Understanding genome to phenotype linkages has been greatly enabled by genomic sequencing. However, most genome analysis is typically confined to the nuclear genome. We conducted a metabolomic QTL analysis on a reciprocal RIL population structured to examine how variation in the organelle genomes affects phenotypic variation. This showed that the cytoplasmic variation had effects similar to, if not larger than, the largest individual nuclear locus. Inclusion of cytoplasmic variation into the genetic model greatly increased the explained phenotypic variation. Cytoplasmic genetic variation was a central hub in the epistatic network controlling the plant metabolome. This epistatic influence manifested such that the cytoplasmic background could alter or hide pairwise epistasis between nuclear loci. Thus, cytoplasmic genetic variation plays a central role in controlling natural variation in metabolomic networks. This suggests that cytoplasmic genomes must be included in any future analysis of natural variation.DOI:http://dx.doi.org/10.7554/eLife.00776.001 The vast majority of genes in plant and animal cells are located on chromosomes within the nucleus. However, cells also contain a small number of genes outside the nucleus in cellular organelles such as the mitochondria, which generate energy, and the chloroplasts, which carry out photosynthesis. All these non-nuclear genes comprise the organellar genome.When trying to explain how variation in genes leads to differences in the characteristics of animals and plants, geneticists have historically paid most attention to the genes inside the nucleus. However, more recent work has shown that variation in the organellar genome can also contribute to differences between individuals, although the relative contribution of organellar genes versus nuclear genes remains unclear.Now, Joseph et al. have performed the first large-scale analysis of how variation in the organellar genome affects the characteristics (or phenotype) of the plant model organism, Arabidopsis. The study examined the degree to which variation in each of roughly 13,000 nuclear genes and 200 organellar genes affected the levels of thousands of metabolites inside cells.This metabolomics analysis revealed that variation in the organellar genome contributed to variation in the levels of more than 80% of the metabolites studied. Organellar genes also helped to regulate the effect of nuclear genes. This combination of direct and indirect influences helps to explain how a small number of organellar genes can have a disproportionately large effect on phenotype.The work of Joseph et al. suggests that the role of the organellar genome has been significantly underestimated to date, and that geneticists should consider variation in both the nuclear and organellar genome when attempting to determine how genes affect phenotype.DOI:http://dx.doi.org/10.7554/eLife.00776.002 A central goal of modern biology is to understand how the integration of gene functions across a genome lead to the individual’s specific phenotype. A key facet to this effort is to develop models that would allow directly inferring a species phenotypic variation from its genetic variation. This goal of mathematically linking genetic to phenotypic variation is central to all studies of quantitative genetics ranging from human genetics to plant breeding to ecology and has led to massive genome resequencing projects focused on developing the genomic databases to allow these studies . HoweverGenomic variation in human organelles has been linked to several severe diseases . HoweverIn plants, genetic variation in mitochondria is also linked with large qualitative phenotypes, such as cytoplasmic male sterility . Plant bThe above studies have shown that cytoplasmic genome variation can influence phenotypic variation. Additionally, genes underlying qualitative interactions between the nucleus and cytoplasm leading to cytoplasmic male sterility and interspecific isolation have been identified. There are, however, numerous open questions remaining about how cytoplasmic variation influences quantitative phenotypic variation. What is the level of phenotypic variation influenced by genetic variation in the cytoplasm in comparison to individual nuclear loci? How much epistatic interaction is there between genetic variation in nuclear loci and the cytoplasmic genomes? What is the breadth of phenotypes that might be influenced by cytoplasmic variation?To begin answering these questions, we utilized metabolomics to investigate how genetic variation in the cytoplasmic and nuclear genomes interacts to control metabolome variation in the reciprocal Arabidopsis Kas × Tsu recombinant inbred line (RIL) population . We focuWe measured the metabolome within the Kas × Tsu RIL population to test how cytoplasmic variation can affect quantitative variation within the metabolome. This population was generated from a reciprocal cross and approximately half of the resulting lines carry Kas organelles while the other half carry Tsu organelles allowing for explicit analysis of the influence of cytoplasmic genetic variation . AnalysiA. thaliana metabolome, we identified and measured metabolite levels, using non-targeted GC-TOF-MS, in leaf tissues of 316 lines of the Kas × Tsu A. thaliana RIL population harvested with fourfold replication across two separate experiments. Within the 316 lines for this population, 136 have the Kas cytoplasm and 180 have the Tsu cytoplasm. A total of 2435 metabolites were identified in over 25% of the RILs with 215 of these being known compounds and 2220 being unidentified compounds. Of these 2435 metabolites, 559 were identified in both experiments (161 known and 398 unknown) while the rest were specific to one of the two experiments.To partition phenotypic variance between the effects of the nuclear and cytoplasmic genomes upon the Classical breeding studies utilize reciprocal crosses with linear modeling to partition heritability between the nuclear and cytoplasmic genomes . In lineWe next moved beyond the classical line heritability approach and directly test if cytoplasmic variation may have similar effects to individual nuclear loci. We mapped QTLs in the Kas × Tsu RILs controlling the mean accumulation of all 2435 measured metabolites (215 known and 2220 unidentified compounds) using 1069 markers with a median spacing of 0.35 cM  Jansen,. This idTo compare nuclear and cytoplasmic genetic variation effects upon metabolism, we utilized these metabolomic QTL hotspots to develop an additive model. This model uses the genetic marker at the center of each metabolomic QTL hotspot as separate terms and also incorporates the cytoplasmic variation as an additional term equivalent to each nuclear locus. We used this additive model to directly test all QTL hotspot-metabolite linkages and obtain the mean effect of variation at each hotspot on the metabolome . For allWe next proceeded to use the additive model to directly compare the role of cytoplasmic genome variation to that of individual nuclear loci in controlling metabolome variation . In compUsing the additive model, we generated per locus estimates of heritability that showed the cytoplasmic genome explained twice the variance as any individual nuclear locus on average . InteresrpoC2 in the plastid, several unknown genes, and key energy genes, such as Rubisco large subunit. The most striking changes were the large number of polymorphisms within the NADH deyhdrogenases in both the mitochondria and the plastid  . The M.IThe large number of significant epistatic interactions between nuclear and cytoplasmic genetic variation forms a cohesive network but the network approach does not let us visualize or directly quantify the effects of each locus in an epistatic pair. Thus, we wanted to develop a better approach to visualize and compare epistatic effects . We utilTo compare the role of each locus in a pairwise epistatic interaction, we plotted the phenotypic center for only the metabolites that showed significant epistasis for each pairwise interaction in our pairwise marker model analysis . For allThe above analysis showed that the cytoplasmic genetic variation plays an important role in mediating variation within the plant metabolome. To quantify how much the inclusion of the cytoplasm improved the genetic models in describing metabolomic variation, we analyzed our additive and pairwise epistasis model models with and without the cytoplasmic terms. For each metabolite for each model, we estimated the percent of variance explained by the significant terms in the model . This sht-test p<0.001).The epistatic network diagram showed that there were several instances of triangles where two nuclear loci showing pairwise epistasis also interacted with the cytoplasmic variation . This coTo examine how cytoplasmic genetic variation influences nuclear epistasis we visualized all significant three-way interactions using the phenotypic center approach, . This shEven though maternal contribution to complex phenotypes has long been suspected, most previous genomic surveys of natural variation using transcriptomics or metabolomics have either not had the capacity to directly assess the influence of cytoplasmic genetic variation or just ignore it completely. Thus, we used the reciprocal Kas × Tsu Arabidopsis RIL population to directly quantify the role of cytoplasmic genetic variation in quantitative variation of metabolomics traits. Our analysis showed that the cytoplasmic genome variation affected the phenotypic variation for over 80% of metabolites. The affected metabolites included key parts of central metabolism and some of the most specialized metabolites . InteresWe also identified a high level of significant epistatic interaction between cytoplasmic genetic variation and nuclear genetic variation, as cytonuclear epistasis . This cyThe effect of the cytoplasmic genetic variation was spread out across nearly all of primary metabolism making it impossible to ascribe a causal link with solely plastidic or mitochondrial genes . SimilarThe plant cytoplasmic genomes contain only about 1% of the number of genes as found within the nuclear genome . Yet genIn this work, we report a first genomic survey of how genetic variation within cytoplasmic genomes influences metabolomic variation. Cytoplasmic genetic variation alters metabolite variation with effects that are equivalent to, if not greater than, individual nuclear loci. More importantly, the cytoplasmic background significantly influences the ability to detect epistasis between nuclear loci. Thus cytoplasmic genomes should be included in any future analysis of natural variation, either by being included as a genotype in GWA studies or by designing future populations as reciprocal populations to allow for direct analysis of the cytoplasmic genomic variation in controlling the phenotype. This inclusion will allow direct assessment of how cytoplasmic genomic variation influences other phenotypic classes, such as transcriptomics or broader physiological phenotypes. Natural genetic variation in the organellar genomes while frequently ignored will have to be kept at the front of future experimental approaches designed to understand the evolution and genetic architecture of organismal phenotypes.Seeds of the 341 lines of the Kas × Tsu recombinant inbred population were obtained from the Arabidopsis Biological Resource Center  . We grewhttp://fiehnlab.ucdavis.edu/Metabolite-Library-2007; 31 days after sowing, we harvested plants for metabolomics analysis. One leaf from the first fully mature adult leaf pair of each plant was removed and ground in extraction solution as previously described . Metabol2g/σ2p , where σ2g was estimated for both the RIL genotypes and cytoplasmic genotypes and σ2p was the total phenotypic variance for a trait (gmeb) was: c = the Kas or Tsu cytoplasm; g = the 1…316 for the 316 RILs, e = experiment 1 or 2 and b = block 1…8 nested within experiment. This