefficient reflected the size of the epistatic effect. For the epistatic traits, the number of main eQTL effects was one, two or none. The coefficients of all effects were set to levels that allowed flexibility in the contribution to heritability and the detection power.A simulation study was conducted in order to assess (i) an improvement in epistasis detection power and in heritability assigned to epistasis as a result of using multi-trait complexes and of using hierarchical testing, and (ii) the FDR control level achieved by the procedure under the dependence structure typical to the tree of hypotheses tested here. Intensities were generated from multivariate normal distribution with mean similar to the observed intensity mean and with standard deviation of 2.5, which allowed variability in power. Non-epistatic clusters were generated with a correlation of 0.4 between the traits. Genotypic information was based on real markers on the Arabidopsis RIL map. In the second step, the scan was performed with higher resolution on six “secondary”, more densely positioned markers neighboring each of the framework markers identified in the first step. The proposed approach was compared to the Bayesian model selection approach of The proposed algorithm was implemented for all configurations of simulated data, starting by calculating the first principal component of the gene-expression traits included in each cluster. Next, for the first step of the hierarchical testing procedure, a scan for epistasis was performed by fitting a NOIA model  the hierarchical testing procedure was also implemented on single traits, and (ii) the analysis on meta-traits was also implemented directly, skipping the initial screen, and the BH procedure was used in order to control the FDR.ftp://ftp.arabidopsis.org/home/tair/Microarrays/analyzed_data/affy_data_1436_10132005.zip). This data contains intensities for 22,810 traits from all five chromosomes of the Arabidopsis thaliana genome. A sample of 211 RIL population individuals derived from a cross between two inbred accessions, Bayreuth-0 (Bay-0) and Shahdara (Sha), was used. Transcript (mRNA) levels were quantified using Affymetrix whole-genome microarrays with two replications (arrays) for each individual http://elp.ucdavis.edu/data/analysis/211_RILs_SFP_map/211_RILs_SFP_map.html. The genotypic data was preprocessed using the MultiPoint software (http://www.multiqtl.com) for the purpose of eliminating non informative, overlapping markers and those markers that cause local neighborhood instability in the mapGene expression data was downloaded from the TAIR database website . The TOM-based clustering followed by the Dynamic Tree Cut procedure discovered 314 trait clusters ranging from two to 1959 in size with mean of 23. Following the cluster identification, a meta-trait was generated for each cluster as the first principal component of the corresponding set of gene expression traits. The individual proportion of cluster variance explained by the corresponding meta-traits ranged between 0.2 and 0.93 with a median of 0.73.The proposed two-stage search for epistasis was used for the analysis of the Next, the two-step hierarchical testing procedure was employed. In the first step, a rough two-dimensional scan for epistasis was performed for each of the 314 meta-traits obtained in the previous step, using 47 sparse framework markers. Thus in the first step 1,081 pairs of markers were considered for each meta-trait, resulting in a total of 1,081*314 = 339,434 tests. Since the interest is in epistasis at all loci, epistatic effects attributed to either framework or secondary markers are of importance. Thus the rejection threshold should be chosen such that the full-tree FDR will be controlled. The multiplicative factor δ* was estimated by employing the hierarchical procedure repeatedly 10,000 times at level q = 0.1, resulting in an estimate of 1.015 (SE = 0.008). From (3), in order to control the full-tree FDR at level 0.1, q* = 0.1/2δ = 0.0472 was used. Twelve epistatic effects were identified at the first step. As can be seen in In the second step, only the combinations of meta-trait and marker pair showing significant epistasis in the first step were tested for epistasis with increased resolution, using secondary markers neighboring the corresponding framework markers. The number of secondary marker pairs in the family of each identified framework marker-pair varied between 100 and 200, and the total number of tests in the second step was 1,673. For six families in the second step all hypotheses were rejected, and for the other five families, the proportion of discoveries varied between 0.6 and 0.97. In total, 1,506 epistatic effects were found in the second stage, summing up to 1,518 epistatic effects in total for both steps. The FDR control level can be obtained from (2), using We examined what would be the results for the discovered effects on meta-traits, if instead the analysis was performed on single traits. Interestingly, the same pairwise effects on the corresponding single traits were not found significant. This may be explained by the poor testing power found by the simulation study for single traits. Yet, their p-values are clearly differentiated from those of all other non-significant effects on single traits , as theiThe markers associated with the detected epistatic effects are all concentrated in chromosomes 2, 4 and 5. Most epistatic effects are in sub-telomeric regions (telomers are repetitive DNA regions at the ends of chromosomes). Seven of the epistatic effects were found between eQTLs of two different chromosomes, and