Rapid advances in next-generation sequencing technologies facilitate genetic association studies of an increasingly wide array of rare variants. To capture the rare or less common variants, a large number of individuals will be needed. However, the cost of a large scale study using whole genome or exome sequencing is still high. DNA pooling can serve as a cost-effective approach, but with a potential limitation that the identity of individual genomes would be lost and therefore individual characteristics and environmental factors could not be adjusted in association analysis, which may result in power loss and a biased estimate of genetic effect.For case-control studies, we propose a design strategy for pool creation and an analysis strategy that allows covariate adjustment, using multiple imputation technique.Simulations show that our approach can obtain reasonable estimate for genotypic effect with only slight loss of power compared to the much more expensive approach of sequencing individual genomes.Our design and analysis strategies enable more powerful and cost-effective sequencing studies of complex diseases, while allowing incorporation of covariate adjustment. Samples with similar characteristics will be pooled for sequencing.Genotype Imputation: Assuming a random binomial process, we calculate the probabilities of genotype for each sample in the pool, given the total number of reads from sequencing. The genotypes will then be randomly drawn following these probabilities.Association test: We use logistic regression to assess the association between candidate markers and disease status, controlling for other genetic or environmental factors. Using multiple imputation technique We will pool samples by their similarity in covariates. When the covariates are all categorical and have a limited number of categories, an exact match can be applied. In this paper, we consider a matching approach based on the predicted probability of being affected.y denote the observed disease status , g be the genetic marker, and Z  =   be the vector of covariates. We fit a logistic regression model of the disease risk on the covariates (without the genetic marker)s asLet We then create the pools by dividing samples into multiple groups according to quantiles of the predicted probabilities. , m follows a binomial distribution Bin. When the variant is less common, p is small and n is the total number of reads at the locus and x the number of reads with allele a. Denote e the sequencing error rate, and then a. The joint probability:m given observed reads x is c(0) = c(2K) = 0.We consider a DNA pool with p and sequence error rate e can be jointly estimated using the EM algorithm developed by Wang et al. Utilizing the blocked design, the allele frequency impute as follows:To impute the genotype for each individual from the pooled sequence data, we draw  from m – a1(impute) is odd, redraw a1(impute). Once we have a1, we calculate a2(impute) = (m – a1(impute))/2 and a0(impute) = K – a1(impute)– a2(impute).Given the value of AA, Aa, or aa to the K samples in the pool such that there are a0(impute) samples with AA, a1(impute) samples with Aa, and a2(impute) samples with aa.Randomly assign the genotype Repeat (1)-(3) multiple times.After the individual genotypes are imputed from pooled sequence data, standard logistic regression can be used to test for disease-marker association, with the covariates being adjusted in the model. To take into account the uncertainty of imputed data and obtain valid estimates, multiple imputation technique will be applied. Specifically, we will repeat the genotype imputation and association test multiple times , and combine the results to produce estimated effects and confidence intervals G) at a disease locus. We assumed the allele frequency of causal allele at 1%, and an odds ratio (OR) of 1.0 (no association) and 3.5 (disease-causing) as the primary simulation model, but also considered models with different allele frequencies and effect sizes. We randomly sample equal numbers of cases and controls (n = 1000 cases/controls), and consider a pool size of 12. For sequencing of pooled samples, we assume an average coverage of 200X at the disease locus. The actual coverage for each sample is randomly drawn from a normal distribution with standard deviation of 20X. We assume 5 additional risk factors (Z) that are associated with the disease with equal or unequal ORs  is correlated with G and serve as a confounder. We also vary the allele frequency and effect size of G and effect size of Z, using simulation settings similar to those in model 5.In the simulations, we first assume that the genotype is not associated with the disease (model 1–4) and evaluate the type I error of our proposed method; model 5–12 assume an OR of 3.5 for the causal allele to compare power of different methods. We vary the correlation between covariate −4 using a large sample size  to evaluate the type 1 error and power of proposed method. In model 4 and 10, we simulate situations where the DNA samples are not equally represented in the pool, reflecting potential technical errors in pool creation (see below). At last, we simulate the sequence data with different sequencing errors , and evaluate the type 1 errors, using model 2 and model 6 as an example.We further consider simulation models to reflect possible scenarios of a real study. In practice, we often do not have information on all risk factors. In model 7, we assume that only two of the five risk factors are included in analysis. In model 8, we assume different effect sizes for the risk factors. We also consider a more stringent significance level of 10For each model, we simulate 1,000 datasets , and use 5 imputations in our proposed method.MI”) to individual sequencing of all cases and controls  and standard DNA pooling without considering other risk factors (“poolunivariate”), where “seqall” would provide the maximum power when budget is not a factor for experiment design. We calculate type 1 error and power as the proportion of simulated replicates where the association p-value is <.05 or 10−4 at the locus.We compare the power of our method . In the simulations, we set αmax to be 1. The weights are further normalized and used as sampling proportions in the pool. We perform association tests using our approach under the equal proportion assumption, and evaluate type 1 error and power.Although equal concentration for individual samples in the pool is desired, in practice their contributions can vary due to technical variability. We further carry out simulations in which the samples have unequal proportions in the pool (model 4 and 10). We randomly generate weight of an individual sample as 1/K*(1+α), where K is the pool size and (1+α) is the scale parameter with α being randomly drawn from  randomly, and assign rest of the samples one at a time to their closest pool defined by the minimum Euclidian distance to the center sample. If the closest pool reaches the desired pool size K, the sample will be assigned to the next closest pool. Simulations (data not shown) show slightly lower power and more variable estimates of genetic effect using this approach. In practice, well-matched samples can be pooled with equal pool size while “outlier” samples are sequenced individually. Another advantage of this unbalanced “blocked pooling” design is that the pools with a single individual can provide accurate estimate for sequence errors, and pools with a large number of individuals provide accurate estimate for allele frequency.Our new method tackles the problem of covariate adjustment by matching samples in the pooling stage. We consider a matching strategy based on quantiles of predicted probabilities. Other matching strategy can also be implemented, for example, K-means or K-median clustering The advantage of using predicted probabilities over Euclidean distance is that it weighs the covariates by their estimated effect sizes in a model without the genetic variant. In presence of a confounding variable such as ethnicity, the estimated effect size of such variable can be biased in this model. However, given the current GWAS results for common variants and the low frequency of rare variants, we expect that a single variant can only explain a small proportion of total variance of outcome and the bias will be small. Our simulation results show that when the effect size of covariates vary, matching based on predicted probabilities performs slightly better than that based on Euclidean distance.P(m) needs to be modified to reflect the true disease model.When imputing the genotypes for individuals in the pool, we assume HWE to derive the posterior distribution Besides the assumption of HWE, our proposed method also relies on accurate estimation of allele frequency to draw valid imputations. In practice, unequal contribution of samples to the pool and sequencing errors can both lead to biased estimation. First, individual DNA samples may not be pooled with equal concentration due to technical variability There are also several practical issues for our proposed methods. First, we consider a pool size of 12 in our simulations. Gautier et. al. In our simulation study, we consider association test based on a single variant, which is often applied in targeted re-sequencing studies to identify or validate potential causal variants. Alternatively, analysis of low-frequency genetic variant (MAF <.01) often model multiple variants simultaneously within a gene or targeted region e.g.,  to increhttp://www.biostat.umn.edu/~wguan/software/, which demonstrates the pool creation and multiple imputation pipeline. We expect our method will aid analyses of sequencing-based association studies for complex traits.In summary, we have proposed a new framework to match samples using the covariate information to create sequencing pools and use multiple imputation technique for association test that allows covariate adjustment. Our method is specifically designed to improve power to detect the disease-marker association using the cost effective DNA pooling approach, and correctly control the false positives in presence of confounding effect. A sample Stata code is available freely at The proposed design for DNA pooling is described in K individuals. Let p and q = 1 - p be the frequencies of alleles a and A, respectively. Let m be the number of allele a in the pool of 2K alleles. Assuming Hardy-Weinberg equilibrium (HWE), m follows a binomial distribution Bin. Let n is the total number of reads at the locus and x the number of reads with allele a. Denote e the sequencing error rate, and then a. The joint probability:m given observed reads x is c(0) = c(2K) = 0.We first consider a DNA pool with p and sequence error rate e, an EM algorithm was described by Wang et al. ps and es from multiple groups of pools  and multiple lanes. Let i denote the lane, and assuming the sequence error is consistent for pools within the same lane, we denote the error rate by k by k = 1 or 2 for group of cases and controls, respectively. For pool j, let j is nested within group k and within lane i, but k is in general not nested within i. Let Lk denote the number of pools in group k, and Li denote the number of pools in lane i.To estimate the allele frequency j-th pool in group k, lane i.E step:, for the M step:k≈20, to estimate the allele frequency. This approach will oversimplify the distribution of allele frequencies, but performs fairly well in our simulation results.When the covariates are continuous, no exact match can be done for pooling samples. In practice, we can divide the samples by quantiles of matching score, e.g., S1 TableType 1 error (model 2) for pool size of 12, 30, and 50. Number of simulations is 1000.(DOCX)Click here for additional data file.S2 TableType 1 error (model 2) and power (model 6) for multiple-imputation based pooling method using 5, 10, and 100 imputations. Number of simulations is 1000.(DOCX)Click here for additional data file.