allowed cytoplasmic effects to be directly tested in the C term and each RIL genotype (G) nested within the appropriate cytoplasmic class, either Kas or Tsu. Experiment and block nested within experiment were treated as random terms within the model to better parse the variation. All resulting variance estimates, p values and heritability terms are presented (2g for RIL was pulled from the Gg(Cc) term while σ2g for cytoplasmic variation was pulled directly from the CcMm term. We used mean values for the RILs for further analysis as we had a randomized complete block design with no missing lines. Additionally, means and LSmeans were correlated with an average r2 of 0.96 for the 159 known metabolites present in both experiments.All RIL lines were represented in every block in both experiments creating a perfectly balanced randomized complete block design. All phenotypic data was used to calculate estimates of broad-sense heritability (H) for each phenotype as H = σ a trait . The ANOresented . σ2g forWe the previously reported genetic map for these lines of the Kas × Tsu RIL population . To deteQTL clusters were identified using a QTL summation approach where the position of each QTL for each trait was plotted on the chromosome by placing a 1 at the peak of the QTL. This was then used to sum the number of traits that had a detected QTL at a given position using a 5 cM sliding window across the genome . The QTLg at marker m was shown as ygm. The model (Additive Model) for each metabolite in each line (ygm) was: g = Kas(1) or Tsu(2); m = 1, …,14. The main effect of the markers was denoted as M involving 15 markers (m). The cytoplasmic genome was included as an additional marker to test for cytoplasmic genome effects. We tested all metabolites with the appropriate model using lm function implemented in the R/car package, which returned all p values, Type III sums-of-squares for the complete model and each main effect. QTL main-effect estimates  were estimated for each marker  for each metabolite in each line (ygm) was: g = Kas(1) or Tsu(2); m = 1, …,14 and n was the identity of the second marker for an interaction. The main effect of the markers was denoted as M having a model involving 15 markers. The cytoplasmic genome was included as an additional single-locus marker to test for interactions between the cytoplasmic and nuclear genomes. p values, Type III sums-of-squares for the complete model and each individual term and QTL pairwise-effect estimates in terms of allelic substitution values were obtained as described for additive model ANOVA  of all the metabolites significant for an interaction were plotted to visualize the distribution centers of phenotype for each pairwise interaction.To plot the epistatic effect of QTLs upon a set of metabolites, we utilized the center of mass calculations. To do this we transitioned the physical distance metric in center of mass to a genetic distance metric for mapping the center of phenotype. In this, we classify one locus of each interaction as being on the x-axis and the other locus being positioned on the y-axis. On each axis, the allelic value of each specific genetic locus is plotted in relation to the heterozygote. For instance, in a two QTL situation the x-axis would be the alleles of QTL1 with the Kas having an allelic value of 1 and the Tsu having an allelic value of −1 while the other axis would be the same for QTL2 there by positioning each of the four homozygous genotypic class in one of the four quadrants. For each metabolite, the center of phenotype was calculated using center of mass calculations as www.ncbi.nlm.nih.gov/, accessions SRX246466 and SRX246442 respectively) and aligned using Bowtie2 (www.arabidopsis.org/) (http://picard.sourceforge.net) and the Genome Analysis Toolkit (GATK) (Kas-1 and Tsu-1 reads were obtained from NCBI ( Bowtie2  to the Cis.org/) . Alignedis.org/) , Picard t (GATK) . SNP dist (GATK) . review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.eLife posts the editorial decision letter and author response on a selection of the published articles . An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent  The authors’ explanation for the average heritability due to the organellar genome being much lower than the one coming from the nuclear genomes seems reasonable. However, both reviewers had a hard time trying to understand why there are apparently no metabolites that show cytoplasmic heritability greater than 0.15. Two different models were used to estimate nuclear and cytoplasmic heritability, but why? Along these lines, how do cytoplasmic and nuclear heritability compare for the metabolites significant for both? And on a related note, please explain why significant effects of the nuclear genome were estimated by partitioning the variance across 316 RIL genomes. These are not independent: surely you want the estimates produced by linkage mapping? Finally, that the complete cytoplasmic genome has a larger effect than individual nuclear loci  does not2) A substantial criticism is that the authors do not tell us anything about sequence differences in the organellar genomes of the RIL parents. The short read data are available, so it would not be too much of a burden to determine how many coding variants there are, and how the distribution of coding variants compares between biosynthetic genes in the organellar and nuclear genomes. We note that the Discussion states that differences have been found in the organellar genomes.3) You discuss whether RILs have less phenotypic variation because they have less genetic variation. You write “A common concern of RIL populations is that they only sample two alleles per locus and thus might be limited in their genetic variation relative to species-wide diversity .” This may or may not be common concern, but it is not the chief one, in our opinion, and it is also not the point made in the papers cited. As far as one can tell, Kim et al. (2007) does not discuss this issue at all, and Nordborg and Weigel (2008) make a completely different point, namely that RILs have greater power to detect rare alleles of large effect that “may not be important from an evolutionary perspective”. This is central to your paper because of the very real possibility that the observed QTL hotspots (which mostly differ from another RIL population) are due to rare alleles of large effect, which may well be deleterious. This does not invalidate the results, but changes their interpretation, in particular with respect to their evolutionary significance.4) There is little consideration of existing knowledge of the contribution of organellar biosynthesis steps to metabolic pathways. An important question is whether metabolites that are known to be made in organelles are more likely to be affected by variation in the organellar genomes than those that are not.Finally, the authors make the important point that the organellar genotypes would add greatly to GWA studies. We agree. Since the authors have metabolome data for 96 accessions , one wonOverall, the clarity of the manuscript should be improved considerably. The text is replete with jargon and technical terms that are not properly introduced. That the models used are not always clearly stated also contributes to the paper being hard to read. The main model(s) need to be in the main text, so it is clear where the results come from. Starting with the title, “control” is clearly too strong.We have changed the title to reflect influence rather than control. Additionally, we have worked to better caveat the work throughout to reflect the link to quantitative analysis of organelles in a genomic phenotype.First, the authors should spell out what fraction of the genetic variation is attributable to cytoplasmic variants, what fraction is due to C×G interactions, and how does this compare to straight G effects?We have worked to make this clearer by dissecting all variance components into the individual main effect (nuclear v cytoplasmic) and epistatic (cytonuclear v nuclear x nuclear) and included this in the description to help with the interpretation of our results. This is also specifically shown in Figure 6–figure supplement 1 where we parse genetic variation to each specific term of main effect or interaction for all metabolites.Second, how representative the findings of the paper are of other phenotypes remains unknown, and the authors should be more circumspect when extending their claims to phenotypes that might have no or only a very indirect connection to metabolites.We have worked to better lay out that while this manuscript focuses on metabolomic variation, further work is required to test how this extends to other phenotypes. As a respectful point, we find it hard to imagine a phenotype that has no, or even an indirect connection to metabolites given the fundamental basis that metabolism plays in providing the energy and structure for any other phenotype to properly occur.Furthermore, both reviewers found the paper hard to followthe presentation needs to be greatly simplified, so that the important points come across better.We have worked to improve the writing and hope that this has been achieved.Specific criticisms:1) The authors’ explanation for the average heritability due to the organellar genome being much lower than the one coming from the nuclear genomes seems reasonable. However, both reviewers had a hard time trying to understand why there are apparently no metabolites that show cytoplasmic heritability greater than 0.15. Two different models were used to estimate nuclear and cytoplasmic heritability, but why? Along these lines, how do cytoplasmic and nuclear heritability compare for the metabolites significant for both? And on a related note, please explain why significant effects of the nuclear genome were estimated by partitioning the variance across 316 RIL genomes. These are not independent: surely you want the estimates produced by linkage mapping? Finally, that the complete cytoplasmic genome has a larger effect than individual nuclear loci  does not seem surprising, given that the mtDNA and cpDNA represent contain dozens of genes.We are slightly confused by the first question as the analysis in question used a single model to estimate nuclear and cytoplasmic heritability that is shown in We are unsure as to why no metabolites had a cytoplasmic heritability above 0.15 using this analysis but this is what the data showed and by doing the classical approach we can now show that this number is misleading based upon the ensuing linkage mapping. To also help with the analysis, we have provided locus and interaction specific estimates of heritability (per locus/interaction R2) that is now discussed in the section on epistatic interactions. This analysis is shown in Figure 6–figure supplement 1. This analysis shows that if we parse the nuclear genetic variation into individual nuclear hotspot variation, the cytoplasmic heritability is actually greater on average than any specific nuclear hotspot.Finally, we have also mentioned in the Discussion that the organellar genomes have roughly the same number of genes as an individual nuclear locus because given the genetic resolution of recombination these loci still represent a region of >100 genes.2) A substantial criticism is that the authors do not tell us anything about sequence differences in the organellar genomes of the RIL parents. The short read data are available, so it would not be too much of a burden to determine how many coding variants there are, and how the distribution of coding variants compares between biosynthetic genes in the organellar and nuclear genomes. We note that the Discussion states that differences have been found in the organellar genomes.We have obtained suitable short reads and provided a list of polymorphisms between the Kas and Tsu mitochondria and organelle as Figure 7–source data 1. This has been added into the section on cytoplasmic effects along with a commentary on how the