Klf7 gene may influence gene transcripts in bone marrow-derived myeloid cells, which in turn affect 17 behavioral traits following morphine injection; this predicted effect of Klf7 is consistent with an in vitro perturbation of Klf7 in bone marrow cells. Our analysis demonstrates the utility of studying hidden causative mechanisms that lead to relationships between complex traits.There is growing recognition that co-morbidity and co-occurrence of disease traits are often determined by shared genetic and molecular mechanisms. In most cases, however, the specific mechanisms that lead to such trait–trait relationships are yet unknown. Here we present an analysis of a broad spectrum of behavioral and physiological traits together with gene-expression measurements across genetically diverse mouse strains. We develop an unbiased methodology that constructs potentially overlapping groups of traits and resolves their underlying combination of genetic loci and molecular mechanisms. For example, our method predicts that genetic variation in the DOI:http://dx.doi.org/10.7554/eLife.04346.001 Many individuals who have diabetes also have other diseases that affect the heart and blood vessels. It is not uncommon for human diseases to occur together like this; and understanding the relationships between diseases and other traits can make it easier to diagnose conditions. Furthermore, it can also help researchers develop treatments that are more precisely targeted to each condition and cause fewer side effects.Two conditions or traits tend to occur together if they are caused by mutations in the same gene or genes; or if they involve processes within cells that share the same proteins and other molecules. However, in most cases the genes and molecular mechanisms involved are not yet known so it is more difficult to work out how the traits are connected.Computing techniques make it possible to assess the relationships between hundreds or thousands of traits at the same time. These high volume analyses can also allow scientists to identify less obvious relationships that might be missed in more traditional types of study.Here, Oren et al. created a new computer algorithm to identify related traits, their shared genetic basis, and the molecular mechanisms behind them. The algorithm is called GEMOT and uses a three-step approach to sift through a large amount of data. Oren et al. tested GEMOT using a database of 1738 documented traits—including diseases and behaviors—in laboratory mice.Klf7 affected the expression of other genes that are involved in making new cells in the bone marrow. In turn, these changes influenced 17 different behaviors in the mice after they were injected with the painkiller morphine.Oren et al. identified many clusters of traits in the mice and the underlying genetic and molecular mechanisms that link them. For example, they found that a mutation in a gene called In humans, the same genes that underlie behaviors related to morphine treatment have been linked to the survival rate of patients with a form of brain cancer. This suggests that—alongside providing pain-relief—morphine may influence how the tumor grows. The algorithm developed by Oren et al. can now be used to further explore the impact of the environment on the relationships between traits.DOI:http://dx.doi.org/10.7554/eLife.04346.002 Epidemiological and clinical research has identified a profusion of correlated physiological traits, as well as a remarkably high incidence of co-occurrence and comorbidity among disorders. Various studies have shown that such connections among diseases are typically attributable to a common underlying genetic or molecular mechanism . Disclosg2 is reactive to the p4 trait but does not cause it  translating between a genetic layer and a layer of traits. In particular, a GEMOT module is focused specifically on causative, non-environmental relationships rather than on relationships of any kind, and accordingly it includes only transcripts that are part of causative relationships . We useGlobal identification of traits that share common causal transcripts and genetic mechanisms requires a reliable reconstruction of a global causal network among variants, transcripts and traits—a notoriously difficult problem, particularly in the case of a large collection of traits and high throughput data. We designed GEMOT, a scalable algorithm for the systematic construction of three-layer modules, each consisting of a group of traits, their shared causal driver transcripts and a genetic variant. GEMOT is based on the notion of ‘linked relationships’ between a variant, a transcript, and a trait. Such relationships incorporate a transcript that is both associated with a variant and correlated with a trait, without a direct evaluation of the causative relationship between the three components. In particular, it relies on the observation that causative relationships are expected also to be linked relationships (but not vice versa). It is therefore possible to start by constructing candidate modules based on the potential of variants and traits to be linked through transcripts. The internal structure is then constructed within each of these modules. Notably, the linked relationships are exploited to avoid global reconstruction of the particular types of relationships, which are then confirmed only at the validation stage.p1, p3, p4 and variant v1 in g1–g3, g1, g3; traits p1, p4; variant v1 in I. We start by calculating associations between each transcript and each variant (a ‘variant–transcript association’) and correlations between each transcript and each trait (a ‘transcript–trait correlation’). We combine these two measures in a statistical test to identify variant–trait pairs that have high potential to be linked through many transcripts. We call this scoring scheme a ‘link potential’ . From thII. We next apply a statistical test to identify transcripts whose linked relationships in the module are higher than expected by chance. This is done by evaluating the correlations and associations of transcripts with the module's traits and genomic interval respectively, computing ‘transcript link scores’, and using it to filter promising ‘candidate transcripts’ . We thenIII. In the third stage the aim is to investigate the internal relationships within a module, thus allowing identification of driver transcripts and their affected traits. Recent methods allow structural reconstruction of a causality network e.g., , and canGEMOT's input is a collection of traits, genotyping, and molecular data across a population of individuals. GEMOT consists of three main stages  to show that the quality of these pairs is not lower than in existing methods. We focused on three main properties of trait pairs: the correlation among traits in a pair; the correlation between a trait pair and the transcripts; and the knowledge-based relationships among traits. As a reference we demonstrate these properties for modules that were generated using three alternative methods: (i) the trait-based hierarchical clustering approach , and were comparable to those obtained by the gene-based INVAMOD approach but weaker than those from the trait-based HC approach  and is comparable to the trait-based method.For each trait pair we searched for a potential shared transcript that showed the best correlation (on average) with both traits. We found that GEMOT's predicted trait pairs were supported by the best-correlated transcripts across a wide range of trait–trait correlations . As expeWe next aimed at determining whether trait pairs predicted by GEMOT were supported by previously known connections between traits. Evaluation of such distinct trait pairs in light of previously known trait connections is a general problem, and no suitable systematic annotation is currently available. To tackle this problem we constructed an unbiased matched-annotation set of connections, and used it in our analysis as the gold standard. To systematically cover, independently of the correlation and co-association measures, the qualitative knowledge about connections among traits, we adopted the descriptive title of each trait in the GeneNetwork Phenotype Database . If the In the following we demonstrate three reconstructed modules, demonstrating GEMOT's ability to identify a model for a collection of tightly related traits, and for a previously uncharacterized combination of traits.r| values ranged from 0.6 to 0.99, The morphine module , all associated with the module's genotype and strongly correlated with each other and with the module traits , but utilized a cis-associated gene (Klf7 or Idh1) as the transcript positioned between the module's genomic interval and another module transcript. Using these scores we found that the causative p values of Klf7 on the remaining module transcripts were substantially more significant than the causative p values of Idh1 on those transcripts . This finding holds for each of the driver groups I and II , it had no influence in group II . Indeede traits . Overexpe traits , right, iversity .p35/Cdk5 driver directly phosphorylates the opioid receptor . Both t drivers  are resp drivers  that may neurons , here wed tissue . We cannd tissue  and the phocytes  potentiaphocytes , in agrenjection . Taken tIn the following we demonstrate GEMOT's ability to identify a model for previously uncharacterized connections, with either strong (module no. 3) or weak (module no. 4) correlations among traits.r| values ranging from 0.67 to 0.9 , but not when using data from the lymphoid, eye, or brain tissues. This suggests that Eya3 and Cd52 play a role in pain processes and eye conditions mainly through their functionality in myeloid cells.Module no. 3  shows th7 to 0.9 . Eya3 anelopment  and the ignaling . Figure r| values ranging from 0.01 to 0.58 . We compared GEMOT to two alternative trait-grouping methods: the trait-based iterative clique enumeration (ICE) approach  and the We set out to identify the molecular and genetic mechanisms underlying connections among groups of traits. To that end, we combined module identification  with cauOur study emphasizes the need for methodologies for constructing causative models that underlie connections among traits. Whereas previous trait-grouping methods have used genetic or molecular data separately, and thus did not validate causative transcripts e.g., , the GEMKlf7 in Our methodology opens the door to a variety of future research directions. One possibility is that GEMOT will be applied on a compendium of molecular data from multiple tissues. In such cases, GEMOT predictions can be used to simultaneously identify both the biological mechanism and its relevant tissue. Second, GEMOT is applicable to a variety of molecular data types in addition to gene-expression data. For example, its application in blood cytokines or plasma lipids  is expecOverall, our approach paves the way to the simultaneous study of several mechanistic layers underlying connections among traits, providing a multilayered view of phenotypic connections. Because the GEMOT methodology is a general one and can be applied to the study of