P < 5e−8 in the discovery GWAS) from 4,397,962 participants across nine phenotypes. The overall replication rate was 85.0%; although lower for binary than quantitative phenotypes (58.1% versus 94.8% respectively). There was a 18.0% decrease in SNV effect size for binary phenotypes, but a 12.0% increase for quantitative phenotypes. Using the discovery SNV effect size, phenotype trait (binary or quantitative), and discovery P value, we built and validated a model that predicted SNV replication with area under the Receiver Operator Curve = 0.90. While non-replication may reflect lack of power rather than genuine false-positives, these results provide insights about which discovered associations are likely to be replicated across subsequent GWAS.With the establishment of large biobanks, discovery of single nucleotide variants ) associated with various phenotypes has accelerated. An open question is whether genome-wide significant SNVs identified in earlier genome-wide association studies (GWAS) are replicated in later GWAS conducted in biobanks. To address this, we examined a publicly available GWAS database and identified two, independent GWAS on the same phenotype . The analysis evaluated 136,318,924 SNVs (of which 6289 reached  Genome-wide association studies investigate the association of individual single nucleotide variants (SNVs) on a phenotype of interest (for example coronary artery diseases)4. Most GWAS identify SNVs with, individually, small effects4. This supports the notion that most diseases are polygenic, rather than monogenic, in nature5.Genome-wide association studies (GWAS) have resulted in the discovery of tens of thousands of genetic associations for various traits and phenotypes. Polygenic risk scores4. Recent advances have seen rapidly increasing sample sizes, particularly with the establishment of large biobanks. The most widely used and analyzed biobank in human genetics is the UK Biobank (UKBB)6. Analyses done in the UKBB and other similar biobanks have the opportunity not only to identify new associations but also to replicate previously proposed associations that arose from other GWAS investigations. It is not unexpected that some SNVs that were considered to be associated with a phenotype in an earlier GWAS may not be replicated in a subsequent GWAS. Even if they are replicated, their effect size may change, e.g. because of the winner’s curse phenomenon7, where early discoveries see attenuation of their effect size when they are replicated in subsequent studies. This has implications for all scientific progress, and even patient care, (i.e. polygenic risk scores) reliant on GWAS results, if these scores include variants that have null effects or effects that are smaller than those anticipated based on their earlier discovery profile.To observe the small effect of individual SNVs, GWAS have relied on increasingly larger sample sizesP values, across varying effect sizes, and how effect sizes change between earlier, smaller GWAS and later, larger GWAS examining the same phenotype. A most interesting comparison would be to contrast earlier GWAS versus the UKBB, which has become a standard, widely used resource. We set out to address these questions, and, from our results, built a model to predict SNV replication.Although several studies have looked at SNV replication for specific phenotypes, it remains broadly unclear across phenotypes how often SNVs replicate, how this varies between binary and quantitative traits, at different https://atlas.ctglab.nl/)8 for GWAS that had been conducted for the same trait (e.g. systolic blood pressure) first using data independent of the UKBB and then a second, independent GWAS using exclusively UKBB data. Thus a trait was eligible if there were two independent GWAS available for it; one not using UKBB data (hereafter referred to as: discovery GWAS) and one using UKBB data (hereafter: replication GWAS). All discovery GWAS occured before the replication GWAS. Further inclusion criteria was GWAS conducted in European subjects (or results available for exclusively Europeans) and GWAS with more than 50 genome-wide significant SNVs, so as to allow having a meaningful number of discoveries to be assessed for replication. More information on the GWAS database we searched and its accompanying paper8 are available in the appendix. Upon acceptance, we will make all the data available and its accompanying code .To determine the reproducibility of SNVs between an earlier GWAS and the UKBB, we identified two, independent GWAS on the same trait, one without data from the UKBB and the second being done on UKBB data. To do this, we systematically searched a publically available database of genome-wide association studies (GWAS)  in the discovery GWAS—these were the SNVs we determined the reproducibility of. (2) Aligned the effect allele between the discovery and replication GWAS, and consequently inverted the effect size if effect alleles did not originally match and (3) Classified SNVs as replicated if they reached genome-wide significant (P < 5e−8) in both discovery and replication GWAS and had congruent effect directions in both GWAS (e.g. odds ratio (OR) above 1 in both GWAS). All SNV effect sizes were converted to OR before reproducibility was determined via the Chinn formula9. Thus, SNV effect sizes that were originally produced from linear models for quantitative (continuous) traits were converted to OR. Lastly, as a sensitivity analysis we explored the reproducibility of SNVs using the more lenient significance of P < 10e−6. For this analysis we tested the reproducibility of SNVs that had a P value < 10e−6 in the discovery cohort, and used a reproducibility P value threshold of P < 10e−6 in the reproducibility cohort. Further details appear in the appendix.To determine the reproducibility of SNVs in the discovery and replication GWAS we performed three broad steps: (1) Determined overlap of SNVs between discovery and replication GWAS (via rsID) and only included SNVs shared between two GWAS cohorts. We then identified the SNVs that reached genome-wide significance  or on a continuous scale, respectively. To explore the replication rate across P values and odd ratios, we also performed meta-analysis assessing the replication of SNVs with certain P value and OR characteristics (from the discovery GWAS). We calculated the reproducibility of SNVs across the following discovery GWAS P value categories: 5e−8 to 5e–9, 5e−9 to 5e−10, 5e−10 to 5e−11, and < 5e−11. We calculated the reproducibility of SNVs across the following discovery GWAS OR categories: 1–1.05, 1.05–1.1, 1.1–1.15, 1.15–1.2, 1.2–1.3, 1.3–1.4, > 1.4.We calculated the replication rate for each included trait individually, for all traits collectively, and for binary (e.g. coronary artery disease) and quantitative (e.g. diastolic blood pressure) traits separately. To calculate replication rate for each individual trait we calculated a simple proportion (e.g. [number of SNVs replicated]/[number of SNVs shared between discovery and replication GWAS]). To calculate the replication rate for all traits collectively we constructed a inverse-variance meta-analysisDetermination of reproducibility’), we converted all SNV effect sizes to an OR via the Chinn formula9. Then, to help interpret the output from this model, we converted all OR values to above 1  Finally we combined SNVs across all traits for the model. From the regression model, we determined the regression coefficient for the discovery OR and interpreted this coefficient as the change in OR between GWAS (e.g. a regression coefficient of 0.80 would imply that 20% decrease in OR between discovery and replication GWAS). We only quantified the change in effect size of SNVs that were replicated, and also for all SNVs that had reached genome-wide significance in the discovery GWAS, regardless of whether they were replicated or not in the replication GWAS. We performed similar analyses for binary and quantitative traits individually.To determine if a change in SNV effect size occured between the earlier, discovery GWAS and the later, replication GWAS in the UKBB we constructed a single variate linear model, with the discovery OR as the predictor variable and replication OR as the outcome variable. As stated above , and trait characteristic (binary vs. quantitative) on replication. We initially split our data into test and train sets . Using the train set, we constructed a logistic regression model using the following predictors: odds ratio , P value category, trait characteristic (binary vs. quantitative), minor allele frequency (taken from the