The accessibility of almost complete genome sequences of uncultivable microbial species from metagenomes necessitates computational methods predicting microbial phenotypes solely based on genomic data. Here we investigate how comparative genomics can be utilized for the prediction of microbial phenotypes. The PICA framework facilitates application and comparison of different machine learning techniques for phenotypic trait prediction. We have improved and extended PICA's support vector machine plug-in and suggest its applicability to large-scale genome databases and incomplete genome sequences.We have demonstrated the stability of the predictive power for phenotypic traits, not perturbed by the rapid growth of genome databases. A new software tool facilitates the in-depth analysis of phenotype models, which associate expected and unexpected protein functions with particular traits. Most of the traits can be reliably predicted in only 60-70% complete genomes. We have established a new phenotypic model that predicts intracellular microorganisms. Thereby we could demonstrate that also independently evolved phenotypic traits, characterized by genome reduction, can be reliably predicted based on comparative genomics.Our results suggest that the extended PICA framework can be used to automatically annotate phenotypes in near-complete microbial genome sequences, as generated in large numbers in current metagenomics studies. Microorganisms, comprising bacteria, archaea and unicellular eukaryotes, are key components of all ecosystems on earth. Their tremendous phylogenetic, ecological and functional diversity is so far only insufficiently understood. Although genome sequencing has within the last two decades enormously advanced the investigation of microbes, microbial genomes have mainly been sequenced from DNA obtained from well-characterized, pure lab cultures. The majority of microbes, however, cannot be cultivated and was therefore inaccessible for genome research . MetagenThe representation of microbial genomes by their protein-coding genes, associated to orthologous or homologous groups, is the most widely used approach for the organization of large-scale genomic data -8. A widPhenotypic traits of microbes can be very diverse. Structured and computer-readable organization of trait descriptions has been suggested e.g. in the Ontology of Microbial Phenotypes . They raamoA gene encoding ammonia monooxygenase . All. All29]]Association rule mining in PICA is based on the CPAR algorithm . SupportLegend: TP, TN, FP, FN signify the number of true positive, true negative, false positive and false negative predictions, respectively.In order to estimate run time and memory consumption in a scenario of increasing input data sizes, 5000 virtual species were created. They comprise genotype profiles of sizes comparable to average genomes in eggNOG 4.0  with virhttps://github.com/univieCUBE/PICAThe PICA framework was initially released in 2010 and has not received further improvements by the original developers since then. We downloaded the open-source code from the project's webpage. The initial release did not highlight SVM as a stand-alone method. Therefore, we re-wrote parts of PICA's SVM plug-in as to enable its use for phenotype prediction in novel genomes. For instance, we ensured that all COGs are always mapped to correct SVM features, especially if not all COGs in the prediction set had already been present in the training data. In addition, we extended the software by implementing a function to extract the most predictive features from linear SVM models. Dumping and ranking features enables the user to interpret the models from a biological perspective: the COGs with the highest discriminative power for presence or absence of a phenotype are ranked at the top. If specific proteins are already known to be part of the genetic underpinning of a phenotype of interest, the user finding the according COGs ranked highly in the list might gain confidence in the biological relevance of the predictions. Unexpected high-ranking COGs hint at previously unknown protein functions associated with the phenotype. However, these may also derive from taxonomic correlations rather than a shared phenotype, which can be caused by insufficient training data. Several minor changes were applied to the software in order to improve code quality. The current release can be obtained from the PICA website or directly from The original publication for PICA focused primarily on association rule mining for phenotype prediction . The autWe initially evaluated PICA with its example data set, which comprises COG profiles based on eggNOG 2.0 . This daFurthermore, we created virtual species to assess the effect of an increasing number of genomes in training sets in terms of run time and memory consumption. For real traits, it will be impossible to increase the sizes of genome sets to arbitrary numbers, because of insufficient biological knowledge. Several sets of increasing size were compiled and cross-validations were performed for virtual phenotypic traits. Our results indicate that problem sizes of 5,000 genomes with approximately 200,000 different COGs in the training set are still computationally feasible Figure . A typicx percent of the total number of COGs per genome . Consequently, phenotypic trait prediction was conducted on these incomplete genomes. All models show approximately sigmoidal response curves for increasing completeness  for obligate intracellular lifestyle. A total of 169 species is predicted intracellular, which consists of 160 bacteria  genotypic signals. Currently ongoing work indicates very good performance of phenotypic trait prediction also for further, ecologically important traits, as soon as sufficient training data are available. Although these models recover known functional markers, they substantially extend the marker concept by associating many further genes to the phenotypic traits. Our results suggest that the extended PICA framework developed in this study can be used to automatically annotate phenotypes in near-complete microbial genome sequences, as generated in large numbers by modern metagenomics.COG: cluster of orthologous groups; NOG: non-supervised cluster of orthologous groups; LUCA: last universal common ancestor; ARM: association rule mining; CPAR: classification based on predictive association rules; SVM: support vector machine; RBF: radial basis function (Gaussian kernel).The authors declare that they have no competing interests.TR initiated and supervised the study. RF and TR designed the computational experiments. RF performed the computational analyses. FS and MH extracted the phenotype data for intracellular/free-living species and compiled the training dataset. RF, MH and TR analyzed the data and wrote the manuscript. All authors read and approved the final manuscript.Supplementary tables and supplementary figures (Microsoft Word).Click here for file


Arabidopsis thaliana defensive compounds, glucosinolates (GSL) control field fitness and are therefore subject to natural selection, we conducted a multi-year field trial using lines that vary in only specific causal genes. Interestingly, we found that variation in these naturally polymorphic GSL genes affected fitness in each of our environments but the pattern fluctuated such that highly fit genotypes in one trial displayed lower fitness in another and that no GSL genotype or genotypes consistently out-performed the others. This was true both across locations and within the same location across years. These results indicate that environmental heterogeneity may contribute to the maintenance of GSL variation observed within Arabidopsis thaliana.Natural populations persist in complex environments, where biotic stressors, such as pathogen and insect communities, fluctuate temporally and spatially. These shifting biotic pressures generate heterogeneous selective forces that can maintain standing natural variation within a species. To directly test if genes containing causal variation for the DOI:http://dx.doi.org/10.7554/eLife.05604.001 ‘Genetic variation’ describes the naturally occurring differences in DNA sequences that are found among individuals of the same species. These genetic differences arise from random mutations and may be passed on to their offspring. Some of these mutations may improve the ability of an individual to survive and reproduce—known as fitness—and are likely to become more common in the population. Other mutations may reduce an individual's fitness and are likely to be lost. However, it is believed that most of the mutations will have no effect on the fitness of individuals.It is not known why many of these ‘neutral’ genetic differences are maintained in populations. Some researchers have proposed that they are kept by chance and that there is no direct advantage to the population of keeping them unless these neutral mutations later become beneficial. However, other researchers think that the genetic variation itself may improve the fitness of the population by allowing it to quickly adapt to changes in the environment.Arabidopsis thaliana is a small plant that lives in many different environments and has high levels of genetic variation in many of its physical traits. One of these traits is the production of molecules called glucosinolates, which help the plants to defend against herbivores and infection by microbes. Previous studies have suggested that variation in the genes that make glucosinolates may improve the fitness of A. thaliana populations.A. thaliana plants that were genetically identical except for some of the genes involved in the production of glucosinolates. Kerwin et al. grew the plants in several different environments over several years. The field trial shows that variation in these genes affected the fitness of the plants in each of the different environments. However, the fitness benefit depended on the environment, and no single gene variant provided the best fitness across all environments, or over all the years of the trial.To test this idea, Kerwin et al. carried out a field trial using Kerwin et al.'s findings suggest that changes in the environment may contribute to the maintenance of genetic variation in the genes that make glucosinolates. This raises the questions of how many other genes in plants (or other species such as humans) have genetic variation that contributes to fitness across varied environments; and how can this link be tested in natural settings.DOI:http://dx.doi.org/10.7554/eLife.05604.002 Arabidopsis thaliana, which exhibits variation both within and among natural populations and/or accessions  , which recreated observed natural variation in the aliphatic GSL pathway found among accessions  . GSLs cof tissue . These af tissue   GSL into alkenyl GSL   GSL and a 60% reduction in short chain (3C and 4C) GSL  GSL than does Col-0, due to reduced expression of a flavin-monooxygenase that converts the MT to MSO GSL  . Addition 4C GSL   GSL  (Hirai e 4C) GSL , 2010. Ahain GSL   and UWY2011  but strongly diverged in UWY2012   . It has ctively) . In addictively) . It is lArabidopsis accessions with potential selective and non-selective evolutionary processes. To test if the GSL genotypes alter plant fitness in the three environments, we measured fecundity of each individual grown in the field. Plants were harvested from the field at maturity and the numbers of fruits, flowers and buds per plant were counted in the laboratory to yield total fruit count (TFC). TFC has previously been shown to be a good proxy for fecundity in Arabidopsis where total number of seeds per plant is highly correlated with total number of siliques  . However, there was significant variation in silique length across GSL genotypes as well as a significant genotype by environment interaction  . Among teraction . We concA. thaliana in an environmentally dependent manner.In this study, GSL genotype had a significant impact on absolute field fitness . There wmyb28/AOP2 shows the greatest fitness in the UCD2012 environment and the lowest fitness in UWY2012. In contrast, myb28/gsoh shows an opposite pattern while other genotypes showing a diversity of other patterns , ESP (At1g54040), MYB28 (At5g61420), MYB29 (At5g07690), GSOH (At2g25450), MAM1 (At5g23010), GSOX1 (At1g65860), GSOX3 (At1g62560). The following knockout or complementation lines for the following loci in A. thaliana Col-0 were used to generate the lab population: AOP2 = 35S:AOP2  in Laramie, WY during Summer 2011, the second at UC Davis in Davis, CA Spring 2012, and the third at UWY during Summer 2012. Seeds were sown into flats with 2 inch 50-celled inserts using Sunshine #5  potting soil containing slow release fertilizer and stratified at 4°C for 4 days before being transferred into the greenhouse at either the University of Wyoming in Laramie (UWY) or the University of California at Davis (UCD) to facilitate germination synchrony. In the UWY greenhouse, plants received 15 hr light/9 hr dark natural phototoperiod with temperatures fluctuating diurnally from 10°C to 30°C. In the UCD greenhouse, plants received 14 hr light/10 hr dark natural photoperiod with temperatures fluctuating from 15°C to 35°C. Further, starting all the plants in the greenhouse minimizes variation in the initial seedling conditions. After germination, seedlings were thinned to one per pot and GSL genotypes were randomly organized into 40 blocks per field trial, for a total of 120 blocks total and also 120 GSL genotype replicates total. Individuals were transplanted from the greenhouse into the field 2 weeks post germination. A single plant of each genotype was present in each block in all three environments and blocks were arranged into four rows of ten blocks each . Each ro2O was transferred to each well using a multichannel pipet and allowed to incubate at room temp 1 hr. Excess H2O was removed from the Sephadex by placing filter plate on top of a 96 deep well discard plate (used to catch the flow through) and centrifuged at 1000 rpm for 2 min. To homogenize the samples, 96 deep well plates containing a single A. thaliana leaf, two 2.3 mm ball bearings and 400 μl of 90% methanol in each well were shaken in a Harbil 5-Gallon Mixer  for 3–5 min. Plates were centrifuged at 4000 rpm for 20 min. To bind GSL to Sephadex, 150 μl of supernatant from each well (containing the extracted organic compounds) was transferred to the corresponding well of the 96 well filter plate containing hydrated Sephadex and centrifuged at 1200 rpm for 3 min on top of the 96 deep well discard plate. To wash away all the non-binding organic compounds from the Sephadex, 150 μl of 90% methanol was added to each well and the plate was centrifuged at 1200 rpm for 3 min. To remove excess methanol, two wash steps were conducted by adding 150 μl of H2O to the plate followed by centrifugation at 1200 rpm for 3 min. To release the GSL from the Sephadex, 10 μl of Sulfatase (Sigma–Alrich) and 100 μl of water were added to each well of the 96 well filter plate then incubated overnight in the dark. The desulfoglucosinolates were then eluted into a 96 well round bottom plate via centrifugation at 1200 rpm for 3 min. For each GSL sample, 50 μl of the 110 μl of extract was injected on an Agilent 1100 HPLC  using a Lichrocart 250–4 RP18e column . Individual GSL compounds were detected at 229 nm and separated utilizing the following program with an aqueous acetonitrile gradient: a 6-min gradient from 1.5% to 5.0% (vol/vol) acetonitrile, followed by a 2-min gradient from 5% to 7% (vol/vol) acetonitrile, a 7-min gradient from 7% to 25% (vol/vol) acetonitrile, a 2-min gradient from 25% to 92% (vol/vol) acetonitrile, 6 min at 92% (vol/vol) acetonitrile, a 1-min gradient from 92% to 1.5% (vol/vol) acetonitrile, and a final 5 min at 1.5% (vol/vol) acetonitrile . The photographed leaves were then placed directly into 96 deep well plates containing 400 μl 90% methanol and stored in the freezer until extraction. For the UWY field trial, the leaves were stored at −20°C for 3–4 weeks and shipped overnight to Davis, CA on dry ice. For the Davis field trial, all plates were stored at −20°C until extraction. After harvest, desulfoglucosinolates were extracted from all samples using a high-throughput protocol briefly described below . One graonitrile . For eacy ImageJ .Leaf damage estimates were visually taken in the field at 4 weeks of age, just before tissue collection for GSL extraction. A scale from 0–10 was used to determine amount of pest damage incurred on each plant, with 0 representing no damage and 10 representing complete destruction of the plant .Absolute fitness was calculated as total fruit count (TFC) × silique length × survival. TFC was measured as the count of fruits (siliques) + flowers + buds per individual. Silique length was measured in ImageJ from digital images of harvested field plants taken using a Nikon D3100 as follows: each plant was placed flat on a white sheet of paper next to a ruler and pictures were taken using auto focus. After setting the scale in ImageJ using the ruler placed in each image, the segmented line tool was used to draw a line from the pedicle to the tip of the silique. For each plant, eight siliques were measured at random and these values were averaged to get a value for each plant. Survival was scored on a binary (0–1) scale. Plants that germinated, were transplanted into the field and survived to harvest were given a survival score of 1 and plants that germinated and were transplanted but did not survive to harvest were given a score of 0. Individuals that did not germinate or did not survive to transplantation were given an NA. Relative fitness was calculated for each GSL genotype within each environment relative to Col-0. To do this, average absolute fitness of a GSL genotype was divided by the average absolute fitness of Col-0 within a environment. Col-0 was chosen as the reference genotype given that it is the background genotype.All statistical analyses were carried out using the R statistical computing language . The fielmer(Trait ∼ Genotype*Environment*Treatment + (1|Plot(Treatment:Environment))).The Anova function from the car package in R was utilized to determine which fixed effects variables significantly altered the mean of each trait  . We esti review process). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.eLife posts the editorial decision letter and author response on a selection of the published articles . An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent  and three reviewers, one of whom is a member of our Board of Reviewing Editors.Thank you for sending your work entitled “Natural Genetic Variation in The following individuals responsible for the peer review of your submission have agreed to reveal their identity: Merijn Kant (Reviewing editor) and Michael Turelli (who was consulted by the referees for advice). The other two reviewers remain anonymous.The Reviewing editor and the other reviewers discussed their comments before we reached this decision, and the Reviewing editor has assembled the following comments to help you prepare a revised submission.Arabidopsis. These mutants were designed such that in each mutant line distinct branches of the glucosinolate pathway were removed selectively and these predicted phenotypes were validated. Then they composed variable populations by transplanting these mutants together at several field sites during several years to monitor several fitness proxies. The manuscript revolves around the question to which extent specific genes can affect fitness under different environmental conditions differently. The value of this work is that it provides a comprehensive assessment on known genes and fluctuating patterns of herbivory and fitness in nature. Hence, Kerwin and colleagues argue that that fluctuating selection may maintain polymorphisms in glucosinolate biosynthesis genes in natural populations.Kerwin and colleagues created a range of glucosinolate mutants in a single genetic background of Arabidopsis populations and their analysis suggests that it does. In addition, they collected 144 Arabidopsis accessions to assess if the signature of fluctuating selection can be seen among these accessions as well and this analysis shows non-random variation of glucosinolate haplotypes suggesting that fluctuating selection may maintain genetic variation here as well.The authors extend beyond their data after reasoning that these different environments basically reflect environmental fluctuations and they use their data to parametrize a model of We all agreed that the manuscript reads very well and that the data set is extremely interesting and comprehensive. However, we also have significant concerns with respect to the usage of the model of Turelli and Barton (subsection “Fluctuating selection estimates”) and the interpretation of the analysis performed on the 144 accessions (in the subsection “Non-random variation of GSL loci among field collected accessions”).1) Firstly, the model of Turelli and Barton cannot be used for this type of data. During our discussion we consulted Michael Turelli directly and together we reached the following conclusion: although these data certainly warrant a discussion on fluctuating selection to play a role here, there is no simple formula to provide the appropriate polymorphism condition in this case, to the best of our knowledge. The detailed comments of Turelli are below and can form an excellent basis for a revised discussion on known genes and fluctuations in herbivory and fitness in nature (we were missing 2) Secondly, we all agreed that the interpretation of the analysis on the 144 field collected accessions is too opportunistic. Non-random variation of glucosinolate loci among natural accessions could be caused by fluctuating selection but there are equally valid alternatives  such as drift, gene flow or historical population structure etc. Now the conclusions worded in the subsection headed “Non-random variation of GSL loci among field collected accessions” are much too selectively biased towards the first. We strongly suggest you rephrase the interpretation thoroughly doing just the alternatives or, and this may be the better alternative, to remove this analysis from your study altogether.eLife.We hope that this letter, the minor comments of the referees and the report of Dr. Turelli will help you to revise your manuscript for Please find below detailed comments of Michael Turelli in response to the manuscript and the discussion among the referees:“This is indeed deep water. Given the technical nature of the relevant theory it should be no surprise that both the authors and the reviewers make incorrect assertions, but both make important points.First, the relevance of the any genetic variants in Arabidopsis thaliana, which is predominantly selfing. Arabidopsis thaliana were completely selfing, which I believe is reasonable as a first approximation, populations would be effectively composed of competing clonal genotypes . In this case, the distinction between variants at one locus vs multiple loci is irrelevant, as is the distinction between diploidy and haploidy. Hence, the diploid-random-mating conditions provided by cannot maintain variation for a haploid, the genotype with the highest geometric mean fitness will prevail  and/or spatial variation with gene flow. The exact conditions will be subtle and depend on biological details that are surely not known.”The conditions provided by Reviewer #2 minor comments:1) Abstract: “fitness effects were significant in each environment but the pattern fluctuated such that highly fit alleles in one year displayed lower fitness in another.” This experiment doesn't compare alleles, it compares multilocus genotypes.2) In the subsection headed “Environment interacts with GSL genotype to impact leaf damage”: “no particular GSL genotype showed a consistent maximal or minimal level of leaf damage across the three field trials”. This conclusion that no genotype has consistently highest or lowest damage level obscures the highly significant main effect of genetic differences in damage levels .3) Discussion: “it has been complicated to validate that specific polymorphic loci within a pathway are the actual causative basis of any changes in fitness due to the use of polygenic populations”. Unfortunately, this study shares the same shortcoming, because the chosen combination of multilocus genotypes prevents a clear test for antagonistic pleiotropy at individual loci.4) Discussion: “we can directly conclude that it is these specific