changes are focused on NADH related metabolic genes, which would explain the widespread consequences in the metabolic grid of the organellar genetic variation because NADH is central to nitrate assimilation, the GOGAT cycle, lipid metabolism, and any process involving a cytochrome P450.3) You discuss whether RILs have less phenotypic variation because they have less genetic variation. You write “A common concern of RIL populations is that they only sample two alleles per locus and thus might be limited in their genetic variation relative to species-wide diversity .” This may or may not be common concern, but it is not the chief one, in our opinion, and it is also not the point made in the papers cited. As far as one can tell, Kim et al. (2007) does not discuss this issue at all, and Nordborg and Weigel (2008) make a completely different point, namely that RILs have greater power to detect rare alleles of large effect that “may not be important from an evolutionary perspective”. This is central to your paper because of the very real possibility that the observed QTL hotspots (which mostly differ from another RIL population) are due to rare alleles of large effect, which may well be deleterious. This does not invalidate the results, but changes their interpretation, in particular with respect to their evolutionary significance.We have worked to better clarify this section to reflect both the power and rarity concern. The specific paragraph in question now attempts to show that while the RIL population may be susceptible to the rare allele issues, we have similar if not greater phenotypic variation than the accessions, meaning that we actually have better power to detect loci and interactions.4) There is little consideration of existing knowledge of the contribution of organellar biosynthesis steps to metabolic pathways. An important question is whether metabolites that are known to be made in organelles are more likely to be affected by variation in the organellar genomes than those that are not.We have added in a commentary in the first results section on the organellar variation of how most metabolites, even those specifically synthesized in a single compartment, are then transported throughout the plant cell even from one organelle to the other. Additionally, a number of metabolites are made in multiple compartments including the organelles and the cytosol, as such ascribing individual compartmental function is not as straightforward as is required for a hypergeometric test or the like. Additionally, our extraction protocol cannot differentiate between the different pools within a cell. Given that nearly all primary metabolites are influenced by the organellar genomic variation this analysis doesn’t have the power to refine the mechanistic basis of this change.Finally, the authors make the important point that the organellar genotypes would add greatly to GWA studies. We agree. Since the authors have metabolome data for 96 accessions , one wonders how much effort it would be to download existing read data, identify polymorphisms in the mitochondrial and chloroplast genomes, and include them in the GWA analysis.  Such an analysis would greatly elevate the study and the authors are strongly encouraged to consider this very seriously.We agree that this would be nice, but for several reasons we feel that this is more appropriate for a follow-up study. The first is technical in that the available short read data were largely made with protocols to enrich the nuclear genomic DNA at the cost of the organellar sequences and as such, we had to identify specific Kas and Tsu samples prepped with a different protocol. The other available short read archive sequences did not provide us sufficient coverage on the organellar genomes to call polymorphisms. The second reason is genetic in that all published literature on the Arabidopsis organellar genetic variation using targeted gene analysis shows that the organelles do not show any evidence of independent assortment and instead they behave in a more clonal fashion which greatly complicates any potential for GWA as the entire organelles are essentially within complete LD. The final reason is for clarity, as the reviewers have rightly noted, we need to improve the manuscript’s clarity and adding a completely additional section on accessions and the organelles would require the equivalent of a full manuscript’s worth of analysis to assess the link between the organelle and population structure, LD, and then finally GWA with metabolites. Thus, we feel that this request is an excellent foundation for another complete manuscript, but it would not help to clarify this manuscript mechanistically, genetically, or editorially.Overall, the clarity of the manuscript should be improved considerably. The text is replete with jargon and technical terms that are not properly introduced. That the models used are not always clearly stated also contributes to the paper being hard to read. The main model(s) need to be in the main text, so it is clear where the results come from.We have worked throughout to better clarify the text and more explicitly link to the proper model.


CLUSTER”), which is extended from the adaptive combination of P-values. Our method combines the association signals of variants that are more likely to be causal. Furthermore, the statistic incorporates the spatial information of variants. With extensive simulations, we show that our method outperforms several commonly-used methods in many scenarios. To demonstrate its use in real data analyses, we also apply this CLUSTER test to the Dallas Heart Study data. CLUSTER is among the best methods when the effects of causal variants are all in the same direction. As variants located in close proximity are more likely to have similar impact on disease risk, CLUSTER is recommended for association testing of clustered rare causal variants in case-control studies.Biological evidence suggests that multiple causal variants in a gene may cluster physically. Variants within the same protein functional domain or gene regulatory element would locate in close proximity on the DNA sequence. However, spatial information of variants is usually not used in current rare variant association analyses. We here propose a clustering method (abbreviated as “ The development in next-generation sequencing technologies has allowed a comprehensive investigation of the role of rare variants  <1%) on complex diseases IL-K” because it is extended from the popular Kulldorff scan statistic P-values Ionita-Laza et al. KERNEL” hereafter). The statistic is P-values. Schaid et al. IL-K outperforms KERNEL over a range of clustering scenarios, but KERNEL takes approximately half the computational time of IL-K.Schaid et al. P-values P-values which are more likely to be neutral variants. With extensive simulations, we have shown that our method outperforms KERNELWS”) VT”) IL-KSKAT) We here propose a clustering method that is extended from the adaptive combination of K variant sites in a region of interest. We name the sites with larger variant frequencies in cases than in controls “deleterious-inclined variant sites”, and those with larger variant frequencies in controls than in cases “protective-inclined variant sites”. For a case-control study, the association of each variant with the disease status can be tested by the Fisher's exact test P-values of the K variants be P-values that are smaller than some truncation threshold. Suppose we consider J candidate truncation thresholds, Suppose that there are P-values jth truncation threshold , and P-value of the ith site is smaller than the jth truncation threshold th element of ith and the jth variants, and The ures see .jth truncation threshold, a test statistic regardless of the directions of effects (deleterious or protective) is B permutations by randomly shuffling the case/control status, we obtain the permuted statistics P-value of the observed statistic P-value of the J candidate truncation thresholds, the minimum P-value of the observed sample is P-value of the B permutations, we compare P-value” is estimated by CLUSTER”, as it is proposed for detecting clusters of rare variants.Under the If we ignore the spatial information and let P-values for rare variant association testing” (abbreviated as “ADA”) This is equivalent to the statistic of the “adaptive combination of To simulate real human genomic structure, we used the Cosi program jth causal variant, its genotype relative risk (GRR) is:jth causal variant is protective, and is 0 otherwise. The genotypes of a subject were formed by two chromosomes randomly drawn from the pool of 10,000 chromosomes. For a subject with chromosomes jth site. Chromosome pairs were randomly drawn from the chromosome pool with replacement until 500 cases and 500 controls were recruited.Given PAR . As a representative method of non-burden tests, SKAT was also included into comparisons. SKAT was implemented with the R package “SKAT” jth variant site . When all the 20 causal variants were deleterious, IL-K, SKAT, and CLUSTER were again the more powerful methods. Note that the effect size (measured by the magnitude of odds ratio) of a deleterious variant was larger than that of a protective variant with the same PAR and MAF  relative to that of the methods without spatial information , in clustered situation or in non-clustered situation.In CLUSTER, IL-K, and KERNEL). They were relatively  more powerful when the causal variants were clustered  of a protective variant was smaller than that of a deleterious variant with the same PAR and MAF  in plasma triglyceride levels. The genotypes of 1,045 European Americans were analyzed. We first used a linear regression to adjust the log-transformed triglyceride levels for age, sex, and BMI. Subjects with residuals smaller than the 30th percentile and larger than the 70th percentile were treated as controls and cases, respectively. Then, the subjects with missing genotypes were excluded from the analysis. Finally, 179 cases and 213 controls were left.These six tests were then applied to the Dallas Heart Study IL-K was set as the total region length (∼10 kb). As a result, only CLUSTER and SKAT had P-values smaller than 0.05  to have low power when all the causal variants were protective. No wonder they failed to detect the association here. This result is consistent with the finding from our simulation study.The significant association of KERNEL usually has lower power than IL-K. However, when all the causal variants are protective, IL-K has very low power  is P-values, except SKAT that uses the Davies method P-values. For simulated data sets each containing 500 cases and 500 controls in ∼20 kb regions (including ∼330 nonsynonymous variant sites), the computation time lengths were ordered as CLUSTER (∼151.7 sec) > SKAT (∼30.2 sec) > IL-K (∼20.4 sec) > KERNEL (∼6.7 sec) > VT or WS (∼3.4 sec), where 1000 permutations were used for all the methods except SKAT. This was timed by a Linux workstation with an Intel Xeon E5-2690 2.9 GHz processor and 6 GB memory. CLUSTER takes a longer time to compute because it incorporates the spatial kernel matrix into the search of the optimal P-value truncation threshold.All the methods evaluated here require permutations to obtain accurate et al.IL-K and KERNEL could have higher power than SKAT, when the variants were correlated. Without correlation, SKAT tended to have the highest power among the tests they compared SKAT is better than KERNEL (and sometimes better than IL-K).Schaid KERNEL and CLUSTER have similar forms in test statistics  of variants that are more likely to be causal, i.e., truncates variants with larger P-values. CLUSTER is among the best methods when the effects of causal variants are in one direction. As variants located in close proximity are more likely to have similar impact on disease risk CLUSTER is recommended for association testing of clustered rare causal variants in case-control studies.