discovery cohort), INFO score , and a sample size ratio (ratio of replication cohort sample size divided by discovery cohort sample size). We then tested the constructed model on the test set. We report the model’s predictive accuracy via the following metrics: sensitivity, specificity, and area under the curve (AUC) all with 95% confidence intervals. We further assessed model fit via McFadden’s R2; a measure of explained variation in logistic regression models, defined as the difference between the the (maximized) likelihood value from the fitted model and that of the null model – the model with only an intercept and no covariates.First we constructed a multivariate logistic regression model to examine the association of our predictors  in the discovery GWAS  , the replication rate improved for all phenotypes, particularly the binary phenotypes : 84.1% to 85.8%) . A less consistent pattern was observed with discovery GWAS OR, almost all OR > / = 1.2 were replicated  decrease in replicated SNV OR between discovery and replication cohorts Fig. , for allWhen considering SNVs that reached genome-wide significance in the discovery cohort (and weren’t necessarily replicated), we found a 16.4% (95% CI 82.8% to 84.4%) decrease in SNV OR between discovery and replication cohorts, for all phenotypes collectively. For binary traits this decrease was 13.6% (95% CI 11.4% to 15.9%), whereas we observed a 10.9% (95% CI 9.9% to 11.9%) increase for quantitative traits.P value < 5e−10 & > 5e−11, and discovery cohort SNV P value < 5e−11   eTable . P valuet eTable .2 of 0.36, reflecting a modest explanation of the variation.When we applied our training model to our test data set, we found an area under the Receiver Operator Curve (ROC) of 0.90 (95% CI 0.88 to 0.91) corresponding to a sensitivity and specificity of 82.1% (95% CI 77.5% to 93.8%) and 82.7% (95% CI 70.2% to 87.7%) respectively. We found a McFadden’s RP value and OR of discovery GWAS SNV. We also found that SNV odds ratios (OR) decreased between discovery and replication GWAS for binary phenotypes, but increased for quantitative phenotypes. Lastly, we developed and then validated a model to predict SNV replication, and found it to be accurate (0.90 (95% CI 0.89 to 0.91)).We analysed 136,318,924 SNVs from 4,397,962 participants across nine different phenotypes (18 GWAS). Of these 136,318,924 SNVs, 6,289 SNVs reached genome-wide significance in the respective discovery GWAS, of which 5,343 were replicated in their replication GWAS : 84.1% to 85.8%). Replication rate varied substantially between binary and quantitative phenotypes and it was lower in the former. Further, replication rate varied across 6. While this probably represents the best current method to define phenotypes in large cohorts, EHR data is messy and likely to include some administrative and clinical error11. An improvement in the phenotyping in data used for GWAS of binary phenotypes is likely to result in improved SNV replication. This may be even more crucial for phenotypes where we saw low replication rates, e.g. eczema.Our results have implications for the GWAS results. First, the SNV replication rate for quantitative phenotypes is very high; implying that quantitative GWAS in the UKBB had likely reached sufficient power to accurately detect all SNVs that were truly associated with a phenotype and that had been discovered by earlier GWAS efforts. We also quantified, using non-stimulated data, the concept of winner’s curse; the change in effect size between our smaller discovery cohort and larger replication cohort may be a useful comparison for future studies that aim to quantify winner’s curse. The high replication rate observed for quantitative traits may also reflect the precision and relative ease in which quantitative traits can be measured. The converse of this, the likely measurement error and ultimate definition heterogeneity of binary phenotypes, may be one explanation for the relatively low rate of replication in binary phenotypes. For instance, binary phenotypes often represent complex clinical diseases that can have (a) broad diagnostic criteria  and (b) are defined via an array of data sources, of varying quality. The UKBB, for instance, defines their phenotypes with ICD codes based on linked electronic health records (EHR)13. With improved phenotyping, it seems plausible that these scores will continue to improve. Nevertheless, in the meantime there may be other ways to enhance current binary GWAS results for polygenic risk scores. First, our results clearly show a superior replication rate with quantitative phenotypes. These quantitative phenotypes are often more in line with physiological processes (e.g. systolic blood pressure) than clinical diseases (e.g. coronary artery disease). As such, future GWAS that directly use metabolomic data as outcomes (such as protein expression) are likely to, similarly, have higher accuracy than clinical disease phenotypes. Future research merging metabolomic outcomes and GWAS may be a useful addition to our scientific knowledge. For instance, some evidence suggests that the use of ‘intermediate’ phenotypes—between the genotype and the disease-based phenotype—may improve disease prediction14. For example, a 2021 study showed that the integration of polygenic risk scores for both disease-associated biomarkers and polygenic risk scores for the disease itself showed enhanced prediction over the polygenic risk score for the disease exclusively14. Second, almost all SNVs for binary traits with an OR > / = 1.2 were replicated, whereas the majority of SNVs with an OR below 1.2 were not replicated and this may reflect lack of power in the replication dataset. Of note, many of the replication UKBB datasets that we considered here did not use the full UKBB data, and power is likely to improve as complete biobank data are used and many biobanks are combined.On the one hand, it is encouraging that much scientific progress has been accomplished with current binary GWAS. For instance, polygenic risk scores based on current binary GWAS have been shown to accurately predict complex, common phenotypes8. It is, however, likely that more GWAS are available, but they contain overlapping samples between GWAS (i.e. two GWAS of the same phenotype are not truly independent as they contain similar cohorts of participants), aren’t of sufficient quality to be included in the GWAS Atlas, are conducted in a non-European population, or have not made their summary statistics available. An earlier study15 reports building a model for SNV replication using GWAS for over 50 phenotypes, although it is unclear what, if any, measures were taken to determine if these numerous GWAS were truly independent i.e. did not include overlapping participants. Also, this study validated their model in two, small GWAS of one trait. Furthermore, this study didn’t actually quantify a SNV replication rate, nor did they stratify their results by binary and quantitative phenotypes. A further limitation of our study is that we didn’t include other SNV features, ideally we would have liked to include, for instance, LD as predictors in our model. However, this data was sparsely available. Lastly, it should be acknowledged that large disease-specific consortiums generally qualitatively describe the replication of SNVs as their consortium increases. Our study quantifies this formally and, importantly, quantifies replication across more than one phenotype.We were surprised to find only nine phenotypes where two GWAS had been conducted in truly independent participants and where inclusion or not of UKBB data was a distinguishing feature. It is plausible that further independent GWAS on the same traits exist, although this seems unlikely given the thorough and systematic search we performed of the GWAS atlasWe have identified a number of future research priorities. First, improving the phenotyping of binary phenotypes seems to be a priority for GWAS. Second, to facilitate an assessment of SNV replication, future independent cohorts are likely required. Many efforts to do this are already underway (e.g. AllofUs cohort and Millions Veteran Program).The replication of SNVs discovered from GWAS was high for quantitative phenotypes. Genome-wide Association Studies appear to be entirely sufficient to detect SNVs associated with quantitative traits. For binary traits, however, the replication rate is modest. We have built a simple prediction model that can accurately ascertain SNV replication in later GWAS. It may be of use for researchers and clinicians that utilize GWAS results.Supplementary Information.


