Prostate cancer is a polygenic disease with a large heritable component. A number of common, low-penetrance prostate cancer risk loci have been identified through GWAS. Here we apply the Bayesian multivariate variable selection algorithm JAM to fine-map 84 prostate cancer susceptibility loci, using summary data from a large European ancestry meta-analysis. We observe evidence for multiple independent signals at 12 regions and 99 risk signals overall. Only 15 original GWAS tag SNPs remain among the catalogue of candidate variants identified; the remainder are replaced by more likely candidates. Biological annotation of our credible set of variants indicates significant enrichment within promoter and enhancer elements, and transcription factor-binding sites, including AR, ERG and FOXA1. In 40 regions at least one variant is colocalised with an eQTL in prostate cancer tissue. The refined set of candidate variants substantially increase the proportion of familial relative risk explained by these known susceptibility regions, which highlights the importance of fine-mapping studies and has implications for clinical risk profiling. Prostate cancer (PrCa) involves a large heritable genetic component. Here, the authors perform multivariate fine-mapping of known PrCa GWAS loci, identifying variants enriched for biological function, explaining more familial relative risk, and with potential application in clinical risk profiling. BRCA2 and ATM)2. By comparison, genome-wide association studies (GWAS) have reported >100 low-penetrance PrCa risk signals with small odds ratios (ORs)3. Individually, these GWAS loci only modestly influence risk. However, because the risk alleles are relatively common within the general population their cumulative impact is substantial.Prostate cancer (PrCa) is the most common cancer among males in developed countries. As there is evidence for a large heritable component for PrCa, the identification of genetic variation that increases susceptibility may help to inform screening strategies and clinical management of patients in the future. Currently, only a handful of rare genetic variants with larger effect sizes have been reported that increase the risk of PrCa  of PrCa compared with the original GWAS tags.When an initial GWAS identifies a susceptibility locus, any one (or more) of a large number of variants within the region may underlie the molecular mechanism that modulates risk. This includes correlated variants in linkage disequilibrium (LD) that may capture the same association signal and additional variants with independent associations. Genotyping a denser set of variants in the region facilitates characterisation of the underlying genetic architecture and makes subsequent imputation more precise and complete. Although forward stepwise selection is frequently used for fine-mapping, it has severe limitations, particularly the way LD can lead to misleading results. In this manuscript, we report the findings of a PrCa fine-mapping study in a European ancestry meta-analysis sample set that is the largest to date and utilise the well-established stochastic search and model selection framework, which more accurately represents the uncertainty in determining both the number of signals and the set of single-nucleotide polymorphisms (SNPs) that best describe the association in each region8; due to their complexity, two regions (Chr8q24 and Chr6p21/MHC) were excluded and are subject to separate studies. Some regions contained more than one signal due to close proximity between the reported index SNPs. Summary results from the large European ancestry meta-analysis comprising 82,591 PrCa cases and 61,213 controls from eight GWAS sub-cohorts , imputed to the 1000 Genomes phase 3 reference panel, were used for our fine-mapping analysis.In this study, we examined 92 PrCa GWAS risk associations within 85 distinct genomic regions reported prior to the recent meta-analysis using the OncoArray experimentP-value <5 × 10−8). Five regions had not replicated and were excluded from downstream fine-mapping analyses accordingly  and has low minor allele frequency (MAF), but the signal is also detectable through a cluster of more common variants as a ‘synthetic association’10.We first assessed whether all 92 original associations had replicated with at least one variant in the region at a genome-wide significant level , one failed quality control (QC) due to strongly discordant MAF between individual sub-studies within the meta-analysis (rs6625711) and is also reported as having extremely discordant MAF between 1000 Genomes phase 1 and phase 3 cohorts (MAF in EUR 0.45 vs. 0.16), one was associated with young-onset disease only (rs636291), one only for aggressive PrCa (rs1571801) and the final three were reported in populations of Chinese (rs103294), Japanese (rs2055109) or African (rs7210100) ancestry and had not been confirmed in Europeans to date16, a novel fine-mapping framework that uses summary statistics and explores multi-SNP models while accounting for LD. JAM provides inference of two important measures; (1) the most likely number of independent risk variants in the region and (2) a 95% credible set of variants that drive these signal(s). This credible set includes all variants from regression models that cumulatively reach at least 95% posterior probability in JAM’s stochastic search. Prior to running JAM, the variants were pruned to eliminate high LD P < 5 × 10−5. From this variant set, JAM identified a catalogue of 3700 SNPs as the final 95% credible set of candidate causal variants for the 75 regions successfully fine-mapped . Prioritisation also performed well in these complex regions. In the TERT region at Chr5p15 we observed the highest number of independent signals, 5, and the credible set comprised only 30 SNPs. Similarly, 3 regions each containing 3 signals  returned a combined credible set of 61 variants representing these 9 PrCa associations. Notably, we observed that the regions found to contain multiple independent signals generally had P-values and marginal ORs towards the upper end of the distribution of original GWAS hits in the univariate meta-GWAS  and histone mark  data sets retrieved through the Cistrome Data Browser24, and expression quantitative trait loci (eQTLs) from a set of 359 PrCa samples in the Cancer Genome Atlas (TCGA).We annotated variants for indicators of putative biological functionality using data from publically available databases. Intragenic variants were ascribed to genes relative to GENCODEv19, miRNA variants using MirBasev20 and variants situated within segments of the genome under evolutionary conservation were annotated using conserved element outputs generated by four algorithms 26 at multiple quantiles . These correspond to posterior probabilities ranging from 0.01 to 0.99, with the exact values conditional on the linear combination of the annotations. At each quantile, we used the fitted model to calculate a predicted posterior probability given the SNP’s annotation features. A single expected posterior probability was then calculated from a weighted average of these quantile-specific expected posterior probabilities with the weight reflecting both the fit  and variance of the predicted values from the quantile-specific model to the data. We selected a single data set for each annotation category for the QR analysis to minimise correlation between variables. Whilst the majority of tag probabilities were not notably adjusted during QR, an appreciable subset of variants were up- or downgraded based upon their annotations   for at least one quantile  analysisP = 1.15 × 10−23); intragenic variants within protein-coding genes  but not non-coding transcripts (P = 0.29); promoter (P = 1.66 × 10−8), enhancer (P = 3.42 × 10−6) and transcribed (P = 3.07 × 10−7) ChromHMM states in prostate epithelial cells; DNaseI hypersensitivity sites from all seven ENCODE prostate data sets (P = 1.28 × 10−7 to 7.61 × 10−17); for AR (P = 2.33 × 10−15 to 2.86 × 10−20), ERG (P = 5.33 × 10−12 to 1.00 × 10−20), FOXA1 (P = 9.18 × 10−18 to 1.14 × 10−18), GABPA (P = 8.53 × 10−12), GATA2 (P = 1.24 × 10−12), HOXB13 (P = 8.25 × 10−9) and NKX3.1 (P = 9.44 × 10−5 to 1.43 × 10−15) transcription factor-binding sites from one or more experimental data set; for H3K27Ac (P = 5.34 × 10−19 to 1.39 × 10−21) and H3K4Me3 (P = 1.30 × 10−9 to 8.27 × 10−14) histone marks; and conserved elements within the human genome according to all four algorithms (P = 1.89 × 10−7 to 4.04 × 10−11). Of particular interest, in over half of the regions fine-mapped, at least one variant within our credible set intersected a significantly associated eQTL with a colocalisation score >0.9  in the TCGA PrCa data set. In all, 40 of the 75 regions contained an eQTL variant among the credible set, with 91 distinct genes represented , unlike FARP2, which is ubiquitously expressed across tissue types. Within the credible set 3 tags are selected with particularly high confidence (posterior probabilities 0.72–1); all 3 represent only themselves with no additional proxy variants to consider, and are therefore the most likely causal variants underlying the 3 signals detected. Two of these 3 candidate causal variants (rs77559646 and rs77482050) are non-synonymous SNPs in ANO7 that are uncommon among European ancestry populations, whilst the third (rs62187431) is intronic in ANO7. The 11 remaining variants in the credible set include one more missense SNP within ANO7 (rs76832527), 2 intronic variants in ANO7 (rs111770284 and rs56091437), a synonymous variant in ANO7 (rs2074840) and 7 variants that are all intronic within other genes . Our fine-mapping results therefore strongly implicate the ANO7 gene as a prospective biological effector modulating susceptibility for PrCa.At several regions our catalogue of variants highlighted putative biological mechanisms that may be responsible for the differential risk of PrCa development, as well as credible sets sufficiently small to enable subsequent laboratory follow-up. One example is the Chr2q37 region described by rs3771570 in the original publication29 presents a good example of how variant annotations can assist further prioritisation of the most likely candidate variants even within regions where the credible set remains comparatively large after fine-mapping . Only 14 of these variants demonstrate any plausible biological evidence however, therefore the credible set can be filtered to prioritise this subset of variants. Four of these are proxies of the tag with the greatest statistical evidence, including the variant that demonstrates the greatest biological evidence for functionality; the original index SNP rs339331, which resides within a DNaseI peak, intersects binding sites for multiple transcription factors, including AR, FOXA1, GATA2, HOXB13 and NKX3.1, and is situated within a conserved element. rs339331 would therefore be ranked highest for follow-up based on combined statistical information and biological annotations, and has been demonstrated to alter HOXB13 transcription factor binding and RFX6 transcription during a previous functional investigation of this region30.The region at Chr6q22 described by rs339331 in the original publicationTMPRSS2 region on Chr21q22, we detected a single PrCa risk signal with a credible set of 31 SNPs from 8 tags, all of which are situated within the promoter region or first intron of TMPRSS2  due to lack of overlap with informative biological annotations, therefore it and its proxies may not in fact represent the most likely candidate causal variants. An early and common event in prostate tumour development involves a translocation that forms a TMPRSS2:ERG fusion, bringing the ERG transcription factor under transcriptional control of the more active TMPRSS2 promoter. Our fine-mapping results and biological annotations therefore allude to the possibility that subtle, heritable