Chrysophrys auratus using both SNP and structural variant data. Specifically, we use feature selection methods in machine learning to explore the relative predictive power of both types of genetic variants in explaining growth and discuss the feature selection results of the evaluated methods. Methods: SNP and structural variant callers were used to generate catalogues of variant data from 32 individual fish at ages 1 and 3 years. Three feature selection algorithms  were used to reduce the dataset by selecting the most informative features. Following this selection process, the subset of variants was used as features to classify fish into small, medium, or large size categories using KNN, naïve Bayes, random forest, and logistic regression. The top-scoring features in each feature selection method were subsequently mapped to annotated genomic regions in the zebrafish genome, and a permutation test was conducted to see if the number of mapped regions was greater than when random sampling was applied. Results: Without feature selection, the prediction accuracies ranged from 0 to 0.5 for both structural variants and SNPs. Following feature selection, the prediction accuracy increased only slightly to between 0 and 0.65 for structural variants and between 0 and 0.75 for SNPs. The highest prediction accuracy for the logistic regression was achieved for age 3 fish using SNPs, although generally predictions for age 1 and 3 fish were very similar . The Chi-square feature selection of SNP data was the only method that had a significantly higher number of matches to annotated genomic regions of zebrafish than would be explained by chance alone. Conclusions: Predicting a complex polygenic trait such as growth using data collected from a low number of individuals remains challenging. While we demonstrate that both SNPs and structural variants provide important information to help understand the genetic basis of phenotypic traits such as fish growth, the full complexities that exist within a genome cannot be easily captured by classical machine learning techniques. When using high-dimensional data, feature selection shows some increase in the prediction accuracy of classification models and provides the potential to identify unknown genomic correlates with growth. Our results show that both SNPs and structural variants significantly impact growth, and we therefore recommend that researchers interested in the genotype–phenotype map should strive to go beyond SNPs and incorporate structural variants in their studies as well. We discuss how our machine learning models can be further expanded to serve as a test bed to inform evolutionary studies and the applied management of species.Background: Genetic diversity provides the basic substrate for evolution. Genetic variation consists of changes ranging from single base pairs  to larger-scale structural variants, such as inversions, deletions, and duplications. SNPs have long been used as the general currency for investigations into how genetic diversity fuels evolution. However, structural variants can affect more base pairs in the genome than SNPs and can be responsible for adaptive phenotypes due to their impact on linkage and recombination. In this study, we investigate the first steps needed to explore the genetic basis of an economically important growth trait in the marine teleost finfish  Intraspecific genetic variation provides the substrate for hereditary evolutionary change . GeneticAnopheles gambiae, inversion polymorphisms are linked to desiccation resistance [Populus balsamifera L., copy number variations are linked with adaptive environmental variations linked to biotic and abiotic stress responses [Drosophila melanogaster, where continental replicates of populations show that large cosmopolitan inversions are involved in a parallel adaptive environmental responses [Major advances in the field of computational genomics combined with increasingly high-quality whole-genome data and assemblies for non-model species have led to a re-evaluation of what constitutes important genomic variation between individuals. Recent studies show that structural variation commonly affects a significant portion of the genome ,8 and, isistance , and in esponses . In partesponses . Improving our understanding of the genomic variants that underpin complex phenotypic traits is particularly important for traits that have a polygenic architecture, which is the case for the predominant number of quantitative traits . As postChrysophrys auratus (hereafter referred to as snapper). Our approach outlines an initial framework of how such an exploration could be achieved to highlight the challenges and opportunities and ultimately to guide future research. The study species for this work is a species of significant commercial, recreational, and cultural significance in New Zealand, where it is referred to as tāmure by Māori. Plant and Food Research has a long-term research programme on this species to develop it for aquaculture using selective breeding. The key economic trait that is selected for is growth, to yield an elite strain with superior growth qualities, something that has been achieved for its sister species the red sea bream, Pagrus major, and the related gilthead sea bream, Sparus auratus [Here, we investigate the roles of SNPs and structural variant polymorphisms in explaining the quantitative trait growth in the marine teleost species the Australasian snapper,  auratus . Until n auratus . To quanWe used 32 fish for which we had individual whole-genome Novaseq data  and length data at age 1 and 3. The methods for the DNA extraction and processing from this cohort have been published elsewhere ,17,18, bSnapper cohorts from a three-generation pedigree were reared in tanks at the Nelson Finfish Facility with consistent feeding, light, water flow, aeration, and tank design ,18. For NovaSeq600 S2 150 bp paired-end read data at an average coverage of 15× were generated for 80 snappers, including the 32 snappers used in this study . To reduce the features to those that contribute most to the prediction of size classes, we examined three feature selection methods, ReliefF, Chi-square, and mutual information methods. The ReliefF algorithm performs feature selection by scoring features based on nearest neighbour instance pairs, then selecting the top-scored features. If a feature has different values in the nearest neighbour pair but their classes  are the same, the score of this feature decreases. Conversely, if the feature values are different and their classes are different as well, then the score increases . ReliefFThe Chi-square feature selection algorithm generates an estimated normal distribution of expected values of the different size classes and then tests the dependency between a feature and the class labels by placing it within this distribution. High dependency yields a high score, with the feature assessed as more useful . Chi-squThe mutual-information-based feature selection method measures the shared information between a feature and the class labels or between two features. It achieves feature selection by removing features that have low mutual information with the class labels but high mutual information with other features and retaining those that have high mutual information with the class labels . Mutual We tested the prediction accuracy following feature selection on four common machine learning algorithms: random forest, Gaussian naïve Bayes, logistic regression, and K-neighbours. These were all performed with the default settings of scikit-learn v0.24.0 ,38.The random forest (RF) classification algorithm constructs an ensemble classifier containing a number of decision trees during the training process, each of which is a predictive model. RF combines the prediction of all the decision trees to produce a class label for each instance . LogistiBecause the number of fish in the study was small, predicting a continuous variable  from count data (counts of the number of a type of variant in either a 10 kb or 50 kb window) was deemed impractical. Instead, we converted the continuous size measurement of length from tip to fork into three size classes  by separating the size measurements into 33.33% quantiles see . We alsoFor both the year 1 and year 3 datasets, we randomly split the data into 24 instances in the training set and 8 instances in the test set . This diTo compare the feature selection methods, we extracted the top features selected by TuRF, Chi-square, or mutual information. We then examined their subsequent prediction accuracy using the random forest, Gaussian naïve Bayes, logistic regression, and K-neighbours classification methods. We investigated how the feature number influences the prediction accuracy of growth by extracting the top 25, 50, 200, 250, and 500 ranked features and compared this to using all features . To ask whether features were more likely to be associated with the presence of genes associated with growth within genomic windows, we extracted gene annotations from a gene annotation file described previously , and resCircos plots were generated using the R package circlize v0.4.1  using beA total of 21,573,217 small variants were called from all 80 snapper samples. The conversion of variants into features (counts of genotype categories within windows) resulted in a total of 102,648 features of 50 kb windows and 513,590 features of 10 kb windows. For the structural variants, there were 58,665 features of 50 kb windows and 293,493 features of 10 kb windows. When the structural variants between 5 bp and 50 kb were merged across the full cohort of 80 individuals, 10,789 duplications, 1092 inversions, 2225 insertions, and 78,719 deletions were counted, of which 6926 duplications, 825 inversions, 1731 insertions, and 63,017 deletions were counted within the 32 individuals under study for growth. Once filtered for variants between 5 bp and 1 kb, 1189 duplications, 294 inversions, 1731 insertions, and 43,946 deletions were counted. There were a total of 1,158,928 deletions, 511,009 insertions, 8204 inversions, and 33,290 duplications recorded. Using no feature selection, the prediction accuracies to classify fish into the “small”, “medium” or “large” categories were generally low . The exception for this was for Chi-square feature selection using SNPs at 50 kb for years 1 and 3 and for SNPs called over 10 kb windows for year 3 fish . When thHow different types of genetic variation influence the phenotype is of key biological importance. The ease with which SNP data can be generated has led to significant progress in our understanding of how phenotypic trait variation is modulated by single changes in the base pair composition of the genome e.g. ,49. HoweChrysophrys auratus) because previous research on this species has generated significant genomic resources and an understanding of growth that we could leverage [Here, we explore the