N = 371) was exome sequenced as part of the Autism Sequencing Consortium (ASC) and 241 trios were extensively characterized to be diagnosed with AS following DSM-IV and Gillberg’s criteria (N = 39) or not (N = 202). Following exome imputation, polygenic risk scores (PRS) were calculated for ASD, SCZ, ADHD, MDD, ANX, and OCD (from available summary data from Psychiatric Genomic Consortium (PGC) repository) in the Spanish trios’ cohort. By using polygenic transmission disequilibrium test (pTDT), we reported that risk for SCZ , ADHD , and MDD  is over-transmitted to children with AS but not to Non_AS. Indeed, agnostic clustering procedure with deviation values from pTDT tests suggested two differentiated clusters of subjects, one of which is significantly enriched in AS (P = 0.025). Subsequent analysis with S-Predixcan, a recently developed software to predict gene expression from genotype data, revealed a clear pattern of correlation between cortical gene expression in ADHD and AS (P < 0.001) and a similar strong correlation pattern between MDD and AS, but also extendable to another non-brain tissue such as lung (P < 0.001). Altogether, these results support the idea of AS being qualitatively distinct from Non_AS autism and consistently evidence the genetic overlap between AS and ADHD, MDD, or SCZ.There is great phenotypic heterogeneity within autism spectrum disorders (ASD), which has led to question their classification into a single diagnostic category. The study of the common genetic variation in ASD has suggested a greater contribution of other psychiatric conditions in Asperger syndrome (AS) than in the rest of the DSM-IV ASD subtypes (Non_AS). Here, using available genetic data from previously performed genome-wide association studies (GWAS), we aimed to study the genetic overlap between five of the most related disorders (schizophrenia (SCZ), major depression disorder (MDD), attention deficit hyperactivity disorder (ADHD), obsessive-compulsive disorders (OCD) and anxiety (ANX)), and AS, comparing it with the overlap in Non_AS subtypes. A Spanish cohort of autism trios ( Epidemiological studies reflect that around 1% of worldwide population could have ASD diagnosis2. The lack of empirical evidence to support the appropriateness of different ASD subtypes has led to their classification into one single category. Part of the clinical heterogeneity of ASD has to do with the coexistence with psychiatric and medical conditions9. Differential psychiatric comorbidities may have an etiopathological relationship with the ASD subtype, as previously conceptualized.Autism spectrum disorders (ASD) comprise a group of complex neurodevelopmental disorders characterized by restricted interests, impaired social interaction, and stereotyped and repetitive behaviors14.Major depression (MDD), anxiety (ANX), attention deficit hyperactivity disorder (ADHD), schizophrenia (SCZ), and obsessive-compulsive disorders (OCD) are among the most prevalent psychiatric comorbidities in ASD patients. This clinical overlap has been more extensively studied in high functioning autism (HFA) and in Asperger syndrome (AS), which may be biasing the findings18. While ASD predisposing rare variation shows a clear overlap with severe neurodevelopmental disorders, intellectual disability and, in lesser degree, schizophrenia16, is the common variation that seems to be shared across major psychiatric disorders15. For instance, strong genetic correlations between ASD and MDD , SCZ  or ADHD  have been described in terms of common variation15. In this sense, the latest ASD GWAS to date demonstrated that common variation contribution to Asperger (AS) subtype was almost double the contribution to other DSM-IV ASD subtypes15. Given this main difference in the genetic architecture of AS, a reasonable question is whether common predisposing variation from comorbid disorders may be present to a greater extent in AS than in other ASD subtypes.Recent advances in ASD genomics have demonstrated a clear pattern of biological overlap between ASD and other psychiatric conditions22. In a previous study, our group surveyed subclinical psychopathology in children and adolescents diagnosed with AS following DSM-IV and Gillberg’s criteria, describing high sub-syndromic MDD, OCD, ADHD symptomatology in our AS sample23.In addition, the criteria for an appropriate AS diagnosis is, still, a matter of important debate18, we analyzed polygenic transmission using an ASD cohort of 379 trios and tested whether comorbid disorders were over-transmitted in AS but not in Non_AS trios. We then used hierarchical clustering to classify subjects based on their transmitted polygenic scores. Indeed, to more deeply understand the significance of this polygenic contribution, we used recent developed software, PrediXcan24 and S-PrediXcan25 to analyze how over-transmitted alleles in AS subjects affect brain cortical gene expression.Therefore, in this study, we aimed to assess whether polygenic risk