genes and their GSL phenotypes that are determining the differences in fitness in the field”. True, but that is not sufficient to show that fluctuating selection maintains genetic variation at any particular locus.5) In the subsection “Statistical analysis methods”: Each plot has 10 blocks. Why is there is no block term in the ANOVA?6) Fitness is normalized with respect to performance of Col-0. This is contrary to the usual definition of relative fitness (with a mean of 1.0). Because of this normalization to Col-0, the reported effects on relative fitness may reflect behavior of Col-0 rather that population means.7) What does 8) In the subsection headed “Pleiotropic Links to GSL Genes”: “while the GSL genes are causing pleiotropic effects, these pleiotropic effects are not driving the observed fitness consequences of the GSL genotypes in our field trials.” A simple pairwise correlation analysis is not sufficient to support this conclusion. More complex ANCOVA-like models might be helpful here, perhaps with principal components of GSLs.Reviewer #3 minor comments:1) Introduction: this sentence gives the impression that intermediate frequency variants are frequent in the genome. This is misleading, because the majority of variants do have low frequency. It is just that there are several intriguing examples of intermediate frequency alleles. Furthermore, people have tried to relate FRI to fitness and failed in most cases.2) Also in the Introduction: I wonder why the authors do not mention the work of 3) In the subsection “Leaf damage in the field varies across environments”: pesticide application is somehow unfortunate because it artificially decreases herbivory load and thus might explain why the expected effect of GLS variation on fitness via herbivore defense was not observed. This must be better incorporated in the Discussion.4) In the subsection “Fluctuating selection estimates”: I really appreciate that the authors include now the model of Turelli and Barton, but the model and its predictions should be briefly summarized (for the reader this will come out of the blue!). More explanations are needed in the Methods as well. Did the authors use LSmeans to calculate the parameters? Were LSmeans calculated after correction of error over dispersion?5) In the subsection “Non-random variation of GSL loci among field collected accessions”: this formulation is somehow strange. The words “population structure” should be mentioned so that the right bell rings for the reader.6) In the same subsection: the authors should be clearer here that this analysis cannot exclude the possibility that the skewed haplotype distribution can result from population structure only.7) Discussion: this aspect of the Discussion is still too uncritical for me. The authors should not forget that their findings are not expected and may be driven by processes that were not supposed to play a role. What about insertion effects? Inserted transgenes can disrupt other genes and may result in fitness effects that are unrelated to GLS function. EMS lines initially contain thousands of mutations. They are generally removed by multiple generation of backcrossing to the wild type. Crossing adds some additional backcrossing, is it possible that lines differ in the number of linked mutations? Finally, transgenes are not always stably expressed and could be silenced in one or the other generation, especially if several tDNA insertion lines are coupled. Such problems are well known to (good) molecular biologists but often overseen by ecologists. I believe it is important to critically assess the possibility that the manipulated lines may not be doing exactly what they are supposed to do.[Editors’ note: an earlier version of this manuscript was also reviewed. The previous decision letter after peer review is shown below.]Arabidopsis thaliana Defense” for consideration at eLife. Your full submission has been evaluated by Ian Baldwin (Senior editor) and three peer reviewers, one of whom, Merijn Kant, is a member of our Board of Reviewing Editors, and the decision was reached after discussions between the reviewers.Thank you for choosing to send your work entitled “Field Evidence that Fluctuating Selection Can Maintain Natural Genetic Variation in eLife. The referees were predominantly concerned about three issues: (1) the framing of the story around the fluctuating selection-theme inferred from the genotype distribution of 144 Arabidopsis accessions; (2) the statistical analyses of the field experiment data and (3) on how the fitness proxies came about. I will briefly summarize the main comments which you will also find in more detail in the full referee reports:The referees appreciated the impressive field experiment and are convinced it has delivered a highly valuable data set that deserves publication. However, the current manuscript needs too much work to warrant a revision for Arabidopsis accessions for drawing conclusions on natural selection as a determinant of their genotype distribution.1) The referees feel that “fluctuating selection/ bet hedging” theme should only (at best) appear in the Discussion and certainly not be a central theme. Much of this has to do with the analysis presented in 2) The ANCOVA analysis using the 144 accessions and its interpretation is troublesome, and maybe should be removed altogether. Several of the remaining statistical analyses  should b3) The validity of the fitness-proxy parameters should be better justified.Reviewer #1:General assessment:The field experiment is really very interesting and has delivered a valuable data set. I disagree with several aspects of the analysis pipeline and hence I do not see sufficient support for the main conclusions. The article is not easy to read since phrasing is often vague and imprecise.My main criticisms:Arabidopsis accessions does not work for me:1) The projection of the experimental data onto the genotype-distribution of 144 A) I fail to see why you would expect to see evidence for natural selection within a group of plants (accessions) of which you do not know what the original selection criteria were: for sure these are not ecotypes and it is unclear to which extent they represent the genotypes of their respective original populations . This should at least be discussed in much more detail.B) The analysis presented in C) How does the analysis of the D) You write “field studies confirm lab results” (at the end of the subsection “GSL genetic variation controls GSL profile in the field”), but you do not provide a direct comparative analysis, just a 'visual' interpretation of the data.E) In the subsection “Empirical fluctuating measures of selection in the field predict standing variation in GSL genes”, you conclude that “selection likely played a role”, but you do not explain where in the figures we can see this. Looking at the three plots , I only 2) You used a “deterministic” approach to genotype the 144 accessions i.e. on the basis of their “GSL profiles” but a validation of this approach is missing:A) Throughout the manuscript is remains unclear what is meant with “profile” and how these were evaluated (e.g. which grouping criteria/procedures/assignment to a genotype). Hence its validity cannot be assessed.B) In the subsection “GSL genetic variation controls GSL profile in the field”, it is unclear to which extent actual profile information was used for the downstream analyses or when only the information on the total  glucosinolates was used e.g. see . Figure C) Why was this indirect approach for genotyping preferred over a direct (DNA-based) approach?3) The factors of the statistical analyses are often unclear:A) The factor “location” is misleading: it should be “environment” since the different locations were used at different moments in time. Why do you refer to these differences as 'fluctuation' i.e. how do you know they are not caused solely by differences in starting conditions? Now you infer these differences from B) The statistical “interaction” is misinterpreted and dance around its meaning. Significant interactions indicate that their simultaneous effects are not additive i.e. either the combined effect is greater (synergistic) or smaller (antagonistic) than expected (additive) effect. Pinpointing what they mean is sometimes virtually impossible and requires post hoc statistics.C) The ANCOVA procedure is not explained anywhere.4) Your fitness proxies, and especially how they were normalized, need validation. In “GSL variation impacts fitness in the field”, you describe a normalization procedure (which assumes a linear relationship between silique length and fecundity) which struck me as highly arbitrary. This procedure needs references or a solid validation.Reviewer #2:This manuscript describes the performance in the field of 20 lines differing only in 8 loci controlling glucosinolate synthesis. The author used 20 lines combining one or more variant at these loci. They planted them in a random block design, in 40 replicates, in two consecutive years in WY and in 2012 in UC Davis. In each experimental block, the level of herbivory was manipulated with the help of pesticides.They monitored the glucosinolate profile of these lines in the field and observed that these profiles broadly match with those observed in the lab. They further quantified leaf damage and demonstrated that the genetic differences between these lines alter leaf damage levels. Finally, the authors present evidence that the fitness of individual lines differ within and between sites/years.In order to address the relevance of the specific observations they made at these two sites, the authors also used known glucosinolate levels to predict the relative occurrence of the glucosinolate profiles in a set of 144 natural accessions. They report that the lines that have the highest fitness in one of their field site/year tend to be the ones whose genotype is overrepresented in the natural population.A. thaliana where variation across year and location dramatically alter fitness levels.This work is unique: the system is very well known, the genetic differences between the lines alter glucosinolate production in the field and the match between observed frequencies and fitness is very exciting. To my knowledge, this is the first time that the fitness consequences of an extent molecular system is studied in the field. This work demonstrates that glucosinolate production is important for fitness. I find equally interesting that this fitness relevance cannot be explained by insect damage. This shows that the ecological function of glucosinolate is not as straightforward as one may think. Finally, the authors document the complexity of field studies in eLife.This work is excellent and I strongly recommend it for publication in Reviewer #3:Arabidopsis accessions. The authors conclude that the relationship between field fitness and observed glucosinolate genotype frequencies is due to fluctuating selection pressures that maintain genetic variation in nature. The questions are of great ecological and evolutionary significance, but these conclusions are compromised by statistical and evolutionary shortcomings.This manuscript examines herbivory and fitness in field sites in the USA for a series of transgenic glucosinolate genotypes, and compares these local fitness estimates to the frequency of genotypes in 144 European Statistics:1) This is a split plot design (for insecticide treatment), not a randomized complete blocks design. Correction of this analysis will certainly affect inferences related to the insecticide treatment, and may alter other parts of the model.2) Inclusion of individuals with zero fitness is not compatible with the distributional assumptions of this ANOVA. This should be visible in the residuals, although no statement is made regarding such verification of statistical assumptions. Such zero-inflated data pose a difficult problem in such analyses, which typically alter levels of statistical significance and often cause spurious rejection of the null hypothesis.3) Controls for multiple statistical tests are needed at several points in this manuscript. Examples include tests for non-random distribution of multilocus GSL genotypes  comparisEvolution and Genetics:4) The evolutionary significance of this study is justified as a