other taxa, this approach may facilitate our understanding of the molecular mechanisms underlying human disease.GEMOT is designed to identify three-layer modules in which driver components translate between a single genomic interval and a collection of traits. As input, GEMOT takes three types of objects: (1) a collection of traits across a population of individuals; (2) genotyped genetic variants for these individuals; and (3) high-throughput gene expression data across the same population.http://csgi.tau.ac.il/gemot/.Our algorithm incorporates three stages . The fir. In this study, for the case of homozygous recombinant inbred strains the association score is a −log t-test p value for the different gene-expression values between the strains carrying the two possible variant alleles. For other cases, such as an outbred population, other standard association scores can be applied . Each bipartite cluster is subject to iterative improvements by addition or removal of traits and variants based on this cutoff. We refer to the bipartite clusters as ‘bipartite modules’ and further improve them in the following stages. Notably, ReL provides the same results when applied with or without Boneferroni correction for the gene–variant association −log p values and link potentials scores, since the construction of the biclusters is robust to an additive rescaling of these scores.Within this graph we use the ReL software package  to identIn this stage a rough list of candidate transcripts is constructed for each module . To thisIn the following we first define the causality test and then describe the procedures for identifying driver transcripts and for module refinement.The input for a causality test is a triplet of objects—a variant, a transcript, and a trait—each measured across the same population of individuals. Several types of relationships exist, including causative, reactive, and independent, and the goal of causality testing is to identify causative relationships among a given triplet of objects. Our causality analysis here follows the formulation of Importantly, in the present study we introduce two important modifications in the scheme suggested by Second, we observed that in a GEMOT module a transcript may have a causal effect on a trait even in the presence of additional transcripts through which the variant influences the trait. Accordingly, in the GEMOT framework, both models M1 and M4 should be considered as causative relationships , as opposed to the classical definition of causative relationships according to model M1 only . In the 2k degrees of freedom: gi is the transcript; j = 1,...,k are the module traits; and pij is the causality p value for the transcript gi and a trait j assuming the module's representative variant. Next, in step (ii) those traits that do not have at least one transcript with a significant causality score are filtered out from among the transcripts that were selected in step (i)  , right. step (i) .10-transformed and normalized by Z-score normalization. All 2885 traits and 3796 genetic variants across BXD strains were downloaded from the WebQTL dataset  and transcript causality p value cutoff = 0.005 .To assess the corresponding false discovery rates, we generated negative controls based on a permutation test in which the transcript levels of each transcript were randomly shuffled and the GEMOT modules were recomputed (a process that was repeated 100 times). In each repeat, a variety of statistics (such as the number of identified modules) were recorded. The permutation-based ‘false discovery rate’ (FDR) is the ratio of the averaged number of statistics that were declared significant using the permuted data to the number of statistics that were declared significant using the original (non-permuted) data. In this study, GEMOT was applied using transcript link score cutoff = 10v, a transcript g and a trait p. In all such triplets we assume 100 homozygous individuals. The genotyping of each variant was generated by sampling a vector of values 0 and 1 from a binomial distribution (with p = 0.5). Based on these genotyping values, the values of g and p were generated according to the following five different models (denoted M1–M5), as depicted in v → g → p; M2, an independent model v → g, v → p; M3, a reactive model v → p → g; M4, v → g → p and v → p; and M5, v → p → g and v → g. Each arrow in these five models was simulated as a linear expression with a normally distributed error term. For example, based on model M1, data were generated as g = α⋅v + ε, p = λ⋅g + ε, ε ∼N; similarly, model M4 was generated as g = α⋅v + ε, p = α⋅v + λ⋅g + ε, ε ∼N. A single ‘synthetic collection’ consisted of 250 relationships from each of the five models, a total of 1250 samples. Results are displayed for many different collections, each generated using different combination of λ and σ values with α = 0.5. GEMOT's causality p values were compared to those obtained by two alternative methods: QTLHot  where FPa accounts for imbalanced data by dividing FP by the ratio between the negative and positive synthetic datasets, calculated as FPa = FP/π0, π0 = (FP + TN)/(TP + FN). The method with lowest FDR is regarded as the best method . Notably, GEMOT attains similar performance to that of the compared methods for models M1–M3 , true negative (TN), false positive (FP) and false negative (FN) counts, which were defined according to the broad-sense definition of causality . The arels M1–M3 , but outls M1–M3 .The synthetic data analysis is focused on two simulations with increasing complexity of the input network: (i) sub-network analysis, in which the input is a sub-network where all components are co-mapped to the same variant; and (ii) network analysis, in which the input is a large network comprising several co-mapped sub-networks.v and m transcripts v and are causally related to k traits v such that v, P, G), where Net-1 (Net-2 (Net-3 (k + 2. The simulation data was generated by using for each edge ai → aj in these sub-networks a linear coefficient β such that aj = β⋅ai + ε(β), ε(β) ∼N, σ = qε⋅β, where qε represents the relative proportion of noise referred to as the ‘noise level’. Observe that ε(β) depends on both the linear coefficient of the relationship β and on the noise level qε. We generated ‘synthetic collections’ of 100 sub-networks ; each collection is constructed for a given network structure , a certain total number of traits  and a certain noise level . In all cases we used β = 1.5 for relationships v → p and v → g and β = 0.6 for relationships g → p and p → g.A synthetic co-mapped sub-network consists of one variant as Net-1 , Net-2 /2  and TPR = TP/(TP + FN)). AUC could not be computed because the three compared approaches do not provide a measure of statistical significance.We compared GEMOT's performance on co-mapped sub-networks to that of alternative network construction algorithms, including the QTLNet method , the QPSs1,...,s5 of the form (v(sL), P(sL), G(sL)), and second, the remaining network comprising additional transcripts, variants, and traits. In total, the network consisted of 100 variants, 100 traits, and 200 transcripts that were used to generate synthetic data across 100 individuals. The data for the five sub-networks were generated as in the sub-network analysis , using varying numbers of traits. The remaining data were generated as follows: (i) genotyping of each variant was generated independently, as described in the causality-testing simulation ; (ii) for each trait and individual, data values were sampled from a standard normal distribution; and (iii) gene-expression data were generated while maintaining the correlation between transcripts of the non-module components and between them and the module component. More specifically, for each individual i and transcript j that are not in a sub-network, the gene-expression data zij were generated in two steps: first, to maintain correlation among all non-sub-network transcripts we sampled the real data in murine myeloid cells  kth transcript in the sub-network .The synthetic network consisted of two parts: first, five co-mapped sub-networks PC(su) , which are the groups of traits with the same causative mechanism behind them. Furthermore, we tested an existing trait-based approach (Iterative Clique Enumeration (ICE); The synthetic network was used to test the ability of GEMOT to identify the groups  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 , a Reviewing editor, and 2 reviewers.Thank you for sending your work entitled “Linking traits based on their shared molecular mechanisms: A systems phenomics approach” for consideration at The Reviewing editor and the reviewers discussed their comments before we reached this decision, and the Reviewing editor has assembled the following comments to help you prepare a revised submission.There is an overall appreciation for methods, such as the proposed GEMOT, that predict causative mutations leading to transcript variations that in turn drive phenotypes. However, to convince that the present method provides an advantage over existing approaches, three additions are required:1) GEMOT performance should be compared to existing methods. This includes the qtlnet software  as well as similar methods .2) Simulations should be used to evaluate the method against a 'truth' standard.Klf7 results: a consistent model describing the effect of each allele  should be presented to provide a clear hypothesis of how Klf7 effect is generated.  consistent with corresponding Klf7 expression differences in the BxD population? That is, do Klf7 knockout effects look like a low-expressing Klf7 strain, and do Klf7 overexpression effects look like a high-expressing Klf7 strain? 