Community ecology has experienced a major transition, from a focus on patterns in taxonomic composition, to revealing the processes underlying community assembly through the analysis of species functional traits. The power of the functional trait approach is its generality, predictive capacity such as with respect to environmental change, and, through linkage of response and effect traits, the synthesis of community assembly with ecosystem function and services. Lichens are a potentially rich source of information about how traits govern community structure and function, thereby creating opportunity to better integrate lichens into ‘mainstream’ ecological studies, while lichen ecology and conservation can also benefit from using the trait approach as an investigative tool. This paper brings together a range of author perspectives to review the use of traits in lichenology, particularly with respect to European ecosystems from the Mediterranean to the Arctic-Alpine. It emphasizes the types of traits that lichenologists have used in their studies, both response and effect, the bundling of traits towards the evolution of life-history strategies, and the critical importance of scale  in functional trait ecology. Focusing on groups such as vascular plants and freshwater invertebrates ,2 the ecLichens have an important but still unfulfilled potential in completing this conceptual transition from pattern to process. For example, as the cohabitant combination of fungi and algae (and/or cyanobacteria) they lie within the realm of ‘microorganisms’ but are often of a size and longevity that is suited to practical investigation, and so, being amenable to standard ecological tools, they can open a window on species response and community assembly relevant to a wider spectrum of the Earth’s biodiversity. They are also the outcome of a complex evolutionary process involving the different symbiotic partners, and leading to a diversity of phenotypes that reflect, to varying degrees, adaptive radiation or convergent evolution, so providing the rich multivariate framework required to explore linkages between ecological fitness, environmental gradients and ecosystem function. Applying a trait-based approach to lichens has important practical benefits in conservation too; for example, it is the difference between a taxonomic list such as for lichen indicators observed to associate with ecological continuity ,13,14,15First, the trait-based approach is integrative, since traits can be explored with respect to community composition and richness, explaining the response of species to the environment, but also the effect that species have within ecosystems, bridging therefore between the classic dichotomy of ‘Grinnelian’ and ‘Eltonian’ niche models .Second, it is an approach that links evolutionary biology—the adaptation of the phenotype—with ecology because it focuses on phenotypic attributes that confer fitness differences across environmental space ; these are the outcome of both natural selection and stochastic processes that can explain species distributions, occurrence or abundance, and community structure.Third, it is scalable, since traits can be linked to acclimation if they are labile, explaining community composition and richness with respect to intraspecific trait variation, or explaining interspecific compositional turnover where environmental change  causes the declining and increasing fitness of species at the boundaries of their trait differences .If functional traits can help us explain and understand the species response to the environment , they can also, by extension, invoke consequences for ecosystem processes . The multifaceted power of this functional trait approach, as applied to lichens, is explored in this review. There are three key points that we want to emphasise:As well as bringing these points together, trait-based approaches may also offer a route through problematic application of lichen systematics to lichen ecology, in which taxonomic concepts may become difficult to apply in practice, as exemplified by a lack of discernible field characters among known species ,20,21. ATo date, the application of trait-based research to understanding lichen distributions, occurrence or abundances, and/or lichen community structure, has been demonstrably effective and this is highlighted through our selection of examples below. Nevertheless, the research groups that have been using trait-based approaches lack a common methodological approach; contrasts include the nomenclature applied to classification of different traits, through to differences in the observed relationship of traits to environment response and ecosystem function. There is still much to discover. Although certain traits are now embedded and routinely used in explaining lichen response, such as the physiological difference between green-algal chlorolichens and cyanolichens ,24, receRecognising both the significant opportunity provided by functional trait studies, and the challenges involved, and without wanting to provide overly prescriptive answers, this paper provides a review of trait-based research in lichen ecology, pointing to a series of recommendations that can move the field forwards. It is drawn from the experience of multiple authors, particularly with respect to European ecosystems from the Mediterranean to the Arctic-Alpine. It emphasises the types of traits that lichenologists have used in their studies, both response and effect, the bundling of traits towards life-history strategies, and the critical importance of scale  in functional trait ecology.Functional traits can be considered in two ways. First, they are the phenotypic attributes that explain the ecological response of a species to one or more biotic or abiotic, spatial or temporal gradients constituting the environment. As stated above, these response traits  will conSecond, functional traits may describe the effect of a species on ecosystem processes. These effect traits  are focuIn principle, the ‘trait space’ that lichens might occupy is highly dimensional, since it can combine a wide array of different phenotypic attributes that are measured to varying degrees of precision ,33. Key Trait-based studies often need to strike a balance between the effort required to measure a given trait and its explanatory power. This links to the flexible but subjective concept of ‘hard’ and ‘soft’ traits , which aFurthermore, the higher cost involved in measuring certain traits may not always contribute additional information within a hypothesis, compared to insights gained from using more easily obtained trait data. Thus, Hurtado et al. ,38,39 foAlmost all traits can be assessed either as quantitative or qualitative. For example, metabolite profiles could be considered in the form of a presence/absence matrix (relatively low cost), or concentration ranges for each metabolite could be measured and used in a quantitative form (relatively high cost). The use of presence/absence data for metabolite profiles in lichen communities is common practice e.g., ,40,41), ,41, 40,4Quantitative traits are often based on primary observations made for a particular lichen population or study area but for qualitative traits it can be common practice to combine field knowledge with information from bibliographic sources, such as original research papers, regional floras e.g., ,47), or , or 47])Again, borrowing from niche theory ,52, traiAdvances in lichen trait studies are exploring the importance of functional trait variability among individuals within a population, as well as among species. The range—or plasticity—of a given trait has consequences for acclimation that may link importantly to the species niche ,60. For Rhizocarpon geographicum aggregate )Second, it is important that statistical methods, no matter how powerful, still draw from the selection of traits that are defensibly functional, with the danger that the addition of spurious—functionally unimportant—traits into multivariate analysis could remain hidden while confounding interpretation. It is therefore important that trait analyses across various scales  remain aHypogymnia physodes [Third, conclusions about traits are robust if they stand on multiple pillars of support: (i) They are consistent with field observation, (ii) They align with the results of experimentation, such as traits that are shown to have physiological consequences, and (iii) They show consistency with previously published analytical studies. However, this should not preclude novelty. Many morphological and metabolic characters routinely used in lichen taxonomy are still poorly quantified with regard to their precise functional roles. Few ecological papers include traits such as the presence or density and length of, for example, hairs , the typphysodes . The potphysodes . These dFourth, it is established that lichens are involved in some key ecosystem processes though we know less about how these processes are affected by individual traits. We can therefore recommend screening experiments across large numbers of lichens with contrasting traits to understand their ecosystem effects ,208. Lic


