We propose a new computational framework, probabilistic transcriptome-wide association study (PTWAS), to investigate causal relationships between gene expressions and complex traits. PTWAS applies the established principles from instrumental variables analysis and takes advantage of probabilistic eQTL annotations to delineate and tackle the unique challenges arising in TWAS. PTWAS not only confers higher power than the existing methods but also provides novel functionalities to evaluate the causal assumptions and estimate tissue- or cell-type-specific gene-to-trait effects. We illustrate the power of PTWAS by analyzing the eQTL data across 49 tissues from GTEx (v8) and GWAS summary statistics from 114 complex traits. Over the past two decades, genome-wide association studies (GWAS) have identified an abundance of genetic loci associated with complex traits and diseases . Howevertesting causal relationships from gene expressions to complex traits. IV analysis, in comparison to other competing causal inference frameworks, is particularly suitable for TWAS because of its explicit consideration of confounding factors in the model formulation. However, we note that existing TWAS methods have at least two notable weaknesses when considering under the framework of IV analysis. First, validating the causal implications from the positive association findings from TWAS is mostly unaddressed. Second, efficient estimation of causal effects remains an open problem. The latter issue is particularly crucial for investigating causal molecular mechanisms in different cellular environments. In this paper, we show that the solutions to these problems can be directly derived from the established principles of IV analysis. Compared to the traditional applications of IV/MR analysis, TWAS also presents some unique challenges. Most notably, it deals with tens of thousands of candidate genes for each given complex trait of interest, which warrants a powerful and efficient testing procedure. Such procedures are under-developed in the traditional IV analysis literature. Additionally, it is now well-known that a single gene can be regulated by multiple independent genetic variants, which is known as allelic heterogeneity (AH) [IV analysis naturally integrates genetic, molecular phenotype, and complex trait data and investigates the causal links from molecular phenotypes  leading to complex diseases. Most popular approaches for transcriptome-wide association analysis (TWAS), e.g., PrediXcan , TWAS-Fuity (AH) . Howeverity (AH) , which rprobabilistic analysis of transcriptome-wide association study, or PTWAS, to address three interrelated areas in TWAS analysis:Testing of the causal relationship from genes to complex traitsValidating causal implications through model diagnosisEstimating causal effects from genes to complex traits In this paper, we propose a new analytic framework named as cis-eQTLs. This feature provides excellent convenience and flexibility to account for uncertainty in eQTLs for both testing and estimation purposes. Taking advantage of widespread allelic heterogeneity, PTWAS also provides a principled way to examine the causal implications from the PTWAS analysis. Through theoretical derivation and numerical simulation studies, we illustrate the advantages of PTWAS over the existing methods. We apply PTWAS to analyze the eQTL data from the GTEx project (version 8) [p values) in investigating and interpreting causal molecular mechanisms of complex traits. The software package and utilities implementing the proposed computational approaches and relevant resources are available in https://github.com/xqwen/ptwas[PTWAS is built upon the causal inference framework of IV analysis and is designed specifically to deal with the challenges arising from the TWAS analysis. PTWAS utilizes the probabilistic annotations of eQTLs derived from the state-of-the-art multi-SNP analysis method for fine-mapping of rsion 8)  and 114 rsion 8)  and otheThe causal inference procedure implemented in PTWAS involves three sequential stages that cover hypothesis testing, causal assumption validation, and effect size estimation. PTWAS works with summary-level statistics from GWAS and probabilistic annotations of eQTLs derived from the multi-SNP fine-mapping analysis. The PTWAS procedure starts with a multiple hypothesis testing of causal relations between candidate genes and the complex trait of interest, which yields an outcome that is similar to the results of PrediXcan and TWAS-Fusion. For all the genes rejected in the first stage, PTWAS further performs a model diagnosis procedure to detect potential violations of the critical causal assumptions in the IV analysis. Finally, an estimate of the causal effect on the complex trait of interest is derived for each qualified gene that passes previous screening steps. Figure strong instruments for inference and model diagnosis. Specifically, we use the probabilistic quantifications of cis-eQTLs derived from the fine-mapping analysis to characterize the strength of eQTLs while accounting for allelic heterogeneity and LD [posterior model probability; (ii) the posterior inclusion probability (PIP) for each SNP ; and (iii) the posterior probability for an independent signal cluster, which we refer to as signal-level PIP, or SPIP. A signal cluster consists of a set of SNPs in LD that are deemed to represent the same underlying causal eQTL, but not completely identifiable based on the association data. The Bayesian credible set now commonly used in fine-mapping analyses of genetic associations [p)% Bayesian credible set can be constructed from a signal cluster by selecting the minimum subset of representing SNPs with cumulative PIPs ≥p).A key feature of PTWAS is that we adopt a well-established statistical principle in the IV analysis to construct and utilize y and LD , 13. Forciations  is specicomposite instrumental variable [For hypothesis testing, we construct a variable , 16 as tvariable .strong eQTL signal cluster . The emphasis on exclusive usage of strong eQTLs is because weak eQTLs are considered to be weak instruments, which provides unreliable and severely biased causal effect estimates. Within each selected signal cluster, we first compute a SNP-level estimate, known as the Ward ratio estimate, for each member SNP. We then combine the SNP-level estimates from the member SNPs weighted by their corresponding PIPs. This novel signal cluster-level estimator is derived from the principle of Bayesian model averaging (BMA) and fully accounts for the uncertainty by LD. Across multiple strong eQTL signals, we compute an I2 statistic [I2 statistic range from 0 to 1, with I2=1, indicating the highest level of inconsistency. Of note, we refrain from adopting a hypothesis testing approach to classify low and high heterogeneity and only use I2 as a quantitative measure, following the rationale discussed in [For the genes that pass the initial PTWAS scan, we consider validating the causal assumptions of the IV analysis before formally estimating their gene-to-trait effects. Particularly, the proposed validation procedure aims to guard against the existence of potential pleiotropic effects, which allows eQTLs to act on the complex traits through an alternative casual path, bypassing the genes of interest. Note that all existing hypothesis testing procedures in the TWAS analysis, including the proposed PTWAS scan procedure, can not automatically distinguish pleiotropic effects. Consequently, the causal interpretation of TWAS association testing relies on the causal assumption known as exclusion assumption (ER), which claims no pleiotropic effects. The proposed validation procedure serves as a post hoc filtering procedure that can effectively identify severe violations of the ER assumption and exclude them from the downstream estimation procedure. The intuition behind the proposed procedure is simple: each independent eQTL can yield an independent estimate of the gene-to-trait effect of interest. If the causal assumptions of the IV analysis hold, these independent estimates representing the same underlying gene-to-trait effect should be highly consistent. Conversely, a high level of inconsistency/heterogeneity observed from the estimates are most likely explained by the pleiotropic effects (which unlikely yield the same direction and magnitude for multiple independent eQTLs) . The protatistic  to quantussed in .I2 value, we further aggregate the signal-level estimates by applying a fixed-effect meta-analysis model, which results in a final gene-level estimate of the causal effect by PTWAS. This estimator of gene-to-trait effects is similar to the IVW estimator in the IV analysis literature [For the genes with small terature , which iterature . Howeverpredicting/imputing gene expression levels from eQTL information. The composite IVs constructed by PTWAS can also be interpreted as a natural ensemble predictions of gene expressions. Additionally, the separation of the hypothesis testing and the effect size estimation procedures is also a unique feature in PTWAS. Particularly, the emphasis on estimation accuracy prompts a slightly different statistical strategy from hypothesis testing. Our proposed estimation and model validation procedures are derived from the well-established principles of the IV analysis and should provide unbiased estimates and calibrated error quantifications while taking advantage of widespread allelic heterogeneity and accounting for LD. Most importantly, these properties enable valid and meaningful comparisons of gene-to-trait effects in different cellular environments within the context of TWAS.PTWAS conceptually connects to all the existing TWAS methods, especially in the stage of scanning candidate genes. However, it also presents some notable distinctions. Both PTWAS and SMR are derived from the IV analysis. However, PTWAS