test whether fluctuating selection maintains genetic variation within and among populations. However, these experiments do not estimate herbivory or fitness for the individual GSL loci, and they do not show change in rank fitness at putatively selected loci, which is a necessary condition for balancing selection to maintain non-neutral genetic polymorphism.5) Even if the patterns in 6) The observation that multi-locus genetic variation controlling aliphatic GSL appears to be non-randomly distributed among the natural accessions is interpreted as evidence for natural selection. However, this may also result from population structure, nonrandom geographic sampling, finite population size, or failure to correct for multiple tests.7) “We observed significant variation in silique lengths across genotypes” How do GSL polymorphisms alter silique length? And, how do these effects differ among pesticide treatments? Alternatively, rather than the effects of GSL polymorphisms, variation in silique length (and fitness) may be due to position effects of the transgene inserts, or untagged Agrobacterium hits, or linked mutations not eliminated following EMS.8) Several points weaken the proposed role of herbivory in shaping the observed patterns in GSL polymorphisms:8A) In 8B) Similarly, the authors note that “the positive correlation between observed genotype frequency and fitness disappeared in the high herbivory WY2012 field trial.” This suggests that these results may not be due to herbivory.8C) To test for herbivory-mediated effects, one could ask whether the ANCOVA is significant if only the no-pesticide treatment is analyzed. Or, what happens to the patterns in  We all agreed that the manuscript reads very well and that the data set is extremely interesting and comprehensive. However, we also have significant concerns with respect to the usage of the model of Turelli and Barton (subsection “Fluctuating selection estimates”) and the interpretation of the analysis performed on the 144 accessions (in the subsection “Non-random variation of GSL loci among field collected accessions”).1) Firstly, the model of Turelli and Barton cannot be used for this type of data. During our discussion we consulted Michael Turelli directly and together we reached the following conclusion: although these data certainly warrant a discussion on fluctuating selection to play a role here, there is no simple formula to provide the appropriate polymorphism condition in this case, to the best of our knowledge. The detailed comments of Turelli are below and can form an excellent basis for a revised discussion on known genes and fluctuations in herbivory and fitness in nature . Furthermore we suggest you make an estimate of the genetic correlation between environments for levels of herbivore resistance among these genotypes. This will be informative, and should not be difficult to calculate from the existing data and will bring depth into the Discussion. Please take this discussion into account that glucosinolates can have effect on fitness also via other effects than herbivore damage alone.Arabidopsis  and provided citational support for these requirements in Arabidopsis within the field. Finally, we have concluded this section with a comment on the dramatic need for further field trials and natural history studies to test for this potential in the field.We have removed the sections using the Turelli approach and we have included a new section in the Discussion commenting on what would be further required to allow for fluctuating selection to maintain diversity in We apologize for having not included the Prasad citation as we had been focusing on single gene manipulations. We have now included this citation.We have now included the genetic correlation of herbivory across the three environments that shows that there is no correlation which agrees with the concept of fluctuating herbivory pressures. We would also like to note that we have an entire paragraph in the Discussion (third paragraph) on glucosinolates altering fitness via their effects on other processes that may influence resistance to unmeasured abiotic fluctuations. We hope that this is sufficient.2) Secondly, we all agreed that the interpretation of the analysis on the 144 field collected accessions is too opportunistic. Non-random variation of glucosinolate loci among natural accessions could be caused by fluctuating selection but there are equally valid alternatives  such as drift, gene flow or historical population structure etc. Now the conclusions worded in the subsection headed “Non-random variation of GSL loci among field collected accessions” are much too selectively biased towards the first. We strongly suggest you rephrase the interpretation thoroughly doing just the alternatives or, and this may be the better alternative, to remove this analysis from your study altogether.We would like to keep this analysis as we feel it nicely connects to the empirical data and provides an alternative explanation for the distribution of variation in the accessions. We have added the following material to this section in the hopes of properly caveating the data and saying that future work needs to be done to clarify any of the hypotheses about the data: “It is similarly possible that this non-random variation is caused by non-selective processes like migration, population structure and local bottlenecks. Significant future efforts will be required to test the extent to which this non-random variation is caused by neutral demographic processes vs potential fluctuating selection.” We feel that we would be remise if we did not include this data and hope that this more detailed caveating of all possible explanations for interpretation helps. If it is still felt that this is too much we will remove it.We hope that this letter, the minor comments of the referees and the report of Dr. Turelli will help you to revise your manuscript for eLife.Please find below detailed comments of Michael Turelli in response to the manuscript and the discussion among the referees:This is indeed deep water. Given the technical nature of the relevant theory it should be no surprise that both the authors and the reviewers make incorrect assertions, but both make important points.“First, the relevance of theconditions to maintenance of variation involving genotypes created from “mutants [involving] two or three mutated alleles (different loci) [brought] together to get the desired phenotype.” Theconditions involve the effects of alleles at individual loci. Hence, one cannot invoke conditions for multilocus genotypes. As I understand this is a key criticism of the reviewers . This criticism is correct, but see below.Second, the relevance of theconditions to any genetic variants in Arabidopsis thaliana, which is predominantly selfing.explicitly assume random mating. If Arabidopsis thaliana were completely selfing, which I believe is reasonable as a first approximation, populations would be effectively composed of competing clonal genotypes . In this case, the distinction between variants at one locus versus multiple loci is irrelevant, as is the distinction between diploidy and haploidy. Hence, the diploid-random-mating conditions provided byare irrelevant to the maintenance of variation. In general, temporal fluctuations alone cannot maintain variation for a haploid, the genotype with the highest geometric mean fitness will prevail . For such populations, one must invoke either spatially varying fitness or temporal variation with a seed bank. The exact conditions for the maintenance of variation will depend on the nature of gene flow between patches with alternative selection regimes and the extent to which the seed bank creates overlapping generations. These issues are discussed byThe conditions provided bycannot be directly applied to the system of Kliebenstein system. However, showing that different genotypes are favored under different conditions does indeed suggest that fluctuating selection (in time and/or space) may contribute to the maintenance of this polymorphism. The exact mathematical conditions relevant to this system have probably not been worked out. However, assuming near-complete selfing, maintenance of variation will require overlapping generations via a seed bank  and/or spatial variation with gene flow. The exact conditions will be subtle and depend on biological details that are surely not known.”Arabidopsis would require either a seed bank and/or spatial separation of selection. We then cited papers providing evidence of both and commented on the need for more natural history to provide detailed parameters to these to allow for more detailed models to be built for this situation. We hope that this helps.We have added in a point in the Discussion section, stating that for fluctuating selection to maintain diversity in Reviewer #2 minor comments:1) Abstract: “fitness effects were significant in each environment but the pattern fluctuated such that highly fit alleles in one year displayed lower fitness in another.” This experiment doesn't compare alleles, it compares multilocus genotypes.We agree that this experiment compares different multilocus genotypes rather than alleles. The text has been changed and “alleles” has been changed to “genotypes”.2) In the subsection headed “Environment interacts with GSL genotype to impact leaf damage”: “no particular GSL genotype showed a consistent maximal or minimal level of leaf damage across the three field trials”. This conclusion that no genotype has consistently highest or lowest damage level obscures the highly significant main effect of genetic differences in damage levels .We agree that genotype is significant but the genotype x environment term is more significant and contains more than two times the variance even though linear models are known to overweight the main effect terms at the cost of the interaction terms. This is in agreement with the visual analysis in the figures where the maximal and minimally fit genotypes are inconsistent. We think the middle is where the main effect variance is coming from. Thus, we prefer keeping our original conclusion.3) Discussion: “it has been complicated to validate that specific polymorphic loci within a pathway are the actual causative basis of any changes in fitness due to the use of polygenic populations”. Unfortunately, this study shares the same shortcoming, because the chosen combination of multilocus genotypes prevents a clear test for antagonistic pleiotropy at individual loci.We feel that this shortcoming is by no means the same scale as the existing polygenic populations that are segregating for thousands of genes some in extreme linkage . In our case, we have a mere handful of discrete gene manipulations all within a single pathway that allows us to focus our interpretation in a way that was not previously possible. We have commented on how it would be optimal to have the full 256 line matrix containing all combinations of alleles between all loci to fully interrogate the effects of all loci in all possible backgrounds (please see the Discussion).4) Discussion: “we can directly conclude that it is these specific genes and their GSL phenotypes that are determining the differences in fitness in the field”. True, but that is not sufficient to show that fluctuating selection maintains genetic variation at any particular locus.We tried very carefully to re-edit the manuscript to ensure that we aren’t making specific allele claims but instead talking in general about the group of loci that we manipulated (i.e. genotypes). We hope that our significant caveats throughout this paper are sufficient to convey to the reader that we are simply providing evidence supporting a role of fluctuating selection in maintaining variance and are not arguing that we have proven this as the sole mechanism at play. As stated earlier in the letter from the editor, there are almost no studies providing similar evidence and we hope that by leaving the paper as written with it being a hypothesis that we can stimulate further research.5) In the subsection “Statistical analysis methods”: Each plot has 10 blocks. Why is there is no block term in the ANOVA?The blocks were subtended to the plot term as suggested in the previous round of review for the split-plot