The genetic basis of traits shapes and constrains how adaptation proceeds in nature; rapid adaptation can proceed using stores of polygenic standing genetic variation or hard selective sweeps, and increasing polygenicity fuels genetic redundancy, reducing gene re-use (genetic convergence). Guppy life history traits evolve rapidly and convergently among natural high- and low-predation environments in northern Trinidad. This system has been studied extensively at the phenotypic level, but little is known about the underlying genetic architecture. Here, we use four independent F2 QTL crosses to examine the genetic basis of seven  guppy life history phenotypes and discuss how these genetic architectures may facilitate or constrain rapid adaptation and convergence. We use RAD-sequencing data  from 370 male and 267 female F2 individuals. We perform linkage mapping, estimates of genome-wide and per-chromosome heritability (multi-locus associations), and QTL mapping (single-locus associations). Our results are consistent with architectures of many loci of small-effect for male age and size at maturity and female interbrood period. Male trait associations are clustered on specific chromosomes, but female interbrood period exhibits a weak genome-wide signal suggesting a potentially highly polygenic component. Offspring weight and female size at maturity are also associated with a single significant QTL each. These results suggest rapid, repeatable phenotypic evolution of guppies may be facilitated by polygenic trait architectures, but subsequent genetic redundancy may limit gene re-use across populations, in agreement with an absence of strong signatures of genetic convergence from recent analyses of wild guppies. Recent evidence that phenotypes can evolve rapidly  to be exploited  and upstream/low-predation (LP) habitats, with LP-adapted guppies evolving independently from HP sources. HP and LP sites within rivers exhibit contrasting levels of gene flow  , male size at maturity is linked to a large-effect locus, where non-signal transducing copies of Mapping large-effect loci is often achieved with quantitative trait locus (QTL) crosses or genome-wide association studies. However, these approaches can inflate the prominence of individual loci and have come under scrutiny Rockman . Indeed,Using an F2 QTL breeding cross design, we examine the genetic basis of seven life history traits in guppies: female age (1) and size (2) at first brood, first brood size (3), interbrood period (4), average dry offspring weight in the first brood (5), and male age (6) and size (7) at maturity. Our aims are to assess the relative extent to which different facets of life history have significant genetic bases, and whether guppy life history traits are better explained by polygenic, or monogenic/oligogenic models. By exploring the genetic bases of these traits, we can begin to understand the role that their genetic architecture has played in their rapid and convergent evolution in the wild.Fish were second- and third-generation laboratory-reared individuals from an HP site in the Yarra river  and an LP site in the Quare river  Fig. . These pLife history phenotyping and rearing followed Reznick ; full restep from a full additive model including family, temperature, and DOB. Relevant model assumptions were checked by comparing residuals to simulated residuals in the R package DHARMa ) and family effects on phenotypes were explored using generalised linear models (GLM) in R  and within-family structure (VG2). At the per-chromosome level, including this additional GRM prevented model convergence in some cases (11/138 chromosome-phenotype pairs), but we observed negligible differences in heritability estimated with and without this additional GRM at the whole-genome level.We used genome-wide complex trait analysis (GCTA) , we took two approaches: (1) we partitioned phenotypic variance using a model with a GRM derived from the focal chromosome and quantitative covariates; (2) we used a likelihood-ratio test (LRT) approach following Santure et al.  to a reduced model b . Quantitative covariates were included in both models. Models were compared with a LRT according to (1), with p values taken from the χ2 distribution with one degree of freedom.To estimate the heritability associated with specific chromosomes  due to issues with model convergence at low h2c under approach 2 , and allowed for analysis of all individuals together to increase biological power, where individuals could inherit an HP (H) or LP (L) allele. The second dataset comprised four separate datasets, one for each family in which family-informative SNPs were included for each family . Numbers of family-informative SNPs for each family were similar . These datasets provided increased SNP resolution within families, and allowed us to examine alleles that may have only been segregating in single crosses. These latter datasets cannot be used to assess loci that are Y-linked, because all males within a family carry the same Y, and the effect of different Y-loci among families cannot be separated from general genome-wide relatedness.scan1 function in R/qtl2  and size at maturity  of F2s varied significantly between the four cross families , and for size at maturity, cross QF4YHM8 F2s matured at a larger size. Rearing conditions affected both male phenotypes. Males matured earlier under increased temperatures  and if born later in the experiment . Larger males at maturity tended to be born later in the experiment , but the temperature did not affect size at maturity. Family status explained 10.4 and 11.7% of phenotypic variance for age and size at maturity, respectively, an effect that will not be captured by our subsequent mapping approaches. Male age and size at maturity were not strongly associated with one another , but a GLM of male size at maturity predicted by an interaction between age at maturity and family revealed a significant effect , with both positive and negative associations depending on the family.Both male age  and offspring weight  differed significantly between families . Increased temperature also reduced interbrood period  and females born later in the experiment had longer interbrood periods . Other female phenotypes were not associated with rearing conditions  was greater than the variance explained by the specific SNPs themselves (VG1). This is expected given RAD-sequencing is designed to capture SNPs in linkage with causal variants, rather than the causal variants themselves. Estimates of heritability were greatest for male size at maturity (43.4%), offspring weight (33.4%), male age at maturity (31.3%), and interbrood period (30.2%). Estimates for the remaining female life history traits were lower, not exceeding 9.7% , with standard errors that overlapped 0 (Table N = 267) and comparable statistical power   the variance explained by within-family structure . Whilst this correlation is strong, there is a clear downward biasing of p values from single-chromosome GRMs, evident as a shift away from the y=x relationship  and male size at maturity ; however, these were not significant following HC-correction. Other traits exhibited negative and non-significant correlations, and in some cases, correlations were clearly driven by one or a few chromosomes, rather than describing a wider whole-genome effect  across all 267 females. Applying a permuted 5% threshold (N = 1000), we detected two QTLs . We also observe several significant QTLs within specific families. Of these, the QTL associated with interbrood period in cross YHF5QM6 (YHF5QM6-chr12:60.71) is of particular interest given its proximity to the sex-determining region and relatively narrow confidence intervals. We therefore explored these three regions further for candidate genes.ythdc1, on scaffold 000149F_0 (000149F_0:131600). This scaffold was placed at the distal end of chromosome 12 near the sex-determining region, in agreement with other mapping studies . The chr22 QTL peak (for size at first brood) was on scaffold 000111F_0:651336 with confidence intervals extended over the scaffold (00111F_0:528180-1199617) and the distal end of chromosome 22 (chr22:23415429-24223839), covering 45 genes. The interbrood period QTL on chr12 overlapped the YTH domain containing 1 gene, Using an F2 cross design of outbred populations with divergent life history phenotypes, we have demonstrated evidence of both small-effect (polygenic) and large-effect (oligogenic/monogenic) trait architectures underlying guppy life history evolution. Both male size and age at maturity, exhibit significant heritability associated with particular chromosomes, suggesting polygenic traits, but little evidence of genome-wide polygenicity or large-effect loci. This suggests these traits are underwritten by many small-effect loci on specific chromosomes, which may be clustered together. For the five female traits, we recovered significant genome-wide heritability for interbrood period and offspring weight. For offspring weight, all per-chromosome estimates of heritability were generally weak, but a large-effect locus detected on chromosome 19 may represent a significant proportion of genome-wide heritability. For interbrood period, we detected a weak genome-wide polygenic signal as an association between chromosome size and per-chromosome heritability and found evidence of a large-effect locus on the sex chromosome, LG12, in a single family. We also detected a significant large-effect QTL associated with female size at first brood with a small effect size, but negligible estimates of genome-wide heritability for this trait. Finally, we found no evidence for heritable genetic architectures for female first brood size and age at first brood, although we observed a within-family QTL associated with first brood size on chr23.We applied genome-wide and chromosome-scale heritability analyses with QTL scans to rule out some uncertainty. For example, estimates of heritability in the absence of a QTL are most likely due to small-effect loci. Furthermore, a weak genome-wide signal of heritability coupled with detecting an individual QTL is likely due to a monogenic/oligogenic architecture. It is more difficult however at our level of sequencing resolution to distinguish between