3) With regards to the 4) The manuscript would be more convincing if the authors identify a group of traits that show low Pearson correlation among themselves, but share the same driver genes.5) Considering the many methods already available (see above), the motivation for the present study should be better clarified.P value; why not refer to it as such? In some cases the new nomenclature can be potentially misleading, such as in the Klf7 discussion where a P value is referred to as a “perturbation effect”. Effect size and significance are different concepts with different biological interpretations.6) The manuscript can be difficult to read at times, primarily due to a reliance on its own jargon. In some cases new nomenclature might be necessary, but many of the new terms seem to be very similar  to widely-used, existing terms. In such cases, the paper should conform to standard nomenclature or define why such standards will not suffice. Notable examples are: “variant-gene associations” instead of eQTL; “linked relationships” instead of Pearson correlation and “link potential” instead of averaged correlation; “bipartite module” instead of pleiotropy. Furthermore, “gene drivers” and the “drivers layer” can probably be more simply referred to as “transcripts” and a “transcript layer” with appropriate context. “Causality score” appears to be a P values systematically corrected for multiple tests? It is also important to estimate false discovery rates for a given significance threshold, which are not addressed in the manuscript. Additionally, the sample size in this study is very small, and BxD lines often exhibit non-local linkage disequilibrium due to limited recombination across few individuals. This can lead to many false-positive associations. How has this potential issue been addressed in the current study?7) High-dimensional approaches like GEMOT are prone to generating false positive associations, especially in such small experimental populations. Are  There is an overall appreciation for methods, such as the proposed GEMOT, that predict causative mutations leading to transcript variations that in turn drive phenotypes. However, to convince that the present method provides an advantage over existing approaches, three additions are required:1) GEMOT performance should be compared to existing methods. This includes the qtlnet software  as well as similar methods .We thank the reviewers for their suggestion, which we believe improves our conclusions. The specified publications are focused on three different aspects: (1) Testing causative relationships ; (2) Network reconstruction ; and (3) grouping traits (Chesler 2005). As suggested by the reviewers, in the revised manuscript we added simulations that relate to each of these three aspects, with a focus on comparison to the suggested methods.P-value score. Rather, we aimed to use an existing methodology with minor modifications that were required in our particular case. In accordance, we used a methodology that is very similar to Neto et al. 2013, with two small modifications: first, we use empirical rather than theoretical evaluation of the likelihood ratio distribution; second, Neto et al. was interested in a 'classical' definition of causality, where a transcript translates between a variant and a trait. Here, we were interested in an additional objective function: identifying causal transcripts in the presence of other transcripts. This situation is common in our case of GEMOT modules harboring multiple causal transcripts translating between the same variant and a group of traits. We have therefore slightly modified the method suggested by Neto et al. to capture this 'broad' definition of causality. We apologize for omitting this important information from the original submission. We now added a detailed description of the methodology and alterations from Neto et al. to the subsection headed “GEMOT stage III: Refine module . We also added a new simulation study (new (1) Testing causative relationships. We agree with the reviewers that our original manuscript did not provide assessment of our causality testing methodology. Notably, our goal was not to develop a new method for a causality tudy new , which s(2) Network reconstruction. In the third stage of the GEMOT algorithm, GEMOT aims to identify the groups of traits that share causal drivers within the given tripartite modules. Such identification can also be performed by constructing a detailed network within a module (using existing methods) and using this solution to identify the desired group of traits. Notably, our goal was not to better construct any given network. Rather, we aimed to develop scalable methodology for the identification of the shared drivers of the module's traits, which can scale to the large tripartite modules we found in real mouse data . According to our observations, the accuracy of the existing methods dropped drastically with an increased number of components, and had an unrealistic running time for our BXD modules. This led us to develop an alternative methodology in GEMOT phase III for identifying the players behind the group of traits without a full reconstruction of the network. However, the GEMOT pipeline is general and existing network reconstruction methods may be used in phase III of the pipeline, alongside or instead of our suggested phase-III approach. We now clarify these points in the Introduction, Results and Methods sections.In the revised manuscript, we added a new simulation study that takes as input co-mapped subnetworks that mimic tripartite modules so as to identify the desired group of traits that share the same transcript players behind them. Notably, GEMOT does not construct a causal network but only predicts a subset of traits sharing the same mechanism. To avoid biases, we therefore based our systematic evaluation on the ability to identify the correct group of traits sharing a mechanism, thus ignoring irrelevant additional information produced by the compared network reconstruction methods. We now provide a detailed description of the simulated sub-networks and comparisons in the Results and Methods  and new five figures new . These s(3) Grouping traits. We have added a relevant simulation of a large biological network that harbors small groups of traits that share the same causal transcripts within it. We now discuss the simulation of this large network in the Methods  and Results  sections. GEMOT's performance is compared to two alternative methods: (I) the ICE algorithm , which wImportantly, an equivalent systematic comparison between GEMOT and the alternative network reconstruction algorithms on the entire network is not feasible due to the long running time of the network reconstruction algorithm. Therefore, the entire 3-phase GEMOT pipeline, which can be applied on thousands of components, cannot be directly compared to the network reconstruction methods. We now highlight this point and exemplify the running time of the compared methods for the case of small sub-networks new .Notably, three additional suggested publications  have not been directly compared since they do not provide or develop any code that we could systematically apply to the synthetic data; these publications, however, discuss methodologies that are similar to the methods by Chesler 2005, Neto 2013 and Lee 2009, which were compared in our revised manuscript, as detailed above.2) Simulations should be used to evaluate the method against a 'truth' standard.We addressed this issue above (in our answer to comment 1). As noted, we now added simulations to evaluate GEMOT's accuracy. In particular, using a gold standard, we present the superiority of GEMOT for the goal of identifying groups of traits with causative players behind them. This is shown for synthetic networks of increasing complexity:(I) Small network fragments including triplets of components new , legend.(II) Co-mapped sub-networks (new (III) Full large networks (in the same subsections).3) With regards to the Klf7 results: a consistent model describing the effect of each allele  should be presented to provide a clear hypothesis of how Klf7 effect is generated.  consistent with corresponding Klf7 expression differences in the BxD population? That is, do Klf7 knockout effects look like a low-expressing Klf7 strain, and do Klf7 overexpression effects look like a high-expressing Klf7 strain?is also confusing as it appears to combine the knockout and overexpression experiments into summary scores. It would be useful to clearly see how these data support the inferred BxD model.)Klf7 transcript and negatively correlated with the morphine-related traits; group II is negatively correlated with Klf7 and positively correlated with these traits. Consistently, strain DBA/2J shows higher levels of group I and Klf7 transcripts, whereas strain C57BL/6J shows higher levels of group II transcripts and of the morphine-related trait measurements. These results suggest that Klf7 acts as an activator of group I drivers and as a repressor of group II drivers. In accordance with this prediction, Klf7 overexpression in the C57BL/6J strain background up-regulated group I and down-regulated group II. Furthermore, Klf7 knockdown in the C57BL/6J strain background down-regulated group I, as expected. . We thank the reviewers for this suggestion, which we believe strengthened our results.Following the reviewers' suggestion, we first extended the analysis of module number 2 using the BxD data, and then demonstrated the agreement between this data and the perturbation experiment. In the revised manuscript we present a full consistency between the experimental perturbation results and the BxD-based model. Our extended analysis shows that the drivers in module number 2 can be partitioned into two types: group I is positively correlated with the Klf7 as an activator of drivers in group I and repressor of drivers in group II , and present new We have substantially revised the manuscript to include these new results that now support a causal role for 4) The manuscript would be more convincing if the authors identify a group of traits that show low Pearson correlation among themselves, but share the same driver genes.We agree with the reviewers, and apologize for the missing details in our description of the modules in the original submission. The original submission already exemplified two modules with high trait-trait correlations (modules nos. 2 and 3) and one module with poor trait-trait correlations  Considering the many methods already available (see above), the motivation for the present study should be better clarified.The comment pointed out to a lack of clarity in comparison to existing methods, which we now address in full. First, we clarify the difference from existing methods. Whereas many trait-clustering methods are available, these do not rely on causative molecular players behind the grouped traits. Furthermore, whereas many causal network construction methods exist, such methods construct the entire networks and therefore cannot scale to large networks that include thousands of genes and traits . We have revised the text in the Introduction, Results , and Discussion sections to clarify these points. Second, in the revised manuscript, we use simulations to demonstrate the advantages of GEMOT over various existing methods  The manuscript can be difficult to read at times, primarily due to a reliance on its own jargon. In some cases new nomenclature might be necessary, but many of the new terms seem to be very similar  to widely-used, existing terms. In such cases, the paper should conform to standard nomenclature or define why such standards will not suffice. Notable examples are: “variant-gene associations” instead of eQTL; “linked relationships” instead of Pearson correlation and “link potential” instead of averaged correlation; “bipartite module” instead of pleiotropy. Furthermore, “gene drivers” and the “drivers layer” can probably be more simply referred to as “transcripts” and a “transcript layer” with appropriate context. “Causality score” appears to be a P value; why not refer to it as such? In some cases the new nomenclature can be potentially misleading, such as in the Klf7 discussion where a P value is referred to as a “perturbation effect”. Effect size and significance are different concepts with different biological interpretations.We thank the reviewers for this suggestion, and made the following changes accordingly:1) Transcripts: The term 'gene' was replaced with ‘transcript’, and