first steps towards understanding the predictive power of both SNPs and structural variant polymorphisms in explaining a complex quantitative growth trait by applying feature selection methods and machine learning models to our dataset. For our work, we chose the non-model species snapper , only a small proportion of total phenotypic variance was accounted for by structural variants [Homarus americanus) from 21 sampling sites revealed that copy number variants accounted for a higher genetic differentiation than SNP markers and were significantly associated with the annual variance in sea surface temperature, providing a strong empirical case that structural variants contribute to local adaptation [Solanum lycopersicum), structural variants detected through long-read nanopore sequencing in 100 individual genomes were shown to be responsible for not just the difference in allele dosage but also a range of expression of phenotypes [Apis mellifera), where chromosomal inversions have been linked to local adaption [Second, in some instances we were able to achieve prediction accuracies of 62% or higher for both the SNP and structural variant data. Thus, it does suggest that structural variants do provide some useful information that associate with the complex growth trait in this snapper population. This has not always been found to be the case. For example, in a study of 35,000 Holstein and Jersey cattle , high p (parameter number) problem. This problem is described by the fact that it is generally more cost and time effective to screen for a large number of variants within an individual than it is to screen large numbers of individuals  as is coIn conclusion, our work outlines a promising approach to finding genetic variants associated with complex traits and showcases how one can go beyond SNP data to also account for structural variant data. While our results indicate that SNPs can account for some of the variation in phenotypic traits, our results also highlight that structural variants should not be overlooked and that they carry significant additional phenotype information. Therefore, we recommend that researchers interested in the genotype–phenotype map should strive to go beyond SNPs in their work to capture the underpinnings of quantitative traits, such as growth. This will allow researchers to harness more of the available catalogue of genetic variants in the genome that are ultimately impacting the phenotype. In addition, future efforts need to increase the sample size of fish to better account for the genetic variation underlying this complex trait and to minimise to some extent the large n, small p issue in many biological datasets used for machine learning approaches.


Understanding how genetic variation shapes a complex trait relies on accurately quantifying both the additive genetic and genotype–environment interaction effects in an age-dependent manner. We used a linear mixed model to quantify diet-dependent genetic contributions to body weight measured through adulthood in diversity outbred female mice under five diets. We observed that heritability of body weight declined with age under all diets, except the 40% calorie restriction diet. We identified 14 loci with age-dependent associations and 19 loci with age- and diet-dependent associations, with many diet-dependent loci previously linked to neurological function and behavior in mice or humans. We found their allelic effects to be dynamic with respect to genomic background, age, and diet, identifying several loci where distinct alleles affect body weight at different ages. These results enable us to more fully understand and predict the effectiveness of dietary intervention on overall health throughout age in distinct genetic backgrounds. Body weight is one trait influenced by genes, age and environmental factors. Both internal and external environmental pressures are known to affect genetic variation over time. However, it is largely unknown how all factors – including age – interact to shape metabolism and bodyweight.Wright et al. set out to quantify the interactions between genes and diet in ageing mice and found that the effect of genetics on mouse body weight changes with age. In the experiments, Wright et al. weighed 960 female mice with diverse genetic backgrounds, starting at two months of age into adulthood. The animals were randomized to different diets at six months of age. Some mice had unlimited food access, others received 20% or 40% less calories than a typical mouse diet, and some fasted one or two days per week.Variations in their genetic background explained about 80% of differences in mice’s weight, but the influence of genetics relative to non-genetic factors decreased as they aged. Mice on the 40% calorie restriction diet were an exception to this rule and genetics accounted for 80% of their weight throughout adulthood, likely due to reduced influence from diet and reduced interactions between diet and genes. Several genes involved in metabolism, neurological function, or behavior, were associated with mouse weight.The experiments highlight the importance of considering interactions between genetics, environment, and age in determining complex traits like body weight. The results and the approaches used by Wright et al. may help other scientists learn more about how the genetic predisposition to disease changes with environmental stimuli and age. Quantifying the contributions of genetic and environmental factors to population variation in an age-dependent phenotype is critical to understanding how phenotypes change over time and in response to external perturbations. The identification of genetic loci that are associated with a complex trait in an age- and environment-dependent manner allows us to elucidate the dynamics and context dependence of the genetic architecture of the trait and facilitates trait prediction. For health-related traits, these genetic loci may also facilitate greater understanding and prediction of age-related disease etiology, which is an important step to genetically or pharmacologically manipulating these traits to improve health.Standard approaches used to identify genetic loci associated with quantitative traits can be confounded by nonadditive genetic effects such as genotype–environment (G×E) and genotype–age (G×A) interactions , contribIn this study, we used an LMM to investigate the classic quantitative trait, body weight, in a large population of diversity outbred (DO) mice. Body weight was measured longitudinally from early development to late adulthood, before and after the imposition of dietary intervention at 6 months of age. We expect diet and age to be important factors affecting body weight and growth rate; however, it remains to be determined how these factors will interact with genetic variation to shape growth. Two early studies found significant genetic correlations for body weight and growth rate during the first 10 weeks of mouse development, which supported the hypothesis that growth rates during early and late development were affected by pleiotropic loci . SubsequWe expect the interaction of dietary interventions, such as calorie restriction (CR) or intermittent fasting (IF), with genetics to greatly impact the body weight trajectories of mice. Researchers have observed genotype-dependent reductions in body weight in the 7–50 weeks after imposing a 40% CR diet, and variation in heritability of this trait with age from 42% to 54% . A seconIn order to address these questions, we measured the body weight of multiple cohorts of genetically diverse mice from the DO population  from 60 In the following sections, we first describe the study design and collection of the genetic and body weight measurements. Second, we motivate the use of the gene–environment mixed model (G×EMM)  to modelMus musculus) population was derived from eight inbred founder strains and is maintained at Jackson Labs as an outbred heterozygous population , so that no mice in the study were siblings and maximum genetic diversity was achieved. Mice were housed in pressurized, individually ventilated cages at a density of eight animals per cage (cage assignments were random). Mice were subject to a 12 hr:12 hr light:dark cycle beginning at 06:00 hr. Animals exit the study upon death. All animal procedures were approved by the Animal Care and Use Committee at The Jackson Laboratory.From enrollment until 6 months of age, all mice were on an AL diet of standard rodent chow 5KOG from LabDiet. At 6 months of age, each cage of eight animals was randomly assigned to one of five dietary treatments, with each cohort equally split between the five groups (N = 192/group): AL, 20% CR (20), 40% CR (40), 1 day per week fast (1D), and 2 days per week fast (2D) see . In a prMice on AL diet had unlimited food access; they were fed when the cage was changed once a week. In rare instances when the AL mice consumed all food before the end of the week, the grain was topped off midweek. Mice on 20% and 40% CR diets were fed daily. We gave them a triple feeding on Friday afternoon to last till Monday afternoon. As the number of these mice in each cage decreased over time, the amount of food given to each cage was adjusted to reflect the number of mice in that cage. Fasting was imposed weekly from Wednesday noon to Thursday noon for mice on 1D diet and Wednesday noon to Friday noon for mice on 2D diet. Mice on 1D and 2D diets have unlimited food access (similar to AL mice) on their nonfasting days.From enrollment until 660 days of age, each animal underwent a number of phenotypic assays to assess a wide range of physiological health parameters. These included two 7-day stints in Sable Systems Promethion metabolic cages at 120 and 390 days of age, two blood draws at 160 and 480 days of age, and one of each of the following challenge-based assays at 300–330 days of age: 3-day stint in a cage with wheel, rotarod, grip strength, dual-energy X-ray absorptiometry, echocardiogram, Y-maze spontaneous alternation, and acoustic startle.body weight and growth rate refer to the predicted fits from Body weight was measured once every week for each mouse throughout its life. The body weight measurements for this analysis were collated on February 1, 2020, at which point 941 mice (98%) had measurements at 180 days, 890 (93%) at 365 days, 813 (85%) at 550 days, and 719 (75%) at 660 days. For these analyses, we included all body weight measures for each mouse up to 660 days of age. We smoothed out measurement noise, either due to errors in measurement or swaps in assigning measurements to mice, using an lgorithm , which cWe present the average trends in body weight and growth rate, stratified by dietary intervention, in http://agingmice.jax.org/protocols). Samples were genotyped using the 143,259-probe GigaMUGA array from the Illumina Infinium II platform (genomics.neogen.com/). We evaluated genotype quality using the R package: qtl2 (https://kbroman.org/MUGAarrays/muga_annotations.html). After filtering genetic markers for uniquely mapped probes, genotype quality, and a 20% genotype missingness threshold, our dataset contained 110,807 markers.We collected tail clippings and extracted DNA from 954 animals  to account for both additive environment-dependent fixed effects and polygenic gene–environment interactions. We considered two different types of environments: diet and generation. The five diet groups were applied from 180 to 660 days and the 12 generations were applied from 30 to 660 days. Next, we performed genome-wide QTL mapping for body weight at each age independently, testing for association between body weight and the inferred founder-of-origin at each genotyped marker. For ages 180–660 days, we additionally tested for association between body weight and the interaction of diet and founder-of-origin at each marker. We computed p-values using a sequential permutation procedure  at each First, we quantified the overall contribution of genetics to variation in body weight and, importantly, how this contribution changed with age. We applied both EMMA and G×EMM to body weight estimated every 10 days. Since the mice from each generation cohort were measured at the same time every week, we used generation as a proxy for the shared environment that mice are exposed to as part of the study design. We accounted for generation-specific fixed effects α in  in both In E40≈0.8)  and low nt noise . MoreoveThe kinship matrix used for estimating these PVE values was computed based on the founder-of-origin of marker variants . When usWhen using kinship computed from genotypes, we note that the PVE in the permuted dataset does not drop to zero, suggesting that genotype-based kinship includes some background relatedness that can explain some of the phenotypic variation even after permuting the labels  and not a decrease in the genetic variance of body weight . Even thWe sought to identify loci significantly associated with body weight in a diet-dependent and age-dependent manner. To this end, we tested for association between the inferred founder-of-origin of each typed variant and body weight at each age independently. We note that body weight measurements taken at different ages are not independent; that is, we may detect a locus at a specific age if it has small effects on body weight acting over a long period of time or a large effect on body weight, resulting in rapid bursts in growth. Thus, a locus identified as significant at a specific age indicates its cumulative contribution to body weight at that age.Data Release: Results for a comparison of the number of significant loci with those obtained using the EMMA model).We identified 29 loci significantly associated with body weight at any age in the additive or interaction models using a genome-wide Bonferroni-corrected on tests . Additiog method . In ordeg method , resulti10−5 see . Notably10−5 see , we reteOur fine-mapping analysis confirmed 24 candidate loci: 5 loci unique to the additive model, 10 loci unique to the interaction model, and 9 loci significant in both models . We idenData Release: Results), while representing the age- and diet-dependent effects of these loci in terms of the effects of its top FAP groups. We further narrowed the number of candidates by intersecting the variants in top FAP groups with functional annotations . For many loci, this procedure identified candidate regions containing 1–3 genes . For the diet-dependent locus, at age 600 days, we identified 617 variants as significant; of these, 507 could be assigned to the lead FAP and shared a similarly high LOD score . For the diet-independent and diet-dependent loci, we found 2 and 101 variants, respectively, that were located in regions of open chromatin , Plekhh1, and Rad51b  gene, a candidate linked to body weight in mid-late adulthood via the lead 129/CAST/WSB FAP group within a diet-dependent locus on chromosome 3. This gene is highly expressed in the cerebral cortex and hippocampus in the rat brain  implicated by two distinct FAP groups in the diet-dependent locus on chromosome 12 (Trmt1l (Trmt1-like), a gene with sequence similarity to orthologous tRNA methyltransferases in other species, was linked to body weight during early adulthood . We observed similar PVE values to those from the full dataset, across the full age range, suggesting that survival bias has very little effect on the results presented in this paper  again has two terms, as in and the numerator of the second term is written asThe expected total sample phenotypic variance can be decomposed as follows:The proportion of variance explained by genetics conditional on environment can be computed by substituting the above in The proportion of phenotypic variance explained by genetic effects is equivalent to narrow-sense heritability, once variation due to additive effects of environment, batch, and other study design artifacts have been removed. In this work, we use the more general term, proportion of variance explained, to accommodate variation due to effects of diet and environment.Under the EMMA model, the expected total sample phenotypic variance simplifies towhere To test for additive effect of a genetic variant on the phenotype, we include the focal variant among the fixed effects in the model while treating all other variants to have random effects.Applying the priors described above for where  variant . The tesTo test for effects of interaction between genotype and environment on the phenotype, we include a fixed effect for the focal variant and its interactions with the set of all environments of interest , we focus our attention to tests for nonlinear trends in the effect sizes of the founder alleles and the effect sizes of the interaction between founder alleles and diet.Specifically, the estimated effects and the two models of the effect size trends arewhere where We apply this test for each of the founder effects in each of the 14 diet-independent loci (112 tests) and each of the 19 founder-x-diet interaction effects in each of the diet-dependent loci (760 tests). We assign a diet-independent trend as significantly nonlinear if we observe a Data used in this study, and significant QTLs, can be downloaded from the following links:https://doi.org/10.6084/m9.figshare.13190735Genotypes: https://doi.org/10.6084/m9.figshare.13190702Body Weight: https://doi.org/10.6084/m9.figshare.13190615Covariates: https://doi.org/10.6084/m9.figshare.13190708Results : https://github.com/calico/do_qtl; (swh:1:rev:3d23d3fbd7768b74b0bba6183de1570a65a2d93d).Our Python implementation of the EMMA and G×EMM models can be downloaded from  This is an outstanding dissection of the genetic architecture of body weight at the genome-wide level across time and across environments. The use of a multiparental mouse population permits high-resolution mapping. The statistical analyses are advanced, leveraging new models, as well as tools developed specifically for this mouse population. The corresponding results are presented in nice and informative figures. In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.Decision letter after peer review:eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Matt Kaeberlein as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Andrew Dahl (Reviewer #2); Amelie Baud (Reviewer #3).Thank you for submitting your article "Age and diet shape the genetic architecture of body weight in Diversity Outbred mice" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:Wright et al., have empirically studied the subtleties of the genetic architecture of a classic quantitative trait, body weight, providing evidence of gene-by-age and gene-by-diet effects, both at the level of the entire genome and at the level of individual genetic loci. The authors also identified likely causal variants at individual loci. To do so, they used a mouse population descended from multiple, known founders and reconstructed the founder haplotypes at each locus, and also used genomic annotations. Finally, the authors also explored pleiotropy, allelic heterogeneity and locus heterogeneity at the associated loci.eLife community.This is an outstanding dissection of the genetic architecture of a complex trait at the genome-wide level, at the locus level, across time and across environments. The experimental design is excellent, with the use of a multiparental mouse population that also permits high-resolution mapping. The statistical analyses are good and advanced, leveraging the GxEMM model recently published by Dahl et al., as well as tools developed specifically for this mouse population to trace back the origin of each QTL to the progenitors of the population; the corresponding results are presented in very informative figures. Finally, the paper is well structured and written, however, additional clarifications, justifications and possibly small additional analyses are requested to make the paper a better fit to the Major Comments:1. Please justify the p-value thresholds:– Lines 306-7 say that a 10fold weaker threshold is used for the interaction test--why? Also, where do these thresholds come from?– Is it sound to take this two-step approach of first finding loci and then 'fine mapping' variants nearby? It is definitely fine if the thresholds are valid genome-wide--but then why not test genome-wide?2. Please eliminate nonnegativity constraints on VCs in software:– Are you truncating estimates to be nonnegative? If so, this will cause bias, which I believe is visible in your simulations. This is essential to fix for testing, and also for unbiased VC estimates.– Users will test random effects, so it is necessary to validate (or remove) this part of your software.– I don't see an assessment of tests or ses for the VCs. A quick supp figure corresponding to the current simulations would suffice, I think.3. Please assess standard errors/false positive rates/power for testing VCs:– Are there evidence that GxEMM improves power for fixed effect interaction tests? I think just commenting on this is enough, but it does seem important if you want others to use your approach. Comparing power  for EMMA vs GxEMM in real data and/or simulation would work.4. Mouse phenotyping:– the text needs to say upfront that the mice included in this study were subject to a battery of phenotyping beyond weighing, including metabolic cage phenotyping, blood drwas, and "challenge-based phenotyping procedures". Currently this information comes late in the text (L287), and the title of Figure 1 Supplement 1 reads "Raw phenotype measurements", which does not alert the reader to these additional phenotypes. Some details about this phenotyping are needed, in particular how many blood draws were taken and which specific procedures are included under "challenge-based phenotyping".This extra phenotyping means that the body weight results presented in this study could be study-specific. In particular, the decrease in PVE observed with age in this study, which contrasts with increased heritability with age observed in previous studies (see Introduction), could be the result of increased noise due to extra phenotyping. The implications of this extra phenotyping need to be discussed.Importantly, it does not mean that this study is any less relevant than mouse studies without challenging life events, humans also experience challenging life events5. Clarifications on Figure 4:– What do PVE_tot and PVE_e represent (more on this below)? In particular, L291 "total genetic variance for the 40% CR group" is non-sensical to me because I thought PVE_tot was across all mice – as suggested by the fact that there is a single dark grey line in Figure 4 showing PVE_tot. Also, I was expecting PVE_tot  to be the sum of non diet-dependent genetic effects + all 5 PVE_e (colored lines). Yet the dark grey line is below the coloured lines. Hence I don't have the right intuition for what PVE_tot and PVE_e are. Looking at the equations didn't help: shouldn't it be PVE_e in Equation (7) and PVE_tot in Equation (13)?Clarifications are needed.