the remaining four were between two eQTLs of the same chromosome. As shown in Epistasis is a genetic phenomenon that is challenging for detection within a genome-wide scan. It has been given relatively small attention until recently, even though it possesses a significant biological meaning and may contribute substantially to the understanding of complex gene networks that can lead to deciphering important biological mechanisms. This paper proposes a searching approach for epistasis effect on gene expression traits. It offers an analytical framework that, unlike other alternatives, combines the treatment of several important issues for the benefit of power gain and deeper biological interpretability. By taking advantage of the correlations between traits, the proposed two-stage algorithm is capable of identifying small epistatic effects which are otherwise challenging for detection, without relying on additional biological information. It performs an initial screen that is driven by the local dependence between markers, for potential epistatic regions. It guarantees control of the FDR at the desired level by using a procedure that accounts for the hierarchical testing structure generated by the screen. It shows advantage in power over similar procedures that do not include one of the key components of trait complexes and hierarchical testing. It allows flexibility in the choice of epistasis modeling approach, which should be in accordance with the interpretation of epistasis that is of interest for the researcher. The NOIA system, which is used in this study, models simple-to-interpret epistatic effects and can be tuned to match the type of population in hand.A major strategy of the proposed approach is to reduce the very large number of tests for epistasis typical for a genome-wide scan. First, correlations between traits affected by epistasis are accounted for by considering unified representations of the expression quantitative traits. Aside from the reduction in the number of traits, a multi-trait complex (meta-trait) that is defined based on correlation may also provide a firmer base of evidence for phenotype-genotype relationships by relying on many traits altogether Arabidopsis thaliana, a considerable reduction in the number of tests for epistasis was achieved by constructing 314 meta-traits by clustering expression data of 7,244 genes. Using the two-step hierarchical testing on the generated multi-trait complexes, 1,081*314+1,673 = 341,107 hypotheses were tested. If, instead, all possible combinations of markers and single traits were tested directly, namely 121,278 marker pairs for each one of the 7,244 traits, 878,537,832 tests would have been performed. Thus the overall number of tests was reduced by 2,575 folds.The use of multi-trait complexes and the hierarchical search together achieves a dramatic reduction in the number of statistical tests. In the exemplifying analysis of the publicly available genome expression data for a RIL mapping population of the central plant model species A simulation study revealed the gain in both epistasis detection power and the contribution to heritability by the epistatic effects resulting from using multi-trait complexes rather than single traits. These observations are consistent with the initial findings of Arabidopsis meta-traits, of which variances were partly explained by epistasis, were based on clusters of a relatively small number of traits (5–23). This result may indicate that traits included in relatively large clusters are more likely to be related to each other by reasons other than being subjected together to the same epistatic effect, such as linkage and co-regulation of expression. Yet, they may also be affected by several different epistatic effects, in which case they must be further divided into sub-clusters, or alternatively the next principal components may be used.Cluster size may play an important role in epistasis identification. The obtained The methodology used for the purpose of constructing multi-trait complexes based on the expression trait data should be a relatively minor stage. As many clustering techniques can be used, the chosen one must achieve high stability for the given data. The hierarchical clustering utilized in this study was based on a TOM-based dissimilarity measure and attained stability by merging a Dynamic Tree Cut algorithm The hierarchical testing enabled control of the FDR across all tests for epistasis, thereby making our approach competitive in restraining the expected rate of false positive identifications. The hierarchical testing procedure achieved a considerable gain in power compared to direct testing of all combinations of marker-pairs and meta-traits. Under the dependence structure characterizing the tree of hypotheses used in this study, the FDR was controlled at a level lower than the boundary level established in The implementation of the hierarchical testing scheme of the proposed approach may be further investigated in two aspects. First, the methods by which markers are chosen may take the genome-wide marker distribution into consideration. In this work, framework markers were chosen such that their regions will contain the same number of secondary markers. However, this may result in highly variable regional density of the secondary markers. An alternative strategy is also to account for distances between the markers. For example, it has been proposed to use biological information, such as locations with common mutation incidence, in order to choose the genotypic marker pairs for testing epistatic effects Aspergillus niger showed that fitness