explicitly takes advantage of the widespread allelic heterogeneity by constructing the composite IV and testing causal effects from multiple independent eQTLs. Both TWAS-Fusion and PrediXcan focus on z-statistics from single-SNP analysis, by including both strong sparse association signals and weak polygenic background effects.We perform simulation studies to validate the proposed PTWAS method and compare its performance to the existing approaches. Our simulated datasets attempt to match the features of observed eQTL and GWAS data in practice, e.g., the distribution of We compare the PTWAS scan procedure to the existing methods, including PrediXcan, TWAS-Fusion, and SMR. We find that all examined approaches effectively control the type I errors in the scan procedure of testing causal genes Fig. . HoweverUsing the simulated data, we inspect the weight distribution over SNPs from the composite IVs constructed by different approaches. Specifically, we measure the concentration/dispersion of the (absolute) weights among SNPs using the Gini coefficient, which effectively measures the sparsity of weights ). ParticThe observations from this set of simulations seem to confirm that our design principle of PTWAS for explicitly accounting for allelic heterogeneity and LD contributes to the improved scan performance.We further examine the estimation procedure by PTWAS and various TWAS methods using simulations. In this particular experiment, we focus on estimating the effects of genes that pass the initial PTWAS scan. It is important to note that our criteria to evaluate the estimation procedures differ from the hypothesis testing, and has a distinct focus on the estimation accuracy  on the gene-to-trait effects.It might be intuitive to estimate the causal effect from a target gene to the complex trait of interest by simply regressing the complex trait phenotype on the composite IV or genetically predicted gene expression of the target gene. This approach, however, is not principled mainly because it ignores substantial uncertainty associated with the imputed gene expression levels. In practice, such ad hoc approach shows both noticeable bias and large variance in estimation Fig. .Fig. 3BWe evaluate the proposed effect estimation procedure and compare its performance to SMR, which implements a standard two-stage least square (2SLS) algorithm by utilizing the strongest eQTL SNP  as the sole instrument. In our simulation studies, both PTWAS and SMR yield seemingly unbiased estimates Fig. . HoweverI2 in Fig. I2 computed from multiple independent eQTLs with modest strength (SPIP >0.50) is expected to be less than 0.10.In all cases, we find that the estimation accuracy is directly correlated with the strength of instruments , which is quantified by the corresponding signal-level PIPs Fig. . By emplz-statistic from the estimated causal effect and the corresponding standard error. We find this approach has slightly better power (0.725 at FDR 5% level) than the SMR test (0.713). However, both are markedly less powerful than the Fusion (0.781), PrediXcan (0.784), and the proposed PTWAS scan procedure (0.800) at the same rejection threshold. We suspect this phenomenon is mainly due to the difficulty in estimating the SNP-level standard errors (used by both SMR and the proposed estimation procedure). The estimated standard errors tend to be conservative in the lack of sufficiently large samples. Therefore, we do not recommend to replace the proposed PTWAS scan procedure with the SMR-like test.Last, we consider the possibility of conducting the scan procedure using the estimated causal effects as the SMR test. Specifically, we construct a In summary, we conclude that both principled effect estimation approaches, SMR and PTWAS, produce unbiased estimates in causal effect estimation. PTWAS shows improved precision by accounting for LD, the strength of the eQTL instruments, and the multiple independent eQTLs. The simulations also provide us some practical guidelines on the threshold values for strong instruments. Informed by the simulation results, we decide to admit eQTLs with signal-level PIP >0.50 for model validation and effect size estimation in our real data analysis.cis-eQTLs across 49 tissues. A total of 32,363 candidate genes are selected for the PTWAS analysis. For the analyses that we present in this paper, we utilize only the GWAS summary-level association statistics derived from the single-SNP analysis. Additional summary-level statistics for unreported GWAS SNPs in each trait are imputed to match the cis-SNPs in the GTEx panel.We perform the PTWAS analysis on 114 complex traits from the UK Biobank (45 traits) and multiple large-scale consortia 69 traits), including CARDiOGRAM, PGC, and GIANT, by the GTEx GWAS working group  . The complete list of significant gene-traits is provided in Additional file ρ=0.55, p value =1.1×10−4) between the TWAS discovery and the estimated heritability . Figure p values of height-associated genes from UK biobank data and GIANT consortium. The strong linear trend indicates that both studies consistently give higher ranks of association for the same set of genes. However, the evidence from the UK Biobank data, with a much larger sample size, is often orders of magnitude stronger.Across 114 traits, we reject the global null hypothesis for 115,327 gene-trait pairs at the false discovery rate (FDR) 5% level  of the cases with I2 values exceeding 0.5. As expected, we find that the ability to detect high degrees of heterogeneity in estimated causal effects improves with the increased availability of independent eQTL instruments. Nevertheless, the main feature of the I2 distribution remains the same for different numbers of available IVs  in artery tibial (I2=0.94), CTB-171A8.1 to LDL cholesterol in artery aorta (I2=0.96), and HLA-DQB2 to height in muscle skeletal (I2=0.98)  In these examples, we observe the common pattern that the SNP-level estimates from correlated SNPs within each signal cluster are highly consistent, yet between the signal clusters, the estimates show high levels of inconsistency. In literature, GUCY1A1 is considered a potential causal gene to CAD. Despite the association evidence discovered in a seemingly relevant tissue, the substantial inconsistency of the estimated gene-to-trait effects indicates that the role of the gene to the underlying disease can be complicated. In the case of the gene HLA-DQB2 where we compute the I2 from the UK Biobank data, a similar high I2 value is also confirmed by the height data from the GIANT consortium (I2=0.77). Similarly in the case of CTB-171A8.1 where the original I2 is computed from the LDL data from the global lipid genetics consortium (GLGC), a confirmative I2=0.97 is also found from the data of self-reported high cholesterol levels (binary outcomes) in the UK Biobank.We show some examples of PTWAS scan signals that seemingly violate the exclusion restriction in Fig. p value =5.71×10−10 via Fisher’s exact test).As an additional empirical validation, we select 739 high-confidence heart disease-related trait-gene associations, consisting of 395 unique genes, obtained from the Online Mendelian Inheritance in Man (OMIM) catalog.  We oveI2>0.5) but include all the trait-gene-tissue combinations with only a single eligible eQTL instrument. In the end, we estimate the causal effects for 1,883,367 trait-gene-tissue combinations, corresponding to 114,083 gene-trait pairs, implicated by the PTWAS scan using the proposed estimation procedure. On average, each gene-trait pair is estimated in ∼17 different tissues.We proceed to estimate the potential causal effects from the genes implicated in the PTWAS scan to the complex traits of interest. For this analysis, we remove the 211,291 trait-gene-tissue combinations flagged in the ER validating analysis . The median and the mean of all the cross-tissue I2 statistics are 0.30 and 0.18, respectively. Note that the tissue-specific effects of eQTLs drive the observed heterogeneity of the estimated gene-to-trait effects across tissues. The overall pattern that we observe from this analysis is qualitatively similar to the reported tissue specificity of cis-eQTLs in the literature: while a good proportion of eQTLs behaves in a tissue-consistent manner, a noticeable proportion shows strong evidence of tissue-specific eQTL effects [We examine the heterogeneity of the estimated gene-to-trait effects across multiple tissues, for which we again compute an  effects –31. ThisSORT1 gene for LDL cholesterol, CETP gene for HDL cholesterol, and PHACTR1 and MRAS genes for cardiovascular disease (CAD). In some cases, we find that the strongest or most confident effect size estimates are obtained from the biologically most relevant tissues, e.g., SORT1 in the liver and PHACTR1 in artery coronary. In other cases, the estimated effects are similar in a group of similar tissues which possibly share some common cell types. The estimates also confirm the directional effects from the genes to corresponding traits.The estimated tissue-specific gene-to-trait effects provide potential insights for understanding the molecular mechanisms of complex diseases, many of which have been well-documented in the literature. In Fig. p value <2.2×10−16.We compare the results from our multi-tissue PTWAS scan to the results from the colocalization analysis implemented in the software package ENLOC . Colocalp values from PTWAS. The plot displays a clear linear trend with high probabilities of colocalization corresponding to significant PTWAS p values. However, the correlation is imperfect, as some most significant TWAS genes only exhibit weak evidence of colocalization, which is likely due to the differences of LD patterns in the GWAS and eQTL data for the relevant genomic regions.For a closer inspection, we examine the joint analyses of GWAS data of CAD from the