accordingly, the terms ‘driver layer’ and 'molecular layer' were replaced with ‘transcripts layer’. We modified the text throughout the manuscript accordingly.2) Driver-related terms: We simplified the terminology by replacing the term 'candidate driver' with 'candidate transcript', and 'driver' with 'driver transcript'. Notably, we could not completely replace the term 'driver' and use the term 'transcript' instead, since we have two kinds of transcripts: the candidate transcripts in stage number II and the transcripts that were identified as drivers in stage number III.P value', and the term 'gene causality score' was replaced by 'transcript causality P value', as suggested.3) Causative scores: The term 'causative score' was replaced with 'causality Klf7 discussion: In the results referring to module number 2 we now conformed to the standard terminology, where 'effect size' refers to difference between strains, and 'significance of effect' refers to the P value for these differences.4) The two existing terms: one is a simple 'correlation' between a transcript and a trait, and the second is an 'association' of a variant and a transcript. Therefore, there is no existing term referring to this combination. We now have the text slightly refined accordingly. Notably, since the term 'link potential' refers to an aggregation of 'linked relationships', we therefore could not use an existing term in this case.5) Linked relationships and link potential: In both cases, the term could not be replaced with an existing term. In the case of 'Linked relationships', we believe that replacing it with the term 'correlation' is misleading since 'correlation' refers to relations between two objects, whereas 'linked relationships' refers to the relations between three objects. In particular, 'linked relationships' refers to the combination of e.g., Tanay et al., Bioinformatics 2002).6). Bipartite modules: In the GEMOT pipeline, bipartite modules do not represent any kind of pleiotropy, but only pleiotropy that is likely mediated through transcripts. The term 'Bipartite module' is therefore not equivalent to 'pleiotropy' and cannot be replaced. We now clarify this in the revised manuscript. Notably, bipartite graphs and sub-graphs conform to the standard terminology in the biclustering literature (7) Variants: In some cases along the GEMOT pipeline, using the term 'eQTL' instead of 'variant' may be misleading. In particular, for the output GEMOT modules and association scores, the variant can be also terms an eQTL. However, in the remaining manuscript, the variant is not an eQTL. For example, during phase 1 of GEMOT, the variant only has linked relationships with a trait, therefore it cannot be declared as an eQTL; in bipartite and tripartite modules and also throughout the simulation studies , reactivOverall, in the revised manuscript, we changed 8 terms so as to conform to the standard terminology according to the reviewers’ suggestion.7) High-dimensional approaches like GEMOT are prone to generating false positive associations, especially in such small experimental populations. Are P value systematically corrected for multiple tests? It is also important to estimate false discovery rates for a given significance threshold, which are not addressed in the manuscript. Additionally, the sample size in this study is very small, and BxD lines often exhibit non-local linkage disequilibrium due to limited recombination across few individuals. This can lead to many false-positive associations. How has this potential issue been addressed in the current study?The reviewer raises two concerns regarding false positives. The first refers to the evaluation of FDR and the multiple testing problem, and the second relates to the linkage disequilibrium issue.P values throughout the manuscript. Notably, GEMOT provides the same results when applied with or without Boneferroni correction for the gene-variant association and link potential scores, since the construction of the bipartite modules is not sensitive to scaling of these values. We clarify this in the revised text.1) Multiple testing correction and FDR: In the revised manuscript, we now systematically correct for multiple testing and estimate FDR. First, in the case of real data, FDR is estimated based on a permutation test. We assessed the FDR for various predictions along the GEMOT pipeline, including the thresholds for identifying candidate transcripts and driver transcripts. We have substantially revised the Methods section accordingly. Second, we provide direct evaluation of FDR for the grouping of traits in synthetic networks, when the actual solution is known new . Finally2) Non-local linkage disequilibrium: We certainly agree that in some cases it would not be possible to discern between several potential genomic intervals due to non-local linkage disequilibrium. To address this issue, we tested the linkage disequilibrium (LD) between the genomic interval of each of our identified modules and the entire genome. We added a new


The etiology of immune-related diseases or traits is often complex, involving many genetic and environmental factors and their interactions. While methodological approaches focusing on an outcome measured at one time point have succeeded in identifying genetic factors involved in immune-related traits, they fail to capture complex disease mechanisms that fluctuate over time. It is increasingly recognized that longitudinal studies, where an outcome is measured at multiple time points, have great potential to shed light on complex disease mechanisms involving genetic factors. However, longitudinal data require specialized statistical methods, especially in family studies where multiple sources of correlation in the data must be modeled. Using simulated data with known genetic effects, we examined the performance of different analytical methods for investigating associations between genetic factors and longitudinal phenotypes in twin data. The simulations were modeled on data from the Québec Newborn Twin Study, an ongoing population-based longitudinal study of twin births with multiple phenotypes, such as cortisol levels and body mass index, collected multiple times in infancy and early childhood and with sequencing data on immune-related genes and pathways. We compared approaches that we classify as (1) family-based methods applied to summaries of the observations over time, (2) longitudinal-based methods with simplifications of the familial correlation, and (3) Bayesian family-based method with simplifications of the temporal correlation. We found that for estimation of the genetic main and interaction effects, all methods gave estimates close to the true values and had similar power. If heritability estimation is desired, approaches of type (1) also provide heritability estimates close to the true value. Our work shows that the simpler approaches are likely adequate to detect genetic effects; however, interpretation of these effects is more challenging. It is increasingly recognized that longitudinal studies – where an outcome, or phenotype, is measured on each individual at multiple time points – have great potential to shed light on complex disease mechanisms involving genetic factors. The Quebec Newborn Twin Study (QNTS) is a prospective longitudinal investigation on twin pairs born between April 1, 1995 and December 31, 1998 in the Greater Montreal Area –4.α (TNF-α), interleukins (IL)-1b and -6, and chemokine ligand 2 (CCL2)  . Inflamm2 (CCL2) , 6. Calo2 (CCL2) , 7, 8. V2 (CCL2) . In addioung men . A systeoung men . Thus, gSince the QNTS contains longitudinal data on twin pairs, a challenge with the analysis of QNTS data is accounting for the correlation due to both repeated measurements over time and repeated measurements within a family. Many different approaches have been developed to analyze longitudinal data on unrelated samples , comWe evaluated several different approaches for the analysis of longitudinal family data. In the next section, we describe the methods that we evaluated. We then describe our simulations and our metrics for judging each approach.We divide the approaches into three categories (1) those that use a summary statistic of the phenotype over time, (2) those that simplify the correlation due to sampling multiple members of the same family, and (3) methods that simplify the correlation due to repeated measurements over time.The simplest form of analysis for a longitudinal outcome measure is to summarize the repeated measures for each individual. The analysis based on the summary measure can then be done using standard methods for family-based designs. We used the following individual summary measures: (1) the average over the time points, (2) the intercept and the slope calculated using a linear regression of BMI on age for each individual, and (3) the area under the curve (AUC) calculated using the trapz R function [pracma package ] implemeijY is the trait value for twin j in twin pair i, β is a vector of fixed effects corresponding to the vector of covariates xij to be included in the model and including an intercept, a, d, c, and e are the path coefficients and ijA, ijD, ijC, and ijE are mutually independent with standard normal distributions. The variance components for additive genetic a, d, c, and e, respectively. We fit the “ACE” model, including additive genetic, common environmental and residual variance components . Heritability can be estimated from this model as the ratio Since we are analyzing twin data, we then used the classical twin model  as impleFor all methods, covariates in the linear model included sex and genotype.We then considered methods that simplify the familial correlation. In the case of twin data, this means that the correlation structure corresponding to twin zygosity (MZ and DZ) is not correctly modeled. With the simplified correlation structure, conventional statistical methods for longitudinal data can be used. We evaluated two models described in Choi et al. . The firA third strategy involves modeling the correlation of phenotype that is due to kinship, as in the approaches of type (1). However, rather than use a summary of all time measurements, each time point is included in the analysis and the correlation between time points is assumed to be due to kinship. A Bayesian-based approach to estimate the variance components that could handle arbitrary family structure and continuous and binary traits was proposed by Burton et al.  and impln twin pairs are measured at six time points. Let the trait value for individual j of twin pair i at age k be denoted by ijkY for ijG and ijS represent the genotype  and sex of the individual j in twin pair i, and ijkT represent the age at the kth time point, the full model describing the association between trait and covariates isβ0, βS, βG, βT, and βGT are all considered fixed effects, β0ij is the random intercept, and Tijβ is the random time effect. We now describe our Bayesian model, which includes both genotype and genotype-by-age effects and assumes the twin study design. We assume ith twin pair isith twin pair isV0 is the covariance