analysis and as such we did not investigate the block term.6) Fitness is normalized with respect to performance of Col-0. This is contrary to the usual definition of relative fitness (with a mean of 1.0). Because of this normalization to Col-0, the reported effects on relative fitness may reflect behavior of Col-0 rather that population means.We have adjusted the normalization to make relative fitness to reflect the population mean. Figures and tables have been adjusted accordingly.The results of the mixed model analysis do not change depending on whether fitness is normalized relative to Col-0 or the population mean. However, we understand that it might be more common to see relative fitness calculated based on the population mean. We have changed accordingly and apologize for any confusion it may have caused.7) What doestell us, beyond the main and interaction effects already reported inTable X?This is a graphical representation of the data presented in the table along with the hierarchical clustering of the genotypes. Some readers approach data more graphically while others prefer the tabular form and as such we felt it was best to include both presentations.8) In the subsection headed “Pleiotropic Links to GSL Genes”: “while the GSL genes are causing pleiotropic effects, these pleiotropic effects are not driving the observed fitness consequences of the GSL genotypes in our field trials.” A simple pairwise correlation analysis is not sufficient to support this conclusion. More complex ANCOVA-like models might be helpful here, perhaps with principal components of GSLs.We feel that a simple pairwise correlation is sufficient to state that pleiotropic effects of flowering time are not sufficient to explain the entirety of the data. If flowering time was the sole driver, then there should have been a simple pairwise correlation. A more involved ANCOVA or path analysis would be required to delve even further into cause and effect but we feel that this is beyond the scope of this manuscript which is solely working to show that there can be fluctuating selection without giving the specific mechanism which as we stated in the discussion may be beyond our current measurements and require further work.Reviewer #3 minor comments:1) Introduction: this sentence gives the impression that intermediate frequency variants are frequent in the genome. This is misleading, because the majority of variants do have low frequency. It is just that there are several intriguing examples of intermediate frequency alleles. Furthermore, people have tried to relate FRI to fitness and failed in most cases.We have changed this section completely to better relate the frequency of alleles topic better. We hope that this works.2) Also in the Introduction: I wonder why the authors do not mention the work ofwhich does relate underlying genes to fitness.Thank you for this suggestion. We have added this citation and another study on local adaptation using GWA studies . We apologize for not including these previously as we were focused on citing studies using specific single locus manipulations in the field.3) In the subsection “Leaf damage in the field varies across environments”: pesticide application is somehow unfortunate because it artificially decreases herbivory load and thus might explain why the expected effect of GLS variation on fitness via herbivore defense was not observed. This must be better incorporated in the Discussion.We had intentionally included the pesticide treatment to enable us to test the effect of herbivory load upon the fitness effects. Unfortunately the fluctuating environments lead to most years having lower than expected herbivory load in these experiments causing the treatment to have minimal impact on the results. We have incorporated a new sentence in this section of the manuscript stating that another explanation for this lack of linkage is that the experiment was too small and needs to be larger. We hope that this is sufficient. We would prefer to not focus too much effort on the lack of an observation, as this is in all likelihood an issue of power.4) In the subsection “Fluctuating selection estimates”: I really appreciate that the authors include now the model of Turelli and Barton, but the model and its predictions should be briefly summarized (for the reader this will come out of the blue!). More explanations are needed in the Methods as well. Did the authors use LSmeans to calculate the parameters? Were LSmeans calculated after correction of error over dispersion?As suggested by the reviewing editor, we have removed the Turelli and Barton equation work.5) In the subsection “Non-random variation of GSL loci among field collected accessions”: this formulation is somehow strange. The words “population structure” should be mentioned so that the right bell rings for the reader.We have better stated the set of demographic/non-selective processes that could have generated a non-random population structure in this section.6) In the same subsection: the authors should be clearer here that this analysis cannot exclude the possibility that the skewed haplotype distribution can result from population structure only.Please see the comment to the editor at the beginning on how we have more fully caveated this section and said that future work needs to be done in the field to assess the relative contribution of selective and non-selective processes to this distribution.7) Discussion: this aspect of the Discussion is still too uncritical for me. The authors should not forget that their findings are not expected and may be driven by processes that were not supposed to play a role. What about insertion effects? Inserted transgenes can disrupt other genes and may result in fitness effects that are unrelated to GLS function. EMS lines initially contain thousands of mutations. They are generally removed by multiple generation of backcrossing to the wild type. Crossing adds some additional backcrossing, is it possible that lines differ in the number of linked mutations? Finally, transgenes are not always stably expressed and could be silenced in one or the other generation, especially if several tDNA insertion lines are coupled. Such problems are well known to (good) molecular biologists but often overseen by ecologists. I believe it is important to critically assess the possibility that the manipulated lines may not be doing exactly what they are supposed to do.We have added in the following material to the Discussion: “We should also note that even with all of our efforts to clean up the respective backgrounds and validate that the mutant phenotypes are similar to the segregating natural genotypes, it remains possible that some of the observed effects are caused by unexpected changes in the lines”.We hope that with the significant efforts at cleaning up the material as described in the Materials and methods that this is sufficient. We would like to note that we can rule out T-DNA silencing as we phenotyped every plant in the analysis using HPLC so that we can be sure that all insertions were generating the appropriate biochemical phenotype in each and every line and as such the insertions were not silenced.8) Finally, the manuscript relies on quantitative analyses of variation. One should not dismiss the possibility that means were not correctly estimated, especially with over dispersed measurement of fitness. There is no such thing as a perfect statistical analysis.We hope that the manuscript is now sufficiently caveated throughout to represent the potential pitfalls. We would like to note that as in the previous round of reviews that we had gone through the data to limit any effects of over-dispersion on the mean estimation.[Editors’ note: the author responses to the previous round of peer review follow.]1) The referees feel that “fluctuating selection/bet hedging” theme should only (at best) appear in the Discussion and certainly not be a central theme. Much of this has to do with the analysis presented inusing the 144 Arabidopsis accessions for drawing conclusions on natural selection as a determinant of their genotype distribution.We have extensively rewritten the entire manuscript to focus on validating fitness effects using specific genetic manipulations and field trials. As per the suggestion by the reviewers, we have introduced a new section where we utilize the 2) The ANCOVA analysis using the 144 accessions and its interpretation is troublesome and maybe should be removed altogether.As suggested by the reviewer, we have removed the ANCOVA analysis.Several of the remaining statistical analyses  should be adjusted.We have redone all the statistics using the split-plot model structure and previous Survival and zeroes:We have run all the statistics using absolute fitness with and without survivorship to show that the models have the same result and that the non-survivors are not driving the observed link between genotype and fitness. We hope that this rectifies any concerns.Multiple testing:We have removed previous 3) The validity of the fitness-proxy parameters should be better justified.Arabidopsis is linear to seed size, we have a better approximation of seed production in these individuals. The linearity argument arises from the fact that Arabidopsis siliques contain only two lines of seeds per silique and as such a silique is really a two-dimensional fruit with regards to seed number. Therefore, we calculated absolute fitness as total fruit count (TFC) x silique length with and without survivorship  The projection of the experimental data onto the genotype-distribution of 144 Arabidopsis accessions does not work for me:A) I fail to see why you would expect to see evidence for natural selection within a group of plants (accessions) of which you do not know what the original selection criteria were: for sure these are not ecotypes and it is unclear to which extent they represent the genotypes of their respective original populations . This should at least be discussed in much more detail.We have worked to address this concern in several ways. The first is that we have included a new figure showing geographic origin of the accessions  that shoB) The analysis presented inthat justifies the field experiment  is not strong since a test for the goodness of fit of the overall observed versus expected relative frequency distributions is missing (e.g. chi square test for goodness of fit).We have now given the goodness of fit for the overall model as requested, which was highly significant .C) How does the analysis of thedata exclude non-selective processes as an alternative for random assortment .As stated above, we have moved this figure to the end of the manuscript and made it clearer that this is not proof of selective processes but does support our conclusions. We also discuss that more field trials over successive years as well as more extensive accession sampling would be necessary to fully validate a fluctuating selection model.D) You write “field studies confirm lab results” (at the end of the subsection “GSL genetic variation controls GSL profile in the field”), but you do not provide a direct comparative analysis, just a 'visual' interpretation of the data.We have now included a direct comparative analysis using PCA and correlation to show that the GSL profiles of the lab and field grown plants are highly comparable.E) In the subsection “Empirical fluctuating measures of selection in the field predict standing variation in GSL genes”, you conclude that “selection likely played a role”, but you do not explain where in the figures we can see this. Looking at the three plots , I only see that the correlation between frequency and your relative fitness-proxy is weak (probably due to UWY2012).We agree that the 2) You used a “deterministic” approach to genotype the 144 accessions i.e. on the basis of their “GSL profiles” but a validation of this approach is missing:A) Throughout the manuscript is remains unclear what is meant with “profile” and how these were evaluated (e.g. which grouping criteria/procedures/assignment to a genotype). Hence its validity cannot be assessed.We have worked to better explain that profile is the mixture of GSLs within a genotype and their relative abundance. To support this description, we have included new figure supplements