CARDiOGRAM consortium and the GTEx eQTL data from the whole blood. Figure TWAS presents some unique challenges for the traditional causal inference methodologies like the IV analysis. Notably, the large number of candidate genes is rarely encountered in the application scenarios from econometrics and epidemiology. This unique feature prompts developing efficient multiple hypothesis testing procedures to screen candidate genes effectively. It is equally important to note that hypothesis testing may not be the endpoint of a sound causal inference: interpreting and validating the scan results have essential implications on follow-up studies. In this paper, we also illustrate that robust estimation of the causal effect, which has been emphasized in the traditional IV analysis, is critical to uncovering the impacts of cellular environments on disease etiology. Thus, we conclude that all three aspects of the PTWAS analysis: multiple hypothesis testing, model validation, and causal effect estimation, should be an integral part of causal inference in TWAS.In PTWAS, our statistical strategies vary for different stages of the analysis. As noted by many authors , 34, altIn this paper, we regard the commonly referred “genetic predictions of gene expressions" in the scan procedure as composite instrumental variables for investigating the causal relationships between candidate genes and the complex trait of interest. Although it is conceptually correct to interpret the composite IVs as genetic predictions of gene expression phenotype, we note that such predictions are generally inaccurate. The evidence here is two-fold: first, existing studies suggest the overall heritability of gene expressions, on average, is quite low ; second,One of the advantages of the proposed PTWAS framework is its utilization of multiple independent eQTLs throughout the three stages of the analysis. This has been shown to improve the power of multiple hypothesis testing, enable the model validation, and increase the estimation efficiency. Importantly, our computational approaches carefully distinguish SNPs representing different independent eQTL signals and SNPs tagging the same eQTL signal. We note that regarding highly correlated SNPs as independent instruments are theoretically invalid. Instead, our approach uses a set of eQTL SNPs in LD  to represent an instrument and weight the evidence from individual SNPs through Bayesian model averaging (BMA). This strategy is proven effective in our simulations and real data analysis by carrying over the SNP-level uncertainty from the eQTL analysis. Recently,  propose p values derived from our novel PTWAS scan procedure can be directly plugged into the fine-mapping methods implemented in FOCUS and yield desired credible sets of causal genes. We will continuously pursue this direction in our follow-up work.Recently emerged TWAS methods, represented by FOCUS  and TWMRprove the assumptions are true but only indicate that they are reasonable given the data at hand. Should such caveat deter our efforts to apply the proposed approaches, or more generally, formulate and perform observational-data-based causal inference in TWAS? Our opinion is no. The challenge is not unique to the field of genetics and genomics. We believe that our proposed approach falls into the category of “shoe leather” methodology advocated by David Freedman [Finally, we acknowledge that, like any observational data based causal inference approach, the proposed procedure is imperfect. It is mainly because some critical causal assumptions can not be rigorously verified, and some required conditions are not satisfied for every gene-trait pair in practice. In our application context, a good proportion of genes lack discoveries of multiple independent and strong eQTLs. Thus, the proposed model validation procedure is not applicable. The emergence of large-scale eQTL datasets will alleviate this problem in the near future as the ability to uncover multiple eQTLs is directly correlated with the sample size of eQTL . NeverthFreedman , which “In this paper, we propose a new computational framework to systematically investigate potential causal mechanisms from tens of thousands of candidate molecular phenotypes leading to complex diseases. Utilizing this approach, our analysis of multi-tissue eQTL data from the GTEx project (v8) and GWAS data from 114 complex traits reveals an abundance of genes with strong evidence of causal relationships with a variety of complex traits and diseases. More importantly, with the ability of accurate quantification of tissue-specific gene-to-trait effects, our analysis highlights the heterogeneity and tissue relevance of these effects across complex traits.Mi) is assessed by a posterior model probability, SNP-level posterior inclusion probability, pj, characterizes if a particular SNP j is a causal eQTL . In the presence of LD, causal eQTLs may not be statistically identifiable even if the evidence for the existence of an eQTL can be overwhelmingly strong [signal-level PIP to quantify the overall strength of an independent eQTL. Specifically for each potential eQTL signal k, we identify a set of SNPs in LD that represent the same association signal. The corresponding signal-level PIP is computed by The probabilistic annotations of eQTLs used by PTWAS require comprehensive characterizations of the strengths and uncertainty of the genetic associations of expression traits at different levels. The Bayesian multi-SNP eQTL mapping analysis considers a wide range of multiple linear regression models consisting of different SNPs. At the model level, each plausible multi-SNP association model , i.e., genetic variants, must be associated with the expression of the target gene (X); (ii) randomization assumption: the instrument is  independent of confounders (U); and (iii) exclusion restriction: the selected genetic variants affect the complex trait of interest (Y) only through the target gene. Notably, the inclusion restriction (IR) requires the instruments are eQTLs, and the exclusion restriction (ER) explicitly excludes the possibility of  pleiotropy. Under these causal assumptions, the evidence of the association between G and Y, i.e., G ⊥̸ ⊥Y, is sufficient to reject the null hypothesis that states no causal link between the target gene and the complex trait of interest [The instrumental variable analysis can be represented by the graphical model in Additional file interest , 34, 42.G,X, and Y are not taken from the same samples. Instead, the eQTL data  and the GWAS data  are measured from two sets of non-overlapping samples. The two-sample design has some important implications on the IV analysis, especially the estimation bias of causal effects introduced by the weak instruments . In a one-sample design, the weak instruments can cause severe type I errors in testing causal relationships, whereas in a two-sample design, the bias is always towards 0, therefore, results only in the loss of power but not inflation of type I errors.The two-sample design refers to the setting that The weighted sum of IVs, i.e., terature , 16. ForIf the true causal eQTLs are known, the principled inference procedure in the IV analysis is the two-stage least squares (2SLS) method . In the model averaging approach that utilizes the posterior model probabilities L sparse candidate association models identified from the eQTL analysis, we fit each model Mi by the least square algorithm. We obtain an effect size estimate, j in model Mi (j∉Mi.) We then compute an overall weight for SNP j by averaging its estimated effects across all L candidate models, i.e.,We propose a Finally, the proposed composite instrumental variable, Mi. Therefore, the resulting composite IV can be naturally interpreted as an ensemble prediction of expression levels for the target gene . Subsequently, by the law of total expectation, we combine the individual estimate from each member SNP weighted by its conditional causal probability, i.e.,which corresponds to the conditional probability of SNP Similarly, by the law of total variance, we obtainFor each independent instrument/eQTL, the proposed estimator provides an intuitive and principled approach to fully account for LD.Under the IV assumptions, each independent eQTL provides an independent estimate of the underlying causal effects. If the causal link from the target gene to the complex trait is indeed true, the multiple estimates from independent eQTLs are analogous to the multiple estimates from a meta-analysis, where the underlying true causal effect should be constant regardless of the instruments used for measurement. By this logic, it becomes natural to adopt a fixed-effect meta-analysis model to combine the individual severe departures from ER when multiple independent instruments become available. If ER holds, the causal effects estimated from multiple independent eQTLs (using the procedure in the above section) should be highly consistent, and low levels of heterogeneity among estimates are expected. In contrast, observations of elevated heterogeneity levels should flag potential violations of ER.The causality implications inferred from TWAS analysis are subject to the validity of the IV assumptions, especially the exclusion restriction (ER). Although rigorous validation of ER based on observed data is considered theoretically implausible , 34, 44,I2 statistic [To implement this idea, we compute an tatistic  based onT represents the number of independent eQTLs used for effect estimation, and Q is the Cochran’s Q statistic and is given bykth independent eQTL, and I2 statistic ranges from 0 to 1 and is designed initially to represent the percentage of the variance observed in a meta-analysis that can be attributed to the heterogeneity among participating studies. In the application context of TWAS, I2→0 indicates reasonable consistency among