matrix for the random intercept effects and TV is the covariance matrix for the random slope effect. The variance components accounting for correlation due to kinship, the additive polygenic variances are The random effects are further decomposed into a random effect due to kinship and a random effect due to common environment. Letting MZ and DZ represent MZ and DZ twins, respectively, the model for the random intercepts for the Ind) is shared between the two twins and can be combined with the pair effect (Pair), which leads to the following model0ijTo implement this model, we used the twin model parameterization described in Visscher et al. , which in et al.  mention As this is a Bayesian approach, prior distributions are required for all model parameters. Following Burton et al. , flat prk ≤ 2 and k > 2. We considered several values of the simulation parameters, as described in Table Our simulations were performed using the model described in Section “We simulated 788 children (226 DZ pairs and 168 MZ pairs) based on the number of QNTS twins with at least three time points available. Sex and age values were defined as observed in the QNTS data. In order to get a complete dataset with six time points per individual, we imputed each missing visit (age) value by randomly sampling an existing age value at that visit. We chose to perform simulations on a complete dataset to facilitate the comparison of methods see . Genotypp-value of the genotype effect, or the genotype–time interaction effect when included, was smaller than 0.05. For the Bayesian approach, our estimate of power is the percentage of replicates where the 95% credible interval excluded 0.All analyses were performed in R  except wFigure In general, all methods of analysis yielded accurate estimates for most of the fixed effects of main interest . Estimates of variance components by the Bayesian model were very poorly estimated ; we discuss this further below.Variance components partitioning genetic, environmental and residual variance are estimated by two of the tested methods: the classical twin analysis and the Bayesian model. The classical twin analysis of the mean summary statistic provided accurate estimates of variance components and heritability of the mean (over time) phenotype . As it is challenging to implement methods with more complicated correlation structures, such as the approach of Burton et al. , the power to detect the genetic effect stayed high with the mean phenotype analysis. The main limitation in using summary measures is that it is difficult to clearly distinguish between a genetic effect on the mean phenotype or on the rate of change in the phenotype since the mean also captures the effect on change.Since we were analyzing twin data, we evaluated the performance of summary measures mainly with the classical twin analysis as implemented in twinlm. A benefit to twinlm is the ability to estimate the variance components; a disadvantage is that this software is only applicable to twin family structures. Therefore, with other family structures a general pedigree approach, such as that implemented in ASSOC of SAGE  would beAlthough generally power was similar and the genetic fixed effects were well estimated by all methods, not all methods provide estimates of the additive genetic variance. This estimate is important if heritability estimation is one of the goals of the analysis. Estimation of variance components parameters is done using twinlm and the Bayesian approach (discussed below). For the standard longitudinal approaches, the GEE approach treats the variance as a nuisance parameter and is not recommended if the variance components are of direct interest. The multi-level modeling does provide variance estimates but the variance that is estimated is not the additive genetic variance because of the simplification of the family structure. It may be possible to extend to longitudinal data existing mixed model parametrization of the biometrical twin models , althouFor our simulated data, we assumed no missing data. Specifically, all individuals in the dataset were observed at exactly six time points. We assumed an equal number of observations per individual to simplify the scripting of the Bayesian approach described in Burton et al. ; however6) to more informative (100 and 500). For the variance components, we modified the uniform range to include negative values and also to be less wide [U and ]. The results are essentially unchanged (results not shown).Because we were interested in comparing the Burton method to the other methods, we chose to implement the approach with the same non-informative prior distributions. Burton et al.  justify a priori it might be expected to perform poorly . Suo et al.  provide KB and MHRG designed the study, performed part of the programming and data analysis, supervised the simulations and analyses, and wrote the manuscript. JFL ran the simulations and also performed part of the programming and data analysis. LD, BFB, and CW provided content knowledge and wrote part of the manuscript. All authors reviewed and approved the manuscript.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.


The environment can play an important role in the evolution of senescence because the optimal allocation between somatic maintenance and reproduction depends on external factors influencing life expectancy.The aims of this study were to experimentally test whether environmental conditions during early life can shape senescence schedules, and if so, to examine whether variation among individuals or genotypes with respect to the degree of ageing differs across environments.Gasterosteus aculeatus, Linnaeus) in which F1 families originating from a wild annual population experienced different temperature regimes.We tested life‐history plasticity and quantified genetic effects on the pattern of senescence across different environments within a reaction norm framework by using an experiment on the three‐spined stickleback (Male sticklebacks that had experienced a more benign environment earlier in life subsequently reduced their investment in carotenoid‐based sexual signals early in the breeding season, and consequently senesced at a slower rate later in the season, compared to those that had developed under harsher conditions. This plasticity of ageing was genetically determined. Both antagonistic pleiotropy and genetic variation in the rate of senescence were evident only in the individuals raised in the harsher environment.The experimental demonstration of genotype‐by‐environment interactions influencing the rate of reproductive senescence provides interesting insights into the role of the environment in the evolution of life histories. The results suggest that benign conditions weaken the scope for senescence to evolve and that the dependence on the environment may maintain genetic variation under selection. The ability of a genotype to produce different phenotypes in response to distinct environmental conditions  and body condition as proxies of their investment in reproduction and self‐maintenance. The reproductive success of male sticklebacks depends on the expression of red coloration through improved mating success, nest defence and offspring survival Candolin . Male stThe aims of this study were therefore to use a longitudinal experiment to examine whether male sticklebacks change their investment in sexual signalling and consequent pattern of senescence in response to earlier environmental conditions, and if so, to examine whether this ability is genetically determined. We do the latter by exploring the quantitative genetics of temporal dynamics in sexual signal and condition  and by testing for a genotype‐by‐environment interaction in the pattern of senescence (G × T × E). We show that animals change their senescence schedules in response to environmental conditions, and that this ability is genetically determined.our unpublished data). In Iberian populations, adults disappear in summer and 2‐year‐old breeders have never been recorded  or four (N = 25 families) ‘growth tanks’ , each initially housing 11 or 12 juvenile fish . Two fish per tank were subsequently removed at age 5 months to be used in another experiment (Kim Artemia (from hatching to age 3 months) and a commercial pelleted diet . Natural photoperiod was simulated by programmed illumination.At age 40 days, fry in each full‐sib family were divided among two . Among the four aquaria systems, two were randomly assigned to the normal winter treatment group and the other two to the warm winter group. Therefore, each family was equally allocated into the two experimental groups. Water temperature in the normal winter group was gradually reduced from 14 °C in November to 9 °C in January then increased to 14 °C in March to simulate natural temperature change in the sampling site, whereas the temperature in the warm winter group was maintained at 14 °C from November onwards throughout the winter, so that the fish experienced a more benign juvenile environment .The water temperature in the growth tanks reflected the natural seasonal pattern at the sampling site of the parent fish  until the experimental manipulation of temperatures began in November as shown in Fig. S1. Juvenile fishes that survived until age 6 months were weighed and permanently marked with colour elastomer tags  under a low dose of benzocaine anaesthetic to allow tracking of individual‐specific life histories  were allocated into individual tanks containing a sponge filter and provided with sand and polyester thread as nesting materials ; they were then monitored for reproductive investment across the breeding season until August.N = 209) was shown a gravid female enclosed in a transparent glass for 5 min twice a week to prompt expression of nuptial colour and behavioural investment in nest construction and courtship    from the digital images by using In July, the level of mating competition was manipulated in order to test whether senescent males that had earlier experienced different temperature schemes differed in male–male competition strategies and terminal investment. Any effect of this competition treatment  on red coloration has been taken into account in all statistical analyses .N = 1020 observations from 104 males; warm‐treatment: N = 1061 observations from 105 males). In a linear mixed‐effect (LME) model fitted to each trait, experimental treatment (control or warm winter), hatching date, date of initiation of breeding (i.e. first expression of red throat coloration), strength of competition (strong or weak treatment), time (unit of 2 weeks between 26 March and 21 August) and interactions of interest were included as fixed effects, and individual identity, growth tank and full‐sib family were included as nested random effects. Additionally, body condition was also analysed in a LME model fitted to body mass and including standard body length as an additional covariate . Non‐significant fixed effects were dropped sequentially by using deletion tests, and then, the final LME model was fitted using the default restricted maximum likelihood (REML) to