– Figure 4: I love this figure, but worry a bit about the role of GxGeneration:– The legend gave me a strong (and wrong) sense that the GxE was all about diet. If possible, disentangling the two GxE contributions visually would be helpful.– I don't understand why generation is included .– Why not have an apples-to-apples comparison using GxGeneration as the baseline for questions about GxDiet?– What is dark grey? The hom estimate from GxEMM? The hom+GxGeneration (but then shouldn't there be one estimate for each generation)?– More generally, I don't follow how generation is being used in this paper. Is it just always in the background as a random effect, and if so, why? Why don't you test for locus-x-generation effects--if they're not expected to be interesting, why do they explain so much variance? If they are absorbing confounding, why not also adjust for cage (perhaps with the GxEMM 'IID' model to save degrees of freedom)? I suspect whatever you're doing is reasonable, but maybe just explain a bit more clearly.Figure 4—figure supplement 2, (b), right – isn't it concerning that the permuted phenotypes are heritable? How can this be? I recognize you don't use this kinship in your real analyses (though believe you do use the genotypes from which the kinship is built), but some explanation here would increase confidence in the overall approach.I'd like to see versions of Figure 4 that: overlay the interventions, as in supplement Figure 1; only show the E-specific genetic variances (ie substracting the sig2g_hom terms); and show the heritabilities . These would make nice supplement Figures if easy to generate.6. GWAS-related comments:– The GWAS section and the corresponding figures are overwhelming. I think it would benefit from shortening and using sub-headings. I think it would be good to show first how likely causal variants can be identified , with the chr6 and chr 12 loci as examples, and THEN show these loci across age and diets to discuss pleiotropy and heterogeneity.– except if we consider triallelic SNPs, the distinction between allelic heterogeneity  and  "a single genomic region contains multiple functional body weight loci that are only revealed with sufficient fine-mapping resolution" (L346-349) is difficult to make because noise can blur genetic associations, making it impossible to know the exact position of the causal variant(s). Consistent with the difficulty I just mentioned, in the section L419-443 and corresponding Supplementary Figures, I find that the assignments of the loci to either allelic or locus heterogeneity not obvious/robust.I think it would be best to focus on distinguishing between pleiotropy  affecting body weight at different ages or in different diets) and non-pleiotropy , rather than trying to distinguish between allelic and locus heterogeneity.Statistical tests exist to test the null hypothesis {same locus affects both traits} in multiparental populations (doi.org/10.1534/g3.119.400098). In addition, looking at the FAPs of the lead variants, as the authors do here, would be a great way to complement this statistical test. Statistical evidence of different loci + differing top FAPS would provide strong evidence for some form of heterogeneity.If you are going to focus on pleiotropy yes/no, it would be good to show a locus with likely pleiotropic effects .An idea now, not a request: It would be interesting to know whether the loci for which different causal variants are predicted to affect different traits (e.g. different ages) are also loci for which multiple causal variants are predicted to affect either trait (see doi:10.1038/ng.2644).7. Gene enrichment:– is there a significant enrichment in genes affecting neurological behavior in this study, to support the claim that the fine-mapped genes implicate neurological and metabolic processes? If not, probably best to move the corresponding section of the text to the discussion. Also discuss whether the associations between neurological genes and body weight could arise due to the stressful extra phenotyping of the mice eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Matt Kaeberlein as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: Andrew Dahl (Reviewer #2); Amelie Baud (Reviewer #3).Thank you for submitting a revised version of your article "Age and diet shape the genetic architecture of body weight in Diversity Outbred mice" for consideration by The manuscript has improved since last submission, however, few comments many for clarity need to be addressed before the manuscript can be accepted for publication.Essential Revisions:1) The methods used to calculate the genome-wide significance threshold for the GWAS are now explained with sufficient detail but I believe the thresholds used are much less stringent than commonly accepted (commonly accepted = some estimate of a genome-wide threshold of 0.05). Two lines of evidence for this:– The authors "used the number of top singular values that explain at least 90% of variation across markers (500), as a proxy for the number of independent QTL signals,", from which they calculated the Bonferroni corrected threshold. They mention in their response to the reviewers that this approach is similar to what is used in human GWAS. However, based on the results presented in Table 1 of https://onlinelibrary.wiley.com/doi/epdf/10.1002/gepi.20430 for example, I believe a value much greater than 90% of variation needs is used when applying this approach to human GWAS data to get close to the commonly accepted threshold of 5.10-8. SimpleM (presented in Table 1 of the paper above) uses a cutoff of 99.5% and still yields a more lenient threshold than 5.10-8.– Other GWAS in DO mice have used much more stringent thresholds than p-value of 10-4: for example, https://link.springer.com/article/10.1007/s00335-018-9745-8#Sec11 used a P value threshold of 7.3.10-7 to claim genome-wide significance at 0.05; https://reader.elsevier.com/reader/sd/pii/S0168952519300654?token=DEFE149F2C71C5E4EA274AB6AE3638597EEACA678E9451C00AEE8CCD806BDA0E20ACE4BAA8DEF5D6BE37F274132E9F61&originRegion=eu-west-1&originCreation=20210602135101 used an even more stringent threshold – see Figure 3C.As a consequence of the likely very lenient significance thresholds used in GWAS, all the claims from GWAS and subsequent analyses are supported by limited statistical evidence. In particular, it is difficult to be confident that the apparent lack of pleiotropic signals observed across loci is a real feature of the architecture of body weight: the different FAPs observed etc. could be the result of noise. The genes identified in Table 1 are also supported by limited statistical evidence.2) I find the GWAS-related text still poorly organised and overwhelming. For example, effects as a function of age are discussed in three different sections . Similarly pleiotropy is discussed in three different sections, and functional variants are discussed in different sections too. Perhaps group everything related to pleiotropy in one section, effects as a function of age in another, and candidate variants/genes in a third?The non-linearity in diet is hard to understand and appreciate in the current manuscript. It is quite interesting (surprising), if true. Perhaps give it its own section?3) Using a diagonal omega matrix is problematic not only for pairs of diets but also for pairs of generations I think, as interaction effect sizes could well be correlated in pairs of generations. The response from the authors to this issue is not entirely satisfactory to me, as they acknowledge that biases are possible but suggest biases will be small without really explaining why they will be small.– Lines 291-5 – I don't understand why permutations don't fully break the correspondence between both sources of relatedness and phenotype? The kinship is just a matrix, and I don't see how substructures in this matrix could be invariant to random permutation. . In other words, what null are you testing if the permutations are also significant? Why doesn't your claim imply that a pure noise phenotype would have significant GxE?4) For negative VC estimates -- the new supp Figure is great, as is the new flag, but don't see these mentioned in the text? I suggest you acknowledge your constrained approach causes bias (cf your simulations), but that you address it in principle with the new flag and also there is no reason to worry about your real data analyses . I think it's important to have unbiased inference for GxE h2 (much more than for additive h2). Major Comments:1. Please justify the p-value thresholds:– Lines 306-7 say that a 10fold weaker threshold is used for the interaction test--why? Also, where do these thresholds come from?