a QTL made up of individual loci of large-effect, or tightly linked clusters of small-effect loci. In terms of response to selection, however, a tightly clustered collection of small-effect loci may carry more comparable expectations to a large-effect allele than a disparate assortment of small-effect loci  in LP sites  and genome-wide heritability should therefore be treated with caution. Our combining of single-chromosome GRMs with a LRT approach however may be useful more generally to alleviate reciprocal issues of inflated p values with single-chromosome GRMs, and model convergence for chromosomes with minimal effects under the LRT approach.Whilst we detected both polygenic and large-effect architectures for life history phenotypes, our study is limited by sample size. In part, this is due to the modest brood sizes of guppies, which restricted larger F2 families, and our focus on sex-specific phenotypes. It is well known within quantitative genetics studies that small sample sizes can inflate estimates of heritability and QTL effect sizes, termed the ‘Beavis Effect’ Beavis . We thersox11a. While selection scans of HP-LP comparisons cannot determine which phenotype selection might be acting on, our results here suggest this region may be involved in female growth. We also observed a number of within-family QTLs, which most likely represent segregating variation within populations . Interestingly, each of these chromosome-phenotype pairings was also detected  by our multi-locus approaches. This suggests that these regions may be reasonably large, such that the peak  only represents a portion of the variance explained by the wider region. Neither of these regions has been strongly implicated in HP-LP adaptation in previous population genomic analyses (Fraser et al. Laupala crickets (Blankers et al. If new optima can be reached by a subset of available SGV, the absence of prominent large-effect loci observed here is expected to fuel redundancy and limit molecular convergence; allowing independent populations to use different sets of alleles to produce convergent phenotypes (Barghi et al. Trait architectures can also be informative for understanding the mechanisms driving rapid adaptation. Guppies evolve rapidly over the course of a few generations when translocated to LP environments (Reznick and Bryga Our results provide regions of the genome and candidate genes to explore further. For instance, an appreciation that much of the genetic basis of guppy life history traits may be polygenic informs experimental and sampling designs for future evolutionary studies of this system. In particular, temporal sampling and quantifying genome-wide temporal autocovariances of allele frequencies offers a promising avenue for studying the role of polygenic architectures in rapid adaptation (Buffalo and Coop Supplementary methods, results and figuresTable S1Table S2Table S3Table S4Table S5Table S6Table S7Table S8Table S9Table S10Table S11Table S12


Evidence for mediation, that perturbation of gene expression in a given tissue or developmental context will induce a change in the downstream GWAS trait, can be provided by two-sample Mendelian Randomization (MR). Here, we introduce a new statistical method, MRLocus, for Bayesian estimation of the gene-to-trait effect from eQTL and GWAS summary data for loci with evidence of allelic heterogeneity, that is, containing multiple causal variants. MRLocus makes use of a colocalization step applied to each nearly-LD-independent eQTL, followed by an MR analysis step across eQTLs. Additionally, our method involves estimation of the extent of allelic heterogeneity through a dispersion parameter, indicating variable mediation effects from each individual eQTL on the downstream trait. Our method is evaluated against other state-of-the-art methods for estimation of the gene-to-trait mediation effect, using an existing simulation framework. In simulation, MRLocus often has the highest accuracy among competing methods, and in each case provides more accurate estimation of uncertainty as assessed through interval coverage. MRLocus is then applied to five candidate causal genes for mediation of particular GWAS traits, where gene-to-trait effects are concordant with those previously reported. We find that MRLocus’s estimation of the causal effect across eQTLs within a locus provides useful information for determining how perturbation of gene expression or individual regulatory elements will affect downstream traits. The MRLocus method is implemented as an R package available at  Genome-wide association studies (GWAS) have identified many loci associated with complex traits and diseases. Expression quantitative trait loci (eQTL) may help to explain mechanisms of GWAS associations, if the gene has a role as a mediator of the trait or disease. Loci that exhibit allelic heterogeneity, that is, loci containing multiple causal variants, offer the opportunity to investigate whether effects are concordant and proportional across eQTL and GWAS; if the gene is a partial mediator of the trait, the sign and size of the effects across distinct eQTL variants should be reflected in GWAS associations. Such a Mendelian Randomization (MR) analysis of individual loci is complicated by moderate sample sizes in eQTL studies and linkage disequilibrium (LD), resulting in complex patterns of estimated effect sizes for eQTL and GWAS. We develop a statistical model, MRLocus, with two steps: selection of eQTL SNPs to act as instruments in the MR analysis of a genetic locus, and estimation of the gene-to-trait mediation effect taking instrument uncertainty into account. In simulation, the method has higher accuracy and better uncertainty measures compared to other competing methods, and we compare its estimates on candidate causal gene-trait pairs from literature. Genome-wide association studies (GWAS) have identified many loci associated with complex traits and diseases. A major goal now is to understand the mechanism by which non-coding genetic variation influences trait levels through changes in gene expression. This involves identifying the causal variants at a locus, determining if the same variants are associated with both gene expression and trait, and disambiguating mediation from pleiotropy . ProposiCurrent efforts to identify the genes underlying GWAS risk often make use of either colocalization of GWAS signal with eQTLs, or expression imputation. In colocalization, statistical models are used to probabilistically assess if the same genetic variants within a locus are likely to be causally contributing to both eQTL and GWAS signals, taking into account the structure of linkage disequilibrium (LD) for a given population –8. ExpreThough colocalization and expression imputation suggest genes involved in a trait, neither method is designed to disambiguate between pleiotropy and mediation. The latest generation of methods for determining those genes involved in mediating GWAS signal have combined the approaches of colocalization and expression imputation with statistical techniques from the field of Mendelian randomization (MR) –14, as eallelic heterogeneity, that is, having more than one independent cis-eQTL per gene, with estimates varying by tissue and study sample size , while the mean vector for the GWAS (B) study was centered on the origin, such that the true gene-to-trait slope is α = 0. These coefficients and their standard errors were provided to the slope estimation step of MRLocus, and 80% credible intervals were calculated for 400 iterations per combination of J and r2. The code for this simulation is provided in the corr_instr_sim directory of the mrlocusPaper GitHub repository.In order to assess whether trimming signal clusters to obtain pairwise reQTL simulation using—clump-p1 0.0001 (F-statistic > ~15.1), and re-ran TWMR and MRLocus. Such estimates for TWMR and MRLocus are referred to using "_p1e-4" in the Results. As PTWAS did not always produce estimates on simulated loci due to insufficient signal clusters with posterior inclusion probability (PIP) > 0.5, we additionally tested PTWAS on the A and high NeQTL simulations using signal clusters with PIP > 0.1, referred to as "_t0.1" in the Results.By producing signal clusters with PLINK clump using—clump-p1 0.001, this ensures that the index eSNP for each signal cluster has an absolute Z-score of > ~3.3, or equivalently an F-statistic > ~10.8. In order to assess whether even stronger criteria on the strength of the signal clusters provided to MRLocus would improve accuracy of the gene-to-trait effect, we re-ran PLINK clump on the main (A) simulation and the high N2g of 10% , we calculated the bias for TWMR, PTWAS, MRLocus, and eCAVIAR-MRLocus, using the sample mean of the estimates and the population-level true alpha value of (h2med / h2g)-1/2. We then re-computed the interval coverage after subtracting the bias. While these "oracle" bias-adjusted coverage values could not be obtained in real settings, they help to answer whether correction of estimation bias alone would resolve problems with insufficient coverage.Two additional assessments of the simulation datasets were performed, to better understand underlying factors that may explain differences in method performance. For MRLocus and eCAVIAR colocalization steps, the accuracy in recovering the causal eSNPs was assessed across the different simulation settings. Specifically, for signal clusters containing a true causal eSNP, the SNP chosen as the candidate instrument from each signal cluster for slope fitting was evaluated as to whether it was equal to or in high correlation (r > 0.95) with the causal eSNP. The accuracy was then computed by averaging over all signal