declined linearly with the number of mutations, without any evidence of epistasis on average Second, the discovery of epistasis may depend also on the definition of epistasis within the statistical model. Indeed, some reports suggest that the way in which alleles interact is highly variable. For instance, the findings in this work suggest that several regions are involved in interactions with more than one region, and that the epistatic effects of one particular locus with several other loci may vary in form. In addition, for pairs of epistatic loci originating from two given regions, the corresponding effects sometimes may be of different form. Such effects were studied by A. thaliana chromosomes 2, 4 or 5, were identified as epistatic effect at the first step of the hierarchical search. For each of these marker pairs, most of the neighboring secondary markers were found to have an effect on the corresponding meta-trait. This further validates the already acknowledged regional association in functional roles of genomic sequences and supports an initial screen based on framework markers for the purpose of identifying epistatic eQTLs. Notably, one of the twelve framework marker pairs included a locus that has no main effect, thus strategies that test for epistasis only among pairs with main effects would fail to detect many of the effects identified here.Twelve combinations of meta-traits and framework marker pairs, all residing in Arabidopsis data did not identify the effects corresponding to the ones identified in the analysis on meta-traits, but included marker pairs from the same DNA regions, which may be suspected as epistatic hotspots. The traits detected in single-trait analysis which also had strong epistatic effects were poorly correlated, while those that were not detected may have suffered a very low chance to be identified in a single trait analysis, as indicated by the simulation study for correlated single traits. These findings may suggest the existence of epistatic gene networks, having common epistatic effect and relatively small individual effects, as well as common involved chromosome regions. These are difficult to identify by a genome-wide association study due to low power. But analyzing them based on multi-trait complexes can dramatically increase the probability of their identification. Yet, the expression of some genes is not correlated with other expression traits but controlled by “individual” epistatic marker pairs that have a relatively large epistatic effect. These pairs can be effectively identified by single-trait analysis.Single-trait eQTL analysis of the S1 FigA schematic representation of the epistatic findings on a genomic map – the Arabidopsis data. Epistatic effects are shown on a partial map that includes only chromosomes found to contain epistasis . An ellipse represents a meta-trait (of which id is specified on top), and the single traits it is based on are schematically shown inside. The ellipse is connected by two lines to two interacting markers located on the map. The vertical lines on the chromosomes mark the groups of “secondary” markers that make up the “framework” markers”. Each color corresponds to a particular epistatic effect on a particular meta-trait. The meta trait 75(19) was found to be affected by two pairs of markers that have one common marker (id 237). See (TIF)Click here for additional data file.


Genomic selection is still to be evaluated and optimized in many species. Mathematical modeling of selection schemes prior to their implementation is a classical and useful tool for that purpose. These models include formalization of a number of entities including the precision of the estimated breeding value. To model genomic selection schemes, equations that predict this reliability as a function of factors such as the size of the reference population, its diversity, its genetic distance from the group of selection candidates genotyped, number of markers and strength of linkage disequilibrium are needed. The present paper aims at exploring new approximations of this reliability.i.e. an “equivalent number of independent loci” which would give a GEBV reliability for unrelated individuals by considering a sub-set of independent markers that is identical to the reliability obtained by considering the full set of markers.Two alternative approximations are proposed for the estimation of the reliability of genomic estimated breeding values (GEBV) in the case of non-independence between candidate and reference populations. Both were derived from the Taylor series heuristic approach suggested by Goddard in 2009. A numerical exploration of their properties showed that the series were not equivalent in terms of convergence to the exact reliability, that the approximations may overestimate the precision of GEBV and that they converged towards their theoretical expectations. Formulae derived for these approximations were simple to handle in the case of independent markers. A few parameters that describe the markers’ genotypic variability  can be estimated from genomic data corresponding to the population of interest or after making assumptions about their distribution. When markers are not in linkage equilibrium, replacing the real number of markers and QTL by the “effective number of independent loci”, as proposed earlier is a practical solution. In this paper, we considered an alternative, This paper is a further step towards the development of deterministic models that describe breeding plans based on the use of genomic information. Such deterministic models carry low computational burden, which allows design