obtain estimates and significance levels of fixed effects in r (version 3.0.2).We first explored the effects of the temperature manipulation on the temporal dynamics of relative red area and body condition of the male sticklebacks by using longitudinal analyses of repeated measures . The random regression (RR) is the most widely applied function‐valued trait approach, and when applied to longitudinal data, RR can provide a direct test of individual variation in ageing rates. We followed recently described methods to construct RRAMs for the quantitative genetics of ageing  for relative red area and body condition, while permanent environment , maternal  and common environment  effects were negligible . Therefore, clutch and growth tank were not included as random effects in the RRAM analyses, but individual identity was included to account for the repeated sampling and individual (co)variance. Body condition was analysed using only mass‐standard length residuals and not body mass, because the latter requires including standard length as a covariate. Since body length itself is a heritable trait that is genetically correlated with body mass, including this covariate as a fixed effect in the RRAM analysis can severely bias estimates of the genetic parameters variances across time in relative red area and body condition  by using pedigree‐based REML random regression animal models (RRAMs), implemented in s Wilson .i was expressed as a function of standardized time t (unit of 2 weeks) to a scale from −1 to 1. By using univariate RRAMs fitted to the control and warm winter groups separately, we first estimated the between‐individual variations in average trait (elevation) and ageing rates (linear and quadratic slopes of the trait measurement over standardized time) and the covariances between elevation and slopes. Then, the individual level RR function  was partitioned further to estimate the contributions of genetic effects (G) and non‐genetic effects due to individual‐specific past environmental conditions  to the individual variations in average trait and ageing rate (G × T and PE × T). Thus, we fitted the hierarchical univariate models for a trait T of individual i at time t as:In the RRAMs, relative red area and body condition in individual i,t). Apart from the overall trait mean μ, timeF and compF are factorial fixed effects that denote time (an 11 level factor) and competition treatment (a two level factor). Then, f was fitted as the RR function of zero order (x = 0), which specifies the between‐individual variation in the average trait. When x = 0, the variance across individuals (ind0) is estimated at the average time value of the individual‐specific variation. In subsequent models, f was partitioned into additive genetic and permanent environment components, f and f, then different orthogonal polynomial functions of time were specified to examine how the effects differed between constant , linear  and quadratic forms . Therefore, a0 and pe0 refer to the variances in reaction norm elevations, representing additive genetic and permanent environmental effects on the average trait value; a1, a2, pe1 and pe2 refer to the variances in reaction norm slopes, representing genetic and permanent environmental effects on ageing rates of either linear or quadratic form. In addition, the RRAMs also estimated the covariances among elevation and slopes. Significance of (co)variance components was assessed by using model comparisons based on likelihood ratio tests (LRT).We fitted the models in hierarchical order, starting from only fixed effects and heterogeneous residual error . The univariate model structures were the same as above, but here we considered linear reaction norms only by fitting polynomial functions of a zero and first order because the analyses based on the full data set suggested linear reaction norm patterns during this period.Senescence (i.e. a decline) in red coloration commenced in mid‐May see . TherefoG × T and PE × T) differed between the control and warm winter groups, we used bivariate RRAMs. A G × T × E interaction is expected if genetic effects on ageing differ between environments. We combined the data sets and pedigree information from the two groups and tested for G × T × E and PE × T × E interactions. For example, relative red area of the two treatment groups was fitted as two response variables to a bivariate RRAM. Here, all covariances between the two treatment groups were constrained to be zero by modelling the genetic, permanent environment and residual variances as treatment‐specific matrices. For the comparison between the treatment groups, the respective (co)variance components  in the two groups were constrained to be equal, assuming that they have the same genetic and permanent environmental variances in average trait and ageing rate. The likelihood optimized under the constrained model was compared to that of the unconstrained model by using LRT , and also had a higher peak coloration .The date of initiation of breeding was significantly earlier for the warm‐treated than the control males  and PE × T2 (pe2)] in both control and warm winter groups . There was significant improvement in the model when fitting a G × T (a1) component ; the inclusion of a second‐order a2 term did not significantly improve the model . In the analysis of changes in relative red area from the onset of senescence onwards (≥9th week), there was significant individual (PE × T) and genetic (G × T) variance in the rate of senescence in the control males, but only the individual variance (PE × T) was significant in the warm‐treated males .In the analysis of the full data set, the relative area of the red throat showed significant linear and quadratic individual‐by‐time interactions [PE × T × E and G × T × E interactions , and Cova0,a1 differed significantly from zero  values of the best‐fit univariate RRAMs, in order to illustrate the patterns of the significant PE × ons Fig. . The perons Fig. . In othero Table . In contro Table .I × T2 interaction in both control and warm winter groups , with no difference in pattern between them . In the control males , this could be decomposed into significant G × T2 and PE × T2 components (P = 0·016), since additive genetic variance for body condition increased over the breeding season whereas permanent environment variance decreased over the same period . There was no significant covariance between any elevation–slope combinations of body condition in either temperature treatment group .Univariate RRAMs of body condition suggested the presence of a significant G × T (genetic variance in the rate of senescence) between the experimental groups suggests that the importance of antagonistic pleiotropic effects depends on environmental conditions, such that these can shape senescence schedules in natural populations through heritable differences in life‐history plasticity.The association shown here between the effort invested by male sticklebacks in sexual signalling early in the breeding season and the rate of ageing later in the season provides experimental support for the disposable soma theory. Meanwhile, our results on the quantitative genetics of senescence in sexual signals support the antagonistic pleiotropy theory of ageing. But perhaps most importantly, we experimentally demonstrated the expression of significant G × E interactions influencing the pattern of senescence. The environment experienced by males prior to the breeding season influenced their investment in early reproduction and subsequent rate of ageing. The difference in et al. In accordance with previous studies of sticklebacks showing that warm temperatures prior to the breeding season prompt a slower lifestyle and delayed senescence , and that the pattern of ageing also showed heritable variation, at least in control males. While the three‐spined stickleback has frequently been used as a model system to study the evolution of sexual signals  suggests that a male's strategy for the timing of allocation of carotenoids and other resources into sexual signalling vs. somatic maintenance through the reproductive season is heritable and should also be subject to evolution under selection. An interesting question here is how the genetic variation in senescence rates is maintained – possibly due to fluctuating selection , which support two important ideas. First, the data support the antagonistic pleiotropy theory of ageing that predicts a genetic link between enhanced performance earlier in life and an accelerated rate of senescence (Kirkwood & Rose et al. et al. et al. G × T × E effects (Schlichting & Pigliucci G × T × E in red coloration appeared mainly because the redder genotypes reduced their colour expression early in the breeding season after experiencing benign environmental conditions. Although the temperature at the beginning of the breeding season was the same in the two environmental treatments, the males raised in warm winter conditions experienced lower seasonality than the control males. It is possible that the reduced seasonal difference in temperatures might prompt the warm‐treated breeders, particularly those of redder genotypes, to suppress the expression of red ornamentation via a downregulation of their sexual hormones (Gonzalez et al. Most interestingly, this present study provides evidence for genotype‐by‐environment interactions in the rate of senescence (This study provides interesting insights into the role of environment in the evolution of life histories and sexual signals. We have shown experimentally that environmental conditions experienced by individuals during early life can determine life‐history integration and trade‐offs by shaping their investment in sexual signalling and senescence schedules. Importantly, genetic variation in the rate of senescence was reduced to a non‐significant level among individuals raised in a benign environment. Therefore, more benign environmental conditions weaken the scope for evolution in the pattern of senescence. The environmental dependence may also explain the maintenance of genetic variation in life‐history and secondary sexual traits against the eroding effects of strong natural and sexual selection in natural populations.http://dx.doi.org/10.5061/dryad.s6h6b (Kim, Metcalfe & Velando Data available from the Dryad Digital Repository Appendix S1. Sampling of monitored sticklebacks.Appendix S2. Male–male competition experiment.Table S1. Results from the linear mixed model of body mass of male sticklebacks.Table S2. Variance components, heritability and environmental effects from univariate animal models.Table S3. Results from the random regression animal models of relative red area and body condition.Figure S1. Seasonal change in the water temperature of the F1 growth tanks of normal and warm winter treatment groups.Figure S2. Relationship between seasonal change in body condition and time of maturation of males from the control and warm winter groups.Figure S3. Plots of the reaction norms for body condition of individual sticklebacks of the control and warm winter schemes.Click here for additional data file.