N = 2,417) from the European Prospective Investigation of Cancer (EPIC)-Norfolk study, a region in FTO was found to have stronger association (rs7204609∼rs9939881 at the first intron P = 4.29×10−7) than single SNP analysis  and a latent quantitative phenotype was obtained using a subset sample of EPIC-Norfolk . We believe our method is appropriate for assessment of regional association and polygenic effect on a single or multiple traits.Genetic association studies are now routinely used to identify single nucleotide polymorphisms (SNPs) linked with human diseases or traits through single SNP-single trait tests. Here we introduced partial least squares path modeling (PLSPM) for association between single or multiple SNPs and a latent trait that can involve single or multiple correlated measurement(s). Furthermore, the framework naturally provides estimators of polygenic effect by appropriately weighting trait-attributing alleles. We conducted computer simulations to assess the performance via multiple SNPs and human obesity-related traits as measured by body mass index (BMI), waist and hip circumferences. Our results showed that the associate statistics had type I error rates close to nominal level and were powerful for a range of effect and sample sizes. When applied to 12 candidate regions in data ( Current genetic association studies in humans, including genome-wide association studies (GWASs) We set to exploit association between multiple SNPs and multiple traits through a latent variable partial least squares path modeling (PLSPM) N = 2,566) was a random sample of the study cohort at baseline and cases were part of the remaining individuals with BMI≥30 kg/m2 . A total of 2,417 individuals in the subcohort and 1,135 cases with 446,861 SNPs passed quality control and in silico genotypes were obtained according to HapMap (http://www.hapmap.org) NEGR1 (rs3101336), SEC16B (rs10913469), TMEM18 (rs6548238), ETV15 (rs7647305), GNPDA2 (rs10938397), BDNF (rs925646), MTCH2 (rs10838738), SH2B1 (rs7498665), FAIM2 (rs7132908), FTO (rs1121980), MC4R (rs17782313), and KCTD15 (rs369784).Participants in the EPIC-Norfolk study were men and women aged between 45 and 74 from Norwich and the surrounding towns and rural areas http://en.wikipedia.org/wiki/Body_shape.The influence of body fat distribution has been linked with body shape named crudely after the fruits and vegetable(s) they resemble most As hinted earlier, our framework resembles structural equation modeling (SEM) with three types of parameters defined: (1) Latent variable scores  SNP set .CEU data at the brain-derived neurotrophic factor (BDNF) region (Chr 11∶27633610..27692970 with 24 SNPs) were used to generate the simulated genotypic data; (2) Based on (1), a large sample of 500,000 individuals was obtained via software gs 2.0 th SNP being the causal variant; (3) Quantitative genetic data was generated according to a trivariate normal distribution . Assume that the causal SNP had no effect on body shape , and quantitative genetics models with the given δ were created by the R mvtnorm package. The window size had 10 SNPs from the 3th to the 12th SNP. Under H0, 10,000 simulations given various sample sizes were conducted to assess the type I error. Under H1, for each model and a given δ, 10,000 simulations were conducted under various sample sizes to assess power. The procedures were implemented with Linux and the R plspm package. Both mvtnorm and plspm packages are available from CRAN. (http://cran.r-project.org/)Simulations were conducted as follows: (1) HapMap phase II α-level was defined as Scan statistics were built through the subcohort for association between the 12 regions and body shape, and to contrast with a SNP-wise single trait test performed by linear regressions (δ), or nominal level (α) (2c–2f). Even with a very small α, for effect size greater than 0.15 and the sample size of up to 4,500, the scan statistics remained to have >80% power .As shown in The model provided the usual association results for single trait adjusted for sex and age including effect size estimate, proportion of variance explained and statistical significance. −4 level according to single-SNP –single-trait tests nor according to sliding window sizes of 1–4 SNPs at the 10−5 level, but smaller p values were obtained for window sizes of 5–11 and 12–15 SNPs. Of particular interest was rs7204609∼rs9939881 at the first intron of FTO with P = 4.29×10−7 for a sliding window of size 10; its model structure is shown in As shown in SNP⋅21β) (95%CI) per allele on body shape was 0.08 . The proportion of variance explained was 0.8% by PRS. All genetic variants showed associations with body shape, though some loadings of the SNPs were not significant at α = 0.05 (FTO) and rs925646 (BDNF) for all the four traits, followed by rs6538238 (TMEM18), rs17782313 (MC4R) for BMI and hip; rs17782313 (MC4R), rs7132908 (FAIM2) for waist and body shape. Non-standardized effect sizes were largest with rs1121980 (FTO) (0.39), but smallest with rs7647305 (ETV5) (0.05)  of 2.28 (7.91×10−24).Shown in χ2 = 1556.8, P<.0001), especially in types 4, 5, 6, 9, 2, 3; (2) for both men and women, along with the risk of obesity, body shape score was seen to be monotonically increasing from types 1 to 9 . Linear regression between the scores and types had good fit for men  and women   , suggest = 0.74) ; (4) The = 0.74)  in both A latent variable PLSPM framework is outlined for association of multiple SNPs with multiple traits, the behavior of such an association was investigated by simulation study through type I error rate and power. Meanwhile, a polygenic statistic was developed for quantification of a polygenic effect by appropriately weighting trait-attributing alleles. These methods were applied to the study of obesity-related variables in the EPIC-Norfolk study for which a latent score was obtained. Below we compare these with available methods, discuss implications of our findings as with other issues involved and indicate some further work.Compared to SEM, PLSPM is robust to multicollinearity commonly encountered in GWAS data (such as strong linkage disequilibrium between SNPs and high correlation between traits). It is a “soft modelling” approach requiring very few distributional assumptions, variables can be numerical, ordinal or nominal, and no need for normality assumptions, while covariance-based SEM is a “hard modeling” with heavy distributional assumptions FTO gene is of interest, as with some of the reported obesity-susceptibility SNPs near or in the 12 genes Analysis of the EPIC-Norfolk discovery sample involving 12 gene regions suggested that the scan statistics are more powerful than single SNP – single trait tests with the size 10 providing the strongest evidence. In particular, the region (rs7204609∼rs9939811) within the first intron 1 of A reviewer has indicated previous work on multiple linked quantitative trait loci (QTLs) A reviewer has questioned the adequacy of body shape as with PLS with a view that body share should be supported by various other measurements such as limb lengths, shoulder widths, etc. However, our interest lies more in utilizing the anthropometric traits from a population study for investigation of health risks. Indeed our results showed that BSS is approximately normal  and servhttp://www.broadinstitute.org/collaboration/giant/index.php/Main_Page) teleconference, a colleague instantly questioned the feasibility across the whole consortium. Secondly, the scan statistics seemed slightly anticonservative and a parametric counterpart is preferable. Thirdly, it will be desirable to catch both linear and nonlinear effects between genome region and latent quantitative trait.There will be several lines of further research. Firstly, there is an important need to examine the precise nature of regional or polygenic effect on a single trait or a collection of traits, as it may involve both polygenic and pleiotropic effects. This is also the case with GWAS. Long before this work when we reported work using SEM to differentiate pleiotropic effect on obesity-related traits in a GIANT consortium  as with distribution of their PRS and cumulative effects of these variants .(TIF)Click here for additional data file.Figure S2The distribution of body shape score (BSS).(TIF)Click here for additional data file.Table S1Nine types of human body shape defined by BMI combination with WHR.(DOC)Click here for additional data file.Table S2Loadings, P values, indirect and overall effects of 12 SNPs and PRS on BMI, waist and hip with adjustment for sex and age.(DOC)Click here for additional data file.Information S1Some theoretical results.(DOC)Click here for additional data file.Information S2Single trait results from the EPIC-Norfolk replication sample.(DOC)Click here for additional data file.