estimates by multiple eQTLs, whereas I2→1 implies severe departures from ER.where We note that the underlying idea of the proposed model diagnosis approach is similar to the intuition behind Egger regression  that is I2 as a quantitative metric to measure the effect size heterogeneity in a comprehensible scale. It is theoretically possible to set up a hypothesis testing procedure to select genes with consistent eQTL-level estimates. Note that in this case, the null hypothesis has to assert heterogeneity in the underlying effect sizes. We have not seen any successful applications of such hypothesis testing. In practice, some authors suggest setting up the null hypothesis as in the Cochran’s Q test  and attempting to “accept” the null hypothesis. This, in our view, is a statistical mistake.We use Throughout our simulation studies, we use the real genotype data from 706 whole blood samples of the GTEx v8 data to simulate expression and complex trait phenotype data. To mimic the two-sample design, we randomly select 400 individuals and 1000 genes to simulate their expression data. The remaining 306 individuals are used to simulate complex trait data.cis-SNPs and independently sample the causal eQTLs from a Bernoulli distribution with the frequency =0.002. Thus, on average, each gene has three causal eQTLs. The effect size of each causal gene is sampled from a Gaussian distribution with mean 0 and variance 0.5. We also add a polygenic background effect to all candidate SNPs, such that the heritability of the expression phenotype is roughly 50% . More specifically, for individual i, the expression level for a candidate gene, xi, is simulated byFor each gene, we select 1500 gi,j represents the genotype of SNP j for the ith individual, βj and αj represent the (strong) sparse genetic effect and the polygenic effect, respectively, and γj is the latent Bernoulli random variable. The corresponding complex trait for individual i, yi, is subsequently simulated by a simple structural equation,where η represents the causal gene-to-trait effects. To investigate the power and type I error control of the PTWAS scan procedure, we sample η from a Gaussian distribution η=1 for all simulated datasets. We simulate the expression data for all 706 individuals but use only the subset of 400 individuals for eQTL analysis. We only simulate the complex trait data for the subset of 306 individuals.where For the proposed PTWAS procedure, we analyze the eQTL data and construct the composite IVs using the software package DAP. For PrediXcan method, we apply the elastic net algorithm with cross-validation to find the genetic predictions of gene expressions. We also run the software package BSLMM to produce the predicted gene expression functions for TWAS-Fusion. When running the BSLMM, we apply the default settings except resetting the number of sampling steps to 200,000 and the burn-in steps to 100,000 for computational considerations.cis-eQTL data from 49 tissues (version 8) and 114 complex traits from the UK Biobank and other consortia. We perform multi-SNP fine-mapping of cis-eQTL analysis for each GTEx tissue using DAP and generate the all three required levels of probabilistic annotations  for the proposed PTWAS analysis.For multi-tissue TWAS analysis, we utilize the GTEx The 114 complex trait datasets are selected and harmonized by the GTEx GWAS analysis subgroup. For each complex trait, only summary statistics are extracted, and additional summary statistics are imputed for the GTEx SNPs that are not directly available from the original studies. The details of the GWAS data processing are documented in .The probabilistic eQTL annotations required by PTWAS are derived from the GTEx release v8 data across 49 tissues using DAP , 13. Thex to trait y in the ith tissue. We apply a multi-tissue PTWAS scan to test a global null hypothesis that statesp value, ith tissue for the target gene-trait pair. We then apply the ACAT method [p values for each gene-trait pair, p value for testing the global null hypothesis. For each trait, we finally apply Storey’s q value procedure to control the false discovery rate at 5% level and identify the genes that reject the global null hypothesis.Let T method  to the sWe benchmark the computational time and resources for the scan procedure: the analysis of a single tissue  with a single complex trait  takes about 12 min of real computational time and 3.5 Gb of memory on a 24-core Linux system with 2.7 GHz CPUs. The computational time grows linearly with additional number of tissues used. The joint analysis of 49 tissues for a single trait (GIANT height data) takes 468 min and 24 GB of memory on the same system.For each complex trait, we focus on the set of genes implicated from the PTWAS scan procedure. For a gene rejected at the scan stage (at FDR 5% level) for the trait of interest, we consider all its gene-tissue pairs (not just the most significant tissue) for the effect estimation and the model validation. We then select the gene-tissue-trait combination that contain at least one eQTL signal cluster with SPIP ≥0.50 for estimation purpose. This particular threshold is mainly informed by our simulation studies, where we observe reliable estimation results for signals with SPIP ≥0.50. To validate ER assumption, we require the selected gene-tissue-trait combinations to have more than two eQTL signal clusters with SPIP ≥0.50.For each selected gene-tissue-trait combination, we carry out the proposed effect estimation and/or model validation procedures separately.Additional file 1 Figure S1: Diagram representing instrumental variable analysis. Figure S2: Distribution of Gini coefficients summarizing the sparsity of the composite IVs in different TWAS scan methods. Figure S3: Allelic heterogeneity in implicated PTWAS signal genes. Figure S4: Heterogeneity of gene-to-trait effects across tissues. Figure S5: Comparison of distributions of colocalization probabilities between all genes and PTWAS significant genes.Additional file 2 Table S1: Descriptions of 114 complex trait datasets used in the PTWAS analysis.Additional file 3 Table S2: Complete list of significant gene-trait pairs at 5% FDR level identified in the multi-tissue PTWAS scan of 114 complex traits.Additional file 4 Table S3: Heart disease-related PTWAS significant genes validated in OMIM.Additional file 5 Table S4: Complete list of estimation and model validation results for all gene-trait-tissue combinations.Additional file 6 Table S5: Complete cross-tissue heterogeneity results for all gene-trait pairs.Additional file 7 Review history.


The baseline LCNN, containing one local convolutional layer (kernel size: 10) and two fully connected layers with 64 nodes each, is outperforming commonly proposed ANNs  for basically all considered traits. For traits with high heritability and large training population as present in the simulated data, LCNN are even outperforming state-of-the-art methods like genomic best linear unbiased prediction (GBLUP), Bayesian models and extended GBLUP, indicated by an increase in predictive ability of up to 24%. However, for small training populations, these state-of-the-art methods outperform all considered ANNs. Nevertheless, the LCNN still outperforms all other considered ANNs by around 10%. Minor improvements to the tested baseline network architecture of the LCNN were obtained by increasing the kernel size and of reducing the stride, whereas the number of subsequent fully connected layers and their node sizes had neglectable impact. Although gains in predictive ability were obtained for large scale data sets by using LCNNs, the practical use of ANNs comes with additional problems, such as the need of genotyping all considered individuals, the lack of estimation of heritability and reliability. Furthermore, breeding values are additive by design, whereas ANN-based estimates are not. However, ANNs also comes with new opportunities, as networks can easily be extended to account for additional inputs  and outputs (multi-trait models), and computing time increases linearly with the number of individuals. With advances in high-throughput phenotyping and cheaper genotyping, ANNs can become a valid alternative for genomic prediction.The prediction of breeding values and phenotypes is of central importance for both livestock and crop breeding. In this study, we analyze the use of artificial neural networks (ANN) and, in particular, local convolutional neural networks (LCNN) for genomic prediction, as a region-specific filter corresponds much better with our prior genetic knowledge on the genetic architecture of traits than traditional convolutional neural networks. Model performances are evaluated on a simulated maize data panel ( The prediction of breeding values and phenotypes is of central importance for both livestock and crop breeding. Obtaining accurate estimates of breeding values at an earlier stage can impact the decision on which individuals should remain in a breeding programs, shorten the generation interval and thus lead to higher genetic gains per year  and Bayesian linear models   in genetics ] would be linked to all nodes of the first layer. For example, a FCL with 64 nodes would result in about 64 times more parameters than a LCL between input and the first layer. Furthermore, a CL layer with a filter linking 10 markers would only lead to 11 parameter (10 + intercept) while in a LCL the number of parameters would be slightly higher than the number of SNPs. As subsequent layer will typically have far more parameters, differences in this layer should still be neglectable. The aim here is to analyze the usefulness of the LCNN compared to traditional network architectures and state-of-the-art methods for a variety of trait architectures, heritabilities and population sizes. Furthermore, the ideal network architectures of a LCNN is investigated by