optimization through intensive numerical exploration.The online version of this article (doi:10.1186/s12711-016-0183-3) contains supplementary material, which is available to authorized users. The effectiveness of genomic selection comes from the possibility of predicting breeding values on un-phenotyped and young animals . GenomicAn extensive literature exists on the mathematical modeling of selection schemes prior to their implementation, in order, for instance, to optimize their design, or to evaluate the usefulness of new technologies such as embryo transfer, sperm selection, DNA markers and others  was assessed by simulation studies , 27, 28.A Taylor expansion of a matrix inverse involved in the reliability formula was suggested , which lAfter a formalization of the genomic selection context, the principles that underlie these approximations are presented and their properties are compared by using a simple example. Then, the new approximation is derived when reference and candidate animals are related. This is illustrated by some numerical examples. Finally, the extension to the linkage disequilibrium situation is described.Although the prediction equations derived below were based on a number of simplifying assumptions, it is important to first draw a complete description of the biological framework, as a basis to subsequently simplify the discussion.r, comprising nr individuals. The genomic estimated breeding values (GEBV) are calculated for a population of candidates for selection and used in breeding, Pc, comprising nc individuals.The SNP effects are estimated in a reference population, PLet nM markers (observed) and at nQ QTL (unknown). Alleles will be noted Am and Bm for the marker m and Aq and Bq for the QTL q. Let atim ∊ {0, 1, 2} and atiq ∊ {0, 1, 2} be the numbers of Bm  alleles that an individual i from population Pt (Pr or Pc) carries at marker m . Let ptm and ptq be the frequencies of alleles Bm and Bq in Pt.Individuals are characterized by their genotypes at xtim = atim − 2ptm and wtiq = atiq − 2ptq. Different codifications can be proposed  = Aτ. The limits of this equality will be discussed below. As indicated above, the denominator of the expected reliability τσβ2 = σq2. Approximating cov]E[v(y)]−1E[cov] is useless because it makes an oversimplification of the relationships between the reference and the candidate population: it considers separately the marginal distributions of xcXr′ and (XrXr′ + Iλβ)−1, while these random matrices are correlated. Estimating directly E[covv(y)−1cov] seems impossible in the general case. The approach of Goddard et al. [i.e. the variance V−1 is approximated by a second degree Taylor expansion [I + Dγ],with I + Dγ]−1 will be approximated using a Taylor series. It must be emphasized that the Taylor series I − Dγ + (Dγ)2 − (Dγ)3 + ··· converges towards [I + Dγ]−1 only if the highest Eigen value of Dγ is smaller than 1, i.e. if and V−1 is equal to D] = 0 and i.e.The second order approximation of Finally, the reliability of the candidate GBLUP is approximated by:T term. As an example, consider a reference population composed of nr half-sibs of the candidate, J coefficient will tend to ∞ as soon as A difficulty with this approximation comes from the Using the classical matrix inversion lemma, the variance Xr′Xr] are the following: m and l.Elements of E[Xr′Xr]mm = E[ ∑ i(aim − 2pm)2] = nrσm2. Let Xr′Xr + Iλβ matrix may be written as:E[Xr′Xr + Iλβ = [I + B]C.I − B + B2 − B3 + ··· to (I + B)−1 depends on the structure of the B matrix, which varies depending on the sample. However, we can examine the case of its expectation E[B].The convergence of the Taylor series B]mm = 0 and β is proportional to the number of markers  term in E[B]2, i.e.I + E[B])−1.E will involve expectations of fourth level moments of Xim within m joint distributions: E[XimXjmXkmXlm], and E[Xim4]. Defining and aij the coancestry coefficient between individuals i and j, we found that  = E[xcmXrim].E[xclXril] = 4aci2σm2σl2. Let i reference individuals.The expectations mentclass2pt{minimτ = ∑mσm2 and τ2 = ∑mσm4 that appear in the first approximation, and the parameters mρm2 and k estimated as 1/log2Ne, Ne being the effective size of the reference population. The expectations of the parameters are in Table The parameters  Goddard : \documeτ and τ2 are linked to the number Me of independent segments. This quantity Me was defined by Goddard , or vX(cij) = σβ4(∑qv(XiqXjq) + ∑q∑q′≠qcov). When the markers are in linkage equilibrium, the covariance term is null, and αij22 = 0, γic22 = −4 and aij = 0. Thus, vX(cij) = σβ4τ2. As σq2 = σβ2τ, X(cij) = σq4/Me. Thus: Me, which depends on the variability of allele frequencies, is not the number of markers nM.The parameters  Goddard  as the n Goddard , this vaA = I then T being diagonal, this equation simplifies to ck = 0. Hence The first approximation gives results similar to Goddard et al.  when indd et al.   while still assuming that reference individuals are unrelated. In this situation, the pedigree relationship matrix is T matrix We consider the situation of a candidate that is the son of one of the entclass1pt{minimaformulae  are descxtim = atim − 2ptm and wtiq = atiq − 2ptq. Alternatively, we could define xtim = (atim − 2ptm)/σtm and wtiq = (atiq − 2ptq)/σtq. The relation between genetic and marker variances becomes σq2 = nMσβ2 and the relation between pedigree and genomic matrices becomes E[G*] = AnM. Thus, formulae  = 4nMaikajl. Thus: i.e. when ck = 0, we have:i.e.In all the previous developments, genotypes were coded formulae  and 2)  xtim = amentclass2pt{minimNe − 1) for a uniform distribution.Based