Genetic selection for host resistance offers a desirable complement to chemical treatment to control infectious disease in livestock. Quantitative genetics disease data frequently originate from field studies and are often binary. However, current methods to analyse binary disease data fail to take infection dynamics into account. Moreover, genetic analyses tend to focus on host susceptibility, ignoring potential variation in infectiousness, i.e. the ability of a host to transmit the infection. This stands in contrast to epidemiological studies, which reveal that variation in infectiousness plays an important role in the progression and severity of epidemics. In this study, we aim at filling this gap by deriving an expression for the probability of becoming infected that incorporates infection dynamics and is an explicit function of both host susceptibility and infectiousness. We then validate this expression according to epidemiological theory and by simulating epidemiological scenarios, and explore implications of integrating this expression into genetic analyses.Our simulations show that the derived expression is valid for a range of stochastic genetic-epidemiological scenarios. In the particular case of variation in susceptibility only, the expression can be incorporated into conventional quantitative genetic analyses using a complementary log-log link function (rather than probit or logit). Similarly, if there is moderate variation in both susceptibility and infectiousness, it is possible to use a logarithmic link function, combined with an indirect genetic effects model. However, in the presence of highly infectious individuals, i.e. super-spreaders, the use of any model that is linear in susceptibility and infectiousness causes biased estimates. Thus, in order to identify super-spreaders, novel analytical methods using our derived expression are required.We have derived a genetic-epidemiological function for quantitative genetic analyses of binary infectious disease data, which, unlike current approaches, takes infection dynamics into account and allows for variation in host susceptibility and infectiousness. Infectious diseases constitute the number one threat to livestock production, with potential devastating implications for food security and human health. With the rapid accumulation of data on the genetic regulation of host responses to infectious pathogens, the drive towards strategies that control genetic disease is gaining momentum. Genetic approaches to combat infectious disease tend to focus on improving host resistance, i.e. the ability of a host to block pathogen entry or to counteract pathogen replication within the host. However, despite enormous breakthroughs in genomics, estimating genetic parameters for disease resistance has proven considerably more challenging than analysis of production traits, and this has hampered the incorporation of disease traits into breeding programmes. These challenges partly arise because disease resistance is not a trait that is directly measurable but relies on observable proxies. Due to the requirement of large sample sizes for quantitative genetic analyses, such proxies are often obtained from field data, which are typically binary, indicating whether an individual has become infected or not .Current quantitative genetic methods analyse binary infectious disease data essentially by contrasting the set of individuals diagnosed as infected to those diagnosed as non-infected, assuming that the observed phenotypic differences represent differences in host resistance to the pathogens under consideration . HoweverAll of the above characteristics that are inherent to natural disease outbreaks are likely to affect estimates of genetic parameters for disease traits. Indeed, we have previously demonstrated that conventional quantitative genetics models fail to capture host genetic variation in infectiousness, if present ,4. FurthTherefore, the aim of this study was to derive an analytical expression for the probability of an individual to become infected within a given time period. We demonstrate how this can be achieved by integrating fundamental principles of epidemiology into the quantitative genetics framework. We then validate this analytical expression by comparing it with established theory in the case of homogeneous populations and by using simulated disease data generated for a range of epidemiological scenarios in genetically heterogeneous populations. Finally, we examine the implications for implementing this probability function into quantitative genetic analyses.R0, defined as the expected number of secondary infections that one infectious individual causes in an otherwise susceptible population  during which the infection status of infectious individuals does not change is therefore,The probability Pj(t) be the probability of individual j, which was susceptible at time zero, to have become infected by time t. Then for a small time-step δt,Let t. Rearranging the above equation, dividing by δt and taking the limit δt → 0 leads toNote, that this equation may encompass single and repeated infections  within the time interval from 0 to Note that the expression for δt → 0, leads toUsing the power series expansion of the exponential function, and dividing by δt and taking the limit using the approximation ln(1 − x) ≈ − x  for small x. Substituting this last expression into the differential equation (5) yieldsNow, defineso thatMultiplying both sides of (10) so that by orHence, the solution of the differential equation (10) isPj(0) can be estimated as the prevalence at the beginning of an observation period. For simplicity, however, from now on we will assume that Pj(0) = 0 and hence,The probability Λj(t) defined above can be written asNote that the quantity Dk(t) denotes the duration of time within the interval  during which individual k is infectious. Thus, if k has not become infected by time t, Dk(t) = 0, otherwisewhere m denotes the number of times that individual k got infected during  and where j(t) defined in (15) were carried out. First, we assessed whether in the extreme case of zero heterogeneity in susceptibility and infectiousness, the derived function is consistent with existing epidemiological theory. Second, the function was validated with binary disease data (infected or not infected) generated by simulated stochastic epidemics in closed genetically heterogeneous populations of constant size, as described in detail in [Two forms of validation of the above derived probability function given by equation 14) with Λetail in ,4. Two m with Λetetail in . Here, tn individuals and provides the disease status of individuals (infected/not infected) over time as output. The epidemic was simulated as a Poisson process, starting with one randomly chosen infected individual per group. The times at which subsequent infection and recovery events occurred and which individuals were affected were determined by the pairwise transmission parameters βjk(t) and by the recovery rates γj(t), respectively, as outlined below. It was assumed that infected individuals became immediately infectious and remained infectious until they recovered. No transmission was assumed between groups.The stochastic epidemiological model used for validation simulates disease progression in isolated groups of j its own level of susceptibility gj and infectivity fj. The dynamic, pairwise transmission parameter βjk(t) was then calculated as:Individual variation in host susceptibility and infectiousness was first incorporated into the model by assigning for each individual βjk(t) encapsulates the contact rate and the transmission probability. To reflect whether susceptibility and infectivity are expressed at time t, the individual constants gj and fk are scaled by Xg,j(t) and Xf,k (t), respectively, which are equal to 1 if j is susceptible at time t and if k is infectious at time t, respectively, and 0 otherwise. Similarly, individual recovery rates were assumed to be equal to γj(t) = Xf,j(t)γj, with γj and Xf,j (t) as defined above.as derived in . Thus, ij was set equal to 0.1 for all individuals. For simplicity, it was further assumed that the expected number of contacts per unit time interval between two individuals in the same group was homogeneous and, without loss of generality, was set equal to cjk = 1. This homogeneity assumption is likely to be satisfied in intensive farming conditions. The values of βjk(t) and γj(t) were calculated at each event time, starting from time zero. Based on these, Gillespie’s direct algorithm was used to determine the next event (infection or recovery), the time of the event and the affected individuals, as outlined in [t at which approximately 50% of individuals had become infected.It was initially assumed that host susceptibility and infectivity were the only sources of individual variation. Thus, parameter γlined in . The simβjk(t), as described above. Similarly, all other individual transition speeds were assumed equal to a constant value for individuals in the relevant compartment and 0 otherwise. Specifically, the constants were; 0.5 for L → I, 0.1 for I → R and 0.2 for R → S. Similar to the previous simulation, it was assumed that the expected number of contacts between two individuals per time unit cjk = 1 for all individuals from the same group. This simulation was run until the same value of t as above, which resulted in approximately 58% of individuals becoming infected.In order to demonstrate that the derived probability function given by equations (14) and (15) is valid for a range of epidemiological models, binary disease data were also generated by simulating an epidemic using a stochastic SIR model with additional variation in recovery rate γ and a stochastic SLIRS model, following the same principles as described above. In a SLIRS model, the epidemiological compartments are: Susceptible (S), Latently infected but not infectious (L), Infectious (I), Recovered and temporarily immune (R), and Susceptible (S). The speed of transition between compartments S and L is given by Thus, the different epidemiological models used for simulation were (i) a SIR model with host variation in susceptibility and infectivity only; (ii) a SIR model with host variation in susceptibility, infectivity and recovery rate; and (iii) a SLIRS model with host variation in susceptibility and infectivity only.a,θ), which is representative for a variety of infectious diseases [γj from a right-skewed Gamma distribution Γ. In other words, it was assumed that most individuals recover quickly, that a few individuals may take a very long time to recover, and that the mean time to recovery was ten time units. This simulation was run until the same value of t as above, which resulted in approximately 41% of individuals becoming infected.Each model was run for a population of size N = 100 000 individuals, randomly divided into 10 000 isolated groups of size 10 chosen, which is equivalent to simulating 10 000 independent epidemics. Susceptibility and infectivity were assumed to be distributed according to a right-skewed gamma distribution Г(diseases . Moreovet) for every individual as output. Furthermore, the period of time during which each individual remained infectious (Dk) was recorded for validation purposes. Note that the duration of the infectious period D in equation (15) captures individual variation in the transmission speeds between compartments g and f, allowed calculation of the quantity Λj(t) using equation (15) and hence the probability of becoming infected by a time t, based on equation (14). This was then compared with the observed proportion of individuals that became infected by time t in the simulations, within a given class of Λj(t). The class size for Λj(t) was taken as 0.02 to ensure that sufficient records