for ASD and comorbid disorders are differently transmitted in AS compared with other autism subtypes (Non_AS). Using polygenic transmission disequilibrium test, a method previously performed in a larger ASD cohortN = 379) were recruited in two sites in Spain, Santiago de Compostela , and Madrid . Subjects from Madrid were recruited as part of AMITEA program, at the Department of Child and Adolescent Psychiatry, Hospital General Universitario Gregorio Marañón. Subjects from Santiago were recruited from an ongoing project from the Galician Public Foundation of Genomic Medicine. Informed consent signed by each participating subject or legal guardian and approval from the corresponding Research Ethics Committee were obtained before starting the study. Only individuals with 3 years of age or above and ASD diagnosis were included. All trios recruited were complete. Parents had no diagnosed psychiatric disorder when trios were recruited.ASD complete trios , the ADOS and/or ADI-R were also administered. For the comorbidity study, we used only participants from the Madrid site, with 39 trios with this specific AS diagnosis, and 202 with other ASD diagnoses (Non_AS), since only these 241 trios were phenotyped enough to ensure a possible diagnosis of AS. These subjects were diagnosed with AS if they had an ASD without mental retardation diagnosis and met Gilbert’s criteria for AS19. In fact, 41 probands without mental retardation were included within the 202 Non_AS trios, as they did not meet both DSM and Gilbert’s criteria. No screening for copy number variants (CNVs) carriers was performed. The average age for recruitment and diagnoses was 15.41 years (CI 95%: 14.55–16.66).Diagnosis of ASD for sample 2 was done by Child Psychiatrists with extensive experience in ASD, clinically trained in the autism diagnostic interview-revised (ADI-R) and research-trained in the autism diagnostic observation schedule (ADOS). All diagnoses followed Diagnostic and Statistical Manual of Mental Disorders, Fourth Edition Text Revision and Fifth Edition (DSM-IV-TR and DSM-5) criteriahttps://imputationserver.sph.umich.edu/) using 1000 Genome Project phase 3v.5 reference panel in order to capture genomic variants beyond exome. From 654,286 variants, a total of 38.7 million were obtained. Only biallelic variants with imputation quality score > 0.9 and minor allele frequency (MAF) > 0.1% were considered . Then, exome-based PRS scores were calculated. Briefly, GWAS summary statistics from PGC repository (https://www.med.unc.edu/pgc/results-and-downloads) were used as discovery sample  in the discovery dataset for inclusion of SNPs below these thresholds in PRS and calculated polygenic transmission disequilibrium test (pTDT), using parent-child trios PRS information, as previously performed in ASD18. Briefly, the expected PRS distribution of the offspring is compared with the average PRS distribution of the parents, and its deviations is tested with a one-sample t-test. For each disorder, the P threshold with the highest estimate value of transmission from pTDT on the whole sample (sample 1 and sample 2) was selected and henceforth used for comparison between AS (N = 39) and Non_AS  trios. As a negative control, pTDT analysis was repeated using summary statistics of body mass index (BMI), from recent meta-analysis32, a trait without genetic correlation with ASD.We calculated polygenic risk scores (PRS) in the 379 Spanish ASD trios that were sequenced as part of the Autism Sequencing Consortium (ASC). Firstly, exome-based VCF files were imputed at Michigan Imputation Server , K-means, self-organizing tree algorithm (SOTA), and model-based). The most suitable method is suggested after an internal validation procedure implemented. The internal measures include the connectivity (the degree of connectedness of the clusters), Silhouette Width (the degree of confidence in a particular clustering assignment), and Dunn Index . We then used NbClust R package34 to determine the optimal number of clusters making use of different indexes and varying all combinations of number of clusters, distance measures, and clustering methods.In order to analyze substructure of our ASD cohort based on polygenic transmission, we performed an agnostic procedure of clustering classification (without specifying the number of clusters to be generated). We first determined the more suitable method using the R package hclust function from cluster R package. Goodness of clustering algorithm results was assessed by determining the silhouette width coefficient, which measures how well an observation is clustered and it estimates the average distance between clusters. Observations with negative silhouette width were removed. fviz_silhouette function from factoextra R library was used. Finally, ASD subjects within each cluster were analyzed to test enrichment of AS subjects within any group.Hierarchical clustering using Ward’s minimum variance method was performed with software that imputes