clusters from all iterations of the simulation. Additionally, the coverage of true values by confidence or credible intervals was assessed using information about the true simulated value. As insufficient coverage could occur due to estimation bias or badly calibrated standard errors, for three simulations with hSORT1 (liver)—low-density lipoproteins (LDL), MRAS —coronary artery disease (CAD), PHACTR1 —CAD, CETP (liver)—high-density lipoproteins (HDL), and LIPC —HDL. eQTL and GWAS summary data were obtained as summarized in Table A in 2 normalized expression, according to references. GWAS summary statistics on CAD were obtained from CARDioGRAMplusC4D  plus The Coronary Artery Disease (C4D) Genetics) consortium We are sorry that we cannot be more positive about your manuscript at this stage. Please do not hesitate to contact us if you have any concerns or questions.Yours sincerely,Caroline Relton, PhDAssociate EditorPLOS GeneticsDavid BaldingSection Editor: MethodsPLOS GeneticsComments to the Authors:Reviewer's Reviewer #1: Thank you for the opportunity to review this manuscript. The authors have developed a new method to integrate eQTL data with findings from GWAS to help develop insight into the underlying biology responsible for trait-associated genetic variants. This area of research has been extremely busy in the last few years with new methods seemingly appearing every month or so. That said, I believe the MRLocus method devised by these authors is one of the better and innovative approaches in this space and am interested to apply it myself in future work. However, I do have some comments, mainly concerning choices of parameters and requests for further simulations, which I would kindly ask the authors to address before I believe it is suitable for publication.Comments:1) The authors state in the introduction that MRLocus estimates gene-to-trait effects at loci containing ‘multiple LD-independent’ eQTL. However, in both their simulations and applied analyses they apply a threshold of r2 < 0.2 (based on the 1KG ref panel). I think this is slightly misleading to the reader, as in the applied analysis of SORT1 it suggests there are 12 ‘independent’ eQTL in liver tissue. However, based on this threshold I think that these 12 variants may well be weakly correlated with each other. In a conventional MR analysis I would be very skeptical of an analysis using this threshold as weakly correlated instruments are likely to result in ‘double counting’ which can bias findings.I therefore think it is important that the authors run simulations to investigate this, using a more stringent threshold i.e. r2<0.001 to compare how their method compares to other approaches using truly independent instruments. Furthermore, I would like to see how false positive rates are affected when the r2 threshold is varied. My concern is that MRLocus may be prone to false positive findings using an r2 < 0.2, although it will be interesting to see how this compares to other methods in the field. Additionally, the instances of ‘independent’ eQTL should be changes if the authors can demonstrate that their method performs well under the default setting of r2<0.2.2) Related to my previous point, I think it should be made clear in the applied analysis how many instruments are used at each locus. Although it is available to the reader in the supplementary material, making this clear in the main text means that the reader doesn’t have to seek this information out. The authors highlight SORT1 which had n=12 instruments in their analysis, although for example MRAS only had a single eQTL instrument. Can the authors comment on whether their method provides added value when this is the case (i.e. single instrument MR) over say the eCAVIAR method which their method is built on?3) I’m also concerned by the P<0.001 threshold applied to identify eQTL as instruments. Can the authors please evaluate how a more stringent threshold influences the false positive rates of their method compared to those it is benchmarked against? In a conventional MR setting an F-stat < 10 is typically used to indicate weak instruments, which will likely be the case when eQTL have P=10-03. This issue is not highlighted in this work as the authors have selected 5 genes which have strong prior knowledge that they are involved in disease risk/trait variation. However, if readers are interested in applying MRLocus to detect novel genes responsible for GWAS signals (which should be its primary purpose I would’ve thought?) then the choice of p-value threshold will likely be important in mitigating false positive rates.In my opinion applying conventional MR instrument criteria of P<5x10-08 and r2<0.001 is not necessary for cis-QTL analyses, however I think the authors should simulate this to investigate how these parameters influence the performance of their method. Some discussion regarding this would also be welcome for readers interested in applying their approach but perhaps have not studied MR extensively.4) Although the authors have used the 1KG reference panel is their study for LD calculations and clumping, this dataset consisting of 503 European individuals which based on modern standards is severely outdated. Although I won’t ask the authors to re-run their analyses, I would ask that they mention in their discussion that their method (as with others in the field) would really benefit from larger reference panel for more accurate LD calculations. Even though they have restricted variants to MAF > 0.01, n=503 is going to be unreliable for low frequency SNPs in my experience.5) The authors do an excellent job of providing a summary of genetic colocalization & TWAS methodologies in their introduction, as well as why introducing MR to address the challenges of deciphering GWAS signals is important. This is a minor suggestion, but I felt that paragraphs 4-6 of the introduction slightly got away from the core message of this paper and may be slightly overwhelming for readers not primarily involved in this topic of research. Perhaps these paragraphs could therefore be streamline, focusing on the methods which are used to benchmark MRLocus, rather than the plethora of other approaches in this very busy area of research.Reviewer #2: The authors present a new approach to summary statistics-based causal inference tailored to gene expression-to-trait settings, which includes a preprocessing step of colocalization analysis. They have shown across a wide range of simulation settings that their newly proposed method has lower error, less bias and better coverage of the confidence interval than state-of-the-art competing methods. They also apply their method to real data and replicate well-established causal links between certain expression levels and complex traits. While the method seems solid and the simulation results are promising, I suspect that some of the modelling (and simulation) assumptions are unrealistic and may give an unfair advantage to MRclust. The real data application could be more thorough, but it is acceptable for a mainly method paper. Below I list my comments and questions for the authors that may improve the m/s.Major comments:It would be clearer if the authors stated the exact mathematical model (in equations) for the simulation process instead of referring to another publication and software (twas_sim). It is not clear for example how much horizontal pleiotropy was added to the signals (i.e. violation of the MR assumption)?I feel there is a slight confusion between two concepts: expression mediated heritability [A] (which is the fraction of trait heritability mediated by gene expression) vs mediated trait variance explained [B] (as far as I understand from the authors’ definition: the squared standardized (SD/SD) causal effect). For me the relationship between them is A = h2-expression x B, do I understand well? Would be great if the terminology could be clarified in the paper.While I see the difference between the colocalization step of MRlocus and eCAVIAR, I’m not sure how different results they would give. (Z-scores can be easily transformed back to effect sizes.) Have the authors compared head-to-head their approach to eCAVIAR when applied to the simulated data set to show superior performance?“For all simulations, if there were no SNPs in the simulated locus with eQTL un-adjusted p-value < 0.001 then a new seed was drawn.” – This leads to Winner’s curse bias, since you only use summary statistics that (by chance) pass the significance threshold, i.e. their effects will be overestimated and hence lead to an underestimation of the causal effect.Low coverage can be a consequence of two issues: (unaccounted) bias and/or badly calibrated SE. It would be helpful if the authors could explore what is the main reason for low coverage of all methods. To me it stems mostly from bias – can the authors show how methods compare in terms of bias?Fig 2A shows that MRlocus outperforms the oracle  both in terms of RMAE/MAE. The authors argue that it is due to the re-estimation of the effects using colocalization. This however would only work if there is no pleiotropy present at all. We know from real data, that there is almost always pleiotropy present, so simulation setting must be extended to more realistic situations.  