were available within each class.Each epidemiological model provided the binary disease state , infectivity , contact rate  or any of the other epidemiological parameters, equation (15) becomesWe first demonstrate that for homogeneous populations, equations (14) and (15) are consistent with existing epidemiological theory and with the method of survival analysis. In a homogeneous population, i.e. when there is no variation in susceptibility  = Xf,k(t) = 1), the transmission coefficient isAlso, following equation (16), in the case of homogeneity, for any pair consisting of a susceptible individual g and f.for small values of t, can be written asFurthermore, the sum of the infectious period of each individual in a group, within the time interval from 0 to dR/dt = γI(t), thus yielding the following for the above sum over infectious periodswhere I(τ) denotes the number of infectious individuals at time τ. In an SIR model with constant recovery rate γ, the number of recovered individuals, R, changes over time according to 0 isNote that in an SIR model, the basic reproductive ratio R0 is the number of susceptible individuals at the start of the epidemic [j(t) = Λ(t)where Sepidemic . Substitj(t) = P(t) according to equation (14)and hence for PHence, the expression for the probability of becoming infected derived, as in the paragraph “Epidemiological principles and approaches” for heterogeneous populations, i.e. equation (14), is consistent with equation (1) from epidemiological literature if there is no individual variation.t and is defined as F(t) = 1 − eΛ(t)−, where Λ(t) is the cumulative hazard function [The probability function (14) is also consistent with the notion of failure in survival analysis, where the failure function F(t) represents the probability of failure by time function . In thist in the epidemiological simulations, for a given time t and calculated values of Λj(t), as well as the analytical expression for the probability of becoming infected derived in equations (14) and (15). Figures Figure quations 4 and  and (15) as the classification criterion. According to Figure t, in a manner that is consistent with an accurate probability function, i.e. with an AUC that is close to, but not equal to, 1. Moreover, the predictive ability of the derived probability function is robust across a range of epidemiological scenarios, with an AUC between 96-97% for all simulations.Figure g and infectivity f may harbour substantial genetic variation, the duration of the infectious period D within a given time interval are more likely to depend upon a combination of various genetic  and environmental , or other stochastic factors. In order to determine the importance of estimating these components of Λj(t) for predicting the future disease status of an individual, ROC curves were also generated with the classification criterion estimated by assuming either no (genetic) heterogeneity in g and f  according to equation (17)), or by assuming genetic heterogeneity but equal non-dynamic exposure (k) in the probability function. The first scenario may be considered to be in line with current epidemiological theory, as outlined in the above paragraph “Derivation of a genetic-epidemiological probability function“ (equation (17)), whereas the second scenario may be considered to be more in line with current quantitative genetics theory that ignores dynamic exposure. Note that exact values of Dk(t) may not be available from field data and, therefore, using the further approximation from equation (20) is more in line with current epidemiological practice. However, applying this approximation results in discrete values of Dk(t) rather than a continuous curve (results not shown). Nonetheless, the resulting discrete values are close to the curve obtained without using this approximation. Figure j(t) outlined in equation (15). The ROC curves in Figure The probability function (14), with Λ(t) defined in (15), captures different sources of host (genetic) variation, which may not be easy to estimate in practice. In particular, whereas susceptibility t (1) from homogeneous to heterogeneous populations. Indeed, in line with epidemiological theory, the quantity Λj(t) described in equation (15) may be called the individual force of infection of an individual j at time t. Defining infectiousness of individual k towards individual j until time t as the product ϕjk(t) = cjkfkDk(t), as previously postulated by Lloyd-Smith et al. [j(t) to:Using mathematical principles, a genetic – epidemiological probability function was derived that links binary disease data to the underlying epidemiological traits, host susceptibility and infectiousness. The function is an extension of the established epidemiological equation for the probability of becoming infected by a time h et al. , simplifj is the product of the individual’s susceptibility and the cumulative infectiousness of its group members towards it, which reflects that an infectious disease results from interactions between susceptible and infectious individuals. Note that under the assumption that cjk = ck for each individual k, the infectiousness ϕjk(t) derived here corresponds to the individual reproductive number with population mean R0, as defined in epidemiological literature [Dk(t) during which an individual remains infected may be partly genetically determined since it encapsulates several mechanisms that are determined by the immune system, such as recovery and latency. Thus, there is potentially much to be gained by incorporating epidemiological information into genetic analyses, and vice-versa, as illustrated in Figure Thus, the force of infection for an individual terature . In the terature , the indThe concept that an individual’s phenotype is not only controlled by its own genes but also by the genes of interacting individuals is not new in quantitative genetics, and has already been successfully incorporated in the form of indirect (or associative) genetics effect (IGE) models -22. We hj(t) (equation (14) with Λj(t) defined in equation (23)), the parameters of interest, i.e. the epidemiological traits susceptibility and infectiousness, enter in a multiplicative rather than in a linear manner. However, if there was genetic variation in susceptibility only, it follows from equations (14) and (23) that the probability Pj(t) can be linked to the following linear model in susceptibility using a complementary log-log link function:In order to incorporate susceptibility and infectiousness into genetic selection programs, knowledge of the respective genetic (co)variances is required. Moreover, it might be desirable to use estimated breeding values of these traits for genetic selection or for genome-wide association studies. Estimation of breeding values by best linear unbiased prediction requires not only knowledge of the genetic variance  but alsocjk, fk and Dk that underlie infectiousness, the second summand of equation (24) can be considered to be an error term ej(t). However, in contrast to using the canonical logit and probit link functions, this model captures and completely separates the individual’s susceptibility from the dynamic aspects of exposure.Assuming no genetic variation in the epidemiological traits j(t) of becoming infected to a linear model that includes both susceptibility and infectiousness. Indeed, the complementary log-log link function (24) is no longer adequate when there is variation in infectiousness since the logarithm of a sum does not equal the sum of the logarithms. It is, however, possible to linearize the force of infection from equation (23), in both susceptibility and infectiousness, using e.g. the Taylor series expansion of t:However, when there is genetic variation in both susceptibility and infectiousness, it is not straightforward to link the probability Pj(t) in equation (25) is not truncated and that it includes only one non-linear term in susceptibility and infectiousness. Following a GL(M)M framework, if the last term of equation (25) was negligible, the expression for Λj(t) would be linear and thus an appropriate link between observed binary disease data (infected or not infected) and the underlying epidemiological traits, host susceptibility and infectiousness.Note that the Taylor series of Λgj and ϕjk(t) corresponds to an IGE model for the individual force of infection Λj(t). IGE models describe the phenotype Pj (here Pj = Λj(t)) of an individual j as a linear combination of the individual’s direct effect PDj, and the cumulate indirect (or associative) effect PSk of its group members, i.e.Note that truncating equation (25) after the linear terms in j (expressed as deviation from the population mean susceptibility), scaled by the cumulative average infectiousness of the group members up to time t, and the indirect (or associative) effect of a group member corresponds to its infectiousness (expressed as deviation from the population mean infectiousness until time t), scaled by the average population susceptibility. Furthermore, equation (25) may shed some light on potential causes for the previously observed bias in the genetic parameter estimates in infectivity [ϕ from the population mean. This is illustrated in Figure f) from genetic variation in the duration of the infectious period (i.e. variation in D). These sources of variation likely correspond to different immunological processes (e.g. shedding vs. recovery) and may therefore be controlled by different sets of genes. However, separating infectiousness components in genetic analyses may come with additional data requirements. For example, repeated binary measurement of an individual’s disease status over time rather than one single snapshot in time may be required to infer genetic variation in the duration of the infectious period. These measurements may be taken from on-going epidemics by using equation (13) instead of (14), with Pj(0) equal to the prevalence of the disease in the first observation. Markov Chain Monte Carlo methods [with an underlying genetic component for both the direct and indirect effects and with μ denoting the population mean phenotype, e.g. ,21. The ectivity . This bi methods , with thWe have derived a genetic epidemiological function for quantitative genetic analyses of binary infectious disease data that takes genetic variation and the dynamic expression of host infectiousness into account. The function describes the probability of an individual to become infected given its own susceptibility and the infectiousness of its group mates. When variation is limited to host susceptibility, it is possible to estimate genetic variation for this trait in a manner compatible with epidemiological dynamics using the complementary log-log link function. When there is genetic variation in both susceptibility and infectiousness, it is possible to use the logarithmic link function with a linear IGE model but this is likely to generate prediction bias if there is a large variation in infectiousness. Future work will concentrate on developing computational algorithms that can incorporate the genetic epidemiological function without linear approximations, in order to identify potential genetic super-spreaders. These algorithms would enable us to uncover the genetics underlying epidemics and thus shape the epidemics of tomorrow.The authors declare that they have no competing interests.DLP carried out and extended the initial outline of the derivations, wrote the simulation program, carried out the validation, and drafted the manuscripts. JAW conceived the study with an initial outline of derivations, and helped to draft the manuscript. ABDW led the supervision, steered the development and interpretation of the study, and carried out major revisions to the manuscript in the editing process. All authors read and approved the final manuscript.