differences in TMPRSS2 expression could potentially operate in conjunction with a common somatic alteration to influence development of PrCa. Intriguingly, we also observed significant enrichment for variants intersecting ERG transcription factor-binding sites among our combined credible set of candidate variants across all regions using Fisher’s exact test  of which were nominally significant at P < 0.05 in the AA meta-analysis. In addition, of the 175 variants that reached genome-wide significance within the five regions in which JAM did not resolve candidate variants, 111 were nominally significant in the AA data. We would hypothesise that variants demonstrating no evidence of association in the AA data set would generally represent less likely candidate causal variants than any nominally significant variants within their region specific credible set and should be assigned lower priority when considering variants for functional confirmation studies. This extra prioritisation step does not enable us to formally exclude any variants from our credible set however, as the AA analysis may be underpowered to detect association with PrCa at specific SNPs, and additional variants within the regions fine-mapped in Europeans but not included in our credible set were not examined for association in AA data.Since LD patterns and allele frequencies of variants frequently differ among ancestral populations, as an additional prioritisation strategy we cross-checked meta-analysis results for variants in our 95% credible set against data from a meta-analysis of 10,202 cases and 10,810 controls with African Ancestry (AA)HOXB13 rs138213197 variant, which demonstrated the greatest contribution at 6.87%, and the multi-signal TERT locus, which explained the next highest level at 2.57%. Each of the remaining regions of higher FRR contribution contained multiple independent signals, with the exception of the single-signal MSMB locus. The magnitude of increase in proportion of FRR explained by each locus after fine-mapping was also generally greater for regions where additional independent signals were identified; for example, the ANO7 region increased 6.5 fold  and the KLK region 1.9 fold (from 0.45 to 0.86%), partly due the identification of 2 novel signals within each.The proportion of FRR of PrCa explained by these risk loci before and after fine-mapping were calculated using conditional effect estimates and standard errors derived from the OncoArray sample sub-cohort. The post fine-mapping calculation was performed separately for the full set of 99 signals identified and a restricted subset of 84 variants , in order to investigate the relative importance between replacement of GWAS tag SNPs and addition of extra novel signals. Single lead variants representing the independent signals were selected for this calculation. In regions containing a single signal, the JAM tag in the credible set with the highest Bayes factor was designated as the new lead variant, or for the five regions in which JAM did not resolve candidates the most strongly associated SNP in the meta-GWAS was taken instead. Within regions containing multiple independent hits, signals were represented by the combination of tags given the greatest posterior support by JAM. Our FRR calculations use conditional risk estimates incorporating uncertainty for each variant, plus a correction for potential bias due to risk estimation in the same sample as discovery and uncertainty in the specification of the FRR. This novel but more conservative method of risk calculation estimated that: 1) inclusion of only single ‘best’ replacement variants for each tag SNP contributes 26.5%  of the known FRR of PrCa compared to 23.2% (95% CI 19.4–27.9) for the 84 previously known GWAS tag SNPs; and (2) inclusion of lead SNPs representing all of the 99 independent signals contributes 30.3% (95% CI 26.0–35.9)  stochastic model search, which allows application to very large regions and does not require a prior assumption on the maximum number of causal SNPs within each region, making it more applicable to regions with larger or unknown numbers of causal variants. Linear model-based summary data methods such as JAM represent the current state of the art and have demonstrated good performance when applied to transformed logistic ORs from binary traits as opposed to linear effects for continuous traitsTERT gene locus, which is known to contain susceptibility variants for many cancer types38. We observed no consistent pattern of LD relationship between the original GWAS tag SNPs and the independent signals identified through fine-mapping in the regions containing multiple independent signals  is not selected in the credible set and correlated with only 1 of the 3 independent signals detected . In contrast, at the TERT region, the original index SNP (rs2242652) is in moderate or modest LD (r2 0.08–0.43) with 4 of the variants selected by JAM as representative of the 5 independent signals. Previous smaller fine-mapping studies using stepwise selection approaches had also identified evidence for independent association signals within several regions. However, these are potentially more sensitive towards subjective measures such as the P-value threshold chosen for secondary signal inclusion and LD level used to define the final list of candidate variants represented by the selected marker(s). Due to our substantially larger sample size and variant density available and the well-established superiority of Bayesian search procedures over stepwise selection in high-dimensional settings, we therefore consider this the most detailed fine-mapping study to date for variant prioritisation. Comparing our results to the previous iCOGS fine-mapping study28, in which refinement of 64 GWAS loci was attempted in a smaller European ancestry cohort of 25,723 PrCa cases and 26,274 controls, 48 regions corresponding to 52 original index SNPs replicated at genome-wide significance in both studies, of which only 21 regions had been densely genotyped on the iCOGS chip (Supplementary Data TERT (Chr5p15), ANO7 (Chr2q37) and SLC22A3 (Chr6q25) loci, and identified multiple independent association signals for the first time at two further loci, including KLK3 (Chr19q13). Eight regions demonstrating evidence for multiple independent signals in the iCOGS fine-mapping study were however not corroborated in this larger study. Notably, the conditional P-values for these secondary signals in the iCOGS fine-mapping study were below genome-wide significance in all but one of these regions. This may suggest that contrary to general assumptions that a lower burden of evidence is valid for uncorrelated variants in loci for which a genome-wide significant association has previously been observed, instead equally stringent significance thresholds should be applied for both secondary signals and initial primary signals. It is also notable that in this well-powered study, the vast majority of regions containing multiple independent signals were first reported as associated with PrCa in early GWAS using relatively modest sample sizes. This may indicate that regions with lower effect sizes and weaker evidence for association, which require larger sample sizes for their detection, are less likely to contain additional independent risk variants. Alternatively however, it could reflect lower power for the detection of additional independently associated variants within the regions that contain weaker signals, despite the large sample cohort utilised in this study.Use of multivariate models prioritised a 95% credible set of 3700 candidate variants from the 203,211 variants analysed within the 75 regions in which candidate variants were resolved; thereby markedly reducing the number of variants for further consideration. In addition, previous reports of multiple independent signals at several PrCa risk loci were confirmed, with evidence for multiple signals at 12 regions; of which 7 regions contained 2 signals, 4 demonstrated evidence for 3 signals and 5 signals were observed at the Chr5p15 RFX6 (Chr6q22) region. We annotated variants against a number of publically available data sets, observing enrichment of several plausible markers of biological function active in prostate cell lines within our credible set, including intersection with prospective promoter and enhancer elements, DNaseI hypersensitivity sites, histone modification or transcription factor-binding peaks, and variants residing within protein-coding transcripts and conserved regions of the genome. Of particular interest, more than a quarter of the variants within our credible set were also eQTLs within the TCGA prostate adenocarcinoma data set. Given their statistical selection independent of this annotation and demonstrated effects upon gene expression, these eQTL variants should be considered high priority when selecting candidate causal variants for functional confirmation, alongside variants that modify the coding sequence of genes, or appear to reside within reliably annotated promoters or enhancers. Another important discovery of this study is that an appreciable number of highly ranked variants within the credible set are non-synonymous SNPs. This provides evidence that subtle alterations to structure and activity of specific proteins may give rise to the functional mechanisms behind a proportion of GWAS associations.As would be expected, refinement of putative causal risk variants varied between regions, with credible sets ranging from a single variant or handful of variants to >100 variants for a small number of regions. The regions retaining large credible set sizes appear to result primarily from large numbers of variants in high LD with the actual causal variant as opposed to low power within the region however, rendering further refinement of these signals to facilitate functional validation studies more complicated. One approach to further prioritise candidate variants could be to leverage the different LD patterns among different ancestral populations, provided that the underlying casual variants are shared and present at sufficient frequency between populations. Cross-referencing the 3700 variants within our 95% credible set with data for an African American PrCa meta-analysis from the African Ancestry Prostate Cancer GWAS Consortium highlighted a subset of 1155 variants with nominal or genome-wide significant evidence for association in this additional population. An alternative prioritisation approach is to consider pre-existing biological information, as we have described for the 42. These methods can prove useful for enhancing variant prioritisation, provided that the annotation information is reliably indicative of causal variants. We preferred to perform statistical analysis separately from annotation and compare statistical and functional evidence for causality afterwards using conditional QR. We believe this more clearly allows the most informative annotations, and the variants that are characterised by those annotations to be highlighted within the data set, whilst also reducing the potential for penalisation of strong candidate variants due to localised artefacts or cell line-specific effects within the whole-genome biological data sets used for annotation. Our conditional QR analysis resulted in adjustment of posterior probability for a small proportion of variants and may further assist prioritisation of the most likely functional variants among the credible set selected for each region.Some alternative fine-mapping algorithms integrate functional annotations during the statistical analysis when considering evidence for causality for each variant8. This highlights the invaluable importance of fine-mapping studies for risk prediction and their potential utility in helping to inform clinical screening studies.Fine-mapping studies are important to reveal information on the biological