Septoria tritici blotch is an important leaf disease of European winter wheat. In our survey, we analyzed Septoria tritici blotch resistance in field trials with a large population of 1,055 elite hybrids and their 87 parental lines. Entries were fingerprinted with the 9 k SNP array. The accuracy of prediction of Septoria tritici blotch resistance achieved with different genome-wide mapping approaches was evaluated based on robust cross validation scenarios.P < 0.01) larger than zero. The cross validation study revealed an absence of large effect QTL for additive and dominance effects. Application of genomic selection approaches particularly designed to tackle complex agronomic traits allowed to double the accuracy of prediction of Septoria tritici blotch resistance compared to calculation methods suited to detect QTL with large effects.Septoria tritici blotch disease severities were normally distributed, with genotypic variation being significantly  contains supplementary material, which is available to authorized users. Mycosphaerella graminicola (anamorph Septoria tritici) has become one of the most devastating leaf diseases in Central European winter wheat (Triticum aestivum L.). The high input of fungicides in combating this disease has led to a high percentage of fungal strains showing resistance to strobilurines [Septoria tritici blotch disease caused by ilurines . Moreoveilurines . BreedinStb gene  that Stb1-18, , 10 and Stb1-18, . Many Euhe field . A QTL ahe field . QTL anaobserved . Negativregating , 15. ThuDespite success in detecting genomic regions involved in quantitative disease resistance, the underlying complex genetic architecture often prevents marker-assisted selection with high accuracy . As an aThe current study relies on a diverse population of 1,055 European wheat hybrids and their 87 parental lines that were evaluated for adult-plant resistance to Septoria tritici blotch disease as well as fingerprinted with a 9 k SNP array. We applied one targeted association mapping and two genome-wide prediction approaches coupled with cross validations. Our objectives were to (1) study the potential to predict Septoria tritici blotch resistance in wheat and (2) evaluate the importance of additive, dominance and epistatic effects for Septoria tritici blotch resistance.Triticum aestivum L.) hybrids and their 87 parental lines  and Harzhof near Eckernförde , in the year 2012. The experimental design was an alpha design where replication and location effects were confounded. Sowing density ranged from 230 to 250 grains m6 spores/ml for one time when all genotypes had fully expanded flag leaves. In Harzhof, natural infection was followed. Septoria tritici blotch disease severity was visually scored plot wise as coverage of flag leaves with lesions bearing pycnidia on a scale from 1 (fully resistant) to 9 (fully susceptible). Data were recorded on 28th of June in both environments. Heading date (in days since January 1st) and plant height (in cm) were evaluated in addition.In Cecilienkoog, targeted inoculation with a mixture of isolates was performed by spraying a spore suspension with a concentration of 1 × 10Rht-B1 and Rht-D1 were genotyped by two functional markers  in the whole population of parents. Out of the 72 female lines, 25 and 45 lines turned out to carry dwarfing alleles at loci Rht-B1 and Rht-D1, respectively. In addition, two male parents had a dwarfing allele at locus Rht-B1.Genotyping was done with the wheat 9 k SNP array based on the Illumina Infinium assay (for details see ). We perP values were used as an approximation [σ2G) versus the phenotypic variance (σ2P), i.e., σ2G/σ2P. The phenotypic variance σ2P comprises σ2G and the masking variances divided by the number of locations. In addition, we assumed fixed genetic effects and estimated the Best Linear Unbiased Estimates of the 1,142 genotypes.We performed lattice analyses of variance . The varximation . Heritab∞ metric [P < 1.25e-6). All above outlined statistical analyses were performed using the software ASReml 3.0 [We specified the additive and dominance design matrices for the hybrids and their parental lines according to the F∞ metric . Based o∞ metric . We cont∞ metric . To test∞ metric  and diviReml 3.0 . We usedπ[Based on the adjusted entry means of the 1,142 genotypes, we applied Ridge Regression Best Linear Unbiased Prediction (RR-BLUP)  and Bayeπ, 30 consπ. All staπ.We evaluated the accuracy of prediction of Septoria tritici blotch resistance by association mapping and the two genomic selection approaches using cross validations. Since population structure in factorial crosses strongly influences prediction accuracy, we used a cross validation strategy where training and validation sets were not related to each other via common parental lines. We sampled 100 times 400 hybrids derived from 10 male and 47 female parental lines as training set and estimated the additive and dominance effects. Hybrids based on the remaining parental lines formed the validation set in which predictions derived from the training set were tested for their accuracy. For every training set, we applied the genomic selection as well as the association mapping models outlined above. For the association mapping approach, we corrected for population stratification with a kinship matrix and identified significant marker-trait associations using a false discovery rate (FDR) of 0.1. We predicted the hybrid performance using the estimated marker effects. The implementation of RR-BLUP was based on estimates of the genetic variances and heritability of the full population. Prediction accuracy was estimated as Pearson’s correlation coefficient between the observed and the predicted hybrid performance dividing by the square root of the heritability on an entry-mean basis. We used the heritability on an entry-mean basis estimated for the full population, because this estimate possesses a lower standard error compared to the heritability estimated in the training population.P < 0.01). Among the parental lines, males showed a slightly lower Septoria tritici blotch severity than females (5.2 vs. 5.7). Across locations, Septoria tritici blotch severities amounted to on average 4.5 for parental lines and 4.0 for hybrids on the 1–9 scale. The distribution of the genotypic values of both material sets, lines and hybrids, followed approximately a normal distribution . Variance of SCA effects was not significantly larger than zero (0.02). Heritability estimates were high for the lines and moderate for the hybrids.Septoria tritici blotch disease severity revealed higher mean ratings for both lines and hybrids in Cecilienkoog than in Harzhof. The correlation between values estimated at both locations was significant  correlation between plant height and Septoria tritici blotch severity .We observed a moderate, yet significant  correlated. Similarly, Schilly et al. [P < 0.01) different from zero for both lines and hybrids. Because natural S. tritici populations are highly variable in their race composition and most probably differed from the isolates used for inoculation, we can assume that we assessed broad-based adult-plant resistances in this study.Artificial and natural infection led to a broad range of Septoria tritici blotch severity scores among lines and hybrids, illustrating the occurrence of resistance in the population Table . Mean diy et al.  had repoSeptoria tritici blotch resistance is associated with increased plant height , this might at least partially explain why the dwarfing genes did not show association with Septoria tritici blotch resistance at a genome wide level.On the level of genes, this morphological resistance was reflected in previous reports by the co-localization of QTL for Septoria tritici blotch resistance and with dwarfing gene loci , 33 as w. On this chromosome, the race-specific resistance gene Stb1 is located [Stb1, however, prevents a further study in detail. Moreover, the source of the Stb1 gene is a Bulgarian landrace, which has to our knowledge not yet been introgressed into Central European elite wheat lines. Two QTL from History/Rubens  and one QTL from Arina/Forno (44 cM) have been also located in a similar region in a previous study on chromosome 5B [Eight SNPs were significantly associated with Septoria tritici blotch resistance Table  with a S located . Absenceosome 5B . In Histosome 5B . In accoosome 5B  detected∞ metric. A further reason for the low benefit to exploit besides additive also dominance effects is the large proportion of unexplained variation entering the prediction model when dominance effects are included [The analysis of variance revealed a high importance of general combination ability effects as would be expected for quantitative pathogen resistances . Variancincluded .We tested for the presence of epistatic effects among loci by a full two-dimensional scan. As expected for selfing species such as wheat , additivA thorough evaluation of the potential to increase the prediction accuracy in genome-wide mapping approaches through the exploitation of epistasis