Autozygosity occurs when two chromosomal segments that are identical from a common ancestor are inherited from each parent. This occurs at high rates in the offspring of mates who are closely related (inbreeding), but also occurs at lower levels among the offspring of distantly related mates. Here, we use runs of homozygosity in genome-wide SNP data to estimate the proportion of the autosome that exists in autozygous tracts in 9,388 cases with schizophrenia and 12,456 controls. We estimate that the odds of schizophrenia increase by ∼17% for every 1% increase in genome-wide autozygosity. This association is not due to one or a few regions, but results from many autozygous segments spread throughout the genome, and is consistent with a role for multiple recessive or partially recessive alleles in the etiology of schizophrenia. Such a bias towards recessivity suggests that alleles that increase the risk of schizophrenia have been selected against over evolutionary time. Inbreeding occurs when genetic relatives have offspring. Because all humans are related to one another, even if very distantly, all people are inbred to various degrees. From a genetic standpoint, it is well known that inbreeding increases the risk that a child will have a rare recessive genetic disease, but there is also increasing interest in understanding whether inbreeding is a risk factor for more common, complex disorders such as schizophrenia. In this investigation, we used single-nucleotide polymorphism data to quantify the degree to which 9,388 schizophrenia cases and 12,456 controls were inbred, and we tested the hypothesis that people whose genome shows higher evidence of being inbred are at higher risk of having schizophrenia. We estimate that the odds of schizophrenia increase by ∼17% for every 1% increase in inbreeding. This finding is consistent with a role for multiple recessive or partially recessive alleles in the etiology of schizophrenia, and it suggests that genetic variants that increase the risk of schizophrenia have been selected against over evolutionary time. Schizophrenia is a highly (.70–.80) heritable If schizophrenia risk alleles have been selected against across evolutionary time (have been under “purifying” selection), another prediction is that schizophrenia risk alleles will be biased towards being recessive. This bias, called directional dominance, occurs in traits subject to purifying selection because selection more efficiently purges the additive and dominant alleles with the strongest effects, leaving the remaining pool of segregating alleles more recessive than otherwise expected Studies that have investigated inbreeding effects on schizophrenia using pedigree data suggest that close  inbreeding is a risk factor F, is defined as the probability that two randomly chosen alleles at a homologous locus within an individual are identical by descent  F assume that marker data are independent, and provide an aggregate measure of homozygosity at measured variants across the genome runs of homozygosity  to infer autozygososity, and have investigated whether the proportion of the genome that exists in such ROHs, Froh, predicts complex traits The inbreeding coefficient of an individual, F, including F estimated by treating markers independently and F estimated from pedigree information, Keller, Visscher, and Goddard Froh is optimal for inferring the degree of genome-wide autozygosity and for detecting inbreeding effects. However, given the small variation in genome-wide Froh in unselected samples , large sample sizes  are necessary to detect inbreeding depression for likely effect sizes in samples not selected for recent inbreeding Froh on human complex traits with samples sizes <3,000 and that failed to find significant inbreeding effects Froh in schizophrenia n = 322) and was significant only for ROHs caused by common haplotypes.Of several alternative estimates of N = 21,844) that are part of the Psychiatric GWAS Consortium (PGC) Froh is associated with higher risk of schizophrenia. We also use an ROH mapping approach to investigate whether specific areas of the genome are predictive of case-control status when autozygous. This study represents the largest investigation to date on the potential consequences of autozygosity as estimated using Froh, and may help elucidate the genetic architecture and natural history of schizophrenia.The present study uses imputed SNP data from 17 schizophrenia case-control datasets .SNP data from 9,388 schizophrenia cases and 12,456 controls were collected with institutional review board approval from 17 sites in 11 countries . Due to Froh separately in each of the 17 datasets using logistic regression, controlling for potential confounding factors such as population stratification and SNP quality metrics  while 4 were less than one, a result inconsistent with chance . More formally, using a mixed linear effects logistic regression model that treated dataset as a random factor , the overall association between schizophrenia and Froh in the combined sample was highly significant . A slope of Froh on schizophrenia of 16.1 is interpreted as saying that for every 0.01 increase in Froh, the odds of schizophrenia are multiplied by We regressed case-control status on rics see Methods.Froh-schizophrenia association. There was no evidence that the Froh-schizophrenia association differed significantly between datasets (p = 0.88), and the association remained highly significant in 17 models that removed one dataset at a time. To understand if this association was sensitive to the covariates included in the model, we ran additional models that controlled for no covariates, various combinations of covariates, and dataset-by-covariate interactions. In all of these models, the association between Froh and schizophrenia remained significant. We also found that our conclusions were insensitive to the SNP threshold used to define ROHs; the association between Froh and schizophrenia remained relatively unchanged and significant for all SNP thresholds of ≥40 consecutive SNPs in both the imputed , which arose from haplotypes that were observed often in the data, and uncommon ROHs  were predictive of case-control status , comprising about one-fourth of the total sample used here. The median length of a deletion in the MGS2 dataset was ∼10 kb, whereas the median length of a ROH was ∼2,000 kb, suggesting that very few deletions would be long enough to qualify as ROHs. Consistent with this expectation, we found that only 10 of 6,480 ROHs in the MGS2 dataset were possible deletions using the algorithm described by McQuillan et al. Froh-schizophrenia association remained highly significant. We conclude that ROH results reported above are due to autozygosity rather than hemizygosity.Copy number variant deletions can create apparent ROHs in SNP data. We could not systematically catalog the overlap between deletions and ROHs in the full dataset because deletion information is not available on the entire sample. However, Levinson and colleagues Froh-schizophrenia association is possible: people who have a higher “load” of schizophrenia risk alleles (and who transmit this risk to offspring) may be more likely to mate with a relative. This counter-explanation to the causal interpretation of the Froh-schizophrenia relationship is less likely if the relationship holds not only for close inbreeding, but also for autozygosity caused by distant and almost certainly unintended inbreeding (arising from common ancestors who lived many generations ago). One way to investigate this issue is to remove positive outliers on Froh and reassess the Froh-schizophrenia relationship. We reran models after dropping a) two individuals with Froh>0.125, the approximate equivalent of half-sibling inbreeding  = , z = 3.24, p = 0.001); b) 15 individuals with Froh>0.0625, the approximate equivalent of cousin-cousin inbreeding  = , z = 2.73, p = 0.006); c) 56 individuals with Froh>0.03125, the approximate equivalent of half-cousin inbreeding  = , z = 1.27, p = 0.20); d) 942 individuals with Froh>.005, consistent with elevated levels of distant inbreeding  = , z = 0.34, p = .73); and e) 6,101 individuals with Froh scores above the mean level of Froh  = , z = 1.81, p = .07). To test whether the change in significance after dropping outliers was due to the Froh-schizophrenia association being stronger for individuals with high levels of autozygosity, we included a quadratic term (2Froh) in the regression model. In contrast to the highly significant linear term of Froh, the quadratic term of Froh was non-significant (p = .09), suggesting that the effect of autozygosity is linear across the range of Froh observed here.A reverse-causation explanation of the Froh is naturally extremely right-skewed  is contained within every confidence interval above. Thus, the results from dropping outliers demonstrate that the Froh-schizophrenia relationship is not driven by a few highly inbred individuals, but do not allow us to distinguish the effects of distant vs. close inbreeding. Second, individuals with high Froh can arise by chance from the accumulation of many paths of distant inbreeding Froh>0.0625 is more consistent with inbreeding from common ancestors living ∼6 generations ago than with first cousin inbreeding  was similar to the effect of Froh>5 Mb , consistent with the hypothesis that autozygosity arising from distant inbreeding is about as much of a schizophrenia risk factor as autozygosity arising from more recent common ancestors.An alternative and more robust approach for assessing the relative importance of distant versus close inbreeding is to compare the effects of short versus long ROHs. We defined 10 p-values for the 5,742 