tissue-specific gene expression levels from subject’s genetic profile24, was used to assess gene expression differences between patients from AS and Non_AS trios. Briefly, PrediXcan makes use of available expression quantitative trait loci (eQTLs) data from GTEx project35 to predict expression levels in a tissue-dependent manner and compares expression levels across different phenotypes. Genotype files from ASD trios with available diagnose information (N = 241) were converted from.bed to.dosage format. Predixcan was run with --predict and –assoc --logistic arguments to predict expression levels per individual and perform statistical comparisons per gene between AS and Non_AS subjects. Given the extensive literature connecting cortical dysfunctions and autism, either from imaging36, gene expression39 or rare disrupting variation40 studies, GTEx brain frontal cortex was used as reference transcriptome. Differences in predicted gene expression in frontal cortex between AS and Non_AS patients were assessed.PrediXcan, a recently published 25, an extension of PrediXcan software that infers its results using only summary statistics from GWAS, was then used on GWAS summary data from ASD and comorbid disorders with significant polygenic transmission  to estimate gene expression differences between cases and controls using imputed expression data from GTEx .S-PrediXcanZ-values derived from PrediXcan test) and gene expression differences between cases and controls from comorbid disorders  was analyzed. This relation was studied under different P thresholds from S-PrediXcan.Correlation between gene expression differences between AS and Non_AS (measured by per gene 41 were used as comparative controls. Body mass index (BMI) summary statistics32 were also used in S-PrediXcan analyses in same tissues as a negative control, as it has not been associated with ASD across literature and repeatedly used as control. Finally, Alzheimer disease (ALZ) summary statistics42 were used in S-PrediXcan analyses in same tissues as a comparison between neurodevelopment and a neurodegenerative disorder.GTEx expression data from lung and cerebellum, other brain tissue with less consistent evidences in psychiatry that frontal cortext-test were performed in form of pTDT. Full procedure is described in previous work18. Comparisons of polygenic transmission values between AS and Non_AS groups were performed with two-sample t-test. Data normality was contrasted with Shapiro–Wilk test. Paired t-test was used to test significance of transmission across all comorbid disorders in AS and Non_AS subgroups of trios. Correlation analyses were performed using Spearman correlation. In case of multiple test comparison, Benjamini–Hochberg FDR correction was performed.To assess for polygenic over-transmission in AS and Non_AS, one-sided P threshold in which pTDT had higher transmission values at each disorder.After imputation and quality control (QC) of genotypic data, we retained 221,418 SNPs, of which a total of 51,718 variants with MAF > 0.1% were used after clumping (methods). Average pTDT and deviation were calculated in our ASD trios cohort using GWAS data from ASD and five comorbid disorders assessed  were used to compare pTDT values between AS and Non_AS. Polygenic risk for SCZ, ADHD and MDD was significantly over-transmitted to AS affected children in trios . We confirmed these results by conducting 1000 random permutations of diagnosis status . As a negative control, pTDT analysis was repeated using BMI summary statistics. Polygenic over-transmission was neither found in AS nor in Non_AS subgroup  = 0.04562–0.37237).ASD trios with available full diagnosis N = 24 were useCorrelation of pTDT deviations across disorders was assessed  = 2.60 (1.10–6.19)).We finally performed clustering using all psychiatric pTDT deviation values from AS and Non_AS trios. Hierarchical clustering was determined as the most suitable method , to infer gene expression differences between AS and Non_AS, and to compare these differences with expression patterns related with those comorbid disorders.In order to analyze whether polygenic over-transmission related with comorbid disorders  in AS subgroup has biological consequences, we used two recent P < 0.05) in AS vs. Non_AS subjects. However, no gene reached statistical significance in predicted gene expression differences after correcting for multiple testing ). When restricting analysis to genes more differently expressed from S-PrediXcan results (ADHD vs. controls), correlation systematically grows, indicating that the more specific ADHD genes in terms of predicted gene expression, the higher correlation with gene expression differences between AS and Non_AS samples. Interestingly, this growing correlation pattern was neither reproducible in cerebellum nor in lung, reflecting that polygenic overlap between ADHD and AS may have high impact in brain cortex but not in other tissues ), and similar growing patterns of correlation were