on Additional file nM independent segments that each carries a single QTL in LD with a single marker. More typically, the genomic information consists of a large number of non-independent markers. This non-independence comes from long-term effects due to bottlenecks, mutations, migrations, etc. and short-term effects due to family structure.So far, following Goddard , we consxci and tr[M] is the trace of matrix M.We based our developments on the very fruitful concept of the effective number of loci that Goddard defined as “the number of independent loci that gives the same variance of realized relationships as that obtained in the more realistic situation” −1] with In the more general situation, prior to the observation of the  by Sved : \documeIn this simplified situation, the equivalent number of loci is [See Additional file xcmXrimxclXril]. Let gimf and gimd are the “values” of the alleles transmitted to individual i by its father and its dam, with gimf and xcl,Xil. The random variable Mcls is the allele of individual c received from s at locus For a complete treatment of the LD situation, it is necessary to estimate the expectations of the product of four genetic values. For instance, with the second approximation [formula ], we neec as for the reference individual i, the pair of genetic values may originate from the same parent (and coded on the same chromosome) or not, giving four types of c and one for i) are on the same chromosome . In type 2  status between alleles at locus xclxcmXilXim] are given by:Thus, 16 terms involved in E = 4[pm(1 − pm)]2 and i and c are unrelated.um were simulated in a uniform pm, i.e. such as In the following numerical evaluation of the formulae derived above, allele frequencies were simulated following an inverse transform sampling (e.g. ): \documX of nr + 1 individuals were generated and the G matrix was built. The reliability of the candidate individual GEBV, I − Dγ + D2γ2 − D3γ3··· The convergence of the series as predicted by the value (lower or higher than 1) of the matrix’s largest eigenvalue was checked numerically, by estimating the mean of this largest eigenvalue from five simulations in each case studied ]]6)] wereν2 = 0.4. The Taylor series converged when the proportion ν2 of the phenotypic variance explained by the molecular score was low, with oscillations and divergence observed when ν2 = 0.7 with the second approximation. These observations were in accordance with the deviation to one of the largest eigenvalue of the matrix involved in the series . As nM increases, the number nR of the equivalent number of independent loci does not exist in the Goddard’s effective number of loci and clearly shows the difference in nature between these concepts. Three phenomena, observed when considering the extreme case of two markers −1 is a decreasing function of nr: as a consequence, the larger is the population size, the smaller is T, which is proportional to the marker effects conditional variances The trace T of . Convergence of these series is not guaranteed and depends on the behavior of the perturbation (I − E + E2 − E3 → (I + E)−1 if ν2 = 0.7 with the second approximation. This is fully consistent with the deviation to one of the largest eigenvalue of the E matrix.These approximations were based on Taylor expansions of a matrix inverse endix in , this coThe expectation of the proposed approximation, when data were simulated with the model corresponding to the hypotheses underlying their algebraic development, was very close to the mean value after 50 simulations. Thus, extremely fast estimation of the precision is possible, which allows intensive optimization and comparison of selection schemes.When individuals are unrelated and markers are in linkage equilibrium, we obtain an estimation of the GEBV accuracy which differs from that of Goddard et al. . This isxcC−1B2xc′ term.A strong limit of our new approximation comes from the limitation to the first order term of the Taylor series. Deriving algebra was only possible at this stage. The side effect is that no genotypic covariance terms between reference individuals appear in this approximation. As a consequence, only the direct relationships between candidate and reference individuals play a role in the estimation, but not the structure within the reference population. This is unfortunate, because accuracies of genomic prediction are obviously affected by the construction of the reference population. Our last numerical example, in which there is a linear trend with the number of half-sibs, reveals this drawback: two half-sibs of the candidates are treated as unrelated and the information that they carry is just the double of that of a single half-sib. Future developments should focus on this limitation, for instance to derive the expectation of the i.e.