performing benchmark tests with varying kernel sizes in the LCL and layer designs in subsequent FCLs. All tests were conducted on a simulated large scale data set in maize and a variety of smaller real Arabidopsis thaliana data panels.The key idea of convolutional layers (CL) is that effects are assigned to specific sequences of alleles. However, the same sequence of marker variants in different areas of the genome can have totally different effects as adjacent variants on a genotyping array have no direct functional relation . Therefore, CNNs do not seem to be an appropriate network architecture for genomic prediction via array data. In this manuscript, we are proposing the use of local convolutional layers (LCL), as they provide a natural extension to CLs that fixes these issues by applying a region specific filter. As a toy example consider the artificial neural network given in As a first data set, a simulated data panel containing 10,000 maize lines that were genotyped at 34,595 SNPs was generated. This was done by simulating random matings between 235 founder lines, with genotypes for the founder lines being generated by combining two haplotypes from a set of 470 doubled haploid lines of the European maize landrace Kemater Landmais Gelb for each founder. Simulations were executed in the software MoBPS 1,000 linked epistatic QTLs (QTL-markers being at most 5 SNPs apart).h2 of 0.1, 0.3, 0.5, 0.8, and 1. Furthermore, a set of 5 correlated traits with 1,000 underlying additive QTLs each was simulated by the use of shuffle.trait in MoBPS . Source code for the generation of all simulated traits can be found in Individual QTL effect sizes were either assumed to be all the same or drawn from either a gaussian or gamma distribution, as true underlying effect structures in practice are not well known and can be highly dependent on the trait of interest. Since results were similar for the different distributions used to generate the individual QTL effect sizes, we will only report results for the tests conducted with equal QTL effect size for the additive QTLs and effects drawn from a gaussian distribution for the epistatic QTLs. For each trait, residual variances were varied to obtain traits with a heritability Overall, this resulted in a data set of highly related individuals, as commonly present in breeding application and covered a variety of trait architectures ranging from relatively simple traits with purely additive traits caused by a few markers to highly complex traits caused by epistatic interactions between a high number of involved QTLs. It should be noted that all individuals considered in subsequent tests are part of the same generation. Since population structure can vary heavily depending on the species and the applied prediction methods can become more complex to include parental effects or similar, this was neglected there. Likewise, no additional fixed effects were simulated. In principle, these two factors could for example be accounted for by additional input layers and one-hot-encoded variables for the respective effects.Arabidopsis thaliana  as the output layer. In genomic prediction, and especially when using an ANN, the number of parameters is usually substantially higher than the number of individuals that can be used for the model fitting. Thus, leading to n < < p problems Multi-layer perceptrons (MLP)Convolutional neural networks (CNN)Local convolutional neural networks (LCNN).We classify all models that assign linear effects to single parameters as linear models. As a baseline for the class LM, we are considering the GBLUP  was used with an adaptive estimates of lower-order moments (Adam) optimizer . For example, this results in 8,000 individuals being used for model fitting in the maize data, whereas the size of the training panel for the Arabidopsis data will be trait specific.A well-known problem of ANNs is that over-fitting can occur after a high number of training epochs . The size of the validation set was adapted based on the size of the data panel . Note that the relative size of the validation set is higher for smaller data sets as a higher impact of the validation set was observed in such chases. The remaining individuals were all used as part of the test set.As the size of the training panel was already extremely small for the Arabidopsis data, a second study was conducted in which no validation set was used, but instead a fixed number of 25 training epochs was performed, therefore not requiring a validation set.All tests for the simulated maize data/Arabidopsis data were repeated 25/100 times respectively, with randomly sampled training, validation and test sets.In the following, we will report results for a baseline model from each of the three ANN class:MPL: 2 FCL with 64 nodesCNN: CL with kernel size and stride 10 + 2 FCL with 64 nodesLCNN: LCL with kernel size and stride 10 + 2 FCL with 64 nodes.Minor improvements were obtained by tweaking parameter settings for selected traits but overall tendencies of predictive ability across kernel size and number of layers as well as nodes per layer were stable. More details on differences will be provided for the LCNN at the end of the results section. There was no clear best model from the LM class. We will consider GBLUP as the baseline, but also report results for BayesA , outperforming the other three baseline models by around 0.03–0.04 . When inWhen considering a purely epistatic trait architecture with 10 underlying non-linked QTLs, differences between the LCNN and the other three baseline models were also around 0.06–0.08 , whereasIn case the underlying QTLs of the epistatic trait were placed on physically linked markers to imitate a trait caused by local interactions in a gene, both the LCNN and CNN obtained higher predictive ability when only 10 QTLs were involved in the trait, whereas the MLP and GBLUP performed worse . As onlyAs expected, we observed a higher predictive ability for traits with higher heritability. This was not only the case when comparing absolute values but also when dividing by the square root of the heritability to standardize performances. This standardization was applied as this is the highest theoretical achievable predictive ability for a given heritability . OverallWhen comparing the predictive ability depending on the number of individuals used for model fitting, we observed an inferior performance of all three classes of ANN models relative to GBLUP for small training sets , whereas the stride had neglectable impact  in the LCL led to higher accuracies  compared to 0.316 for the MLP and 0.312 for the CNN model . HoweverTests for the ANN models were performed using a GeForce RTX 2080 Ti graphics card and Intel(R) Xeon(R) Gold 6154 processor (3.00 GHz) with 18 cores, whereas all LMs were fitting on a server cluster with Intel E5-2650 (2X12 core 2.2 GHz).When using 8,000 individuals for model training, computing times for the model fitting for the MLP and CNN were lowest with 0.9 min , followeMulti-trait models in ASRemlR  showed substantially worse performance, both in terms of predictive ability and model robustness, of all considered ANN architectures. On the contrary, for large scale data set with up to 8,000 individuals used for training, the LCNN is outperforming GBLUP, or at least performing on a similar level, for basically all simulated trait architectures. As results for the simulated and real data were very similar for smaller training populations, we would expect results to generalize to large scale real data sets. However, as typical data panels in plant breeding contain <1,000 lines, we must conclude that as of today, genomic data sets in plant breeding are usually too small to justify the use of ANNs in breeding application.On the contrary, even larger populations with potentially millions of animals are available in livestock breeding (Masuda et al., On the positive side, ANNs also come with great potential. Most prominently, models are computationally extremely efficient, with computing times only increasing linear in the number of individuals considered. As state-of-the-art methods like GBLUP have a cubic cost or require approximated solutions, we would expect great usefulness of ANNs for large scale data set. Similarly, including additional inputs like other omics (Li et al., Overall, we can conclude that, as of today, ANNs will not be the ideal model in most current breeding applications unless uniform genomic data for all relevant individuals are available. However, with reduced genotyping costs, advances in high-throughput phenotyping and additional inputs and outputs to consider, this might change in the future. Of the tested ANN structures, we see the most potential in the newly proposed LCNN architectures, as negative aspects like the overparametrization in MLPs and filters not being in line with our prior knowledge of genetic traits for CNNs are avoided. This is also empirically supported by the conducted test for both the simulated and real data sets as obtained predictive abilities are increased for basically all considered traits when using a LCNN architecture. Therefore, LCNNs should be a key network architecture to consider when designing artificial neural networks for the use in genomic prediction, or even in general when performing practical applications that are using genomic data from a genotyping array as an input.https://arapheno.1001genomes.org/; https://link.springer.com/article/10.1007/s00122-019-03428-8.Publicly available datasets were analyzed in this study. This data can be found at: TP lead the development of the methodology, performed the analysis, and wrote the initial manuscript. JF, AK, and HS provided critical feedback to both analysis and the manuscript. HS supervised the study. All authors read and approach the final 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.