observed when restricting genes analyzed to those more differentially expressed from S-PrediXcan results (lowering Pthreshold). However, when comparing expression differences across other tissues, significant correlation and same growing correlation trends were observed in cerebellum ) and lung ). Thus, expression similarities between MDD and AS conditions appear not to be restricted to brain cortex but distributed across other tissues.We also identified significant correlation between MDD and AS gene expression patterns in brain frontal cortex ), but to a significant lesser degree than findings in ADHD or MDD.Contrary to MDD and ADHD, polygenic overlap between AS and SCZ could not be explained in terms of predicted expression differences in brain frontal cortex, where no significant correlations were found  instead of the whole ASD sample. Indeed, for the five described comorbid disorders studied here , the polygenic contribution is higher in AS subtype of ASD than in Non_AS autism Fig. . This hi46. In this study, by performing pTDT18, which uses family-based samples, results are not affected by ancestral stratification or other environmental factors that potentially biases case–control studies, such as socioeconomic status.A main utility of PRS is the possibility to evaluate the genetic contributions of different disorders on well-characterized subtypes of a target sample under studyP = 0.025; Supplementary Fig. Given that no correlation between ASD and comorbid disorders  was observed at the pTDT level , which may lead to greater comorbidity with depressive disorders, particularly in adolescence and the transition to adult life. However, the debate whether these features characterize a subtype within HFA or personality traits is beyond the scope of this article. Data presented here are consistent with previous clinical studies23, and we extract from our results that AS meeting Gillberg’s criteria might be a highly polygenic disorder and strongly affected by other psychiatric contributions.One of the greatest novelties of our study is the combination of DSM-IV and Gillberg criteria to diagnose AS subtype. This coincides with Klin et al.15, and place AS, in terms of genetic contributions, closer to conditions as MDD or ADHD rather than to average ASD. From a nosological perspective these results may add to the discussion whether genetic contribution may help subtyping the group of disorders comprised in the term ASD55.However, our observations do contrast with those from other recent studiesNASD_GWAS = 46,351, whereas NMDD_GWAS = 480,359). Moreover, other power dependencies as phenotypic heterogeneity of ASD discovery sample might also explain these results. In this sense, similar inconsistencies have been previously found56, pointing to ASD clinical heterogeneity as a big obstacle for explaining the expected variance in PRS analyses. A deeper phenotypic characterization of the sample  could help better understanding which patients may have higher polygenic risk for comorbid conditions. Indeed, we may not discard the possibility that some forms of high functioning autism, i.e., AS meeting Gillberg criteria, or any HFA with social motivation, could have stronger polygenic psychopathological contributions57 than others.We have to be aware of important limitations in our study, including the small sample size of the sample and its limited phenotypic characterization. Intriguingly, we did not observe significant polygenic over-transmission of ASD common variation in either AS or Non_AS subtypes Fig. . There a23. The data presented here, particularly that related to comorbidity with ADHD, adds on previous elucubrations giving the possibility of a more biological-based explanation of the high psychiatric comorbidity observed in AS.The results herein presented of a polygenic overlap and correlated gene expression profiles between AS and other psychiatric disorders support the idea of AS being qualitatively distinct from Non_AS autism. This adds to previous evidence showing high psychopathological comorbidity (at the symptom level) between AS and SCZ, ADHD, and MDDSupplementary InformationSupplementary Information


Type traits data from 7,714 buffalo cows plus a pedigree file including 18,831 individuals were provided by the Italian National Association of Buffalo Breeders. VCs and EBVs were estimated for each trait fitting a single-trait animal model and using the official DNA-verified pedigree. Successively, EBVs were re-estimated using modified pedigrees with two different proportion of missing genealogies , and two different grouping strategies, year of birth (Y30/Y60) or genetic clustering . The different set of VCs, estimated EBVs and their standard errors were compared with the results obtained using the original pedigree. Results were also compared in terms of efficiency of selection. Differences among VCs varied according to the trait and the scenario considered. The largest effect was observed for two traits, udder