-4. This same threshold is reasonable for our interaction tests since we have only one test per marker (similar to the additive tests); however, we use a weaker threshold of 10-3 for interaction tests to explore suggestive GxE interaction QTLs. Our choice of thresholds, although arbitrary, are intended to help us focus our attention to the strongest QTLs with sufficient statistical support and are not intended to quantify the exact number of QTLs linked to body weight. We have updated the manuscript to better explain our choice of p-value thresholds.The Bonferroni corrected p-value threshold used in the manuscript is a genome-wide threshold and was computed based on the expected number of linkage disequilibrium (LD) blocks  in our study (similar to the strategy used in human GWAS studies). If the LD structure is perfectly block-like, the number of LD blocks can be computed from the number of non-zero singular values of the marker genotype matrix. In practice, we used the number of top singular values that explain at least 90% of variation across markers (500), as a proxy for the number of independent QTL signals, resulting in a p-value threshold of 10– Is it sound to take this two-step approach of first finding loci and then 'fine mapping' variants nearby? It is definitely fine if the thresholds are valid genome-wide--but then why not test genome-wide?The p-value thresholds we used are valid genome-wide and it is certainly reasonable to simply test genome-wide. We chose to take the two-step approach for two reasons:1. At the genotyped markers, testing for association between founder-of-origin and phenotype has higher power than testing for association between allele count and phenotype . Notably, we only have informative founder-of-origin inferences at genotyped markers.2. The two-step approach is much more computationally efficient. While this two-step approach certainly has an increased false-negative rate, evaluating the tests longitudinally through age should mitigate this substantially.2. Please eliminate nonnegativity constraints on VCs in software:– Are you truncating estimates to be nonnegative? If so, this will cause bias, which I believe is visible in your simulations. This is essential to fix for testing, and also for unbiased VC estimates.– Users will test random effects, so it is necessary to validate (or remove) this part of your software.– I don't see an assessment of tests or ses for the VCs. A quick supp figure corresponding to the current simulations would suffice, I think.Thank you for bringing to our attention the possibility that variance components do not need to be constrained to be positive, in order to have valid estimates of heritability. We re-computed the PVE estimates for all ages and diets without truncating the estimates to be non-negative, and found very little difference in the magnitude and trends of PVE with age . We chose to keep the estimates with non-negativity constraints as the main result, since these variance components are more interpretable in the context of our study. We have, however, included an option in the software to relax the non-negativity constraints on the variance components.3. Please assess standard errors/false positive rates/power for testing VCs:– Are there evidence that GxEMM improves power for fixed effect interaction tests? I think just commenting on this is enough, but it does seem important if you want others to use your approach. Comparing power  for EMMA vs GxEMM in real data and/or simulation would work.-3 and 10-4, the EMMA model identified more loci associated with body weight, quantified both by the number of independent genomic regions and average length of time in days per locus. We have updated the Results section, included Figure 5 —figure supplement 2 , and added a table in Supplementary file 3 to highlight this point.To address the question of power for both fixed effect additive and interaction tests, we performed QTL mapping using the EMMA model, at the same set of ages as for the GxEMM model. In order to compare the GxEMM results to the standard linear mixed model, we reran the body weight association analyses at all ages using the EMMA model. We found that for both the additive and interaction models, at p-value thresholds of 10We, however, do not claim the difference in QTLs to be due to a difference in power nor label any model-specific QTLs as false positives. Comparing Figure 5 —figure supplements 1 and 2, we observe that it is rare for a strong association under one model to be completely ablated under the other model; instead we observe subtle differences in likelihood ratio and p-values. Given the high temporal resolution in phenotype measurements, we feel it is more informative to focus on the effect size estimates  of reasonably significant QTLs rather than focusing on the (admittedly arbitrarily and binary) problem of testing for QTLs. We relied on GxEMM since it is a more expressive model and EMMA is a special case of GxEMM.4. Mouse phenotyping:– The text needs to say upfront that the mice included in this study were subject to a battery of phenotyping beyond weighing, including metabolic cage phenotyping, blood drwas, and "challenge-based phenotyping procedures". Currently this information comes late in the text (L287), and the title of Figure 1 Supplement 1 reads "Raw phenotype measurements", which does not alert the reader to these additional phenotypes. Some details about this phenotyping are needed, in particular how many blood draws were taken and which specific procedures are included under "challenge-based phenotyping".This is a good point and we have updated the ‘Data’ section to describe the challenge-based phenotyping procedures (L129 – L134).This extra phenotyping means that the body weight results presented in this study could be study-specific. In particular, the decrease in PVE observed with age in this study, which contrasts with increased heritability with age observed in previous studies (see Introduction), could be the result of increased noise due to extra phenotyping. The implications of this extra phenotyping need to be discussed.Importantly, it does not mean that this study is any less relevant than mouse studies without challenging life events, humans also experience challenging life eventsAgreed; for this reason – and for all the unmeasured factors that we are unaware of – some of these results may be specific to this study. With data from another dietary intervention study in aged, outbred mice, we could assess whether this is the case. We have added text to the ‘Discussion’ to highlight this point (L557 – L559).5. Clarifications on Figure 4:– What do PVE_tot and PVE_e represent (more on this below)? In particular, L291 "total genetic variance for the 40% CR group" is non-sensical to me because I thought PVE_tot was across all mice – as suggested by the fact that there is a single dark grey line in Figure 4 showing PVE_tot. Also, I was expecting PVE_tot  to be the sum of non diet-dependent genetic effects + all 5 PVE_e (colored lines). Yet the dark grey line is below the coloured lines. Hence I don't have the right intuition for what PVE_tot and PVE_e are. Looking at the equations didn't help: shouldn't it be PVE_e in Equation (7) and PVE_tot in Equation (13)?Clarifications are needed.tot is computed using all mice  and PVEe is computed using mice belonging to diet ‘e’ . Since PVEtot and PVEe (for each diet) are computed on different sets of mice, we can’t expect PVEtot to be the sum of all PVEe . This is clear from the equations: the denominator of Equation 7 for PVEtot is VarY , the phenotypic variance computed using all the samples, while the denominator of Equation 13 for PVEe is VarY|e , the variance computed using only samples belonging to diet ‘e’. Crucially, PVEe is not the fraction of PVEtot contributed by diet ‘e’.PVEThank you for pointing out the error on L291; we have removed the term “total” from that sentence.– Figure 4: I love this figure, but worry a bit about the role of GxGeneration:– The legend gave me a strong (and wrong) sense that the GxE was all about diet. If possible, disentangling the two GxE contributions visually would be helpful.– I don't understand why generation is included .– Why not have an apples-to-apples comparison using GxGeneration as the baseline for questions about GxDiet?– More generally, I don't follow how generation is being used in this paper. Is it just always in the background as a random effect, and if so, why? Why don't you test for locus-x-generation effects--if they're not expected to be interesting, why do they explain so much variance? If they are absorbing confounding, why not also adjust for cage (perhaps with the GxEMM 'IID' model to save degrees of freedom)? I suspect whatever you're doing is reasonable, but maybe just explain a bit more clearly.e. We don’t test for GxGeneration fixed effects, both because they are not expected to be interesting and because their contribution to diet-dependent PVE values are relatively small .The GxEMM model includes variance components for interaction terms with ‘diet’ and ‘generation’. In our study design, ‘generation’ is a proxy for the shared environment that the mice are exposed to throughout the study; in particular, mice of the same generation are subject to various phenotyping pipelines together. In this sense, ‘generation’ effects are essentially batch effects. We chose to always control for GxGeneration random effects in the model since this helped give us better and more precise estimates for PVEe is computed using mice on diet ‘e’ and includes contributions from the diet ‘e’ term and from all the ‘generation’ terms. Thus, PVEe for two diets does have some shared components coming from the generation variance components; however, it is difficult to decompose which parts are truly shared and which are diet-specific, since the PVE are computed on different sets of mice, and thus the contribution of kinship is slightly different (see Equation 14). We have added Figure 4 —figure supplement 4 highlighting the contribution of diet-specific variance components and generation-specific variance components for each PVEe.PVEWe could certainly control for GxCage effects, either assuming the same variance component for all cages as in the GxEMM ‘IID’ model or using a hierarchical model for the cage variance components. Assuming that all cages shared the same variance component parameter, we observed that the estimate for the cage-specific variance components was negligibly small, suggesting that either cage effects were negligible or the ‘IID’ model is too restrictive. A hierarchical model for cage effects is an interesting avenue for future work, but is out of the scope for our current study.