mechanisms underlying disease predisposition by pinpointing potential candidate genes, signalling pathways and networks that account for differences in disease risk between individuals. In addition, these studies may help to refine the contribution of GWAS loci to PrCa risk by incorporating more likely candidate variants. This study evaluated almost all previously reported PrCa GWAS regions, apart from the highly complex Chr8q24 and major histocompatibility complex (MHC) regions and associations that did not replicate in the largest European meta-analysis to date. We then subsequently re-evaluated the contribution to FRR of these known PrCa risk loci using an enhanced method in which the overall FRR of PrCa was revised upwards from 2.0 to 2.5 to reflect the most recent estimates and we also accounted for uncertainty of various estimates that can introduce bias in these calculations. Our approach therefore provides more conservative estimates than in previous publications. We demonstrated a substantial increase in the proportion of FRR explained through fine-mapping these GWAS regions (from 23.2 to 30.3%), with detailed investigation showing that a similar proportion of this enhancement was conferred by replacement of the original tag SNPs and discovery of secondary signals. It is also noteworthy that the 7.1% magnitude of increase in FRR explained after fine-mapping known loci is substantially greater than the 4.4% increase achieved through identification of 62 novel PrCa lociFine-mapping of GWAS loci requires comprehensive examination of variation within the region. Logistical constraints generally preclude resequencing of disease-associated loci to achieve complete variant coverage in large sample cohorts and instead mandate the use of genotype array data followed by imputation, in order to achieve sufficient sample sizes. To ensure the accuracy of downstream fine-mapping analyses, stringent variant QC must be applied to imputed data, to exclude low-quality variants that may be indicative of imputation artefacts. In this study, initial pre-imputation QC of the meta-analysis data set was first performed to exclude potential genotyping errors, followed by post-imputation QC in which variants with low MAF or imputation information score, or divergent MAF consistency between dosage and ‘best guess’-derived MAF estimates were excluded. The MAF estimate consistency check was performed to highlight additional variants for which reliability of imputation may be reduced and evaluation of variants excluded in this step revealed that the majority were situated within segments of the genome flagged as repetitive or otherwise ambiguous. Whilst we cannot guarantee that no causal variants at GWAS loci would be located within repetitive elements, we believe that the high proportion of variants filtered during QC that are located within potentially difficult to impute segments indicates an appropriate balance between controlling against both type I and II errors during the subsequent fine-mapping analyses. The inability to directly interrogate this category of variants during this study could however reflect a potential limitation.The multivariate fine-mapping strategy we employed enabled identification of small numbers of prospective causal variants amenable to functional follow-up at many known PrCa susceptibility regions. Within this credible set of variants, we found evidence of enrichment for a number of biologically plausible mechanisms through which PrCa risk could potentially be modulated. We observed multiple independent PrCa associations at 15% of the loci fine-mapped, and several candidate genes were indicated for consideration through functional annotation. As rare variants with MAF < 0.005 were not included in our analyses, we cannot exclude a contribution of rare casual variants exerting a greater effect size giving rise to synthetic associations at any GWAS loci, although our findings indicate that these are unlikely to be widespread. Importantly, replacement of the original GWAS tag SNPs with more likely candidate variants and identification of additional independent signals resulted in a substantial increase in the proportion of the FRR of PrCa explained by these loci. This finding accounts for a portion of the ‘missing heritability’ of PrCa and has important implications for clinical risk profiling and management of patients.12. Six of these lead variants were located within the Chr8q24 region that is associated with multiple cancer types in a highly complex manner, and three within the MHC Chr6p21 region. Due to the large numbers of variants, high levels of correlation and greater complexity within these regions, they are the subject of separate fine-mapping and risk stratification studies and were excluded from consideration in this analysis; the remaining 92 previously reported GWAS SNPs were selected for fine-mapping in this study. For 5 of these originally reported GWAS SNPs, no variant within ±500 kb replicated at genome-wide significance in our larger European meta-analysis and these loci were subsequently excluded from downstream Bayesian analyses and FRR calculations. An additional 2 GWAS SNPs originally reported in non-European ancestral populations and 1 reported in a previous meta-analysis did not replicate, but were situated <500 kb from an independent, replicated European risk association and were therefore still considered within the region boundaries of signals that were fine-mapped.We identified 101 independent PrCa GWAS risk associations within the literature that had been reported at genome-wide significance prior to the start of this study, the majority of which had previously been replicated within a European ancestry population43 were densely genotyped within the OncoArray sample cohort. Region boundaries for dense genotyping were defined as the greater of ±500 kb from the index SNPs or the maximum distance of any variant with r2 > 0.3 to the index SNP in 1KG . All SNPs within these regions with MAF > 0.01 in any ancestral population were extracted and then we obtained Illumina Design Scores for all variants from the 1000 Genomes Project . From designable variants with a Design Score ≥ 0.8, we used Snagger44 to select (a) all variants correlated with the known hits at r2 > 0.6 and P < 0.05 in the iCOGS study, (b) all variants from lists of potentially functional variants, defined through ENCODE and RegulomeDB and (c) a set of SNPs to tag all remaining variants at r2 > 0.9. The 23 risk loci reported in a recent multi-ethnic meta-analysis study12 were not densely genotyped as these loci were reported after the OncoArray design; however, these regions were also fine-mapped in this study.A total of 78 PrCa risk associations that had been reported prior to the design of the OncoArray genotyping platform8. Per-allele ORs and standard errors were generated for the OncoArray and each GWAS, adjusting for principal components (PCs) and study relevant covariates using logistic regression. The OncoArray and iCOGS analyses were additionally stratified by country and study, respectively. We used the first seven PCs for OncoArray and first eight PCs for iCOGS samples, as additional components did not further reduce inflation in the test statistics. OR estimates were derived using either SNPTEST (https://mathgen.stats.ox.ac.uk/genetics_software/snptest/snptest.html) or an in-house software C++ programme. OR estimates and standard errors were combined by a fixed effects inverse variance meta-analysis using METAL45. All statistical tests conducted were two-sided.Genotype data for a combined 82,591 PrCa cases and 61,213 controls of European ancestry from eight GWAS  were used for the meta-analysisr2 > 0.3 to the index SNP in 1KG phase 1 from the originally reported GWAS index SNP in the meta-analysis cohort. For the OncoArray data, un-phased imputation was carried out for all the fine-mapping regions. Where the boundaries of adjacent associations to fine-map overlapped, these were merged for imputation; therefore, imputation was performed as 82 discrete chunks. Within 3 of these chunks the separate signals to analyse were sufficiently dispersed to enable clear demarcation of the individual signals and retention of an appropriate flank distance; these 3 imputation chunks were therefore split prior to statistical analysis and the 92 original index SNPs analysed were fine-mapped as 85 separate regions.IMPUTE2 was used to impute non-genotyped SNPs within a boundary flank of ±500 kb or the maximum distance of any variant with We conducted a two-stage post-imputation QC process. During basic QC, imputed genotype data were filtered to retain variants with INFO ≥ 0.4 and MAF ≥ 0.005. We subsequently instituted an additional QC measure to remove imputed variants with greater genotype uncertainty in which separate MAFs were calculated based on ‘dosage’ and ‘best guess’ genotypes. Large deviations between these MAF estimates for a variant would indicate unreliable imputation performance; variants for which these differed by ≥10% were excluded from analysis. An additional benefit of this methodology is that inherently applies progressively greater stringency of QC filtering the rarer a variant is within the study population. During the post-imputation QC process, 288,033 rare variants were excluded, whilst a further 146,088 variants were removed due to low INFO score or divergent MAF consistency. This resulted in a final post-QC set for analysis of 213,728 SNPs within the 80 fine-map regions that had replicated in the initial meta-GWAS, with a minimum variant INFO score within the final data set of 0.63, and the vast majority of variants having INFO > 0.9  in 1000 Genomes European samples that were retained or excluded during our QC procedure. In total, 186,907 of 227,793 common 1000 Genomes European variants (82.1%) were included in our final post-QC data set for analysis. The vast majority of common variants excluded during QC, 37,830, were removed in the MAF consistency check step. In all, 27,070 (71.5%) of these were situated within segments of the genome flagged as repetitive or otherwise ambiguous , whilst a further 4460 (11.8%) had intermediate INFO score values (0.4–0.8).16 is a novel Bayesian algorithm that searches multi-SNP models in summary data by imputing the correlation structure according to a reference panel. JAM provides inference on the number of independent signals, as well as the set of potential SNPs driving those signals. Under a standard multivariate linear regression, the vector of trait values y are regressed on a matrix of genotypes, X, under the following modelσ2 represents the residual variance, β represents a vector of effects, which are all adjusted for one another, and IN is the N × N identity matrix. Multiplying the standard model above through by the transpose of the genotype matrix, JAM makes inference under the resulting multivariate normal (MVN) model:JAMX′y can be derived from one-at-a-time univariate effect estimates of each variant47 and X′X from an estimate of the genetic correlation matrix. Note that in the case of the PrCa summary statistics, we derive X′y after first mapping the univariate log ORs to approximate linear effects via their z-scores, a strategy adopted for binary traits in other linear model-based summary statistic frameworks48. Consequently, the model residuals have the same interpretation as in a linear regression of a binary outcome; they cannot exceed 1 and, under the null model, their variance σ2 equals the trait variance, p(1 − p) where p is the proportion of cases. Since each region is unlikely to explain much heritability individually, we specify an inverse gamma (Γ−1) prior that loosely targets the PrCa variance in the meta-GWAS:σ2 equal to the PrCa variance in the meta-GWAS, 0.24, and 95% weight over the range . The JAM model is completed by specifying a so-called ‘g-prior’ over the