teat and body depth in the GC60 genetic cluster, whose heritability decreased by −0.07 and increased by +0.04, respectively. Considering buffalo cows with record, the average correlation across traits between official EBVs and EBVs from different scenarios was 0.91, 0.88, 0.84, and 0.79 for Y30, CG30, Y60, and CG60, respectively. In bulls the correlations between EBVs ranged from 0.90 for fore udder attachment and udder depth to 0.96 for stature and body length in the GC30 scenario and from 0.75 for udder depth to 0.90 for stature in the GC60 scenario. When a variable proportion of missing pedigree is present using the appropriate strategy to define genetic groups and including them in VC and EBV is a worth-while and low-demanding solution.The use of genetic evaluations in the Water Buffalo by means of a Best Linear Unbiased Prediction (BLUP) animal model has been increased over the last two-decades across several countries. However, natural mating is still a common reproductive strategy that can increase the proportion of missing pedigree information. The inclusion of genetic groups in variance component (VC) and breeding value (EBV) estimation is a possible solution. The aim of this study was to evaluate two different genetic grouping strategies and their effects on VC and EBV for composite ( Bubalus bubalis) is a large bovid mainly distributed in the Asian continent where the 97% of its world population is concentrated [The Water Buffalo  is still moderate . AccordiDespite being a routine analysis, it is almost impossible for the farmer to bear the total cost of parentage verification and to have his entire herd genotyped. In detail, in 2019 approximately 10,000 individuals have received a type trait evaluation in Italy but only 4,671 were DNA tested . Hence, Moreover, parentage testing is often reserved only for the best animals causing additional biases in the genetic evaluation being eventually based on a selected and non-random sample of the effective population. Furthermore, the possibility of using a larger number of data, albeit with incomplete pedigree, allows to observe all the variability of the trait of interest and therefore to obtain more accurate estimates.The problem of incomplete pedigree has existed for many years and continues to be one of the main issues in genetic evaluations. Several researchers have worked on possible statistical approaches in order to correct for the presence of gaps in the pedigree . The impOne suggested solution when dealing with an incomplete pedigree is the use of “Genetic Groups” approach, suggested over 30 years ago by The inclusion of genetic groups in VC and EBV is a method that has been adopted and extensively validated, as an example, in beef and dairy cattle . The assHowever, a crucial aspect is the strategy used to define the genetic groups. Therefore, the aim of this study was to evaluate the use of different genetic grouping strategies and its effects on VC and EBV estimation for 5 composite and 10 linear traits in the IMB population.Animal welfare and use committee approval was not needed for this study as datasets were obtained from pre-existing databases based on routine animal recording procedures.Data for the present study were provided by the Italian National Association of Buffalo Breeders (ANASB) and consisted of linear appraisal records from years 2004 to 2020. The initial data set included 79,342 IMB cows from 464 herds phenotyped for fifteen type traits. The type traits were five composite traits, namely, final score (FS), structure (ST), feet and legs (FL), yield potential (YP) and udder teat (UT), and 10 linear traits, namely, stature (STAT), body depth (BD), body length (BL), foot angle (FA), fore udder attachment (FUA), rear udder width (RUW), udder depth (UD), teat placement (TP), teat length (TL), and body condition score (BCS). The median age at evaluation was 46 months. The scale used for scoring varied according to the set of observed traits. Composite traits were scored on a 65–100 scale, linear traits were scored on a 1–50 scale and BCS was scored on a 4.5–9.5 scale. Overall 17 official classifiers were enrolled in the scoring procedures. Data editing consisted of retaining only cows from herds with at least two contemporaries  and whose ascendants were confirmed by a DNA parentage test. Finally, 7,714 buffalo cows belonging to 194 herd with a pedigree containing 18,831 individuals were used in the analysis. Descriptive statistics are in The impact of different genetic grouping strategies on VC, EBV, and their accuracies (ACC) was investigated using the original pedigree and a modified pedigree where two different proportion of missing genealogies, namely, 30% (30) and 60%, (60) were randomly introduced. The choice of using these two thresholds was based not only on the need to mimic the real situation observed across ANASB farms but also to investigate the effect of moderate or massive pedigree gaps. After introducing the missing