– What is dark grey? The hom estimate from GxEMM? The hom+GxGeneration (but then shouldn't there be one estimate for each generation)?Dark grey in Figure 4 is the PVE computed using all mice. This includes the contribution from all the diet-specific and generation-specific variance components. We have included Figure 4 —figure supplement 5 showing the contribution of each of these components to the dark grey line.Figure 4—figure supplement 2, (b), right – isn't it concerning that the permuted phenotypes are heritable? How can this be? I recognize you don't use this kinship in your real analyses (though believe you do use the genotypes from which the kinship is built), but some explanation here would increase confidence in the overall approach.The SNP-based kinship can be decomposed into two components: the genetic sharing between the founder strains (the 8 founders have some degree of genetic similarity amongst themselves at the SNP level) and the genetic sharing arising from the breeding strategy used to develop the DO panel. In other words, SNP-based kinship accounts for sharing due to identity-by-state while FAP-based kinship accounts for sharing due to identity-by-descent. Randomly permuting the phenotype labels breaks the link between phenotypic similarity and the latter component of SNP-based kinship, but does not effectively break the link with the former component. Computing kinship using the founder allele probability effectively controls for any genetic similarity between the founder strains . We believe this explains the inflation of PVE after permuting phenotypes with the SNP-based kinship, observed both for the EMMA and GxEMM models. Based on this reasoning, we hypothesize that the observed inflation would have been worse at earlier generations of DO mice and predict that this inflation will continue to decrease with future generations of DO mice. We have added text in the manuscript elaborating on this observation.I'd like to see versions of Figure 4 that: overlay the interventions, as in supplement Figure 1; only show the E-specific genetic variances (ie substracting the sig2g_hom terms); and show the heritabilities . These would make nice supplement Figuresif easy to generate.We have added Figure 4 —figure supplement 2, overlaying the interventions onto the PVE trends. We have also added Figure 4 —figure supplement 5 breaking down each PVE  into contributions from the diet-specific terms and the generation-specific terms.6. GWAS-related comments:– The GWAS section and the corresponding figures are overwhelming. I think it would benefit from shortening and using sub-headings. I think it would be good to show first how likely causal variants can be identified , with the chr6 and chr 12 loci as examples, and THEN show these loci across age and diets to discuss pleiotropy and heterogeneity.We appreciate the comments from this reviewer and agree that the GWAS section as originally constructed was overwhelming. To address this, we have now broken this section up into two subsections and eliminated the confusing discussion about distinguishing between pleiotropy, allelic heterogeneity and tightly linked loci (see below). We believe these changes will greatly increase reader comprehension.In regards to figure 5, we agree there is a lot of information in each subpanel. We have re-organized these results into two figures to first discuss the identification of focal variants and second the effect of a focal variant on body weight at different ages.– except if we consider triallelic SNPs, the distinction between allelic heterogeneity  and  "a single genomic region contains multiple functional body weight loci that are only revealed with sufficient fine-mapping resolution" (L346-349) is difficult to make because noise can blur genetic associations, making it impossible to know the exact position of the causal variant(s). Consistent with the difficulty I just mentioned, in the section L419-443 and corresponding Supplementary Figures, I find that the assignments of the loci to either allelic or locus heterogeneity not obvious/robust.I think it would be best to focus on distinguishing between pleiotropy  affecting body weight at different ages or in different diets) and non-pleiotropy , rather than trying to distinguish between allelic and locus heterogeneity.Yes, this is a good point. We agree that in general we do not have a large enough mapping population for the fine-mapping analysis to distinguish between allelic and locus heterogeneity. We have updated the language in the manuscript to state that these results are not consistent with a single pleiotropic locus.Statistical tests exist to test the null hypothesis {same locus affects both traits} in multiparental populations (doi.org/10.1534/g3.119.400098). In addition, looking at the FAPs of the lead variants, as the authors do here, would be a great way to complement this statistical test. Statistical evidence of different loci + differing top FAPS would provide strong evidence for some form of heterogeneity.If you are going to focus on pleiotropy yes/no, it would be good to show a locus with likely pleiotropic effects .This is a great point. We do not apply this formal test of pleiotropy. We have updated the manuscript to state that when we identify a single FAP associated with body weight at multiple ages  that this is suggestive of pleiotropy.Additionally, we interpret the identification of distinct FAPs at the same genomic region  as strong evidence against a single pleiotropic locus.An idea now, not a request: It would be interesting to know whether the loci for which different causal variants are predicted to affect different traits (e.g. different ages) are also loci for which multiple causal variants are predicted to affect either trait (see doi:10.1038/ng.2644).Yes, we agree this is an interesting idea to pursue in follow-up analyses.7. Gene enrichment:– is there a significant enrichment in genes affecting neurological behavior in this study, to support the claim that the fine-mapped genes implicate neurological and metabolic processes? If not, probably best to move the corresponding section of the text to the discussion. Also discuss whether the associations between neurological genes and body weight could arise due to the stressful extra phenotyping of the mice We have not tested for a specific GO term enrichment of neurological and metabolic processes for the candidate genes. In response to this comment, we have edited this section of the results to make clear that we do not claim any specific enrichment of these processes. In keeping with comments from another reviewer, we feel that highlighting these six specific candidate genes  adds significant value to the paper. Moreover, we believe that highlighting these six genes in the Results section immediately following our discussion of the fine-mapping data is the clearest way to convey this information to the reader and we have kept this in the Results section.We agree with this comment (and previous comments) that this particular result, and nearly any other result we present in the paper could in fact be caused by peculiarities of this experiment rather than the ‘true’ genetic basis of variation in body weight and how that is affected by age and diet. We have emphasized this caveat in the Discussion. Future studies that incorporate longitudinal measurements of body weight in both mice and humans should help identify how much of our results are robust to differences in experimental design.Essential Revisions:1) The methods used to calculate the genome-wide significance threshold for the GWAS are now explained with sufficient detail but I believe the thresholds used are much less stringent than commonly accepted (commonly accepted = some estimate of a genome-wide threshold of 0.05). Two lines of evidence for this:– The authors "used the number of top singular values that explain at least 90% of variation across markers (500), as a proxy for the number of independent QTL signals,", from which they calculated the Bonferroni corrected threshold. They mention in their response to the reviewers that this approach is similar to what is used in human GWAS. However, based on the results presented in Table 1 of https://onlinelibrary.wiley.com/doi/epdf/10.1002/gepi.20430 for example, I believe a value much greater than 90% of variation needs is used when applying this approach to human GWAS data to get close to the commonly accepted threshold of 5.10-8. SimpleM (presented in Table 1 of the paper above) uses a cutoff of 99.5% and still yields a more lenient threshold than 5.10-8.– Other GWAS in DO mice have used much more stringent thresholds than p-value of 10-4: for example, https://link.springer.com/article/10.1007/s00335-018-9745-8#Sec11 used a P value threshold of 7.3.10-7 to claim genome-wide significance at 0.05; https://reader.elsevier.com/reader/sd/pii/S0168952519300654?token=DEFE149F2C71C5E4EA274AB6AE3638597EEACA678E9451C00AEE8CCD806BDA0E20ACE4BAA8DEF5D6BE37F274132E9F61&originRegion=eu-west-1&originCreation=20210602135101 used an even more stringent threshold – see Figure 3C.As a consequence of the likely very lenient significance thresholds used in GWAS, all the claims from GWAS and subsequent analyses are supported by limited statistical evidence. In particular, it is difficult to be confident that the apparent lack of pleiotropic signals observed across loci is a real feature of the architecture of body weight: the different FAPs observed etc. could be the result of noise. The genes identified in Table 1 are also supported by limited statistical evidence.We appreciate the reviewers pointing out evidence from both human GWAS and mouse QTL studies suggesting the need for a more stringent p-value cutoff for claiming significance. While the two papers on GWAS in DO mice used a more stringent p-value threshold to claim genome-wide significance at 0.05, the Yuan et al., paper used a different permutation scheme to generate their null distribution and compute their p-value threshold and the Saul et al., paper does not describe how their threshold was selected.Following the approach in the Gao et al., paper on Bonferroni correction in human GWAS studies, we computed the eigenvalues of the full linkage disequilibrium matrix among genotyped variants and used the top K eigenvalues that explain Y% of total genetic variation as a proxy for the number of independent tests. For Y = 90, we obtained K = 500, leading to a p-value threshold of 1e-4. For Y = 99.5, we obtained K = 4455, leading to a p-value threshold of 1.1e-5. A Bonferroni correction for multiple hypotheses is considered to be highly conservative, particularly for traits like Body Mass that are known to have a strong genetic component. An alternate and less conservative approach would be to use a p-value threshold corresponding to a fixed, expected number of false discoveries. Using the Benjamini-Hochberg method, a procedure that is expected to be robust to correlations due to linkage disequilibrium, we computed a p-value threshold of 1.2e-4 corresponding to a 10% expected false discovery rate.Given the high heritability of Body Mass and the availability of longitudinal Body Mass data, we reasoned that it was excessively conservative to rely on a single Bonferroni-based p-value threshold as the only source of statistical evidence. Instead, in Table 1, we listed loci that (i) passed a more liberal Bonferroni threshold (matching the 10% FDR threshold), (ii) were identified as significant at multiple ages, and (iii) were found to be significant using fine-mapping analysis. In order to clarify the strength of evidence based on p-values alone, we marked in Table 1 loci with p-value less than 1.1e-5 with *** (denoting them as highly significant), loci with p-value less than 1e-4 with ** (denoting them as significant), and p-value less than 1e-3 with * (denoting them as suggestive). Multiple sources of evidence supporting these loci suggest that the observed associations and related aspects of the architecture of body weight are not the result of noise.2) I find the GWAS-related text still poorly organised and overwhelming. For example, effects as a function of age are discussed in three different sections . Similarly pleiotropy is discussed in three different sections, and functional variants are discussed in different sections too. Perhaps group everything related to pleiotropy in one section, effects as a function of age in another, and candidate variants/genes in a third?The non-linearity in diet is hard to understand and appreciate in the current manuscript. It is quite interesting (surprising), if true. Perhaps give it its own section?We have restructured the GWAS-related text to improve readability and organization of information. First, we discussed the use of founder allele patterns, along with functional variants and candidate genes at the two loci we’ve highlighted, then we discussed pleiotropy, and, finally, we discussed effects as a function of age. We have retained a separate, broader discussion on candidate genes that we’ve identified in this study. We have also separated the paragraph on non-linearity in effects with diet into its own section.3) Using a diagonal omega matrix is problematic not only for pairs of diets but also for pairs of generations I think, as interaction effect sizes could well be correlated in pairs of generations. The response from the authors to this issue is not entirely satisfactory to me, as they acknowledge that biases are possible but suggest biases will be small without really explaining why they will be small.We acknowledge the lack of explanation behind our intuition that off-diagonal terms in the omega matrix are expected to be small, leading to small biases in estimates of heritability. To address this, we modified our code to estimate a full omega matrix and computed heritability estimates at each age using the full matrix. We observed that off-diagonal entries of the full omega matrix were often orders of magnitude smaller than the diagonal entries, leading to very small changes in heritability estimates using the full matrix. We have added Figure 4 —figure supplement 5 comparing the heritability estimates between a diagonal omega matrix and a full omega matrix.– Lines 291-5 – I don't understand why permutations don't fully break the correspondence between both sources of relatedness and phenotype? The kinship is just a matrix, and I don't see how substructures in this matrix could be invariant to random permutation. . In other words, what null are you testing if the permutations are also significant? Why doesn't your claim imply that a pure noise phenotype would have significant GxE?The kinship is a matrix of relatedness between pairs of individuals; in this sense, substructures in this matrix (or even the entire kinship matrix) could be invariant to certain permutations of samples depending on whether kinship is computed using genotypes or using founder allele probabilities. This invariance is much more readily observed in the DO mouse population (or other lab-outbred populations) than in natural populations of mice or humans, particularly because the DO population is currently only ~30 generations removed from the inbred Collaborative Cross mouse lines from which they were derived.As an extreme example, if the mice in our study were composed of just “copies” of the 8 founder strains, then the genotype-based kinship matrix would have eight blocks of matrix-of-ones along the diagonal (since the 8 founders are completely homozygous), with off-diagonal blocks capturing the kinship between pairs of founders. Such a kinship matrix is invariant under certain permutations of sample ids; these permutations would give significant heritability estimates and, thus, straightforward permutations would not be a valid approach to construct a null of no association between genotype and phenotype.The current DO population matches a less extreme version of the example above, due to ~30 generations of outbreeding. Thus, permuting the genotype-based kinship matrix does not fully break the association between genotype and phenotype. We believe this effect would have been more extreme in earlier DO generations, and will continue to weaken in later DO generations.4) For negative VC estimates -- the new supp Figure is great, as is the new flag, but don't see these mentioned in the text? I suggest you acknowledge your constrained approach causes bias (cf your simulations), but that you address it in principle with the new flag and also there is no reason to worry about your real data analyses . I think it's important to have unbiased inference for GxE h2 (much more than for additive h2).We have now addressed in the manuscript the possible bias in our constrained approach, shown that we observed little difference with and without the constraint, and highlighted that our software allows for relaxing this constraint via a flag.


People with bipolar disorder (BPD) are more likely to die prematurely, which is partly attributed to comorbid cardiometabolic traits. Previous studies report cardiometabolic abnormalities in BPD, but their shared aetiology remains poorly understood. This study examined the phenotypic associations and shared genetic aetiology between BPD and various cardiometabolic traits.N = 61 508) we investigated phenotypic associations between BPD (ncases = 4186) and cardiometabolic traits, represented by biomarkers, anthropometric traits and cardiometabolic diseases. To determine shared genetic aetiology in European ancestry, polygenic risk scores (PRS) and genetic correlations were calculated between BPD and cardiometabolic traits.In a subset of the UK Biobank sample (Several traits were significantly associated with increased risk for BPD, namely low total cholesterol, low high-density lipoprotein cholesterol, high triglycerides, high glycated haemoglobin, low systolic blood pressure, high body mass index, high waist-to-hip ratio; and stroke, coronary artery disease and type 2 diabetes diagnosis. BPD was associated with higher polygenic risk for triglycerides, waist-to-hip ratio, coronary artery disease and type 2 diabetes. Shared genetic aetiology persisted for coronary artery disease, when correcting PRS associations for cardiometabolic base phenotypes. Associations were not replicated using genetic correlations.This large study identified increased phenotypic cardiometabolic abnormalities in BPD participants. It is found that the comorbidity of coronary artery disease may be based on shared genetic aetiology. These results motivate hypothesis-driven research to consider individual cardiometabolic traits rather than a composite metabolic syndrome when attempting to disentangle driving mechanisms of cardiometabolic abnormalities in BPD. Bipolar disorder (BPD) is among the 20 most debilitating neuropsychiatric diseases  , Stahl et al.  found noindividual-level phenotypic and genetic investigation has been conducted.In summary, evidence for shared genetic aetiology between BPD and cardiometabolic traits in population-based samples is scarce. Their relationships, as well as their influencing factors, are poorly understood; no comprehensive, Here, we investigate the relationship between BPD and cardiometabolic traits on a phenotypic and genetic level in the European UK Biobank (UKB) sample. First, we hypothesise that there is an increased risk of cardiometabolic traits in BPD. We assess phenotypic associations between BPD and three categories of cardiometabolic traits which were selected because they have been shown to be associated with BPD in the existing literature  , did not meet any of these BPD criteria or any other mental health condition . Controls excluded participants with self-reported antipsychotic, antidepressant and mood stabiliser usage (item 20003).BPD status was determined based on self-report questionnaires, a nurse interview and hospital episode statistics. BPD cases matched diagnostic ICD-10 codes for BPD , had a self-report diagnosis of mania, BPD or manic depression at nurse interview (items 20002 and 20544), fulfilled BPD criteria according to the baseline questionnaire of mood disorders ; mood stabiliser codes are in Supplementary Material 8 and all other medication codes in Glanville et al. .Systolic and diastolic blood pressure was corrected for antihypertensive medication based on the recommendations by Tobin, Sheehan, Scurrah, and Burton . If medi2) and the other measured using electrical impedance. Where both measures were available, we calculated the average of the measures and excluded participants who differed between the two measures by over 4.56 standard deviations (n = 1164) , this value was used.Two measures of BMI were available, one as weight/height . The ratio was residualised for BMI to represent abdominal body mass distribution independent of overall body mass.http://biobank.ndph.ox.ac.uk/showcase/showcase/docs/biomarker_issues.pdf). We corrected LDL and total cholesterol levels for individuals taking any cholesterol-lowering medication . LDL cholesterol levels for individuals taking medication were divided by 0.7, while total cholesterol levels were divided by 0.8 , high-density lipoprotein cholesterol (HDL cholesterol) and triglycerides] and glycated haemoglobin (HbA1c). Quality control was performed by UKB using standardised laboratory procedures , the national death register and self-reported questionnaires. Cases had self-reported type 2 or generic diabetes as established in the nurse interview and the touchscreen questionnaire. However, participants were only classified as cases when they reported in the questionnaire that (1) they had not been treated with insulin in the first year after diagnosis, (2) and had been diagnosed after the age of 35 years . Participants self-reporting those conditions in the nurse interview or touchscreen questionnaire were also considered coronary artery disease cases. Coronary artery disease controls did not fulfil coronary artery disease criteria.Stroke status was determined using stroke diagnoses in the hospital in-patient data and the death register. Additionally, participants self-reporting to have had a stroke in the nurse interview or in the touchscreen questionnaire were included as stroke cases  represent lifetime diagnoses (maximum three time points), and continuous variables were based on the first visit at the assessment centre. For a summary of items and codes, refer to Supplementary Material 5. Information on genotype quality control is in Supplementary Material 2.ncases = 4186; ncontrols = 57 322) and cardiometabolic traits, we performed logistic regressions in R v3.6.0  and females  separately to identify sex-specific associations. Phenotypic sensitivity analyses are described in Supplementary Material 3.To assess phenotypic relationships between BPD . PRSicev2 (https://github.com/choishingwan/PRSice)  and to create the PRSs. PRSs were standardised.We created PRSs representing genetic propensity to cardiometabolic traits by aggregating by-variant effects across the autosomes, weighted by effect sizes from GWAS summary statistics. PRSs were created for total