Various methods have been proposed for genomic prediction (GP) in livestock. These methods have mainly focused on statistical considerations and did not include genome annotation information. In this study, to improve the predictive performance of carcass traits in Chinese Simmental beef cattle, we incorporated the genome annotation information into GP. Single nucleotide polymorphisms (SNPs) were annotated to five genomic classes: intergenic, gene, exon, protein coding sequences, and 3′/5′ untranslated region. Haploblocks were constructed for all markers and these five genomic classes by defining a biologically functional unit, and haplotype effects were modeled in both numerical dosage and categorical coding strategies. The first-order epistatic effects among SNPs and haplotypes were modeled using a categorical epistasis model. For all makers, the extension from the SNP-based model to a haplotype-based model improved the accuracy by 5.4–9.8% for carcass weight (CW), live weight (LW), and striploin (SI). For the five genomic classes using the haplotype-based prediction model, the incorporation of gene class information into the model improved the accuracies by an average of 1.4, 2.1, and 1.3% for CW, LW, and SI, respectively, compared with their corresponding results for all markers. Including the first-order epistatic effects into the prediction models improved the accuracies in some traits and genomic classes. Therefore, for traits with moderate-to-high heritability, incorporating genome annotation information of gene class into haplotype-based prediction models could be considered as a promising tool for GP in Chinese Simmental beef cattle, and modeling epistasis in prediction can further increase the accuracy to some degree. Genomic prediction (GP), which uses whole-genome markers to predict genomic breeding value, has been widely used in breeding programs of plants  and domeGiven the availability of genome annotation information, some studies have tried to integrate this information into prediction models to improve the predictive accuracies . Single An alternative is treating haplotypes that are on tuples of SNPs as predictor variables in GP to compensate for the imperfect LD between SNPs and QTLs . The maiIn this study, we used annotation information of the cattle genome to divide Illumina BovineHD BeadChip into five genomic classes, including intergenic regions (IGR), gene, exon, protein coding sequences (CDS), and 3′/5′ untranslated regions (UTR) classes. Then, haploblocks were created  and haplOur dataset includes 1346 Simmental cattle born between 2008 and 2015 from Ulgai, Xilingol League, and Inner Mongolia, China. After weaning, cattle were moved to Jinweifuren Co., Ltd.  for fattening under the same feeding and management conditions. A more detailed description of the management processes was reported in previous studies , 2017. Ap > 10–6) and individual call rate (>0.90). Missing genotypes were imputed using BEAGLE (v4.1) (2) dropped below 0.2 at distances of 34 kb, indicating that the implementation of GS in this population requires at least 77,941 markers  . IndividE (v4.1) . Consequ markers .Phenotypes were adjusted for the environmental fixed effects, including sex, year, and the covariates of body weight upon entering the fattening farm, and the number of fattening days. Subsequently, the adjusted phenotypes were used for further analysis. Variance components were estimated using the following univariate animal model in ASREML (v4.1) :y is the vector of the adjusted phenotypes, 1nis an n × 1 vector with entries equal to 1; μ is the overall mean; G is the additive genetic relationship matrix constructed using all SNPs and Z is incidence matrix associating a; and I is the identity matrix and where 1. According to genome annotation information, the bovine genome was partitioned into five genomic classes: (1) intergenic regions (IGR), (2) gene, (3) exon, (4) protein coding sequences (CDS), and (5) 3′/5′ untranslated regions (UTR) classes. Gene class contained the exon class, and exon class represented a combination of CDS and UTR classes. Thus, overlapping existed among different genomic classes. Then, the SNPs of BovineHD Beadchip were annotated into the corresponding genomic class based on their physical position.The latest bovine genome annotation (Bos_taurus.ARS-UCD1.2) was downloaded from EnsembleFor the gene, exon, CDS, and UTR classes, a genome feature refers to a single gene, exon, CDS, and UTR, respectively; for the IGR class, a genome feature refers to an interval between two adjacent genes. A group of SNPs that were annotated in a certain genome feature of the five genomic classes was called an SNP set. The phased consecutive SNPs were used for haploblock construction via the approach described by Haplotype effects were then modeled using both numerical dosage  and cateG, which were constructed based on respective prediction approaches , except for the different genomic relatedness matrices proaches . In our M denotes the  encoded genotype matrix, pi is the MAF of marker i, m is the number of markers, and P is a matrix with columns equal to 2pi. The haplotype-based genomic best linear unbiased prediction (GHBLUP) was performed for all markers. The haplotype-based genomic relatedness matrix in GHBLUP was constructed as the dot product of the haplotype allele matrix (MH) and expressed as H is the pseudo-markers matrix with entries 0, 1, and 2 representing the number of copies of each haplotype allele in a haploblock, and QH is the total number of haploblocks of whole genome.In numerical dosage models, GBLUP  was perfGHBLUP|GA) was implemented. Similarly, the haplotype-based genomic relatedness matrix in GHBLUP|GA was constructed as For the five genomic classes, haplotype-based genomic best linear unbiased prediction given genome annotation  was applied for all markers as well, in which the number of haploblocks that were in the same state between pairs of individuals were counted. The genomic relatedness matrix in CHM is expressed as SHwith entries jiq was scored 1 if individual i and j share the same haplotype allele configuration on haploblock q; otherwise, φjiq was scored 0; QH was the total number of haploblocks, which is the same with that in GH. Therefore, the entries of SH represented the proportion of haploblocks with an identical state between pairs of individuals. For the five genomic classes, the haplotype-based CM assigned the genome annotation CHM|GA was applied. Similarly, the genomic relatedness matrix was built by counting the number of haploblocks that were in an identical state between pairs of individuals /m2, where # denotes the Hadamard product. The first-order epistasis between pairs of haploblocks was modeled by extending CHM to the haplotype-based categorical epistasis model (CHE)  model . In the el (CHE) , where ts CHE|GA , where tThe accuracy of GP was assessed using fivefold cross-validation (CV), which assigns animals randomly into five separate subsets with near-equal size. Each subset was used as the validation set only once, with phenotype masked, and the remaining four subsets were treated as a training set. In order to reduce random sampling effects, the CV layout described above was replicated twenty times, where a new randomization was implemented for each replicate so that the each of the subset contains different individuals. DGVs were calculated for each validation subset based on the genomic relatedness matrix. For each replicate, the prediction accuracies were assessed by the correlation between the DGVs and the pre-adjusted phenotypes in the validation set divided by square root of heritability. In addition, in order to assess the extent of bias on GP, linear regression coefficients [b ] of the pre-adjusted phenotypes (y) on the DGVs was calculated for individuals in the validation set. Unbiased models are expected to do not significantly different from 1, whereas values greater than 1 indicate a biased deflation prediction of DGVs and values smaller than 1 indicate a biased inflation prediction of DGVs.We annotated 671,204 filtered SNPs into five genomic classes based on their physical positions. The annotation results and descriptive statistics of each genomic class are displayed in GHBLUP and CHM) and the SNP-based prediction models (GBLUP and CM). The results showed that the predictive performances of GHBLUP and CHM were more accurate than GBLUP and CM in CW, LW, and SI , gene class of LW (1.4%), exon class of CW (0.2%) and SI (0.6%), CDS class of CW (0.3%) and SI (0.8%), and UTR class of CW (0.4%) and SI (0.5%).Considering the prediction model including epistatic effects may increase the accuracy and reduce the bias of DGVs. The results showed that incorporation of first-order epistatic effects into prediction model can slightly improve the prediction accuracies for most traits and genomic classes . When inAdvances in high-throughput genotyping technology and the availability of genome annotation information have contributed to the improvement of the predictive performance of complex quantitative traits in livestock species . To bridGHBLUP and CHM) were applied to the whole genome-wide markers, and the result of this scenario was treated as a benchmark. We found that the predictive performance of haplotype-based prediction models was superior to corresponding SNP-based prediction models in the three traits  unaltered. However, mutations in different loci tend to cause major changes in the haplotype frequencies . Thus, wcis-acting causal variants  of the total genes of the reference genome, whereas 4.08% , 3.17% , and 7.26%  of the total exons, CDS, and UTR of reference genome were respectively represented by exon, CDS, and UTR classes. Consequently, the high proportion of biological-functional-unit-like genes may contribute to stronger predictive power. Taken together, these factors may explain the outstanding predictive performance displayed in gene class compared with the other classes.When the genome annotation information was incorporated into the haplotype-based prediction models, we also observed a slight or moderate improvement in prediction accuracies for the three traits. This can be explained by the traits having different genetic architectures . The numThe usage of genome annotation information of the IGR class also led to a slight improvement in prediction accuracy in CW and SI. Studies have suggested that the IGR class, such as non-coding conserved regions, miRNA, and regulatory regions, might harbor important genetic variants associated with complex traits in crops  and humaGBLUP slightly outperformed the SNP-based CM in three traits. CM with GBLUP, and found only slight differences in predictive ability between CM and GBLUP among 13 traits in mouse. The CM does not use the assumption of constant allele substitution effects like GBLUP; instead, it models the independent effect of each genotype at a locus, which enables the modeling of dominance  was downloaded from Ensemble (http://asia.ensembl.org/index.html).Genotype data have been submitted to Dryad: doi: The animal study was reviewed and approved by Science Research Department of the Institute of Animal Sciences, Chinese Academy of Agricultural Sciences (CAAS) .LX simulated and analyzed the data and wrote the manuscript. ZW, LX, and YL collected the data. NG, YC, XG, HG, LYX, LZ, BZ, and JL discussed and improved the manuscript. All authors read and approved the final 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.