to B) In the subsection “GSL genetic variation controls GSL profile in the field”, it is unclear to which extent actual profile information was used for the downstream analyses or when only the information on the total  glucosinolates was used (e.g. see).appears to represent these “profiles” but a statistical evaluation is not provided.We have included statistical analysis on the profile figures as requested and provided visuals on the profiles in C) Why was this indirect approach for genotyping preferred over a direct (DNA-based) approach?Arabidopsis, such as flowering time, there are independently evolved alleles in the GSL pathway that generate the same phenotype but appear as independent genotypes. Thus, we prefer to define the accessions by their functionality at each locus which better reflects the GSL profile differences observed. Additionally, the GSL loci have local rearrangements that make them nearly impossible to obtain accurate genotypic information using Illumina resequencing approaches and as such we have found that the data in the 1001 databases for these loci is inaccurate when we compare to direct BAC sequencing of the same accession. Thus, the available data is unable to provide accurate genotyping information which is another reason to use the indirect approach at this time.As is true for other naturally variable loci in 3) The factors of the statistical analyses are often unclear:A) The factor “location” is misleading: it should be “environment” since the different locations were used at different moments in time. Why do you refer to these differences as 'fluctuation' i.e. how do you know they are not caused solely by differences in starting conditions? Now you infer these differences frombut the patterns across the three panels should be statistically evaluated to decide to which extend they differ.We have changed the term “location” to “environment” as requested. We worked to minimize the differences in starting conditions by working to make the planting time as close as possible. Similarly, all plants were started in a greenhouse to minimize variation in starting conditions on the seedlings. As with any field trial it is very difficult to ascribe specific causes of fitness differences and we have worked to show that flowering time which should be equally susceptible to starting conditions was not linked to the resulting fitness. Even if the planting data was identical, the starting condition across years could be strikingly different and we interpret that as a fluctuation. We have included statistical analysis within B) The statistical “interaction” is misinterpreted and dance around its meaning. Significant interactions indicate that their simultaneous effects are not additive i.e. either the combined effect is greater (synergistic) or smaller (antagonistic) than expected (additive) effect. Pinpointing what they mean is sometimes virtually impossible and requires post hoc statistics.We have included a new set of figures on both herbivory and fitness to show that neither the synergistic nor antagonistic models fit the observed genotype × environment interactions as there are numerous instances of the GSL genotypes crossing, i.e. a genotype’s rank for fitness changing from environment to environment. We hope that this visual analysis and accompanying changes to the statistical model help to show that this fits neither the synergistic or antagonistic model but instead is a better fit to a fluctuating model.C) The ANCOVA procedure is not explained anywhere.The ANCOVA and the corresponding figure have been removed as per requested by other reviewers.4) Your fitness proxies, and especially how they were normalized, need validation. In “GSL variation impacts fitness in the field”, you describe a normalization procedure (which assumes a linear relationship between silique length and fecundity) which struck me as highly arbitrary. This procedure needs references or a solid validation.Arabidopsis, the silique is a linear fruit with two files of seeds. We found that seed size was not different amongst genotypes and thus silique length is directly correlated to the number of seeds that can be within that silique. Thus as we had genetic variation in silique length we had to adjust the approximation of Schmitt and colleagues to appropriately reflect this fact. We have worked to make this clearer within the text. In addition, we conducted all the statistics using total fruit count alone with and without survivorship and got similar results as we did for absolute fitness  This is a split plot design (for insecticide treatment), not a randomized complete blocks design. Correction of this analysis will certainly affect inferences related to the insecticide treatment, and may alter other parts of the model.We have redone the entire analysis with a split plot analysis. All statistics throughout the manuscript have been adjusted to reflect this new analysis. This as suggested by the reviewer lead to a loss of significance of the treatment effect which required us to rework the entire manuscript to remove any inference about the effects of herbivory upon the analysis as there was no difference in the pesticide and control plots. The observation that GSL gene variation and an interaction of GSL gene variation and environment are linked to fitness was still significant.2) Inclusion of individuals with zero fitness is not compatible with the distributional assumptions of this ANOVA. This should be visible in the residuals, although no statement is made regarding such verification of statistical assumptions. Such zero-inflated data pose a difficult problem in such analyses, which typically alter levels of statistical significance and often cause spurious rejection of the null hypothesis.We have empirically tested if the zero fitness individuals were causing spurious significance by running the model using fitness as calculated with the zeros and without the zero individuals. This is now shown in the manuscript in 3) Controls for multiple statistical tests are needed at several points in this manuscript. Examples include tests for non-random distribution of multilocus GSL genotypes  comparison of treatment effects, and variation of GSL among sites .As per the request from Reviewer 1, we now include the whole-model Chi-square goodness of fit for Evolution and Genetics:4) The evolutionary significance of this study is justified as a test whether fluctuating selection maintains genetic variation within and among populations. However, these experiments do not estimate herbivory or fitness for the individual GSL loci, and they do not show change in rank fitness at putatively selected loci, which is a necessary condition for balancing selection to maintain non-neutral genetic polymorphism.vi and the population K to show that the empirical values we have found are sufficient to fit the necessary conditions as modeled by Turelli and Barton to allow for fluctuating selection to maintain multi-locus genetic polymorphisms. Additionally, we have reworked the entire manuscript to focus more on the fact that the GSL genes affect field fitness. We hope that this helps to address these concerns as well as makes for a better manuscript as a whole.We have included a new figure showing that the ranks of the GSL genotypes are changing across the environments . Additio5) Even if the patterns inwere due to selection, they might be attributable to non-equilibrium directional selection in Eurasia, rather than to historical balancing (fluctuating) selection. Consequently, this analysis cannot prove that such patterns are due to fluctuating pressures maintaining standing natural variation within a species.We agree with the reviewer that proof of how historical selection has occurred is nearly impossible to obtain. Throughout the manuscript we had attempted to state that we have generated data that supports a fluctuating hypothesis but that more extensive field trials and more extensive inter and intra population sampling within the species range are required to further validate this hypothesis. We have worked through the manuscript to ensure that we do not state we have generated proof but instead simply support.6) The observation that multi-locus genetic variation controlling aliphatic GSL appears to be non-randomly distributed among the natural accessions is interpreted as evidence for natural selection. However, this may also result from population structure, nonrandom geographic sampling, finite population size, or failure to correct for multiple tests.Arabidopsis thaliana accessions agree with the field trial estimates of the Turelli and Barton parameters that support the hypothesis that fluctuating selection can balance multi-locus polygenic genetic variation within the aliphatic GSL pathway.We apologize for the obvious confusion on this section and figure which we had meant to state that the pattern may result from natural selection, population structure, sampling or any other demographic process and then to state that separating between these options needed field tests of specific genetic variants. Instead of having this analysis at the front, we have moved this to the last figure  to indic7) “We observed significant variation in silique lengths across genotypes” How do GSL polymorphisms alter silique length? And, how do these effects differ among pesticide treatments? Alternatively, rather than the effects of GSL polymorphisms, variation in silique length (and fitness) may be due to position effects of the transgene inserts, or untagged Agrobacterium hits, or linked mutations not eliminated following EMS.Arabidopsis RIL populations and then show the effect using the transgenic validation lines. This was with both enzymatic loci and transcription factor loci showing that this is not a second site effect, but instead a link from GSL to the clock and flowering. We wish we could provide more mechanistic insight into these non-traditional roles of GSLs but these experiments are still underway. We have included a new section showing that these pleiotropic effects on flowering and indole glucosinolate are not correlated with fitness showing that the GSL to fitness link is not an artifact of some secondary indirect random pleiotropy as best we can measure.We have worked to make it clearer in the text that the genetic backgrounds of our GSL genotype are unlikely to have second site insertions due to the fact that they have been back-crossed multiple times to eliminate unlinked effects. Additionally, the majority of lines are specific insertions within the GSL gene to create the natural knockout allele. Further, in reply to Reviewer 2, we have noted that our previous work has shown that unexpected links to non-GSL phenotypes, such as flowering time, have been validated both with the transgenic and natural populations i.e. we could map circadian timing variation to GSL loci in an 8) Several points weaken the proposed role of herbivory in shaping the observed patterns in GSL polymorphisms:We have largely removed the herbivory arguments because the split plot analysis removed any significance associated with treatment meaning that we don’t have the capacity to support this argument.8A) Inwe see that the ranking of herbivore damage (without insecticide) decreases from UWY2012 > UCD2012 > UWY2011. However, the correlations inFigure 12show the opposite pattern: UWY2012 < UCD2012 < UWY2011. This seems incompatible with the conclusion that the herbivory differences in the field reflect natural selection by herbivores in Eurasian Arabidopsis over thousands of generations.We have removed the ANCOVA as requested as well as the corresponding figure.8B) Similarly, the authors note that “the positive correlation between observed genotype frequency and fitness disappeared in the high herbivory WY2012 field trial.” This suggests that these results may not be due to herbivory.We have removed the ANCOVA as requested as well as the corresponding figure.8C) To test for herbivory-mediated effects, one could ask whether the ANCOVA is significant if only the no-pesticide treatment is analyzed. Or, what happens to the patterns inif the change in fitness between insecticide treatments is used as the response variable for the ANCOVA?We have removed the ANCOVA as requested by the reviewers.