genetic effects, β:The motivation for using the model in  rather tX′X, and has been shown to help when modelling highly correlated predictors49. There is a substantial literature on choices for the hyper-parameter, τ; we follow recommendations to set a value equal to the maximum of N and P2, where P is the number of variants in the region51.The conjugate g-prior supports effects inversely proportional to the corresponding genetic co-variances and variances, as estimated from the reference matrix β; JAM is therefore able to approximate inference from a multivariate analysis of individual-level data. Optimal performance is achieved when the correlation structure X′X is taken from the original GWAS population, rather than an external reference population. We applied JAM to summary statistics from the meta-analysis data set using LD estimated according to imputed individual-level data from the OncoArray sub-cohort of 53,449 cases and 36,225 controls in which these regions had been densely genotyped.Crucially, both  and 2)  2) are pγ, for whether each variant should be included . Any specific configuration of indicators then specifies a specific model, M. Using a Bayesian stochastic search, specifically a Reversible Jump MCMC (RJMCMC) algorithm52, JAM searches over different possible models. By specifying a prior on the probability of including any combination of variants, we induce a prior over the ‘model space’, γ. More formally, JAM’s prior over γ induces sparsity and accounts for the multiple testing burden through use of a ‘beta-binomial’ prior on the number of associated variants or variants included in any given model, which consists of a Beta distribution over the proportion of associated variants in a particular region, conditional on which prior probabilities for each possible number of associated variants follow a binomial distribution. All configurations or combinations, including the same number of variants are given identical prior probabilities. For each region we used a beta-binomial  prior, where Pr is the total number of variants in a region r. This places a constant prior probability for any effect in each region  of 0.5, which is split up over all possible models according to the beta-binomial distribution. Since these are previously discovered regions, this is far more generous than our prior belief would be that a random region of the genome is associated with PrCa but is more conservative for the regions in this analysis, where we estimate the false discovery rate is <10%. The marginal prior odds of any particular SNP being selected is 1/Pr, and decreases with the total number of variants in the region, providing an intrinsic multiplicity correction as a function of region size56. The prior probabilities for ≥2, or ≥3 associated variants and so on are weakly effected by Pr, however, for all regions in this analysis they are equal to the second decimal place at 0.25 and 0.12, respectively , and for each combination of variants, Pr(M = 1|data). To determine statistical significance for individual variants, combinations of variants and for the possible number of independent signals we use Bayes factors57, the ratio of the posterior odds to the prior odds. Specifically, we used the inference of the minimum number of independent signals in the model at a regional Bayes factor threshold of 3 to define the evidence for multiple signals.Similar to other Bayesian stochastic variable selection approaches, JAM models a latent vector of binary indicators, http://prioritypruner.sourceforge.net) was used to LD prune the imputed meta-analysis variant set at a threshold of r2 = 0.9 for the 80 regions replicated at genome-wide significance. Pruning was performed agnostic of additional prioritisation criteria (association or annotation data) to ensure unbiased Bayesian model selection. Additional pruning at lower LD levels was performed upon any regions in which the overall Bayes factor for association with PrCa fell below 1. A regional Bayes factor below 1 directly conflicts with our knowledge that these regions are robustly associated with PrCa, and was taken as an indication of collinearity; numerical instability that can occur when fitting multivariate models to highly correlated variables. Where required, the pruning threshold was lowered in r2 = 0.05 increments, to a cut-off level of r2 = 0.6. The pruned data set used in the final Bayesian analyses comprised a total of 38,745 selected tags.Before running JAM, Priority Pruner v0.1.3 (M = 1|data) that summed to a cumulative posterior probability of 0.95, were used to define a run specific 95% credible set. To filter out any low confidence variants, final 95% credible sets for each region were defined according to the intersection between two independent runs of JAM, with any variants with variant-specific BF < 1 additionally removed from the amalgamated variant list due to having greater standalone evidence against association. Overall, 3761 of the 4142 unique SNPs selected by either JAM run were retained in the combined top models from both runs (90.8%), with a further 61 variants with BF < 1 removed to achieve the final 95% credible set.The pruning thresholds used in the final results are listed in Tables Variants were annotated for a number of putative indicators of biological functionality or importance, using a range of publically available data sources. These annotations focussed on either the likely consequence or relevance of the variant resulting from its primary genomic context, or the proximity to annotated regulatory features within cell lines derived from normal prostate or PrCa tissues.58. Variants residing within miRNA transcripts were subsequently added in relation to miRBase release 20 (ftp://mirbase.org/pub/mirbase/20/genomes/hsa.gff3)59. Annotation of variants that reside within genomic elements demonstrating evidence for evolutionary constraint was performed against conserved element peak outputs from comparative genomics analyses by four algorithms; GERP++ (http://mendel.stanford.edu/SidowLab/downloads/gerp/)20, SiPhy_Omega, SiPhy_Pi 21 and PhastCons (ftp://hgdownload.cse.ucsc.edu/goldenPath/hg19/phastCons100way/)22. Variants were also scored for likelihood of prospective pathogenicity using CADDv1.3 (http://cadd.gs.washington.edu/score)60.Gene-based annotation of variants was performed using wANNOVAR in relation to GENCODEv19 transcripts62. Peak data from ChIP-seq experiments for transcription factor-binding sites and histone modifications in the LNCaP, PC3, PrEC and VCaP cell lines and human prostate tumour tissue was downloaded from the Cistrome Data Browser (http://cistrome.org/db/); a resource that accumulates publically available ChIP-seq data sets and re-analyses their raw data through a standardised pipeline and QC procedure24. Downloaded CistromeDB data were converted from GRCh38 to GRCh37/hg19 reference assembly co-ordinates for compatibility with our variant data set using the UCSC Genome Browser LiftOver tool (https://genome.ucsc.edu/cgi-bin/hgLiftOver). Transcription factor-binding site data were obtained for the Androgen Receptor , CTCF (GSM1006874 and GSM1383877), ERG (GSM1193657 and GSM1328978), FOXA1 , GABPA (GSM1193660), GATA2 (GSM1600544), HOXB13 (GSM1716763 and GSM1716764) and NKX3.1 (GSM699633 and GSM989640). Histone modification data were obtained for H3K27Ac (GSM1249447 and GSM1249448), H3K27me3 (GSM1383866 and GSM1383872) and H3K4me3 (GSM1383874 and GSM945240). Finally, to facilitate deeper categorisation of the genomic context of variants within prospective regulatory features, they were annotated with their chromatin state categorisations by ChromHMM from two prostate cell lines , alongside three ENCODE tier 1&2 cell lines  to enable comparison of tissue specificity for prospective regulatory elements64.For annotation against prospective regulatory elements within the genome, which frequently operate in a tissue-specific context, these data sets were primarily retrieved from experiments using prostate-derived cell lines. We annotated variants that intersected DNaseI peaks data in seven individual ENCODE prostate data sets from three cell lines https://gdc-portal.nci.nih.gov). For the genotype data set, QC was performed according to the protocol suggested by Anderson et al.65, removing samples with heterozygosity >2 standard deviations from the mean, individuals with low genotype call rate (<95%), non-male samples and related or duplicated samples . Variants with call rate <95% were also excluded from analysis. PC analysis was performed to induce the ancestry of the TCGA samples, using the 494 TCGA samples plus 2504 samples from the 1000 Genomes Project phase 3, with non-European or Finnish samples removed from the analysis. In total, 108 samples and 106 SNPs were removed after performing QC on genotype data. For the expression data set, we observed that samples from two plates (A31K and A30D) exhibited values substantially higher than samples on the remainder of plates, therefore samples on these plates were also excluded . Out of the 494 samples, 359 therefore passed QC. Genotypes for samples passing QC were subsequently imputed to the 1000 Genomes Project phase 3 reference panel within the region boundaries applied to the fine-mapping data set using IMPUTE2. In all, 227,773 variants within the fine-mapping data set passed QC thresholds in the TCGA imputed data and therefore were available for eQTL analysis. Genes with mean expression across samples of ≤6 counts or with expression variance = 0 were also excluded . Finally, expression values were quantile-normalised by samples and rank-transformed by genes. In total, 16,038 genes passed QC out of the initial 20,531.Genotype and gene expression data for 494 samples with PrCa were downloaded from TCGA , within a non-coding transcript, and whether the variant altered protein structure .All annotations were converted to binary format for the QR analysis, with the exception of CADD RawScore, which was retained as a continuous variable. Separate variables were created for each possible ChromHMM state during conversion from categorical to binary format. QR analysis was performed upon the priority pruner tag variants that were analysed by JAM, using the statistical results from those analyses. Annotations for all proxy SNPs represented by the tag variant were therefore subsequently inherited by the priority pruner tag. For the binary annotation categories, this meant that if one or more proxies had received a given annotation then the tag would also receive that annotation, whilst for the continuous CADD RawScore, the tag inherited the highest value from all associated proxies.