Φa = Φb = Φ, this quantity Φ can be adjusted to fit the distribution of Goddard. Using the Chi2 test as a fitting option, we observed that the adjusted 2 are easily derived from the moments generating function of Beta distribution  corresponding to a given variance of realized relationships. Here, we proposed the alternative equivalent number of independent loci (Mi) which corresponds to a given reliability. We showed that this Mi number depends on the size of the reference population and on heritability, a dependence that does not occur with Me. If we invert the argument, controlling the level of realized relationships variance with the effective number of loci (Me) does not seem to be a good approach to control the estimated GEBV reliability.All the developments shown in this paper are based on the hypothesis that the reliability of GEBV based on non-independent markers for a trait controlled by  Goddard . How man Goddard  was baseAs detailed by Hayes et al. , the effMi, there is no reason that the number of independent loci must equal the number of QTL, which is unknown, contrary to the hypothesis about pairs of marker-QTL . Equating W as well as σβ2 and σα2 has no clear justification. The variance σβ2xcXr′(XrXr′ + Iλβ)−1Xrxc′ but σα2xcXr′(XrXr′ + Iλβ)−1(WrWr′ + Iλα)(XrXr′ + Iλβ)−1Xrxc′. This other formula assembles two sets of unknown parameters: the variances σα2 and σβ2, and the genotypes X and W. It is often assumed that Wr matrix is not observed.Regardless of the definition of mentclass2pt{minimnM markers-QTL pairs with strong LD within pairs and no LD between pairs) is partly retained, a slight improvement is possible considering the element b of the genetic variability explained by SNPs. The idea would be to replace, in the formulae used in this paper, σq2 by b × σg2. Element b can be derived by considering that the markers’ (β) and QTL’ (α) effects are fixed in the genetic and statistical models. Leaving aside the singularity of Xr′Xr when the number of SNPs is large, the marker effects are now estimated by g = Wrα. Given the genotype matrices, the sample genetic variability is vg = α′Wr′Wrα and the sample molecular score variability y′Xr(Xr′Xr)−1Xr′y with an expectation vq = α′Wr′Xr(Xr′Xr)−1Xr′Wrα. The part of the genetic variability explained by the SNPs is the ratio b = vq/vg.If the framework considered so far (nrpm(1 − pm) = nrσm2 in the diagonal, with similar expressions for Wr′Wr elements.Expectations of the matrices’ product elements q is in LD with only one marker m(q), with a LD value vg = nr ∑ qαq2σq2, we get Following Goddard , approxir2. Unfortunately, neither αq2 nor σq2 are known. The unweighted mean c being the distance, in Morgan, between the QTL and its marker. Let L be the total length of the genome, and assume an equal distance L/nM between each successive marker The ratio b is the weighted mean of LD ing Sved , the expN/D] = E[N]/E[D] − cov/E2[D] + v[D]E[N]/E3[D]) could not be used here due to algebra complexity. However, in the case of unrelated individuals and independent markers, numerical evaluation of the difference between exact and approximated results for various reference population sizes and numbers of markers shows a very small underestimation of the reliability  can be estimated from genomic data corresponding to the population of interest or estimated after assumption about their distribution.i.e. there is LD), replacing the real number of markers and QTL by an effective or equivalent number of independent loci, as proposed by Goddard [When markers are not in linkage equilibrium ( Goddard  and Haye Goddard , is a pr


P < 5 × 10−8 for the single locus models of McManus and Annett. The strong conclusion is that handedness is not controlled by a single genetic locus. A consideration of the genetic architecture of height, primary ciliary dyskinesia, and intelligence suggests that handedness inheritance can be explained by a multilocus variant of the McManus DC model, classical effects on family and twins being barely distinguishable from the single locus model. Based on the ENGAGE meta-analysis of GWASs, we estimate at least 40 loci are involved in determining handedness.Right- and left-handedness run in families, show greater concordance in monozygotic than dizygotic twins, and are well described by single-locus Mendelian models. Here we summarize a large genome-wide association study (GWAS) that finds no significant associations with handedness and is consistent with a meta-analysis of GWASs. The GWAS had 99% power to detect a single locus using the conventional criterion of  Right- and left-handedness show many features that suggest that they are under genetic control. For example, left-handedness runs in families,3DC model, which describes additive expression at a single locus with two alleles, D  and C (Chance), and the three genotypes being DD, DC, and CC, although most of the conclusions broadly and similarly apply to other genetic models. In the DC model, the probabilities of left-handedness given the three genotypes, P(L|DD), P(L|DC), and P(L|CC), are 0%, 25%, and 50%. For a typical population rate of left-handedness, P(L) = 10%, and for the frequency of the C allele, P(C) = 20%. The McManus model, as well as the Annett model, is successful in its predictions because the C allele  produces randomness in the phenotypes. The phenotype of the CC genotype with its 50:50 mixture of right- and left-handedness does not indicate remaining genetic or environmental variance, but instead the phenotype itself is what can be called deep chance, corresponding to fluctuating asymmetry in biology;iv gene,iv/+), show situs solitus (ss), where the normal position of the heart is on the left, and the other viscera are in their usual lateral locations . However, iv homozygotes (iv/iv) manifest as 50% with situs solitus and 50% with situs inversus . The absence of remaining genetic variation is shown because crosses between iv/iv mice produce offspring that are independent of parental phenotypes iv/iv × iv/iv and parental pairs, which are phenotypically ss × ss, ss × si, or si × si, all producing 50% si offspring.Most models of the inheritance of handedness, from the early model of RamaleyR × R parents have some left-handed offspring, and L × L parents have, in fact, mostly right-handed offspring .Handedness in families and twins shows several unusual features, which the McManus model  account for successfully. Typical rates of