In addition: it seems to me that in the simulations there were no trait-only effects simulated, which is again a very important omission. Gene->trait causal effects do not mean that all trait-associated SNP at the locus must be expression associated, traits can have additional genetic components. Adding this more realistic setting would show the weakness of MRlocus, because it would artificially pull up the effect of those SNPs on expression. Both these situations should be incorporated into the simulations, otherwise the settings are too artificial and unrealistic.While it is reassuring to see that previous findings are confirmed by MRlocus, but would be nice to see examples of gene-trait associations missed by other methods and only picked up by MRlocus or potentially spurious causal effects (by TWMR or PTWAS) disproved by MRclust.Since the authors point out the importance of allelic heterogeneity, larger eQTL data sets, such as the eQTL-Gen summary statistics  would be more ideal to demonstrate the advantages of their method. Have the authors tried MRclust on such data?I’d move quite some part of the supplementary methods  to the main text Methods – especially given that PLoS Gen has no strict page limit.Minor comments:“the original TWMR paper performed conditional analyses” – TWMR performs approximate conditional analysis, which is designed for summary statistics.“We therefore considered even lower heritability of trait on gene expression of 0.5% and 0.1%” – Please rephrase this sentence, it is currently not understandable, how a trait can have a heritability on expression?Fig 4B vertical whiskers are missing to indicate SE.**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: Yes**********what does this mean?). 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To do this, go to ‘Update my Information’ (in the upper left-hand corner of the main menu), and click on the Fetch/Validate link next to the ORCID field.  This will take you to the ORCID site and allow you to create a new iD or authenticate a pre-existing iD in Editorial Manager.In the meantime, please log into Editorial Manager at If you have a press-related query, or would like to know about making your underlying data available , please see the end of this email. If your institution or institutions have a press office, please notify them about your upcoming article at this point, to enable them to help maximise its impact. Inform journal staff as soon as possible if you are preparing a press release for your article and need a publication date.Thank you again for supporting open-access publishing; we are looking forward to publishing your work in PLOS Genetics!Yours sincerely,Caroline Relton, PhDAssociate EditorPLOS GeneticsDavid BaldingSection Editor: MethodsPLOS Geneticswww.plosgenetics.orgTwitter: @PLOSGenetics----------------------------------------------------Comments from the reviewers (if applicable):Reviewer's Responses to QuestionsComments to the Authors:Please note here if the review is uploaded as an attachment.Reviewer #1: Thank you for addressing my comments and congratulations on an excellent study.Reviewer #2: The authors have done an excellent job addressing my comments. Only a few minor ones I’d like to flag up:1. “βjeQTL ~ N^{-1/2} ).” – I’m not sure why the per SNP variance needs to be raised to the power -1/2?2. “ygene = Z βeQTL + ε,” Define epsilon in the equations, not only buried in the text. Otherwise the reader doesn’t understand why you introduced s_{err}^2.3. Please provide the exact equation for y_trait instead (or at least on top) of the ambiguous description in the text.4. The figures are of very poor resolution, pls change.**********Have all data underlying the figures and results presented in the manuscript been provided?PLOS Geneticsdata availability policy, and numerical data that underlies graphs or summary statistics should be provided in spreadsheet form as supporting information.Large-scale datasets should be made available via a public repository as described in the Reviewer #1: YesReviewer #2: Yes**********what does this mean?). 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PLOS Genetics may also choose to issue a press release for your article. If there's anything the journal should know or you'd like more information, please get in touch via  7 Apr 2021PGENETICS-D-20-01297R1 MRLocus: identifying causal genes mediating a trait through Bayesian estimation of allelic heterogeneity Dear Dr Love, We are pleased to inform you that your manuscript entitled "MRLocus: identifying causal genes mediating a trait through Bayesian estimation of allelic heterogeneity" has been formally accepted for publication in PLOS Genetics! Your manuscript is now with our production department and you will be notified of the publication date in due course.The corresponding author will soon be receiving a typeset proof for review, to ensure errors have not been introduced during production. Please review the PDF proof of your manuscript carefully, as this is the last chance to correct any errors. 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P = 0.042), and APV is 0.73 years later in European compared with Mapuche adolescents (P = 0.023). Further, by performing a GWAS on 774, 433 single-nucleotide polymorphisms, we identified a genetic signal harboring 3 linked variants significantly associated with PV in boys  have identified hundreds of variants involved in traits that result from body growth, like adult height. However, they do not capture many genetic loci involved in growth changes over distinct growth phases. Further, such GWAS have been mostly performed in Europeans, but it is unknown how these findings relate to other continental populations. In this study, we analyzed the genetic basis of three pubertal traits; namely, peak height velocity (PV), age at PV (APV) and height at APV (HAPV). We analyzed a cohort of 904 admixed Chilean children and adolescents with European and Mapuche Native American ancestries. Height was measured on roughly a The online version supplementary material available at 10.1007/s00439-021-02290-3. Puberty is a complex developmental process characterized by distinct as well as shared phenotypes in males and females. For instance, while in boys voice breaking represents a developmental milestone, in females distinct pubertal markers are menarche, namely the onset of the first menstrual bleed . This is also true for the age at PV , age at menarche (12.0 vs. 12.6 years) and the age at attainment of adult height (16.5 vs. 17.1 years)  have been key in identifying genetic variation involved in traits that result from body growth, such as adult height, which is highly heritable and polygenic, involving The Chilean population consists of admixed individuals whose continental ancestry comes from Europe . Indeed, not accounting for Mapuche and Aymara sub-ancestries has shown to markedly underestimate associations with disease phenotypes, as compared to when these sub-ancestries are combined together . Figure To our knowledge, neither comparisons in PV, APV and HAPV between European and Native American children, nor comparisons in pubertal growth between Mapuche and Aymara children have been formally tested. Therefore, we decided to account for the effect of European ancestry as well as Native-American sub-ancestries in the GWAS linear regressions for PV, APV and HAPV. Hence, we performed a global ancestry inference with ADMIXTURE  esv3624175 . In the analysis in boys, we found 2 variant alleles, rs148840332, located in the RP11-184E9.1 lincRNA gene, was associated with APV at PP <10We did not find significant associations for APV. However, one variant, rs75297609 and rs57205007. We used the Trans-Omics for Precision Medicine (TOPMed) server  for APV and − 4.3 cm (P = 0.04) for HAPV in boys and girls combined . In the regression model, we measured the effect of Native American local ancestry and also the interaction term between genotype and Native American local ancestry (see Methods). The variant allele with the strongest genome-wide association with PV for the interaction term between genotype and Native American local ancestry was mentclass2pt{minimmentclass2pt{minimIn this study, we aimed to better understand the genetic architecture of pubertal growth. We conducted GWAS on PV, APV and HAPV. The two former traits are critical antropometric markers of pubertal growth  LCOR gene, namely, rs113497890-G—also on chromosome 10—reaching a P value very close to genome-wide significance  axis that triggers puberty   versus height, where i , age at peak height velocity (APV) and height at the age of peak velocity (HAPV) using the function getapv , and j. ph represents the phenotype that can take on the three phenotypes that we consider  and the subscript i stands for measurements at individual i. Note that the genetic association of SNP j on female children is given by j: (i) For each of the three phenotypes we performed genome-wide associations by implementing linear regression models. The model included boys and girls together. We adjusted for gender, Native American local ancestry at each SNP, global ancestry for each individual and the genotype for each SNP. Global ancestry refers to the proportion of global Mapuche Native American ancestry and local ancestry was measured for each child at each SNP, and it consists of an estimate of the number of alleles that originate from Native America. It takes values 0, 1 or 2. We also included in the model an interaction effect between genotype and local ancestry and an interaction effect between genotype and gender. The linear regression equation for the model was the following:To test associations between imputed SNPs and PV, we implemented a regression model similar to the aforementioned model, but we excluded the effect of Native American local ancestry. The linear regression equation for the model was the following:PVariant annotations corresponding to the GRCh37 (hg19) assembly were retrieved with the web tool Variant Effect Predictor (VEP) from Ensembl Supplementary material 2 (pdf 623 KB)Below is the link to the electronic supplementary material.