genealogy, the individual was assigned to a specific genetic group. Genetic groups (GG) were created following two clustering methods.The first method (Y) was based on the year of birth and on an average generation interval, which for the IMB was defined  as 6 years. Individuals born before 1985 was considered as base animals and assigned to group 1. The remainder of the buffaloes was assigned to six different groups.The second grouping strategy (GC) was based on the genetic distances estimated from the original pedigree. The procedure consisted of two steps. In the first step the pedigree-based additive relationship matrix was calculated and used as input for a hierarchical cluster analysis using a complete-linkage clustering method . This mea priori the cut-off level that will identify the number of clusters . Each individual is then assigned to a particular cluster. Following the above mentioned procedure, fourteen different genetic groups were created . The result is a tree that can be plotted as a dendrogram. In the second step, the dendrogram is visually evaluated to define  created .In detail at the end of the procedures, four scenarios were created according to the grouping strategy (Y or GC) and the proportion of missing genealogies (30 or 60%).gold standard. The estimation of VC, EBV, and ACC was repeated 10 times per each scenario . The average number of animals and its standard deviation per scenario are shown in Successively, VC, EBV, and ACC were estimated for each trait presented in The following single-trait animal model with groups was used to estimate VC, their corresponding heritability, and breeding value for each considered trait:yijklm is the score of each trait for a given buffalo cow; μ is the overall mean; hyci is the fixed effect of the ith herd-year of evaluation-classifier ; PAj is the fixed effect of the jth age nested within parity ; DIMk is the fixed effect of the kth days in milk ; NMl is the fixed effect of the lth number of milking ; am is the random additive genetic effect of the mth buffalo; gn is the fixed group effect based on Y or GG and containing the nth ancestor; tmn is the additive relationship between the nth and mth animals and the summation is over all p ancestors of animal m; and eijklm is the random residual effect.where In matrix notation, the model can be written as:where matrix X is an incidence matrix relating phenotypic records in vector y to fixed effects in vector b, matrix Za is an incidence matrix relating phenotypic records in vector y to animal additive genetic effects in vector a, matrix Qa is an incidence matrix relating animals in vector a to unknown parent groups in vector ga. Vectors a and e have means 0 and variances AThe corresponding mixed-model equations were:m will be:Solving the equations the breeding value of an animal The accuracy of EBV was calculated as recommended by i in trait j, fx corresponds to individual inbreeding and va is the additive variance where SE is the standard error for the animal solution Results from different scenarios were compared based on descriptive statistics  of VC, Pearson’s correlations between EBVs grouped by animal status , re-rankings of first 10 bulls, efficiency of selection (SEf) as defined later and genetic trends, estimated by the linear regression of EBVs on year of birth.The SEf was calculated as proposed by The SEf was calculated for the best 10, 30, and 50% animals, respectively.optiSel  while the most affected trait was FA in the scenario GC60 (r = 0.68).The correlations between EBVs in the different scenarios are shown in In the case of bulls, the correlation between EBVs in the grouping GC30 ranged from 0.90 for FUA to 0.96 for STAT and BL, while, in the GC60 scenario the values range between 0.75 for UD to 0.90 for STAT . As expeThe accuracy of breeding values across traits and scenarios for bulls with at least 10 daughters and buffalo cows with own record are presented in The result of the average selection efficiency for the three different selection intensities  for composite and linear trait are summarized in the Observing the average intensity of selection across scenarios, the highest value was in GC30 (81.27%), followed by 78.75, 67.41, and 65.22% in Y30, GC60, and Y60, respectively. The average intensity of selections for the best 10, 30, and 50% were 73.16, 60.40, and 42.31%, respectively.Within each scenario, selection efficiency in composite traits was more effective than in linear traits. When the best 10% of individuals were selected, four out of five composite traits had a selection efficiency higher than 60%, while only three out of 10 linear traits exceeded such a threshold . A similIn terms of standard deviation, the GC30 scenario showed the lowest standard deviation (average = 4.61), while the values obtained from GC60 and Y60 tend to be higher, with an average SD of 7.94 and 7.82, respectively.h2 = 0.35), UD (h2 = 0.23), and FA (h2 = 0.10). Spearman’s rank correlation calculated on 111 