τ, we first fit a conditional QR model to the estimated posterior probabilities from the JAM analysis for each variant. Second, we use the fitted model to calculate an expected posterior probability for each SNP given the annotation profile for that SNP. Since there is uncertainty in the choice of τ, we analyse the data across a range of τ =  and calculate a weighted average of these expected posterior probabilities to yield a final estimate. Specifically, the posterior probability from JAM, P, is modelled with a conditional QR with annotation, Z. The model is defined by an asymmetric laplace distribution (ALD):v is affected by both P and Zθ, and it suggests a weighted average of P and fitted regression quantiles can approximate v. The density function of ALD distribution isλ, the maximum is achieved atλ to beλ fixed, only the exponential parts of the Gaussian distribution and ALD involve v, to which we assign weight to P and i as Pi. We normalise the weight for Pi to be 1. For v is thenFor a specified quantile, λ0 is the observed FRR to first degree relatives of cases and λm is the FRR due to locus m, calculated assuming a per-allele effect:pm is the frequency of the risk allele for locus m, qm = 1 − pm and rm is the estimated per-allele OR.The contribution and comparison of the newly identified SNPs and the previously known variants to the familial risk, under a multiplicative model, was computed using the formulark, and the value of the observed familial risk, λ0. To correct for potential bias in effect estimation from using the same sample to determine the credible set of SNPs , we implemented a hierarchical model similar in spirit to Zhong and Prentice69 by placing a normal prior distribution on effect estimates of the form βm is the log OR from the conditional model within each region, and τ is a pre-specified variance of the effect distribution reflecting our prior beliefs. For all variants, we used a conservative value of τ = 0.05, reflecting a 95% prior probability density for a per-allele OR in the range of . For the FRR calculation, we specified a prior distribution as 70.This calculation was performed using a Bayesian framework, which allows us to attenuate any ‘winners curse’ bias, and incorporates the uncertainty in estimating the variant-specific per-allele OR, To collapse our catalogue of credible variants identified through fine-mapping into a parsimonious set of SNPs matching the observed number of independent signals, we selected single representative lead variants to represent each signal. For the 63 regions in which JAM identified only a single signal, these were designated as the tag with the highest posterior evidence for association, whereas for the 5 regions in which JAM did not resolve candidate variants the variant most strongly associated with PrCa in the original meta-GWAS was designated as the novel lead variant. For the 12 regions containing multiple independent risk signals, to facilitate unbiased selection of variants representing different signals, JAM exhaustively fitted all possible multi-SNP models for the specified number of signals, and the combinations of SNPs with the highest posterior probability were selected to represent the independent signals. Separate models were run to derive the variant list for the full 99 signals identified and also a reduced set of 84 signals, matching the number of original index variants fine-mapped, to enable comparison between the contributions of replacement of the GWAS tag SNPs and addition of novel signals identified. To yield adjusted effect estimates for each lead variant in regions containing multiple signals, conditional effect estimates and standard errors for the selected ‘representative’ variants used for the FRR calculations were derived from the OncoArray sub-cohort of 53,449 cases and 36,225 controls, for which individual-level data were available.http://practical.icr.ac.uk/blog/?page_id=8164) or GitHub (https://github.com/oncogenetics/LocusExplorer/tree/master/Data/ProstateData). Results from the fine-mapping analyses may be explored interactively through Locus Explorer71 (http://www.oncogenetics.icr.ac.uk/LocusExplorer/).The meta-analysis summary data used in this fine-mapping project are available from the PRACTICAL Consortium (Supplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Data 4Supplementary Data 5


Accumulation of phenolic needle metabolites in Norway spruce is regulated by many genes with small and additive effects and is correlated with the susceptibility against fungal attack.Chrysomyxa rhododendri in an unstructured natural population of Norway spruce. Thirty-one significant genetic associations for the flavonoids gallocatechin, kaempferol 3-glucoside and quercetin 3-glucoside and the stilbenes resveratrol, piceatannol, astringin and isorhapontin were discovered, explaining 22–59% of phenotypic variation, and indicating a regulation of phenolic accumulation by many genes with small and additive effects. The phenolics profile differed between trees with high and low susceptibility to the fungus, underlining the importance of phenolic compounds in the defence mechanisms of Norway spruce to C. rhododendri. Results highlight the utility of association studies in non-model tree species and may enable marker-assisted selection of Norway spruce adapted to severe pathogen attack.Norway spruce accumulates high foliar concentrations of secondary phenolic metabolites, with important functions for pathogen defence responses. However, the molecular genetic basis underlying the quantitative variation of phenolic compounds and their role in enhanced resistance of spruce to infection by needle bladder rust are unknown. To address these questions, a set of 1035 genome-wide single nucleotide polymorphisms (SNPs) was associated to the quantitative variation of four simple phenylpropanoids, eight stilbenes, nine flavonoids, six related arithmetic parameters and the susceptibility to infection by The online version of this article (doi:10.1007/s11103-017-0589-5) contains supplementary material, which is available to authorized users. The chemical composition of tissues plays important roles in the defence of plants against herbivory and pathogens. Of the defence-related plant secondary metabolites, phenolic compounds are particularly important for quantitative resistance to fungal pathogens, which are the most important group of tree pathogens (Hammerschmidt Picea abies (L.) H.Karst), several phenolic compounds were found to be associated with resistance to insects, herbivory and pathogen attack, or showed increased concentration following infection and wounding  de Bary . The individuals were identified by the Tyrolean Forest Department in cooperation with the Institute of Botany of the University of Innsbruck in order to have an association population with a high variation in the susceptibility to Chrysomyxa rhododendri infection degrees for all trees were determined by assessing the percentage of needle loss due to infection on sampled twigs on a scale of 1–5  for the 4 years 2009–2012  extract and to consider the different concentration ranges of the metabolites in the extract. Twenty-one phenolic compounds . Ion spray voltage was set to 4.5 kV, gas 1–40 psi and gas 2–50 psi at a temperature of 500 °C. Both quadrupole mass analysers were operated at unit resolution. Peaks were automatically detected based on retention time and MRM transition. Peak areas were normalized relative to the internal standards to account for variations during sample preparation and analysis, and concentration was calculated according to the compound-specific calibration curves established with authentic standards using the software Analyst and MultiQuant .Healthy 1-year-old needles of the year 2012 were freeze-dried for 72 h and homogenized for 8 min at 2000 rpm in a microdismembrator  using 7 ml Teflon grinding capsules and one agate ball of 1 cm diameter. To avoid warming of the sample, capsules containing the needles were submerged in liquid nitrogen for 2 min before grinding, and to avoid sublimation of water on the powder, the capsules were allowed to equilibrate with room temperature in a desiccator over silica gel before opening  or the Mann–Whitney U test . All tests were performed at a probability level of 5% using SPSS . All values are given as mean ± SE.Correlations were analysed using the Pearson  or the Spearman Rank  correlation coefficient. Comparisons of the subgroups showing high and low susceptibility were performed, after testing normality with the Kolmogorov–Smirnov test, with Picea glauca and later also tested on and found to be variable in a small number of P. abies individuals , and 17 SNPs were designed based on loci available at Genbank from a population resequencing study of different conifer species  was developed by merging SNPs from a number of different resequencing and genotyping projects. The majority of SNPs (1742) were originally identified in and designed for InfiniumBeadChips were manufactured by Illumina in a 24 × 1 format. For each sample, genomic DNA was extracted from freeze-dried needle tissue using a CTAB protocol . Ten independent runs (iterations) were conducted for each putative number of cluster K. Sampling location information was considered by applying the prior model parameter (LOCPRIOR) to the population model  above 0.2. Population stratification was first investigated with the Bayesian model-based software STRUCTURE . The amount of variation explained by a SNP (Rsq_Marker) was calculated for each significant association using a simple general linear model. The q-value for each marker was calculated to adjust for the false discovery rate (Storey and Tibshirani http://www.r-project.org/). Q-value threshold of 10% was used to declare significant associations.Association analysis was performed using TASSEL  or that the sample contains values arising due to other manner, as most likely by true associations  among markers, we calculated the correlations between alleles at two SNP loci rC. rhododendri infection degrees during the four observed years varied from Norway spruce trees with single infected needles to individuals with a needle loss of more than 65%. On average, trees classified as highly susceptible exhibited twice as high infections as trees with low susceptibility , as well as lower cis/trans-ratios of the stilbenes astringin (p = 0.043), isorhapontin (p = 0.027) and piceid (p = 0.047) compared to highly susceptible trees (see Table cis/trans-ratios of astringin (p = 0.003), isorhapontin (p = 0.004) and piceid (p = 0.026), but not with cis-piceid and gallocatechin  and n p = 0.07 and pic6 and n pcis- and trans-forms and arithmetic parameters of each compounds. Similarly, the flavonoids were correlated to each other; kaempferol 3-glucoside and catechin in addition with shikimic acid.The concentrations of several compounds were highly correlated to each other Table , most ofWhen considering tree sampling locations as prior in population structure analysis, the likelihood (LnP) of K decreased with increasing K without reaching a continuous plateau that would be expected in the presence of a genetic structure . The number of genetic groups was also investigated with Evanno’s method, where the Delta K plot showed low values in all K tested . Bar plots demonstrated that all individuals are admixed and none of them was clearly assigned to one group. The alternative scenario, without considering sampling locations, revealed similar results , suggesting that the most probable K is one. This conclusion is reinforced by the PCA using SNP data , where no group was clearly defined. Finally, the cladogram showed that individuals with high and low susceptibility are evenly distributed  and PCA (P) did not show any structure in our population, models correcting for population stratification estimated by both methods are not presented and the GLM model without correction was selected for association analysis. Q-Q plots Fig.  show thecis-astringin, trans-astringin, astringin ratio, astringin sum, cis-isorhapontin, trans-isorhapontin, isorhapontin ratio, isorhapontin sum, cis-piceid, trans-piceid, piceid ratio, piceid sum, trans-piceatannol, trans-resveratrol; flavonoids: kaempferol 3-glucoside, quercetin 3-glucoside, catechin, gallocatechin; simple phenylpropanoids: shikimic acid, picein), two infection traits  and five multivariate traits . For the latter, the first five principal components with the highest eigenvalues  were used  were tested against 20 chemical traits (stilbenes: −5 (p < 0.1). Furthermore, 31 significant associations were found under a q-value threshold of 10%. A total number of 20 markers were associated with the studied traits, and some of them were shared by different traits . No associations were found for simple phenylpropanoids and 8 weak associations were found in just one multivariate trait (PC4); four of these weak associations were also found in flavonoid traits such as kaempferol 3-glucoside and quercetin 3-glucoside.Among the 27,945 marker-trait pairs, 15 significant associations were found under the strictest conditions with a