Drosophila melanogaster and Drosophila C Virus as a host-pathogen model system to dissect the genetic and sex-specific sources of variation in multiple host traits that are central to pathogen transmission. Our findings show complex interactions between genetic background, sex, and female mating status accounting for a substantial proportion of variance in lifespan following infection, viral load, virus shedding, and viral load at death. Two notable findings include the interaction between genetic background and sex accounting for nearly 20% of the variance in viral load, and genetic background alone accounting for ~10% of the variance in viral shedding and in lifespan following infection. To understand how variation in these traits could generate heterogeneity in individual pathogen transmission potential, we combined measures of lifespan following infection, virus shedding, and previously published data on fly social aggregation. We found that the interaction between genetic background and sex explained ~12% of the variance in individual transmission potential. Our results highlight the importance of characterising the sources of variation in multiple host traits to understand the drivers of heterogeneity in disease transmission.Host heterogeneity in disease transmission is widespread but precisely how different host traits drive this heterogeneity remains poorly understood. Part of the difficulty in linking individual variation to population-scale outcomes is that individual hosts can differ on multiple behavioral, physiological and immunological axes, which will together impact their transmission potential. Moreover, we lack well-characterized, empirical systems that enable the quantification of individual variation in key host traits, while also characterizing genetic or sex-based sources of such variation. Here we used  Host heterogeneity in pathogen transmission presents a major hurdle to predicting and minimizing the spread of infectious agents. Part of the difficulty in linking individual variation to epidemic outcomes is that individual hosts can vary on multiple behavioral, physiological, immunological axes that may affect their transmission potential. Moreover, we lack well-characterized empirical systems that allow to measure multiple facets of individual variation in pathogen transmission. In this work, we capitalize on the strengths of the fruit fly Drosophila as an established and powerful model system for genetics, behavior, and immunity. We provide individual-level data on several axes of infection and test how each of these components experiences variation arising from host genetic background, sex, and mating status. We are therefore able to identify the sources of host heterogeneity  and the specific host traits  that are most important in determining disease dynamics. We find that a substantial proportion of between-individual heterogeneity in disease transmission is explained by genotype-by-sex interactions affecting the likelihood that individuals will shed virus, but also how much they are likely to shed. Salmonella typhi while working as a cook in New York during the early 20th century We are sorry that we cannot be more positive about your manuscript at this stage, but if you have any concerns or questions, please do not hesitate to contact us.Sincerely,William B. Ludington, PhDGuest EditorPLOS PathogensSara CherrySection EditorPLOS PathogensKasturi HaldarEditor-in-ChiefPLOS Pathogensorcid.org/0000-0001-5065-158XMichael MalimEditor-in-ChiefPLOS Pathogensorcid.org/0000-0002-7699-2064***********************Reviewer's Responses to QuestionsPart I - SummaryPlease use this section to discuss strengths/weaknesses of study, novelty/significance, general execution and scholarship.Reviewer #1: This study examines the contributions of host sex, mating status, and genetic background to among-host variation in the transmission potential of Drosophila C Virus. The study finds that some of these variables and their interactions account for appreciable variance in transmission-relevant traits like quantitative resistance, viral shedding, and lifespan post infection. The variance in these traits is further used to bootstrap and estimate the distribution of transmission potential among individuals in a population, finding a combination of zero-inflation and a small but potentially epidemiologically important superspreader tail.The motivation for this study is excellent – the field desperately needs work that rigorously connects variation in the within-host dynamics  of infection to between-host dynamics, and this study ambitiously approaches this goal. Thus, I think it is of sufficient novelty and broad interest for the readers of this journal.I struggled in my first reading of this manuscript because it is written in an excessively lean style, given that the methods do not appear till the end. Several key “what” and “why” details should be elaborated upon in the results and discussion, to help readers better understand the experimental design and relevance and limitations of the results (specific suggestions below).Reviewer #2: This manuscript aims to explore how three factors of host identity  interact to produce heterogeneity in pathogen transmission potential. Using a model host-pathogen system (Drosophila and DCV), they found extensive among-individual variation in transmission potential, and a much of this variation is explained by genotype x sex interactions. The experiments are exploratory, but provide interesting empirical data on transmission heterogeneity, and the authors combine these measures with previous data on fly social behavior to estimate V  and present these data very well . Overall, the intellectual merit of this paper is twofold: the authors describe and quantify potential factors contributing to pathogen transmission heterogeneity and their interactions, and they also provide a great foundation for future studies using this model host-pathogen system. Drosophila is clearly recognized as a model for physiology, genetics, and pathology, but these types of studies show how powerful this system can be used as a tool to study ecology and evolution of infectious diseases. I think this will make a fantastic contribution to the literature, and will garner broad readership in PLoS Pathogens.Reviewer #3: The manuscript by Jc fonathon A. Siva-Jothy and Pedro F. Vale has tested how common sources of variation between individuals  contribute to individual heterogeneity in pathogen transmission potential using Drosophila melanogaster and Drosophila C Virus as a model system.The primary weakness of the paper, conceptually and in terms of novelty, is that the effect of host trait on disease transmission has been determined in other host-pathogen system. Indeed, the authors here systemically measure the effect of multiple host traits on disease transmission, which provides new information to fully understand the sources of heterogeneity in pathogen transmission. Overall the paper is succinct and a thorough study of the effect of host trait variation on pathogen transmission.However, I have some lingering questions after reading the paper and suggestions for experiments that could improve or substantiate the work presented here.**********Part II – Major Issues: Key Experiments Required for Acceptanceabsolutely required to validate study conclusions.Please use this section to detail the key new experiments or modifications of existing experiments that should be Generally, there should be no more than 3 such required experiments or major modifications for a "Major Revision" recommendation. If more than 3 experiments are necessary to validate the study conclusions, then you are encouraged to recommend "Reject".Reviewer #1: I also have three intermediate-to-major concerns about the experimental design that at least deserve substantial discussion or clarification, if additional supporting data is not readily achievable:1) I understand that septic infection is convenient in that you can closely control the initial dose (a key source of variation), but this is a fecal-oral virus and you are measuring fecal transmission, correct? Given what is known about the life history of this virus, might you expect different results (e.g. the degree to which different variables and their interactions explain transmission virulence) if infected through the natural transmission mode? Most importantly, would you still predict the same zero-inflated + superspreader distribution? I think the absence of data on this dampens the impact of this paper (but maybe I am missing something about the host-microbe model here).2) The intra-fly correlation between lifespan and viral shedding is not clear, because very few flies  die before 10 days, but shedding is only measured in the first three days. Viral Load at Death is measured when the flies die, but there is no significant correlation between viral load and viral shedding (supp. figs). So, how does variation in lifespan really speak to the transmission period in this model? If this was carefully considered, it is not clear from the text.3) Is the estimated heterogeneity in transmission potential really reflective of a natural population? Fig. 4 distribution shows a lot of variance, but it is worth noting that the data are from the 5 most resistant and susceptible Dmel lines, meaning that the variance has been artificially maximized. The distribution in a natural heterogeneous population is likely much lower.Reviewer #2: 1. I think the term “superspreader” should be de-emphasized in the introduction (and removed from the keywords). Although superspreader events are an extreme form of transmission heterogeneity, this paper does not provide any direct empirical evidence for how superspreader events can be generated by differences in host traits. I think that future studies could certainly use this system to do so, and this paper certainly sets the groundwork for those experiments.2. The abstract might be more meaningful if the authors included some quantitative descriptors of their results, perhaps some of the variance explained by sex, genotype, mating status, or the effect size/magnitude of change found between sexes or the most different genotypes. Saying that one genetic background had X% higher viral shedding, for example, than another is more informative than just saying there are vast differences between genotypes.3. I suggest that the authors be more forthright in the introduction that this is exploratory research aimed at discovering the degree of heterogeneity in pathogen transmission potential, rather than testing hypotheses about specific genotypes, sexes, or their combinations. Given the huge amount of work involved in these experiments, this isn’t a criticism by any means, this type of exploratory work is very important, but the results will be put in a clearer context if the reader knows these aims by the end of the introduction.4. It would be helpful if the authors expounded a bit on the difference between qualitative and quantitative values of shedding. I understand how you measured these things, but what they mean in the context of biology is still unclear.5. Since one of the goals of the paper is to show how this system is a valuable model for studying transmission heterogeneity, I would have liked to see some more information about the natural history of the interaction between Drosophila and DCV, if there is anything known about prevalence in the wild, evidence for epizootics, etc.Reviewer #3: 1. It has been reported in many host-virus systems that genetic and sex-specific variation can affect individual heterogeneity in different components of disease transmission, which is interpreted again in this study, my major concern of this study is the lack of novelty.2. In the main text, only mated females were measured, there is no explanation for not characterizing mated males.3. Figure 2a: do you have any ideas that the proportion of flies with non-zero DCV load differed between virgin and mated females from particular genetic background? It should be somehow discussed.