Numerous studies have reported positive correlations among couples for height. This suggests that humans find individuals of similar height attractive. However, the answer to whether the choice of a mate with a similar phenotype is genetically or environmentally determined has been elusive.Here we provide an estimate of the genetic contribution to height choice in mates in 13,068 genotyped couples. Using a mixed linear model we show that 4.1 % of the variation in the mate height choice is determined by a person’s own genotype, as expected in a model where one’s height determines the choice of mate height. Furthermore, the genotype of an individual predicts their partners’ height in an independent dataset of 15,437 individuals with 13 % accuracy, which is 64 % of the theoretical maximum achievable with a heritability of 0.041. Theoretical predictions suggest that approximately 5 % of the heritability of height is due to the positive covariance between allelic effects at different loci, which is caused by assortative mating. Hence, the coupling of alleles with similar effects could substantially contribute to the missing heritability of height.These estimates provide new insight into the mechanisms that govern mate choice in humans and warrant the search for the genetic causes of choice of mate height. They have important methodological implications and contribute to the missing heritability debate.The online version of this article (doi:10.1186/s13059-015-0833-8) contains supplementary material, which is available to authorized users. The processes that lead humans to choose a particular mate and the extent to which these choices are governed by genes or environment have been widely debated. Here, we use 32,000 human couples and height as a model trait of human attractiveness to shed light onto these processes.Height is a model quantitative trait that is determined by the interplay of large numbers of genetic and environmental factors. Narrow-sense heritability for height, which measures the relative importance of additive genetic factors and environmental factors in the expression of a trait, has been consistently estimated to be high, typically around 0.8 , 2. HeigThe correlation in height between members of a couple is much larger than that expected by chance –10. ThisThe UK Biobank  has genoTo estimate the contribution of genetic and environmental factors to variation in choice of mate height, we estimated relationships . We estimated that the heritability of choice of mate height was 0.041 (standard error 0.014), which indicates that there is a significant genetic component for choice of mate height in humans. This is consistent with a model where mate selection for height is driven by one’s own height see ‘’.We then asked whether the genetic determinants of choice of mate height were shared with the genetic determinants of a person’s own height. To answer this question, we treated the height of the partner as a phenotype of an individual and used a bivariate analysis to estimate the genetic and environmental correlation between the two traits. A genetic correlation equal to zero would imply that one’s own height and the choice of mate by height are not affected by the same genetic variants or that there is no directional pleiotropy, whilst a genetic correlation of one would imply that the two traits share the same genetic determinants, working in the same direction. Similarly, a non-zero environmental correlation would imply that the factors that affect the environmental and non-additive genetic deviations are at least partly shared between the two traits. The bivariate analysis Table  performeP = 7.55 × 10−59), that is, 64 % of the maximum expected correlation; the expected maximum correlation between the additive genetic effect for choice of mate height and phenotype for choice of mate height being 0.2, the square root of the heritability of choice of mate height.To strengthen the evidence for this hypothesis, we estimated, using genetic marker information and a univariate mixed-linear model see ‘’, the adThe genetic consequences of assortative mating depend on whether the primary cause of assortment among partners is phenotypic , genetic (e.g. matings are within differentiated ethnic groups) or environmental . Primary genetic or environmental correlations arise when mating occurs within groups that are either genetically or environmentally differentiated. We argue that for human height the primary source of partner similarity is phenotypic, rather than caused by genetic or environmental structure within the population. We believe that the observed correlation in height between partners is not an artefact of mating within groups or populations that are genetically differentiated, because our analyses were adjusted for the first 20 PCs and because, for mixed-origin couples (those for which a partner is classified as White-British and the other as non White-British), we observed similar heritabilities to those of White-British couples for both height and mate’s height , which is consistent with the primary source of assortment being the phenotype. Moreover, we can use theoretical predictions to estimate what the heritability of height would have been before assortative mating started. If we assume a heritability for height of 0.8 under assortative mating, then we estimate that the heritability under random mating would be 0.76. That is, continuous assortative mating is expected to lead to an increase of heritability for height of ~5 %, which is due to how alleles are assorted in the population under assortative mating and not to additional genetic variants segregating in the population . Individuals were excluded from further analysis if they exhibited excess heterozygosity, as identified by UK Biobank internal QC procedures [P < 10−50) or with minor allele frequency below 0.05 within the subset of couples identified as ethnically White-British as described below, which left 318,852 SNPs for analysis. The genotype QC was performed using PLINK [We obtained data for 152,736 individuals genotyped in phase 1 of the UK Biobank genotyping programme. These comprise 49,979 individuals selected as part of the BiLEVE study based on their lung function phenotypes , 102,750ocedures , if theing PLINK .http://biobank.ctsu.ox.ac.uk/crystal/refer.cgi?id=149744) that passed our SNP QC protocol. Amongst individuals who self-reported their ethnicity as White-British, we then retained individuals for whom the projections onto the leading 20 genomic PCs fell within 3 standard deviations (SD) of the mean.The UK Biobank cohort includes individuals of diverse ethnicities that may confound analyses. We therefore identified a core subset of 123,847 individuals of White-British ethnicity by combining self-reported and genotype information. Specifically, we performed a principal components analysis (PCA) of all individuals passing genotypic QC using an LD-pruned set of 99,101 autosomal markers ’. Hence, for ~90 % of the pairs we have additional confirmatory information that these were couples. Our univariate and bivariate analyses included only those couples whose coefficient of relatedness (r) was less than 0.0625, of which only seven pairs had r > 0.025.Of those 105,381 identified couples, we used 13,068 White-British couples and 3,726 mixed-race couples (where one member of the couple was classified as White-British and the other as non White-British) that had been genotyped in phase 1. The bulk of the analyses in the paper were performed on the 13,068 White-British couples. Our predictions of the partner’s height based on the individual genotype were performed using 15,437 couples where only one of the partners had been genotyped in phase 1. For this, we predicted the total additive effect of height for the person genotyped and estimated the correlation (i.e. the prediction accuracy) of that ‘polygenic score’ with the height of their partner. In this case, and because we could not confirm that the partners were unrelated using genotypes, we set additional filtering criteria. We used only pairs where both individuals were self-reported White-British; the genotyped person was classified as White-British based on genotype; individuals reported different ages for one or both parents; and individuals had an age difference of less than 10 years, were of opposite gender, and reported to live with their partner or partner and children.We defined outliers as males and females that were more than 3 SD from their gender mean, and removed them from the analyses.http://www.dissect.ed.ac.uk) under a GNU GPL v3 license. The availability of the software and access to the UK National Supercomputer (ARCHER) allowed us to fit these computationally intense analyses to the large dataset.The PCA and all mixed linear models were fitted using DISSECT , a softwWe fitted the following univariate mixed linear model:μ is the mean term and ei the residual for individual i. L is the number of fixed effects, xil being the value for fixed effect l for individual i and βl the estimated effect for l. M is the number of markers and zij is the standardised genotype of individual i at marker j. The vector of random SNP effects a is distributed as N. The phenotypic variance-covariance matrix is var(y) = V = ZZTσu2 + Iσe2. The SNP effects are estimated using the equation [where equation :\documenj=1Mzijajis the total additive genetic effect (gi) for individual i, this model can also be expressed as,Because ∑g is distributed as N. Where A is the genetic relationship matrix and σg2 = Mσu2. Accordingly, the total phenotypic variance-covariance matrix is var(y) = V = Aσg2 + Iσe2. From the equivalence between these two models, DISSECT can estimate the total additive effect from the equation:In this model, the vector of genetic effects σg2 and σe2 using the expectation maximization (EM) method for the first step [DISSECT estimates rst step , followerst step , 23.We fitted the following bivariate mixed linear model :\documenμi is a vector of equal mean terms and ei the vector of residuals for the trait i. Xi is the incidence matrix of the fixed effects βi for the trait i. gi is the vector of the individuals' genetic effects for the trait i with covariance matrix:where Ai is the genetic relationship matrix between the individuals measured for trait i and Aij the genetic relationship matrix between the individuals measured for trait i and trait j.V) is,where I is the identity matrix and I12 is a matrix where the elements in row i and column j are 1 if the individual i for the trait 1 is the same than the individual j of the trait 2 and 0 otherwise. As in the univariate case, DISSECT fits the variances and covariances using the expectation maximization (EM) method for the first step [where rst step , followerst step .h02), was estimated as h2 is the current h2 (assumed to be 0.8), and m is the correlation of breeding values among mates [The heritability of height, before the population started assortative mating and reached an equilibrium  which follows the standard additive genetic model, i.e., Pi = Ai + Ei, where Ai and Ei are the additive genetic effect and environmental component for individual i, respectively. If P drives mate selection the phenotype of the partner m(i) for a given individual i can be expressed as Pm(i) = bPi + Em(i). However under the assumption of an ante-dependence model Ai → Pi → Pm(i) for selection, where the additive genetic effect Ai influences the phenotype Pi which in turn influences the choice of i’s partner’s phenotype, we have cov) = 0. HenceLet us assume a standardised phenotype (b2var(Ai) = b2hP2var(Pi) where hP2 is the heritability of P. Since for a standardised phenotype b = rp where rp is the phenotypic correlation and var(Pi) = var(Pm(i)), we have that with the genetic component being h2 = 0.8 and rp = 0.26, the expected heritability for choice of mate’s height is 0.043.Now assuming a heritability for height of The use of the UK Biobank dataset falls within the study’s ethical approval from the North West Medical Research Ethics Committee (Reference 11/NW/0382).http://www.ukbiobank.ac.uk).The data can be accessed through the UK Biobank (