Bonferroni corrected threshold of 9.66 × 10trans-piceatannol (R2 = 0.52–0.24), three of which  were also associated with trans-resveratrol that exhibited a total of four associated markers (R2 = 0.59–0.29). One marker was linked to isorhapontin ratio , and another one was associated with trans-astringin and shared by astringin sum , the latter being associated with the flavonoid quercetin 3-glucoside (R2 = 0.25). For flavonoids, seven markers were associated with quercetin 3-glucoside (R2 = 0.42–0.21), two of which  were also associated with kaempferol 3-glucoside (R2 = 0.30–0.25). In addition, one SNP marker was associated with gallocatechin .Concerning stilbenes, a total of six markers were associated with GQ03011-J06.1.333) or ratio (isorhapontin ratio − GA PBB-PF00847-11-1). Both markers are widely distributed in the studied population . Others 5 markers) belong to introns, downstream regions or gene-empty regions . However, within individual genes and contigs, LD showed strong heterogeneity as shown in the Fig. S3b, c in agreement with previous studies , resveratrol (0.64 µMol g−1) and quercetin 3-glucoside , compared to grapes (0.22–0.44 µMol g−1) and red wine (up to 0.07 µMol ml−1), which are considered major sources of resveratrol , similar or partly higher compared to other conifer studies , an evolutionary conserved protein domain  make this candidate interesting. Marker PBB-PF00847-11-1, associated with isorhapontin ratio, is located in the coding sequence of MA_37766g0010, a putative member of the Apetala2/Ethylene-responsive element-binding protein family (AP2/EREBP). In A. thaliana, ethylene response factors (ERF) are directly responsible for the transcriptional regulation of several jasmonate/ethylene-responsive defence genes  are key players in plant innate immunity and activation of defence pathways. Marker GQ0015-B03.1.189, associated with both flavonoids and stilbenes, is located in the gene MA_804816g0010 that encodes a protein with a leucine-rich repeat (LRR) domain, frequently involved in plant defence Supplementary material 2 (XLSX 405 KB)Supplementary material 3 (DOCX 1194 KB)Supplementary material 4 (TXT 183 KB)Supplementary material 5 (TXT 17 KB)


Left ventricular (LV) hypertrophy is a strong predictor of cardiovascular outcomes, but its genetic regulation remains largely unexplained. Conventional phenotyping relies on manual calculation of LV mass and wall thickness, but advanced cardiac image analysis presents an opportunity for high-throughput mapping of genotype-phenotype associations in three dimensions (3D).High-resolution cardiac magnetic resonance images were automatically segmented in 1124 healthy volunteers to create a 3D shape model of the heart. Mass univariate regression was used to plot a 3D effect-size map for the association between wall thickness and a set of predictors at each vertex in the mesh. The vertices where a significant effect exists were determined by applying threshold-free cluster enhancement to boost areas of signal with spatial contiguity. Experiments on simulated phenotypic signals and SNP replication show that this approach offers a substantial gain in statistical power for cardiac genotype-phenotype associations while providing good control of the false discovery rate. This framework models the effects of genetic variation throughout the heart and can be automatically applied to large population cohorts.https://doi.org/10.5281/zenodo.834610 together with the clinical data used in this work.The proposed approach has been coded in an R package freely available at Bioinformatics online. One of the most complex unanswered questions in cardiovascular biology is how genetic and environmental factors influence the structure and function of the heart as a three-dimensional (3D) structure  Fonseca.One approach to inference is to transform the spatially correlated data into a smaller number of uncorrelated principal components . In thisThe healthy volunteers dataset used in this study is part of the UK Digital Heart Project at Imperial College London (www.uk10k.org). Quality of the genotypes was evaluated both on a per-individual and per-marker level using in-house Perl scripts. SNPs were removed if they had a Impute Information (INFO) score < 0.4, missing call rate in more than 1% of samples, minor allele frequency of less than 1% or deviated significantly from Hardy-Weinberg equilibrium (P > 0.001). Only non-related individuals with ‘CEU’ ethnicity were retained. The total genotyping rate in these individuals was 0.997 and the total number of variants available was 9.4 million.Genotyping of common variants was carried out using an Illumina HumanOmniExpress-12v1-1 single nucleotide polymorphism (SNP) array . Clustering, calling and scoring of SNPs was performed using Illumina GenCall software. Samples were pre-phased with SHAPEIT . A validated cardiac segmentation and co-registration framework was used which has previously been described in detail  , categorical or expressing interaction between them. In particular, categorical variables can be exploited to express either different categories (such as gender or ethnicity) or the presence/absence in a binary form of a clinical condition (such as the presence of genetic mutation or a specific disease). β is the regression coefficient vector to be estimated and Y not explained by the model. The regression coefficient can be standardized by normalizing to mean 0 and unit-variance the columns of X and Y. As a result, β will represent the amount of variation of Y in units of its standard deviation when X is increased by one standard deviation, allowing comparisons between variables.The association between a ventricular phenotype mapped onto a 3D mesh and one or more clinical variables can be described using a general linear model of the form β  and statistics can be extracted and corrected for multiple testing in order to test one or more statistical hypotheses. In a parametric framework, the t-statistic computed as tor of β . The regph is the value of the vertex statistic, e(h) is the extent of the cluster with cluster-forming threshold h that contains p, and E and H are two parameters usually set to 0.5 and 2 for empirical and analytical motivations —the area of all the elements connected to p that have a statistic value greater or equal to h—as a different e(h) needs to be computed for each vertex of the mesh and for each term of the sum. However, the TFCE score associated to a vertex p of a specific h in the summation consists of the same score that should be associated with all the vertices which contribute to e(h). Therefore, the computational time of the TFCE method can be significantly reduced by sampling the interval between the maximum and minimum statistic h in the statistic map so as to use each sampled value as a threshold The value of a statistic h obtained through mass univariate regression at a vertex p—a t-statistic in our context—is transformed by TFCE using the following integral:ivations . In compP-value associated with the regression coefficient computed at each atlas vertex can be derived via permutation testing. In particular, by permuting N times the input data, N TFCE scores maps can be obtained. It is important that the adopted permutation strategy guarantees the exchangeability assumption, i.e. permutations of Y given X do not alter the joint distribution of the dependent variables under the null hypothesis. In the proposed context, the Y values themselves are not exchangeable under the null hypothesis, as the predictors included in the model together with the variable under study are nuisance variables that could explain some portion of variability of Y. In order to address this problem, among a number of available techniques, the Freedman-Lane procedure  procedures. In particular, these procedures can be applied to adjust the voxelwise terature  procedurterature . This coterature .The proposed mass univariate framework has been coded as an R package (mutools3D) which benefits from the use of vectorized operations. Matrices containing the phenotypic data and templates to visualise the 3D models are also available with the software. Linear regression assumptions must be met in order to obtain reliable inferences , using echocardiography for phenotyping . Regardiested in . The numested in  S3, TFCEested in , since tFour SNPs showed a significant association with WT as reported in ificance  S5.snpX of an non-associated SNP (rs4288653) adjusted for age, gender, BSA and SBP was used to generate background noise. A synthetic data signal was generated by summing to the WT values of each subject a term I is the signal intensity and β is a map of regression coefficients. Two contrasting β maps  obtained from real clinical data were chosen and are available in β coefficients covering the 10% of total area of the LV and scaled to the  range in a more extended area covering the 60% of the LV surface. By subsampling the number of subjects N and the signal intensity I, different signals to be detected by the proposed standard mass univariate pipeline were obtained. The number of permutations for each simulation was fixed to 5000 and results were linearly interpolated and plotted on the contour plots shown in Sensitivity, specificity and the rate of false discoveries of the proposed pipeline were estimated using synthetic data. A 3D model showing no correlation between WT and the posterior estimate of the allele frequency N and signal intensities I, reaching the greatest values with the most extended signal  as expected. Given the sample size of our GWAS replication study and the intensity of the associations found, these results would assign a sensitivity of 70% for the first two discovered SNPs and more than 90% for the other two. Moreover, the rate of false discoveries was 0 for all the results of signal A and below 5% except for few simulations involving signal B and sample sizes greater than 1600 (results reported in Sensitivity increased at larger sample sizes Finally, we have performed a comparative study between TFCE and a standard cluster-based thresholding method as reported in the original TFCE paper on brain imaging data , which hThe environmental and genetic determinants of cardiac physiology and function, especially in the earliest stages of disease, remain poorly characterized and morphological classification relies on one-dimensional metrics derived by manual image segmentation (Genetic association studies using conventional 2D imaging leave much of the moderate heritability of LV mass unexplained (One of the main limitations of the presented framework is that high-spatial resolution CMR is not available in all cohorts, although conventional two-dimensional images may be super-resolved to provide similar shape models (Mass univariate approaches do not directly consider the local covariance structure of the data, however this is accounted for when Random Field Theory or permutation tests define a threshold for significant activation . In the As the methods are computationally efficient and require no human input for phenotypic analysis, it is feasible to scale up the pipeline to larger population cohorts such as UK Biobank, which aims to investigate up to 100 000 participants using MR imaging (We report a powerful and flexible framework for statistical parametric modelling of 3D cardiac atlases, encoding multiple phenotypic traits, which offers a substantial gain in power with robust inferences. We have implemented and validated the approach on both synthetic and clinical datasets, showing its suitability for detecting genotype-phenotype interactions on LV geometry. More generally, the proposed method can be applied to population-based studies to increase our understanding of the physiological, genetic and environmental effects on cardiac structure and function.Supplementary FiguresClick here for additional data file.