left-handedness in Western societies are about 10–12%, although there are geographical and historical variations.DC and CC twins each having a 25% or 50% probability of left-handedness, those probabilities being independent in the ontogeny of each twin. Therefore, for CC MZ twins, 0.25 will be R–R, 0.25 will be L–L, and 0.5 will be R–L, while for the more frequent DC MZ twins, the proportions of R–R, R–L, and L–L pairs are 9/16, 6/16, and 1/16. Overall, for 10% population left-handedness, the McManus model predicts that 14% of MZ pairs are discordant, a lower rate than the 16% predicted for DZ twins. Discordant pairs should also be more frequent in twins with left-handed parentsHandedness in MZ twins has traditionally been problematic for genetic models because of the high rate of discordance. A meta-analysis,D and C alleles; the DC and CC genotypes having a 25% and 50% probability, respectively, of right-language lateralization, with this probability being independent of the probability of being right- or left-handed. The result is that 7.8% of right-handers and 30% of left-handers would be expected to have right-language dominance, which fits well with the data.Handedness correlates with key human cognitive processes of language, which, as Dax and Broca showed in the 19th century, are mainly carried out by the left hemisphere of the brain.−8.Since handedness appears to be inherited at a single locus, it might be expected, in an age of molecular genetics, that finding the gene should be straightforward. However, the combination of additive inheritance and the randomness resulting from fluctuating asymmetry substantially reduces the power of standard methods, such as linkage and association. The advent of large-scale genome-wide association studies (GWASs) should change that, as long as sample sizes are sufficient. Because there are only a small number of published GWASs looking at handedness (which are reviewed below), data are analyzed here from a large molecular genetic study in order to look for associations with handedness on a genome-wide basis. These results will be presented in detail in a separate publication,Although our GWAS analysis found no significant associations, a key question is whether those analyses are compelling evidence against a single gene for handedness, or whether perhaps there was simply insufficient power to convincingly be able to come to a negative conclusion. Formal power calculation was therefore carried out, given our sample size of about 3750 individuals, to assess the likelihood of finding an association with a single-locus gene. To ensure that a single locus could be rejected by such data, we set the power level at 99%.−8, calculated as reflecting the usual P < 0.05 α criterion, Bonferroni-corrected for 1 million possible loci (based on 3 billion bases and a possible gene length of 3000 bytes). On that basis, power for the standard McManus model in our GWAS was 99.47% (and 99.17% for the Annett model), adequate power for detecting a single locus.Although it is possible to consider the problem of power analytically  consortium reported meta-analysis of 12 GWASs, based on 2350 left-handers and 21,093 controls. No associations reached conventional GWAS significance, although three approached it, and it was said that, “large-scale replication effects are currently underway.” Since then, in 2010, the International Handedness Consortium reported data from 5429 left-handers and 49,970 right-handers from 32 separate GWASs,Handedness is far from being the only common trait where problems have arisen in finding genetic associations. As Crow has said for psychiatric conditions, where once there was “widespread optimism [that …] all that was necessary was to ‘drain the pond dry’ to reveal the relevant genes”The large GWASs reported here had adequate power to detect a single major gene determining handedness. Even if no single locus accounts for variation in handedness, it does not mean that handedness is not under genetic control. Before looking at handedness in particular, the findings of GWASs will be considered first for understanding traits and conditions such as intelligence and primary ciliary dyskinesia.http://www.ciliaproteome.org), with recent estimates suggesting well over 800 proteins in the ciliary proteome , disruption of any of which might result in dysfunction. It is not surprising that many disease loci have been found despite the broad phenotype being pathophysiologically similar across cases.A key model for thinking about handedness is primary ciliary dyskinesia , which results in chronic bronchiectasis and sinusitis, infertility, and, in 50% of cases, si.Although about half of the variance in intelligence is under genetic control,Both PCD and intelligence can be construed as pathology models, with variance mostly caused by rare, recent, deleterious genes.et al.Our within-families analysis suggests that there is no single gene for handedness. However, our GWAS and the meta-analysis of Medland DC model can readily be reconceptualized with n loci, where n can be from two to some large number. At the ith locus, let there be alleles conceptually equivalent to D and C in the single-locus model, which are labelled iD and iC (i = 1:n). For simplicity, assume that the frequencies of the Ci alleles, ic, are equal . Individuals with only iD alleles at all loci are equivalent to DD individuals in the single-locus model, and all will be right-handed. Similarly, individuals with two iC alleles at just one locus (iCiC) are 50% left-handed, as are CC individuals in the single-locus model, and individuals with a single iC allele  