requires cross validation studies. We have not performed these analyses, due to the high computational demand for two-dimensional scans of epistasis. There exists a strong demand to develop computational efficient methods to tackle epistatic interactions in genome-wide mapping studies based on high-density SNP arrays. Moreover, further research is needed to investigate methods suited to scale the epistatic variance components relative to the variance of the main effects.i.e. training and validation sets did not share any parents. If the information for the female or male parents is additionally implemented in the model, the accuracy rises to 0.6  or 0.87 .Both applied genomic selection procedures had a considerably higher accuracy to predict Septoria tritici blotch resistance than the association mapping approach Figure . ConsequFor our data set, we observed a slight superiority of RR-BLUP compared to BayesCπ. While RR-BLUP approximates the infinitesimal model, BayesCπ relies on the assumption that particular loci contributed stronger to the phenotypic variance than others . ConsequThe data is available from the Dryad Digital Repository: doi:10.5061/dryad.461nc.Additional file 1: Figure S1: Crossing scheme between the 72 female and 15 male wheat lines. Open boxes indicate presence and filled boxes indicate absence of a particular cross. (EPS 807 KB)Additional file 2: Figure S2: Quantile-quantile plots for association mapping based on the combined population of hybrids and lines using two different biometrical approaches, (1) without correction for population structure, and (2) correcting for population structure with a kinship matrix. (EPS 830 KB)Additional file 3: Figure S3: Association of Septoria tritici blotch rating  and plant height for 1,055 hybrids and 135 lines, r = coefficient of correlation, *** = *** Significantly different from zero at 0.001 level of probability. (EPS 809 KB)P values for 4 different types of digenic epistatic effects. (EPS 1 MB)Additional file 4: Figure S4: Distribution of


ULK4 on chromosome 3 suggest that inference obtained from a copula model can be more informative than findings from the SBP-specific and DBP-specific univariate models alone.We conduct genetic association analysis in the subset of unrelated individuals from the San Antonio Family Studies pedigrees, applying a two-stage approach to take account of the dependence between systolic and diastolic blood pressure (SBP and DBP). In the first stage, we adjust blood pressure for the effects of age, sex, smoking, and use of antihypertensive medication based on a novel modification of censored regression. In the second stage, we model the bivariate distribution of the adjusted SBP and DBP phenotypes by a copula function with interpretable SBP-DBP correlation parameters. This allows us to identify genetic variants associated with each of the adjusted blood pressures, as well as variants that explain the association between the two phenotypes. Within this framework, we define a pleiotropic variant as one that reduces the SBP-DBP correlation. Our results for whole genome sequence variants in the gene  A number of genome-wide association studies (GWAS) involving large populations have been conducted to identify genetic variants associated with various single blood pressure (BP) measures: systolic blood pressure (SBP), diastolic blood pressure (DBP), or a linear function of them. Although the correlation between SBP and DBP is high, the results of the GWAS for each separately indicate only partially overlapping sets of variants associated with SBP and DBP. In this report, we model SBP and DBP jointly, taking the association between them into account. Constructing a bivariate model for these two phenotypes can increase the power to detect causal variants for one or both phenotypes, shedding more light onto the complex underlying genetic processes.We apply copula functions  to modelOur analysis has two objectives: (a) to investigate the association of some common variants with SBP and DBP under the joint model of SBP and DBP, and (b) to identify pleiotropic variants, which we define as variants that explain the association between SBP and DBP.ULK4 gene previously found to be associated with DBP [The Genetic Analysis Workshop 18 (GAW18) data set includes 153 unrelated individuals from the San Antonio family studies pedigrees having SBP and DBP measurements at one or more study exams, information regarding current use of antihypertensive medication, and nongenetic covariates sex, age, and current tobacco smoking status at some examinations. To retain all subjects, we imputed missing age values by adding the mean time interval between measurements to the last known age of a subject. Some missing values of smoking status were also imputed by examining the smoking patterns of individuals over the four time points. We later verified that these imputations did not lead to any significant differences in parameter estimates and inference. Among the 153 unrelated individuals with measured phenotype data, 100 have whole genome sequence data. We conducted our genetic analysis on chromosome 3 in this group, considering only the with DBP . We analBefore modeling the joint distribution of SBP and DBP conditional on genetic variants, we first adjusted the observed BPs for the effect of antihypertensive medication and other nongenetic covariates. The GAW18 unrelated pedigree members include hypertensive individuals  and some taking antihypertensive medication , the conditional expectation isj = 1,2,3) separately for SBP and DBP, and took these mean residuals as our adjusted phenotypes.where X are independent of the nongenetic variants Z. In the marginal modelsIn the second stage, we first constructed the marginal models for our adjusted phenotypes C to build the bivariate distribution of we observed no evidence against the normality assumptions for the error terms. We then used a copula function ψ is the vector of copula parameters. To illustrate the approach, consider the 2-parameter copula familywhere Lλ, Uλ, respectively), which explain the amount of dependence between extreme values, and can give more insight in identifying pleiotropic variants. For the copula family in (6), these dependence measures become [with We obtain MLEs of the marginal parameters α=α0,α,σ1, β=β0To address aim (a) concerning the marginal association of a variant with each SBP and DBP under the bivariate model (5), we test the null hypotheses φ and θ, and dependence measures (7) are of interest. We compare estimates of Kendall's φ goes to 0. However, because it is practically impossible to identify all variants, instead of testing independence, we search for variants that reduce the magnitude of the overall dependence measures, such as Kendall's τ.In contrast, for aim (b), which is to identify a variant that explains association between SBP and DBP, the copula model dependence parameters p values of the MLE estimates of the coefficients p values for testing p values 1.7 × 10−4 and 5.1 × 10−5, respectively) are smaller than the p values under the working independence model . This includes variants significantly associated with both BP phenotypes under the joint copula model, although they are not significantly associated at the 1% level with either under the univariate phenotypic models  value under the copula model (6) is much lower than the AIC under a bivariate normal model, indicating that the copula model is a better fit. For example, the AIC value under the copula model (6) reported in Table ULK4, Kendall's tau and lower tail dependence do not differ markedly. We observe that without conditioning on any variant p value = 0.040) and DBP , but the upper tail dependence is reduced from 0.449 obtained under the null model to 0.289 with a CI that includes 0 , and although we observed some reduction in point estimates of lower tail dependence and Kendall's tau, the CIs still overlap with those under the null model. Calling a comparison significant when the CIs fail to overlap is a conservative approach, but it is computationally efficient. As an alternative, a nonparametric bootstrap procedure could be used to estimate the variance of the estimated difference between dependence measures under the null and full models, and to construct an approximate CI. To allow multiple testing adjustments, instead of checking whether the CI for In principle, the extension of our approach to 3 or more quantitative traits is straightforward; however, the copula model 6) may not be ideal in this setting. It involves some restrictions on the association structure, and generally the Gaussian copula is used when there are 3 or more traits. The approach could also be extended to binary traits, but with some caution because there is no unique copula identifying the joint distribution function of discrete variables [ may not The authors declare that they have no competing interests.YEY and SBB designed the overall study, SK conducted statistical analyses, and SK and YEY drafted the manuscript. All authors read and approved the final manuscript.