Motivation: For genetic studies, statistically significant variants explain far less trait variance than ‘sub-threshold’ association signals. To dimension follow-up studies, researchers need to accurately estimate ‘true’ effect sizes at each SNP, e.g. the true mean of odds ratios (ORs)/regression coefficients (RRs) or Z-score noncentralities. Naïve estimates of effect sizes incur winner’s curse biases, which are reduced only by laborious winner’s curse adjustments (WCAs). Given that Z-scores estimates can be theoretically translated on other scales, we propose a simple method to compute WCA for Z-scores, i.e. their true means/noncentralities.Results:WCA of Z-scores shrinks these towards zero while, on P-value scale, multiple testing adjustment (MTA) shrinks P-values toward one, which corresponds to the zero Z-score value. Thus, WCA on Z-scores scale is a proxy for MTA on P-value scale. Therefore, to estimate Z-score noncentralities for all SNPs in genome scans, we propose FDR Inverse Quantile Transformation (FIQT). It (i) performs the simpler MTA of P-values using FDR and (ii) obtains noncentralities by back-transforming MTA P-values on Z-score scale. When compared to competitors, realistic simulations suggest that FIQT is more (i) accurate and (ii) computationally efficient by orders of magnitude. Practical application of FIQT to Psychiatric Genetic Consortium schizophrenia cohort predicts a non-trivial fraction of sub-threshold signals which become significant in much larger supersamples.Conclusions: FIQT is a simple, yet accurate, WCA method for Z-scores .Availability and Implementation: A 10 lines R function implementation is available at https://github.com/bacanusa/FIQT.Contact:sabacanu@vcu.eduSupplementary information:Supplementary data are available at Bioinformatics online. Genome-wide association studies (GWAS) represent a powerful and widely used tool for detecting associations between genetic variants and complex traits. In such studies, researchers directly assay and statistically impute . HoweverZ-scores, ORs and RRs can be theoretically translated from one scale to another, in this paper we concentrate on estimating the true means/noncentrality of Z-scores at each SNP.To successfully dimension future studies, e.g. for detecting as significant a certain number of signals which are only ‘suggestive’ in current cohorts, there is a need for statistical methods that accurately estimate unbiased effect-sizes for suggestive signal SNPs and, even, all variants from genome scans (henceforth denoting not only extant GWAS and whole-exome sequencing but emergent whole-genome sequencing studies as well). Given that effect size estimates such as Z-score. By incorrectly assuming a Gaussian distribution, naïve estimators of extreme statistics have a tendency to overestimate the magnitude of these statistics  method based on Tweedie’s formula , was adaP-values as a measure of association for SNPs will overestimate their statistical significance. This is due to the fact that, due to the large number of tests, many SNPs will attain very low P-values even under the null hypothesis of no association between trait and genotypes. Thus, to be used in assessing genome-wide significance of SNPs, individual P-values need to be first adjusted for multiple testing , we argue that WCA for effect sizes is very similar in spirit with, if not downright the homologue of, MTA for P-values. Thus, MTA can be considered, if not identical to, a very good proxy for the WCA for P-values.Similar to WCA, naïve use of SNP  testing . After mZ-scores from a genome scan, i.e. their true means/noncentralities, we propose a novel two-step method, which is inspired by the strong similarity between MTA and WCA. First, we perform a MTA for P-values, e.g. by using a False Discovery Rate (FDR) approach . When compared to competing methods, we show that the proposed procedure has very good performance in terms of (i) squared error loss, (ii) fraction of the variability in true means of univariate statistics explained and (iii) computational efficiency. A practical application of this approach shows that, due to their good performance, the proposed estimators can be used to predict with reasonable accuracy the number and location of subtreshold signals that are likely to become significant in much larger cohorts.To accurately estimate the WCA of approach . Second,Z-score noncentralities for all SNPs in a genome scan. Below, we first present our proposed method and its competitors, including extensions of these competitors proposed by us. Subsequently, we describe simulation setup and genetic data used for our chosen practical application.As mentioned above, the main issue we address in this paper pertains to the estimation, as opposed to testing, of P-values, respectively. If not reported, Supplementary Material (SM)].Let Z-scores, i.e. estimate their noncentralities, for all SNPs in a genome scan. However, it is extremely simple to MTA the P-values for the genome-wide multiple testing. The Invariance Principle of Mathematical Statistics  good proxy for WCA on the P-value scale, we thus propose to (i) adjust SNP P-values for multiple testing, e.g. using FDR as in this paper and (ii) obtain the Z-score noncentrality estimates for each SNP as the Gaussian quantiles (with the appropriate sign) associated with these adjusted P-values . [While the FDR procedure might be anticonservative for the extreme scenario of numerous negatively correlated variables  we do not expect these local correlations to be mostly negative.]Given the extreme value distribution of scan statistics in the upper and lower tails and different distributions elsewhere, it is unclear  how to properly WCA atistics  implies ariables , in geneq-values . Then, we can estimate the noncentralitiy of Z-scores, In mathematical notation, let P-value adjustments for multiple testing, homologous methods can be constructed using other P-value MTA methods. Many such adjustments are already available in the same p.adjust R function, which we employed for the FDR adjustment. Among others, p.adjust implements more conservative family-wise error rate type of adjustments, such as Bonferroni, Z-score estimates, the assessment of non-FDR based methods are outside the scope of this paper.While we chose FDR as a simple, and less conservative than most, n equally spaced non-overlapping sets  empirically estimate their density and (ii) use the derivatives of the empirical densities to estimate the mean of the statistics and their variance. However, scan statistics are often rather correlated locally (i.e. as a consequence of linkage disequilibrium). This is likely to (i) affect the density estimate (which assumes independent statistics) and (ii) underestimate the variance of mean statistics. To eliminate (most of) the local correlations we propose an EB extension which (i) divides the statistics into n . (Because the soft threshold method (R2 in Section 3) in a cumulative manner, i.e. for all statistics with unadjusted P-values below a large range of thresholds.For comparison, we use the naïve maximum likelihood estimator (MLE), i.e. the statistics themselves, classical EB (EB-1 in the above set notation) and EB-d method  was found method . The orip.adjust base function with the ‘fdr’ option specified for method . Based on the descriptions from  from the output of system.time R function.We implemented all described methods using the R statistical programming environment. For FDR, FIQT employed the Supplementary Material (SM) and We simulate a complex height-like trait by patterning our simulations on the observed effect sizes of the ht study , i.e. m1To assess the performance of methods for underpowered studies, we performed simulations under P-values from PGC-SCZ1. The inference relies on the fact that the Z-score noncentrality increases with the square root of the sample size. Thus, the noncentrality (true mean) of Z-score for SNPs in PGC-SCZ2 are estimated simply as the double of their PGC-SCZ1 homologues. We predict as significant in PGC-SCZ2 only those SNPs for which the P-value associated with their predicted Z-score noncentrality is lower than the commonly used To underline FIQT accuracy and its usefulness in genetics, we applied it to the summary statistics from the discovery phase of the 2005 Psychiatric Genomics Consortium (PGC) GWAS of schizophrenia (PGC-SCZ1) . Our infn methods, we tested EB-1, EB-10, EB-50 and EB-100. EB-10 and EB-50 have intermediate performance between EB-1 and EB-100, with EB-10 closer to EB-1 and EB-50 closer to EB-100 (data not shown). Consequently, we present only the results for EB-1 and EB-100. Measures of prediction accuracy for all of the above methods are assessed based on the simulated and estimated noncentralities for all SNPs in genome scans.Among EB-P-values, where EB-1 slightly outperforms it ], because, when compared with EB  methods, the bias is often somewhat larger . , opens the possibility of future improvement which take into account the local LD of statistics, as alluded in Discussion.) When measuring accuracy by R2, i.e. the explained variability of the Z-score noncentralities, FIQT practically outperforms all other methods ]. FIQT is also faster than the less accurate EB-1 by almost two orders of magnitude (data not shown).Due to its very simple computation, FIQT has much faster running times than competitors. When compared to the next most accurate method, EB-100, the proposed method is faster by more than four orders of magnitude [Fig. S2 in Practical application. Given that discovery phase of PGC-SCZ2 has around four times the sample size of its PGC-SCZ1 homolog, then the Z-score noncentrality in PGC-SCZ2 are expected to be twice as large as the PGC-SCZ1 FIQT estimates . By computing, under a Gaussian distribution assumption, the P-values associated with estimated PCC_SCZ2 noncentralities, we predict 46 regions (Supplementary Table S1) to attain significance in PGC-SCZ2, as opposed to only 11 present in PGC-SCZ1. The 46 regions were obtained by clustering together predicted significant signals within 250 Kb. Of these significant regions, a very high number, 34 (∼75%), overlap the 105 independent chromosomal regions reported by PGC-SCZ2. A total of 18 predicted PGC-SCZ2 regions overlap the extended MHC region (25–33 Mb) on chromosome 6p from the actual PGC-SCZ2 findings, as opposed to only 5 reported by PGC-SCZ1. Of the overall of 34 overlapping regions, 16 are in loci outside MHC regions, as opposed to just 6 reported by PGC-SCZ1.Z-scores by performing a winner’s curse adjustment (WCA) on Z-scores. Due to the high degree of similarity between WCA on Z-score scale and multiple testing adjustment (MTA) on P-value scale, we propose a two stage procedure. First, use FDR for the MTA of P-values. Second, transform the adjusted P-values to upper tail Z-scores and assign to it the sign of the original statistics. When compared to competing methods, FIQT estimators are shown to (i) have a smaller mean squared