Heritability is a central measure in genetics quantifying how much of the variability observed in a trait is attributable to genetic differences. Existing methods for estimating heritability are most often based on random-effect models, typically for computational reasons. The alternative of using a fixed-effect model has received much more limited attention in the literature.“boosting heritability”, by combining the advantageous features of different recent methods to produce an estimate of the heritability with a high-dimensional linear model. Boosting heritability uses in particular a multiple sample splitting strategy which leads in general to a stable and accurate estimate. We use both simulated data and real antibiotic resistance data from a major human pathogen, Sptreptococcus pneumoniae, to demonstrate the attractive features of our inference strategy.In this paper, we propose a generic strategy for heritability inference, termed as Boosting is shown to offer a reliable and practically useful tool for inference about heritability. For this purpose, quantity , 2 and iCurrent studies of heritability in the literature have usually been carried out in the linear mixed-effect model framework , 4. In tSome comparisons of different methods for estimating heritability have been recently conducted, for example, in , 9–11. Hrding to  and onlyrding to . These eIn this paper, we focus on the high-dimensional linear regression model with fixed effects, where no distributional assumption on the effect sizes is made. Although limited from the computational perspective due to the extremely high-dimensional data in GWAS, high-dimensional linear regression is a natural model for GWAS in modelling the whole-genome level contributions of genetic variation. The benefit of this model over the classical univariate approach in GWAS has been demonstrated for example in , 15. TheSome two-step procedures based on high-dimensional regularized regression have been introduced in , 20 thatTo achieve more reliable results, we propose to use a multiple sample splitting procedure so that different structures in the sample are presented in both selection and estimation steps with a sufficiently high probability , 22. BasTo demonstrate our framework, we apply the procedure to bacterial GWAS for estimating the heritability of antibiotic resistant phenotypes. While there are numerous works concerning estimating heritability in human GWAS, the topic has not yet been considered widely in bacteria, for the only prominent example see . This isThe paper is structured as follows. In Section “Model and definition” we present the linear model that relates a trait with a genotype matrix, then narrow-sense heritability is defined together with some discussion regarding the fixed-effect vs. random-effect approach for estimation. In Section “Boosting heritability estimation”, we introduce our “boosting heritability” procedure. Results from a simulation study comparing the different methods as components of the framework presented in Section “Simulation studies” and the application to antibiotic resistance phenotypes are presented in Section i-th row and j-th column. For any index set x containing only the components indexed by S, and A forming by columns of A indexed by S.Notations: Here, we introduce the main notations used in the paper. The y of n samples that is modelled as a linear combination of p genetic covariates Given a phenotype/trait X are random variables. Conversely, in the majority of works in the heritability literature assume that elements of X are assumed fixed.Here we focus on the fixed effects encoded by i-th observation thaty defined asUnder the model , we haveAs we have the relationentclass1pt{minimasee e.g. ) to estiHowever, it is worth noting that as a bi-product from GWAS analysis when using a multivariate regression approach, such as the Elastic net discussed below, one would already have the estimated effect sizes corresponding to the selected covariates. Using these effect sizes to estimate the heritability would bring insight on the heritability corresponding to the selected covariates and thus clearly provide useful ways to understand the genetic architecture of a trait.p, which is usually in the order of hundreds of thousands at minimum. Assume that the true effect size In GWAS the true number of causal loci reported tend to be comparatively small compared with the number of putative genetic markers  defined , 25 as \However, when employing the random-effect assumption, most methods do not use the sparsity constraint. This leads to the target heritability being estimating is e.g. see , 26. Seve.g. see , 25, 27.As the number of biomarkers can be very large, it is natural to first apply some variable selection or variable screening methods to remove the irrelevant variables from the actual heritability estimation phase. This kind of a post-selection approach has been proposed in the literature, more specifically for the fixed-effect model , 20.The HERRA method proposed in  is basedAnother “two-stage” approach with sample-splitting has also been proposed in the paper . The datBoth these approaches clearly suffer from some limitations. Firstly, when the number of covariates is very large, it is expensive to fit a sparse regularization directly as in the “two-stage” approach described above. Using a screening method, as in HERRA, to reduce the dimension of the problem is thus a pragmatic approach for applications. However, as the true number of causal biomarkers is not known, as well as their LD structure is not given, reducing the number of variables below the sample size (as in HERRA) introduces another problem from the practical perspective. Secondly, it is clear that both of these approaches crucially depend on the particular sample splitting employed. One can avoid this dependence by performing the sample splitting and inference procedure many times (e.g. 100 times) and aggregating the corresponding results , 22. ThiThe idea of aggregating different estimates to yield an estimate with improved statistical properties is the central feature of the generic boosting approach widely used in machine learning, such as AdaBoost . The mulWe propose a strategy that uses multiple sample splitting to estimate heritability, called Boosting heritability detailed in Algorithm 1.Step 0) is a screening step that can use a simple measure of association, such as the sample correlation, to remove covariates that are only weakly correlated with the trait of interest. This step is similar to the one used in HERRA [It is noted that the initial step  for variable selection in the setting where B repetitions can be easily implemented in parallel. When the trait of interest is dichotomous, one can use the Robertson transformation [We note that the main cost for Boosting Heritability procedure is fitting a penalized regression :h2aprx, that is calculated through the formula , HERRA and the boosting versions of HERRA denoted by “B_herra” and GCTA method. More specifically, GCTA  is a widFrom the results in Table Elastic net underestimates the target, which can be explained by the downward bias known to influence the naive plug-in lasso-type approaches, such as the Elastic net. The effect is due to shrinkage of some of the coefficients corresponding to weak effect towards zero, while such weak effects may still be significant in terms of the total genetic trait variability. However, we would like to note that estimating heritability through Elastic net provides a good lower bound for the heritability, as indicated by the results.On the other hand, HERRA and its boosting version return stable estimates. More specifically, with a proper choice of the screening step (Step 0) as in Table In our simulations, GCTA generally did not perform well, most likely due to the sample size being too small for random effects based approaches such as GCTA. We note that, for unrelated individuals and common SNPs in human studies, GCTA method is recommended with at least 3160 unrelated samples, see . In studB is a crucial factor in practice. Here we exemplify that as B increases, the resulting estimated heritabilities concentrate around their mean, see Fig. Clearly, choosing the number of data splittings We further investigate the effect of reducing the covariates by using the screening step. Different scenarios for 100 randomly selected SNPs with target heritability entclass1pt{minimaIt is revealed that using the screening step to reduce the irrelevant covariates not only reduces the dimension of the data, but can also improve the heritability estimation, in particular for the scenario of removing 60% of the covariates. This fact has also been reported before in the linear mixed model approach in , where tThe running times for default B_herra on MA data with the splitting step parallelized on 10 CPU cores was 2.335 mins. More specifically, the screening step took 5.25 secs of the total runtime. In the case of removing 60% covariates, the running time is significantly reduced to 1.319 mins. The R codes were run on Linux (Redhat 64-bit) with R version 3.6.0 .We further examine the performances of Enet, HERRA, B_herra and GCTA method when the phenotypes are instead simulated from the GCTA model. We remind that GCTA model is a random effect model that is different to the linear model  and thusThe results, Table Streptococus pneumoniae genomes from an infant cohort study conducted in a refugee camp on the Thailand–Myanmar border [To further illustrate the boosting based approach, we apply our procedure to Maela data which represent 3069 r border , 41. Afttotal heritability, since unmeasured genetic factors are likely to contribute partially to the measured phenotypic variation. We use two different types of resistance phenotypes to investigate their heritability. First we use the binary phenotype corresponding to the labels ’R’ or ’S’ (stand for ’Sensitive’ or ’Resistant’) for each bacterial isolate in the cohort. Second, we use a continuous phenotype corresponding to the inhibition zone diameters measured in the lab. These inhibition zone diameters are in practice used to defined whether a sample is sensitive or resistant to an antibiotic. It is however worthwhile noting that the transformation from inhibition zone diameters to labelling a sample ’S’ vs ’R’ is nonlinear due to the way the inhibition mechanism dynamics in the bacterial culture.The heritability of the antibiotic resistance phenotype is expected to be high, meaning that the variability stems primarily from the observed genetic differences among these bacteria and that the SNPs available for this particular species/dataset and would include majority of the underlying causal mechanisms for resistance. However, despite that the bacterial isolates are related, it cannot be concluded that the reported estimates refer to We apply Enet, HERRA, boosting version of HERRA and GCTA method  to this As a broad summary, heritabilities of these five antibiotic resistances are high, as expected, whether using binary or continuous phenotypes. However, we would like to note that the results for binary responses are on the observed scale (0/1 resistance status), as we are not able to transform them into the underlying threshold model, see . The ElaInterestingly, B_herra yields consistent results with GCTA method. However, the result for heritability of penicillin by GCTA is lower than the one from Enet method while boosting HERRA is not, see Table In this paper, we provide a general framework ’boosting heritability’ for making inference about heritability. The main ingredient of ’boosting heritability’ is a multiple sample splitting strategy. This strategy allows one to employ a variable selection step to remove irrelevant covariates that do not contribute to the variability of a trait and thus produce a reliable estimate of heritability. Moreover, by repeating sample splitting many times, this strategy makes sure that different latent structures are taken into account in both selection and estimation steps.Numerical comparisons of different methods together with our proposal for estimating heritability in linear (fixed-effect) model draw a systematic picture on the behaviour of the current approaches when focusing on an application to bacterial GWAS. The results on real data suggest that the observed variability of the five studied antibiotic resistances is mainly due to the variability in the observed genetic factors, while some unexplained variation still remains.Succeeding in improving and stabilizing HERRA , “boostiFurthermore, our boosting heritability procedure uses a simple aggregation to combine the estimates that is to use their arithmetic mean. Other types of aggregation, see e.g. , 31, cou