bulls in STAT-UD-FA were 0.921–0.884–0.842, 0.913–0.852–0.728, 0.846-0.695-0.659, and 0.811-0.690-0.587 for GC30, Y30, GC60, and Y60, respectively. The consistency of ranking across grouping strategy can also be effectively visualized with a target plot  was +0.032 for composite traits and +0.014 for linear traits . The aveIn this study, the effect of two genetic grouping strategies on the estimation of VC and EBV for type traits in a parentage-tested IMB sub-population was evaluated. In the last three years the IMB has experienced an exponential increase in term of registered animals in the Herd Book. As a consequence, IMB is facing a situation where phenotypic data are available for many animals, but some animals lack complete genealogical data. Records from individuals without pedigree information has been excluded from the genetic evaluation or assumed to have an unknown sire. Such practice results in loss of information and potentially could compromise expected genetic gain . To mitiGenetic groups are normally created according to different criteria, for example on the basis of origin, sex, herd, or year of birth of the individual. The creation of the GG is not a simple procedure and can sometimes present some practical problems. Genetic groups modeling must be balanced as groups with few animals might impair the estimation of the GG effect . At the Results have shown that including GG in the mixed model equation had an effect on the estimates of both VC, which can be observed in As expected, EBVs accuracy decreased when an increased proportion of missing pedigree was simulated . Howeverr = 0.68) was FA, whose h2 was 0.10. In addition, observing the correlations within sex, the Y30/Y60 genetic group strategy showed the highest coefficients for buffalo cows, while for bulls GC30 was the most appropriate for the data. This result was somewhat expected because the strategy based on the hierarchical clustering is strictly related to the relationship matrix, i.e., on the pedigree information. The number of AI bulls in the IMB population is limited (n < 100) and most of them have common ancestors. This means that grouping based on the relationship matrix will be possibly biased by the sire’s pedigree. Actually, all individuals with both parents missing have been assigned to group 1 . Requests to access these datasets should be directed to Ethical review and approval was not required for the animal study because Animal welfare and use committee approval was not needed for this study as datasets were obtained from pre-existing databases based on routine animal recording procedures.SB and MGC conceived and designed the work. DR, RC, GZ, YG, and DA were responsible for updating and editing the data. SB, RDP, and MGC contributed to analyzing the data and interpreting the results. MGC and SB wrote the manuscript with input from all the authors. All authors revised the manuscript, contributed to the article, and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Glycine soja, the wild counterpart to cultivated soybean, Glycine max, harbors much higher genetic diversity and can grow in diverse environments. It can also cross easily with cultivated soybean. Thus, it holds a great potential in developing soybean cultivars with beneficial agronomic traits. In this study, we used 225 wild soybean accessions originally from diverse environments across its geographic distribution in East Asia. We quantified the natural variation of several early vigor traits, investigated the relationships among them, and dissected the genetic basis of these traits by applying a Genome-Wide Association Study (GWAS) with genome-wide single nucleotide polymorphism (SNP) data. Our results showed positive correlation between all early vigor traits studied. A total of 12 SNPs significantly associated with EPH were identified with 4 shared with EGR. We also identified two candidate genes, Glyma.07G055800.1 and Glyma.07G055900.1, playing important roles in influencing trait variation in both EGR and EPH in G. soja.A worldwide food shortage has been projected as a result of the current increase in global population and climate change. In order to provide sufficient food to feed more people, we must develop crops that can produce higher yields. Plant early vigor traits, early growth rate (EGR), early plant height (EPH), inter-node length, and node count are important traits that are related to crop yield.  