error loss, (ii) explain a higher proportion of the true means of the statistics and (iii) have substantially faster running times. The practical application to PGC-SCZ1 data show that FIQT estimators are useful for highlighting, with reasonable specificity, genomic regions likely to attain significance only in much larger supersamples.We propose a novel approach, FIQT, to extract information from genome scan statistics by estimating noncentrality (true mean) of Z-score scale, Delta Method (a first order Taylor approximation) from statistical theory states that the relative performance of methods should be similar on other scales  prediction accuracy. Its performance advantage over EB based methods is especially notable at high sample sizes and a moderate to large number of true signals. [While, the accuracy was assessed only on the r scales , e.g. RRFIQT practical application to PGC SCZ summary statistics, were used to predict a large fraction of future signals discovered in a four times larger cohort. This underscores its useful in predicting moderately large, even if non-significant, signals. While ranking regions and predicting as possibly significant in the future a set number of them, in practice the decision on the magnitude of such number is both complex and subjective. In contrast, FIQT can help to objectively determine the number of signals that likely to be significant in the future based on the (i) estimated non-centralities and the (ii) increase in sample size. Such estimates can be used to adequately design well-powered follow-up studies.Z-scores in a genome scan. Sometimes, Z-scores are not available and the researchers need to estimate them from other summary data (see SM). Conversely, the adjusted Z-scores  can be subsequently used to estimate the adjusted values for the summary statistics of interest. For instance, if summary data contain only log odds ratio, Z-scores is Z-scores (FIQT estimates), FIQT estimates the noncentralities for all Z-score noncentrality estimates. In the future we plan to extend FIQT to be both less conservative and provide such estimates. Heuristically, for each SNP, such a plan might (i), similarly to EB-n, compute FIQT-n mean Z-score noncentrality estimates by using only (quasi-independent) SNPs spaced Z-score noncentrality by interpolation using all FIQT-n which do not include this SNP in its support. Subsequently, for each SNP, (i) the Z-score noncentrality might be estimated as the mean of its n-1 FIQT-n noncentralities and (ii) the SD of the mean of FIQT-n scores can be estimated assuming that the q-values are much less conservative and, in turn, the updated FIQT estimates become less conservative.In its present form, FIQT is conservative and provides only point estimates, i.e. it does not compute the standard deviation (SD) of Z-score noncentralities. For instance, shrinkage estimators are widely used for correlation/covariance matrices  of LD score method . (DISTMIX imputes the statistics at the unmeasured SNPs based only on the statistics at the measured SNPs and the LD patterns estimated from a cosmopolitan reference panel.)FIQT is available from GitHub and


To evolve and respond to natural selection behavioural traits must have a genetic component. Quantifying the genetic component of behaviour can thus reveal its evolutionary significance. In a cooperative breeder, we tested if behavioural traits were consistent, heritable and correlated. We found that our measures of exploratory behaviour were consistent and correlated, and that novel environment exploration, was heritable. This behaviour therefore has the greatest capacity to evolve in response to a changing environment. Acrocephalus sechellensis) on Cousin Island, a lack of breeding vacancies forces individuals into different life-history strategies, and these differences in reproductive state could generate behavioural differences among individuals in the population. We used this population to estimate the repeatability of 4 behavioural traits , and narrow-sense heritability , and evolvability, of the repeatable behavioural traits. We also tested for an among-individual correlation between the repeatable traits. We found that, compared to estimates in other study species, the exploratory behaviours were moderately repeatable (0.23–0.37), there was a positive among-individual correlation (0.51) between novel environment and novel object exploration, and that novel environment exploration was moderately heritable . This study further clarifies the additive genetic variance available for selection to act upon in this cooperatively breeding bird.Quantifying consistent differences in behaviour among individuals is vital to understanding the ecological and evolutionary significance of animal personality. To quantify personality, the phenotypic variation of a behavioural trait is partitioned to assess how it varies among individuals, which is also known as repeatability. If pedigree data are available, the phenotypic variation can then be further partitioned to estimate the additive genetic variance and heritability. Assessing the repeatability and heritability of personality traits therefore allows for a better understanding of what natural selection can act upon, enabling evolution. In a natural population of facultative cooperatively breeding Seychelles warbler ( Animal personality is a phenomenon where individuals exhibit consistent behavioural differences between one another . BehavioTo test the state-dependent model, studies of personality are required in systems where there are multiple states or life-history strategies. Breeding systems where 3 or more individuals help to raise offspring, such that at least one individual helps to raise offspring that are not their own, are known as cooperative breeding systems . IndividParticular theoretical models that can be tested in cooperative breeding system include the asset protection and social state models . When beVP), that is explained by the difference between individuals (VI) can be estimated. Repeatability (R) can then be calculated as: R = VI/ VP  of the variance in behaviour has been shown to be accounted for by consistent differences among individuals  describes the proportion of the total phenotypic variance (VP) that can be explained by additive genetic variance (VA); h2B= VA/ VP (N = 209) of the variance in behaviour has been shown to be accounted for by additive genetic variation (VP. Using this heritability measure (h2P), on average, 0.52  of the variance in personality is explained by additive genetic variation (IA), the mean standardised additive genetic variance (VA / trait mean2), is a further measure that allows comparison when using the same transformation across the same traits and populations with different means  provides an excellent opportunity to investigate personality in a cooperative breeding system. First, habitat saturation limits the number of available breeding territories, forcing some individuals to remain on their natal territory, instead of gaining a primary breeding position elsewhere, and help rear offspring that are not their own  has a carrying capacity of around 320 individuals that reside in ca. 115 territories , and the number of stick touches was lower  in the novel object assay than in the control assay. This confirmed that the behavioural reaction resulted from the novel object and not the stick to which it was attached . Latency had very low repeatability . Behaviour scores in the novel object assay were therefore used as a measure of exploration  the bird was placed in the palm of the hand, but this was changed to prevent hand temperature and movement affecting the measure. Therefore, the method change was accounted for in the analyses.Escape response was recorded back at the territory of capture. The departure time to fly from a man-made perch (consisting of a branch 24 cm in length attached to an 80-cm trunk) was recorded , such that both variance priors were set at 1, and n = 1.002. Furthermore, for the observer identity random effect in the novel object exploration models, we specified the equivalent of a proper Cauchy prior: V = 1, n = 1, alpha.mu = 0, alpha.V = 252 (n = 7). We assessed convergence by inspecting the autocorrelation values (r < 0.1) and time-series plots of the model parameters, and using the heidel.diag and geweke.diag functions. Prior sensitivity analyses showed that our choice of priors had little influence on the results of the model (Supplementary Table S2). Power analyses  were included to account for multiple measures on the same bird and measures taken by different observers. The variance components were extracted from the GLMM, and the raw phenotypic repeatability of the personality trait captured following Generalised linear mixed models (GLMMs) were run using a Poisson distribution with log link for all traits except stress response, where a Gaussian distribution with identity link was used. The dependent variable was the personality trait. We tested fixed effects that we believe may be important and associated with personality in our cooperative breeding study system and have been associated with personality in other systems: social status ; mother identity to account for the maternal effects (VM); individual identity to account for the permanent environment effects (VPE); and, observer identity to account for multiple measures by the same observer (VO). The variance components were extracted from the GLMM, and, extending h2B) calculated as h2B= VA/ VP, the heritability of behaviour excluding observer variance (h2B-O), calculated as h2B-O = VA / (VA + VPE + VM + VRes); and the heritability of personality (h2P) calculated as, h2P= VA/ (VA + VPE + VM), so as to exclude temporary environmental effects . Finally, for escape behaviour, individuals took longer to fly from the perch when it was raining than when it was cloudy, with increasing assay number, in 2013 and 2014 than 2010, with increasing body mass, and when released from the perch rather than the hand .h2B, estimates were moderate for novel environment .A positive among-individual correlation existed between the novel object and novel environment exploration , compared to the mean reported h2B  similar to estimates observed for behavioural traits , and a low IA (<0.01). Low heritability estimates are expected when directional selection has depleted the genetic variation in traits linked to fitness (We have shown that novel environment exploration and novel object exploration are moderately repeatable (0.23–0.37), comparable to the mean reported repeatability of behaviour  and novel object exploration (<0.01 vs 0.01) when measurement error and temporary environmental effects were, in turn, excluded to estimate VA , a Natural Environment Research Council fellowship (NE/I021748/1 to HLD), 2 Schure Beijerinck Popping grants (SBP2013/46 to HAE and SBP2012/26 to HLD) and TB was supported by a Leverhulme Fellowship.Heritability_Supp_BehavEcoClick here for additional data file.