logistic regressions predicting case-control status from ROHs at each 500 kb bin along the autosome. No regions reached genome-wide significance although two (1p13.2 and 3p24.1) exceeded the “suggestive significance” threshold. Froh with the two suggestively significant regions removed, results of the burden analysis remained essentially unchanged, showing that these regions have only a minor influence on the overall Froh-schizophrenia association and suggesting that the effect of autozygosity is diffused across the genome.The top of The bottom of Froh). Given the standard deviation of Froh (0.004), this effect is modest, explaining <0.1% of the risk of schizophrenia in outbred populations (Nagelkerke r = 0.026). Nevertheless, this effect implies that close inbreeding is a significant risk factor for schizophrenia. Cousin-cousin inbreeding is predicted to increase the odds of schizophrenia 2.74-fold (by 174%) and second-cousin inbreeding is expected to increase the odds of schizophrenia 1.29-fold (by 29%). These estimates are roughly in line with previous reports on schizophrenia from samples selected based on pedigree inbreeding These results suggest that the odds of schizophrenia increase by ∼17% for every 0.01 increase in the proportion of estimated autosomal autozygosity  selection There are three main limitations to the current study. The most important is that this was a mega-analysis of SNP data collected at 17 different sites using six different platforms. The collection and handling of samples, the distribution of samples on plates, and the calling of SNPs differed between and within sites in ways that were impossible to quantify in the analysis. This certainly added noise to the results, reducing the apparent effect size, but also may have introduced subtle biases. We have tried to statistically control for as many of these as possible, but the possibility remains that uncorrected biases made these results appear stronger or weaker than they actually are.Froh values are excluded, the case-control difference is no longer significant. On the other hand, there are good statistical reasons to consider the analysis of short versus long ROHs more valid than the analyses that exclude individuals with the highest Froh values. Thus, the authors favor the conclusion that both distant and close inbreeding are risk factors for schizophrenia. A more definitive answer to this question would either require a substantially larger sample size or a sample of similar size to the current one but drawn from a population with greater variation in levels of distant inbreeding.Second, while our results clearly support the hypothesis that autozygosity is a risk factor for schizophrenia, they are less clear about how confidently we can differentiate the roles of distant versus close inbreeding. On one hand, when enough outliers on Froh-schizophrenia association is likely to be causal because the association is consistent with a known genetic mechanism, directional dominance, and because the association appears to be as robust for short ROHs as long ROHs. Short ROHs are likely to represent autozygosity caused by distant inbreeding, and therefore seem less likely to differ between parents as a function of their load of schizophrenia risk alleles. Nevertheless, we cannot eliminate the possibility that parents of offspring who have schizophrenia differ in ways that make distant inbreeding more likely, such as an increased propensity to mate with individuals who have culturally, geographically, or ethnically similar backgrounds.A final limitation has to do with the correlational nature of these findings. We argue that the Froh and schizophrenia is due to directional dominance, such that schizophrenia risk alleles are more recessive than otherwise expected, this suggests that alleles that increase the risk of schizophrenia have been under negative selection ancestrally.Inbreeding has had a central place in population genetics since its inception, but until recently, the effects of inbreeding could only be investigated from careful analysis of pedigrees and only for close inbreeding. SNP data allows investigation into the effects of potentially very distant inbreeding in non-selected samples, and allows insight into where the signal comes from in the genome. However, unless samples are specifically selected based on inbreeding, very large samples are required to reliably detect effects of autozygosity due to the low variation between individuals in their levels of autozygosity. The present investigation used SNP data from a large sample to conclude that autozygosity is a risk factor for schizophrenia. If the relationship between Full methods are given elsewhere −6; b) had missingness >0.02; c) showed a minor allele frequency difference to HapMap CEU>0.15; or d) had a missingness difference between cases and controls >0.02. On average the QC processes excluded 15 individuals (0–100) and 38K SNPs (5K–160K) per dataset. The number of SNPs per dataset after QC varied between 250K and 680K , we could afford to lose a large number of imputed SNPs from QC procedures.To overcome these issues, we imputed dosages for 1,252,901 autosomal SNPs in each dataset using BEAGLE Froh), and in their associations with schizophrenia. We therefore report results on ROHs called from imputed data. However, results for the ROHs called from raw data were similar, and are shown in ROHs called from imputed data were less variable across platform and across datasets in terms of basic descriptive statistics, in the effects of potential artifacts , which reduced false autozygosity calls by removing redundant markers in SNP-dense regions and by making SNP coverage more uniform; and b) defining ROHs as being ≥65 consecutive homozygous SNPs with no heterozygote calls allowed Froh-schizophrenia association , a recent investigation by three of the authors of the current report tion see . This thtion see . FinallyROHs can also be categorized by their frequency (how often a particular haplotype creates ROHs at a given location). We used PLINK's –homozyg-group and –homozyg-match arguments to understand whether uncommon ROHs or common ROHs were particularly predictive of case-control status, defining ROHs in a given region as “uncommon” when they allelically matched with 16 (the median) or fewer other ROHs in the combined data; all other ROHs were defined as “common.”9 bases) to derive Froh, the proportion (0 to 1) of the autosome in ROHs. Froh was used as the predictor of case-control status in ROH burden analyses. Froh can be influenced by confounding factors like population stratification , low quality DNA leading to incorrect SNP calls, and heterozygosity levels that vary across plates, DNA sources, etc. To control for the effects of stratification, we included the first 20 principal components based on ∼30K SNPs genotyped in all datasets. We also controlled for the percentage of missing calls in the raw SNP data and excess heterozygosity as these track the quality of SNP calls Froh to accurately estimate autozygosity is negligibly affected by statistically controlling for excess heterozygosity, and therefore doing so should have minimal effect on results when genotyping error rates are low, but may help elucidate effects of ROHs when such errors are present.For each individual, we summed the total length of all their ROHs in the autosome and divided by the total SNP-mappable autosomal distance  to estimate the overall effect of Froh across datasets, treating dataset as a random factor. This also controlled for SNP platform because dataset was nested within each platform .We regressed case-control status on th most significant p-value was the genome-wide significance threshold and the 100th most significant p-value was the “suggestive” genome-wide significance threshold.To understand whether any genomic area was predictive of case-control status, we divided the autosome into 5,742 segments of length 500 kb each. At each segment, an individual was scored as either having a ROH that partially or completely overlapped the segment or not. We performed 5,742 logistic regressions, regressing case-control status on whether or not individuals had an ROH in each segment, controlling for covariates described above. To derive a genome-wide significance threshold corrected for multiple testing, we permuted case-control status within the 17 datasets and reran the 5,742 logistic regressions, preserving the most significant result of each permutation. We repeated this permutation 1,000 times. The 50Figure S1Froh (right) in the total sample, including individuals with Froh>.0625. Distributions are based on ROHs from the imputed SNP data.Distributions of ROH Lengths (left) and (TIF)Click here for additional data file.Figure S2Froh  and their 95% confidence intervals (bars) across the 17 datasets (colored) and for the total sample (black) from the raw SNP data. Boxes are proportional to the square root of sample sizes . Dataset names are on the x-axis. Although none of the estimated odds ratios are significantly different from one individually, the overall effect (black) is highly significant.Estimated changes in odds of schizophrenia for each 1% increase in (TIF)Click here for additional data file.Figure S3Froh; points) and their 95% confidence intervals (bars) of Froh from raw SNP data predicting schizophrenia for different SNP homozygosity thresholds of calling ROHs. Minimum SNP thresholds for full and reduced models are offset for clarity. All ROH thresholds were significant; the most significant result was for ROHs defined as being 110 or more homozygous SNPs in a row.Slope estimates (the change in log odds for a 1% increase in (TIF)Click here for additional data file.