cholesterol, LDL and HDL cholesterol, triglycerides  and cardiometabolic traits, we calculated logistic regressions with BPD as the dependent variable, and the standardised cardiometabolic PRSs at 11 p-value thresholds. The models were adjusted for assessment centre, genotyping batch and six genetic principal components to control for population stratification. This analysis was repeated for males  and females  separately to identify sex-specific associations.To test for shared genetic aetiology in individuals of European ancestries between BPD  . The sample included 4186 BPD cases and 57 322 unaffected controls . Descriptive statistics of cardiometabolic traits by BPD case–control status are shown in The sample consisted of 61 508 participants , with a mean age of 57 years (p ≤ 5.8 × 10−4 (FDR 5%), we observed positive associations between BPD and the cardiometabolic traits triglycerides, HbA1c, BMI, waist-to-hip ratio, waist-to-hip ratio adjusted for BMI, stroke, type 2 diabetes and coronary artery disease. Total cholesterol, HDL cholesterol and systolic blood pressure were negatively associated with BPD , odds ratios indicated larger effects (e.g. stroke OR increased from 2.44 to 4.94), with larger explained variances . (3) Adding antipsychotic, antidepressant and mood stabiliser medication as covariates showed consistent directions of effects and largely the same significant results between cardiometabolic traits and BPD as found in the primary analysis . However, odds ratios decreased and explained variances reduced drastically . Waist-to-hip ratio adjusted for BMI became non-significant when controlling for either medication, and had the largest decrease in odds ratios from 1.06 (95% CI 1.02–1.09) in primary analysis to 1.00 (95% CI 0.96–1.03) when controlled for mood stabilisers. (4) Residualising CMTs for age and re-calculating their association with BPD yielded similar results to the primary associations; they can be found in online Supplementary Table S8.(1) To analyse whether phenotypic associations with blood pressure traits were biased by the blood pressure medication adjustment, phenotypic associations were re-calculated excluding participants on blood pressure medication. Systolic blood pressure remained negatively associated . Diastolic blood pressure  and hypertension  showed no effect on BPD, indicating that this association was independent of medication intake. (2) When limiting BPD cases to hospital in-patients only , BPD was positively associated with PRSs for triglycerides, waist-to-hip ratio, waist-to-hip ratio adjusted for BMI, coronary artery disease and type 2 diabetes. The highest contribution to explaining variance in BPD was from the waist-to-hip ratio PRS (PRSPT = 0.5) accounting for 0.13% of the variance (full results in online Supplementary Table S10). PRS analyses repeated for males and females separately did not survive correction for multiple testing; however, directions of effects were largely consistent with the primary analysis (online Supplementary Tables S11 and S12).Logistic regressions were performed to test the association between BPD and PRSs at 11 PT 0.4 declined from R2 = 0.081% in the main analysis to R2 = 0.076% in the sensitivity analysis (relative attenuation ⩽5.90%). When excluding type 2 diabetes cases, type 2 diabetes PRS associations had a substantial attenuation in explained variance. For example, for PRSPT 0.4 it declined from R2 = 0.080 in the main analysis to R2 = 0.059% in the sensitivity analysis . For continuous traits, we repeated the PRS analyses adding the base cardiometabolic trait as a covariate; that is, triglycerides, and both waist-to-hip ratios, respectively. In those three cases, explained variance drastically declined. The explained variance by triglycerides PRS (PRSPT 1) dropped from R2 = 0.049% in the primary analysis to R2 = 0.00008% when adding triglycerides as a covariate (relative attenuation in R2 across thresholds between 96% and 100%). Explained variance by waist-to-hip ratio PRS (PRSPT 0.1) declined from R2 = 0.055% in primary analysis to R2 = 0.021% (relative attenuation: 53–62%), and for waist-to-hip ratio adjusted for BMI PRS (PRSPT 0.2), a relatively smaller decrease from R2 = 0.055% to R2 = 0.046% . (2) To test whether the strength of the phenotype influenced the associations, we restricted to BPD cases based on hospital in-patient ICD10 diagnoses (ncases = 920). None of these associations survived correction for multiple testing (online Supplementary Table S13). (3) Predictive abilities of PRSs are displayed in online Supplementary Tables S14 and S15. (4) There were no significant associations when predicting cardiometabolic traits using BPD PRS (online Supplementary Tables S18 and S19).(1) To assess whether significant PRS associations were driven by phenotypic associations between BPD and cardiometabolic traits, we investigated the attenuation of explained variance when controlling for the base cardiometabolic phenotype. For binary traits, we re-calculated associations for significant PRSs with BPD by excluding cases with the corresponding cardiometabolic disease . For coronary artery disease PRSs, explained variance was hardly attenuated. For example, the variance explained with PRSgr = −0.064, p = 0.004) and waist-to-hip ratio adjusted for BMI  were nominally correlated but did not survive correction for multiple testing.Genetic correlations between BPD and cardiometabolic traits were low and not significant after correcting for multiple testing , Fig. 3.This study investigated the relationship between BPD and cardiometabolic traits in UKB on a phenotypic and genetic level, using PRS analyses and genetic correlations.The phenotypic results revealed significant, but weak associations with several cardiometabolic traits, namely low total cholesterol, high triglycerides, low HDL cholesterol, low systolic blood pressure, high BMI, high waist-to-hip ratio, as well as stroke, type 2 diabetes and coronary artery disease status. These findings were largely consistent with our hypothesis that BPD status is associated with increased cardiometabolic risk.Associations with biomarkers were consistent with meta-analytic findings for triglycerides, HDL cholesterol, HbA1c  = 17.92, p < 0.0001) between BPD cases  and controls ]. Controls are likely older because participants must remain healthy until the last measured time point to classify as controls. However, associations between cardiometabolic traits and BPD in this study remained robust when controlled for age. Future studies should further assess these associations and potential age-related influences using longitudinal BPD definitions.The survivor bias is also reflected in significant age differences [We observed a negative association between BPD and systolic blood pressure, whereas diastolic blood pressure and hypertension were not associated. This was unexpected because elevated systolic and diastolic measures were both linked with negative health outcomes, including cardiovascular events  confirmed associations found in primary analyses and explained more variance. This strengthens the evidence that the significant phenotypic associations are not artefactual, because these 920 cases are classified with high confidence having been admitted to hospital for BPD. It is possible that these stronger associations reflect that cardiometabolic traits themselves increase the likelihood for BPD participants to seek medical help and receive a BPD diagnosis.Sensitivity analyses restricted to more severe BPD cases  could further examine the effect of medication use on the association between BPD and cardiometabolic traits.Finally, we controlled the associations between BPD and cardiometabolic traits for antipsychotic, antidepressant and mood stabiliser usage. Directions of effects were consistent compared with the primary analyses, but odds ratios and explained variances were considerably lower suggesting that medications moderate the associations and that effects depend on medication intake. For example, the ncases = 920). The number of cases was probably underpowered to capture significant PRS associations, underlining the importance of future large-scale studies.We discovered evidence for shared genetic aetiology in European ancestries based on PRS associations in primary analyses for five cardiometabolic traits: triglycerides, waist-to-hip ratio unadjusted and adjusted for BMI, coronary artery disease and type 2 diabetes. Associations re-calculated for males and females showed consistent directions of effects but did not survive correction for multiple testing; nor did they when cases were limited to more severe BPD cases , and full relative attenuation for triglycerides (average attenuation 98.76%). This indicates that, when predicting BPD, adding a coronary artery disease PRS seems to explain some additional variance beyond the variance captured by the coronary artery disease phenotype. This indicates shared genetic aetiology with BPD above and beyond their base phenotypes in UKB, which was not the case for triglycerides, and at least partly applied to type 2 diabetes, waist-to-hip ratio unadjusted and adjusted for BMI. Consistent with phenotypic associations reported above, these differing patterns indicate distinct relationships with BPD for individual cardiometabolic traits, some of which probably share some genetic aetiology in UKB with BPD; mainly type 2 diabetes, coronary artery disease and waist-to-hip ratio. Future research is imperative to investigate to what extent those results are prone towards collider bias , and none implicated causal biological mechanisms.There are additional limitations, beyond those highlighted throughout this discussion. The This large-scale, cross-sectional study constitutes a nuanced account of the comorbidity between BPD and various, extensively phenotyped, cardiometabolic traits, considering clinical and self-report data, physical measurements, and biological samples. BMI was most strongly associated with an increased risk of BPD. We found shared genetic aetiology for coronary artery disease, type 2 diabetes, and waist-to-hip ratio unadjusted and adjusted for BMI and triglycerides. These associations only persisted beyond the variance explained by cardiometabolic base phenotypes in the case of coronary artery disease. This was not replicated by genetic correlations, accentuating the importance of choosing appropriate statistical techniques when testing for shared genetic aetiology.Our results underline that cardiometabolic comorbidity in BPD differs between cardiometabolic traits, where effect sizes depend on sex, medication intake and the phenotype strength. This should motivate future hypothesis-driven longitudinal research inside and outside UKB to consider specific cardiometabolic traits for associations with BPD, rather than an overarching global metabolic trait, when attempting to disentangle underlying biological mechanisms.