**********Part III – Minor Issues: Editorial and Data Presentation ModificationsPlease use this section for editorial suggestions as well as relatively minor modifications of existing data that would enhance clarity.Reviewer #1: Other CommentsLines 105-107: More rigorous examples where covariance among traits  would help to underscore the existence of a gap in knowledge here. Also, what is “coupled heterogeneities?” That sounds like a term that I would use as filler if I didn’t know quite what I wanted to say. I think it needs clarification.Lines 107-108: I would change "fully" and "essential" in this sentence; measuring multiple traits may still not allow you to fully understand, and conversely a full understanding may not require the measurement of multiple traits (perhaps one trait explains an outsized amount of variance)Lines 117-120: I think it is essential here that you note which measurements come from the same individual flies  and which are relying on averages among fly groups. For better or for worse, the impact  come from the extent to which these measurements are coupled across time and within flies.Intro: I think it would be helpful somewhere in here to introduce the concept of quantitative vs. qualitative infection outcomes , since it becomes so central to the analysis and interpretation of the results.Results: Overall, the results needs more of an introduction to the general experimental design. How is oral infection carried out? How many genotypes did you infect? How long does it take flies to die, in general? When did you measure viral load? If the methods come at the end of the document, these details need to be here, to provide necessary narration. Otherwise just put the methods before the results; surely PLoS has some leeway there.Lines 126-127: Some summary statistics would be helpful here. On average, how much did infection reduce lifespan?Fig 1A: Kind of hard to eyeball general trends across columns here, other than they aren't precisely rank orderedLine 133: Interesting. Is this because later-dying flies started clearing infection and then died, or do you think that cumulative load, rather than peak load, explains mortality?Line 136: Were they not properly infected/colonized or did they clear infection? This section would benefit from a sentence or two introducing the experiment in question, since the methods are at the end of the documentLine 140: Should this be labeled as “detectable” instead of ‘non-zero’ on the Fig. 2a axis?Line 141: These are collected in first three days after infection. Do flies start to die before this? Do they start to die well after this? What does DCV titres at this stage really tell you?Line 141; Fig. 2a: Not clear from just looking at the figure that those bars are time points. Why not represent the data in the same way that you represent the quantitative data, or show more of a binomial style of plot with actual data points?Line 149-150: Why are these pairwise? Is this better than a quadratic model?Line 156: How is shedding measured? Give us a crumb of a method here.Line 176: did you use individual distribution over time curves for this?Line 180: Fig. 4a distribution is interesting. What does R0 mean for a proportion? Not quite sure I get the x axis there.Line 180, and Line 293: These paragraphs need some substantial revising here and there for grammarLine 208-9: Do those that fail to shed also survive? If not, could there be shedding post mortem?Lines 235-61: This paragraph is long and starts to get a little list-likeLine 267: Would it be worth it to show male vs female V/Vmean distributions, perhaps as overlapping in Fig. 4A?Lines 281-288: I appreciate the connection to other systems, but the testosterone discussion roams pretty far from being relevant for your results.Lines 289-90: This example just hangs there. Are you trying to make a point about vertebrate vs. invertebrate sex bias?Lines 312-313: Do we know what that dose response looks like? Is it threshold-like? Could R0 actually be lower than estimated?Lines 318, and surrounding: I think there needs to be a deeper and more thoughtful discussion of how sampling limitations and within-group variation reflect on covariance among variablesLines 340-1: Which 5 and 5 genotypes? Did your results recapitulate this?Line 362 and Line 373: This is not a huge sample size, given the clear variation in clearance rates and zero-inflation. Probably sums up to a good sample size for single variables, but the interaction effects might be underpowered (e.g. some genotype x trait groups have an N=1). Also, was the experiment repeated multiple times? Where do the error bars come from?Line 370: Did you have a group of flies that were measured for only load without the shedding assay first, to see if it was stressful and/or made a difference for the load results?Fig S1: I think Fig. S1 labels are backwards - shouldn't high load but low VLAD individuals be supersponges?Reviewer #2: 6. Lines 14-15: The abstract sets up the paper as if you will measure the se underlying effects, but rather you manipulate host genotype/sex/mating status and find widespread effects on transmission potential. However, the mechanisms remain unknown. An extra sentence in the abstract to explain that factors of host identity like genetic background and sex can influence these underlying mechanisms that then influence transmission potential.7. Line 88: Since immune traits are a form of physiological traits, I would replace that with “social factors” or something to point out that transmission is influenced by the interaction between infected hosts and susceptible hosts. A relatively recent paper showed that social context can be a predictive factor of disease risk in Drosophila social aggregations:Keiser, C.N., Rudolf, V.H., Sartain, E., Every, E.R. and Saltz, J.B. 2018. Social context alters host behavior and infection risk. Behavioral ecology, 29(4), pp.869-875.8. Line 141: DPI should be defined before its first usage here, as well as what you mean by “DPI effect”.9. Line 182: Ah, here we see some evidence for potential superspreaders. “Long-tail” distributions like this are common in many diseases, and the individuals are the far right end may represent superspreaders (as described in Lloyd-Smith’s Nature paper from 2005). If the authors prefer to keep their references to superspreaders in the introduction (see my comment #1), then this should be highlighted in the discussion more explicitly.10. Line 185: Statements like this, and throughout the results section, would be much more powerful when they include some effect size – what was the sex-difference in proportion here?11. Lines 242-261: This seems like a laundry list of studies that showed genotypic effects on pathogen shedding/transmission – it might read a little easier if they were distilled into main take-away messages, and how they help explain the effects discovered in your experiments.12. Line 267: How is this statement different from the opening sentence of this paragraph?13. Line 279: There are also studies on Drosophila sex-differences in pathogen avoidance, and how that is related to susceptibility . How avoidance behavior related to transmission potential might be an interesting addition to this paragraph.Reviewer #3: 1. The paper has used extensive long sentences without the proper commas resulting in difficulties to follow. It can be simplified by reducing the use of complex sentence structures.2. Figure 1a&b: statistics should be noted for the two figures either in main text or in the legend.3. Figure 2a&b: statistics should be note, and mark for significance should be denoted.4. Carefuly check the writing, such as in Line 161, please carefully check ‘while these were effects were significant’.5. The authors should carefully check the format of reference and keep it consistent, for example, for some journal name, abbreviations were used. The paper also excessively cites publications; less than half of the citations are likely necessary.6. Line 314, the format of the two dashes is different.**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article :Reviewer's Responses to QuestionsPart I - SummaryPlease use this section to discuss strengths/weaknesses of study, novelty/significance, general execution and scholarship.Reviewer #1: In the revised version of the manuscript, the authors have thoughtfully addressed my previous concerns. In particular, they provide a reasonable justification for performing septic rather than oral infections, and (thanks to improved organization and explanation of methods) it is much easier to follow the analyses and comparisons of individual metrics and calculations/distributions of transmission potential. The resulting manuscript is a pleasure to read, the model system is likely to inspire future work, and the results should be of substantial interest to those interested in disease ecology, heterogeneity, and host-microbe interactions. I have no further concerns about the suitability of this manuscript for publication.Reviewer #2: The authors have sufficiently addressed all of my comments. Great job!**********Part II – Major Issues: Key Experiments Required for Acceptanceabsolutely required to validate study conclusions.Please use this section to detail the key new experiments or modifications of existing experiments that should be Generally, there should be no more than 3 such required experiments or major modifications for a "Major Revision" recommendation. If more than 3 experiments are necessary to validate the study conclusions, then you are encouraged to recommend "Reject".Reviewer #1: NoneReviewer #2: (No Response)**********Part III – Minor Issues: Editorial and Data Presentation ModificationsPlease use this section for editorial suggestions as well as relatively minor modifications of existing data that would enhance clarity.Reviewer #1: One tiny thing: there appears to be a typo in Line 27 of the abstract – probably important to fix.Reviewer #2: (No Response)**********what does this mean?). If published, this will include your full peer review and any attached files.PLOS authors have the option to publish the peer review history of their article  are generated on a different schedule and may not be made available as quickly.Soon after your final files are uploaded, the early version of your manuscript, if you opted to have an early version of your article, will be published online. The date of the early version will be your article's publication date. The final article will be published to the same URL, and all versions of the paper will be accessible to readers.Thank you again for supporting open-access publishing; we are looking forward to publishing your work in PLOS Pathogens. Best regards,Kasturi HaldarEditor-in-ChiefPLOS Pathogensorcid.org/0000-0001-5065-158XMichael MalimEditor-in-ChiefPLOS Pathogensorcid.org/0000-0002-7699-2064