are 25% left-handed. Using a damage model akin to that in PCD, if being homozygous for iC at a single locus produces fluctuating asymmetry by preventing ciliary action, then being homozygous at two or more loci will have no greater effect, and hence individuals who are iCiC at multiple loci will also show 50% left-handedness. Likewise, individuals who are heterozygotes at multiple loci (iCiD) will have a 25% chance of left-handedness.The re Table , individith locus, the probability of being iDiD is (1− ic),iDiD for all loci is (1− ic)n2. Likewise, the probability of a single locus being iCiC is ic2, and, therefore, the probability of having no iCiC genotypes is (1 − ic2)n; hence, the probability of having at least one iCiC genotype is 1 − (1 − ic2)n. The probability of having at least one iCiD genotype is then 1-[1- (1− ic2)n] − (1− ic2)n = (1− ic2)n− (1−ic)n2. Since one quarter of iCiD and one half of iCiC are left-handed, thenFor the ic for any value of p(L); see Table p(L) = 10% and n from 1 to 1000.This equation can then be solved for n). The heritability of handedness does decrease slightly with more loci, R × R parents having slightly more left-handed offspring and L × L parents having slightly fewer left-handed offspring. Those differences arise because, although 50% of offspring from two CC parents (CC × CC) would be left-handed in the single-locus case, with multiple loci, the iC alleles may be at different loci , producing only 25% of left-handedness. For MZ twins, the increasing numbers of loci also result in a slightly higher rate of discordant pairs.Analytic solutions for varying numbers of multiple loci are possible, but for ease we have resorted here to a Monte Carlo simulation , has submitted an application to carry out such a study.Since the differences between multi- and single-locus models are small Table , these mn of 23,443, is much more computationally intensive. ENGAGE was estimated to have a power of 99.26% to detect a McManus model with 30 equi-frequent loci, and 98.96% with 40 loci. Although power for larger numbers of loci was lower, it was still about 96% with 100 equi-frequent loci. The much larger sample size of over 55,000 in the meta-analysis of the International Handedness Consortium (see above) will have still larger power. It seems reasonable to conclude, given the lack of any significant results in the ENGAGE analysis, that there are probably at least 30–40 loci involved in handedness, or a significant result would have probably been found.In our own GWAS, the power for detecting a locus was calculated if there were 10 loci at about 85%. Calculation of power for the much larger ENGAGE consortium data, which had an situs lateralization). Primary ciliary dyskinesia might provide a useful model for the type of mechanism we are proposing for handedness, with multiple genes being affected. It must, however, be stressed that the genes for primary ciliary dyskinesia are not the same as those for handedness, since handedness and situs inversus/solitus in PCD are not associated;Little is known about the nature of the biological mechanisms underpinning handedness/cerebral lateralization , or a racemic mixture of right- and left-handers . The most likely possibility for maintenance of left-handedness with a single-locus model is a heterozygote advantage where DC genotypes having greater fitness. Similar selective pressures could in principle work in parallel on all of the iC alleles . It has been speculated that the benefits of DC individuals come from partial randomization resulting in cerebral polymorphisms,Consideration of the details of underlying biological mechanisms that determine right-handedness is far from straightforward, not least because there are strong reasons to believe that there must be at least some selective advantages to being left-handedness or genetic drift would have resulted in fixation of one or other allele, resulting in a population either of right-handers , or, in effect, it could be at the level of the genotype,DD, DC, and CC all having differing phenotypes because of cerebral polymorphism.  More detailed modeling of frequency-dependent selection has been carried out in both of these terms, and with differing degrees of balanced polymorphism . Again, the main conclusion is that single- and multilocus models do not differ in any substantive way.Frequency-dependent selection is also possible, although that is more complicated, not only because selection can either be purely at the level of the handedness phenotype . The erudite and convincing theory of Crow shows how events on the X and Y chromosomes may have been responsible for such a saltatory, species-producing eventiC allele(s)) could then have evolved at a much later stage, seemingly by having advantages of its own, which allowed the iD allele(s) and various iC alleles all to be present in the population at the same time, with left-handers in modern proportions. The human tendency to right-handedness and the existence of a smaller proportion of left-handers are therefore entirely separate and logically independent processes, and should not be confused. The present analysis concerns the nature of the iC alleles, not the origin of the iD allele(s). It is a plausible alternative evolutionary scenario that the iD alleles evolved and went to fixation, with all humans having left-hemisphere dominance for language and being right-handed, with a large minority of left-handers never subsequently appearing in human evolution.Although current human populations are polymorphic for handedness, this may not necessarily have been the case during the evolution of