Glycine max, is an important legume crop that supplies the majority of protein meal and oilseed worldwide [Glycine soja, is analyzed for genetic associations to early vigor traits that are not present in the cultivated population.The cultivated soybean, orldwide . Crop imorldwide . The wilG. max diverged from G. soja 0.27 [G. max have been shown to have a significant effect on diversity on all twenty chromosomes [oja 0.27  or 0.8 moja 0.27 , leavingoja 0.27 . The culoja 0.27 ,6. The gomosomes . By explG. soja are node count, inter-node length, early growth rate, and early plant height. Early growth rate (EGR) and early plant height (EPH) are further analyzed for genotypic dissection using genome-wide association studies (GWAS). These traits have not been studied or used for genetic association in wild soybean thus far. The node count and inter-node length are representative of the density of plant foliage, as each node results in a branching compound leaf. There is a significant correlation between the yield per soybean plant and branch number [Early vigor is a combination of traits that impact the eventual success and yield of a plant. The early vigor phenotypic traits studied in h number . Measureh number , which wh number . All traA genome-wide association study (GWAS) was used in this study to determine genetic associations with complex agronomically beneficial traits, EPH and EGR. GWAS has significant advantages over the tradition approach of complex candidate loci discovery, quantitative trait loci (QTL) mapping. QTL mapping relies on a crossed mapping population from only two individuals to contain all genetic diversity for the trait being analyzed. In addition, QTL mapping is limited by its resolution in the mapping population due to limited recombination events . AlthougG. soja, has been used in the genetic dissection of soybean growth [G. soja to study early vigor phenotypic traits, such as early growth rate, early plant height, node count, and inter-node length, has never been reported. To explore the genetic diversity harbored in the wild soybean, we used GWAS to effectively characterize the genetic architecture of early vigor traits. This study aims to make use of a cutting-edge quantitative trait loci discovery method to dissect the genetic basis of agronomically beneficial traits, EGR and EPH, and their relationships to inter-node length and node count to further crop-improvement techniques.The value of crop wild relatives in crop improvement has been progressively recognized in the past decades . The wiln growth ,25, yieln growth , seed con growth ,27, abion growth ,30,31,32n growth ,40,41,42G. soja, inter-node length to node count, inter-node length to EGR, inter-node length to EPH, node count to EPH, node count to EGR, and EGR to EPH, expressed significant positive correlations, p < 0.001, by Spearman’s correlation test (All trait relationships studied on 225 ecotypes of ion test . As a trp < 0.05 (p < 0.05) by all p-value adjustment and threshold tests . SNP marker ss715598271 explains 10.85% of EGR phenotype variation and 12.42% of EPH phenotype variation. Bracketing markers to ss715598271, ss715598270, and ss715598272 are also shown to be significant by chromosome-wide Bonferroni threshold adjustment in EPH, explaining 8.34% and 8.17% of the phenotypic variation, respectively. Manhattan plots of EGR and EPH  was used for the principle component analysis (PCA) and GWAS. The PCA result was shown in p < 0.05 . All sig and EPH A,B visua and EPH D,E. The The SNP ss715598271, which is significantly associated with both EGR and EPH, and its bracketing markers  associated with EPH, co-localize with a previously identified large QTL, plant height 19-5 . In addiGlyma.07G055800.1, respectively. Two markers, ss715598271 and ss715598272, are within the intron of gene Glyma.07G055900.1. No significant LD is found near the other significant SNPs. These, therefore, were not investigated further for candidate genes.The pairwise linkage disequilibrium (LD) analysis of a 65.3-kb window containing the four significant SNPs  from 4,915,929 bp to 4,928,272 bp on chromosome 7 shows high linkage within this region . Two marp < 0.02)  and studied traits EPH and EGR. The A allele morph is associated with higher EGR and higher EPH than the C allele morph at this marker ( < 0.02) . The sigGlyma.07G055800.1 and Glyma.07G055900.1 are promising candidate genes associated with both EPH and EGR. Glyma.07G055800.1 is predicted to encode a transmembrane protein containing DoH and Cytochrome b-561/ferric reductase transmembrane domains [Arabidopsis is Cytochrome b561/ferric reductase transmembrane with DOMON-related domain protein (CYB561). This protein is responsible for catalyzing transmembrane electron transfer by ascorbate, which is a key metabolite in growth and development of plants [Glyma.07G055900.1 is predicted to encode a Tetratricopeptide repeat (TPR)-like super family protein, playing a role in protein binding and translation initiation [ domains . Its clof plants . Glyma.0itiation .Significant correlations were found between all traits studied, suggesting that EPH, EGR, inter-node length, and node count are all related phenotypic traits . The posG. soja as previously described in the finding of a G. soja-unique salt-tolerant gene GmCHX1 [G. soja. This is supported by significant surrounding markers and high LD in this region.We identified a total of 12 significant SNPs for EPH with 4 shared significant SNPs for EPH and EGR. The most compelling results were found on chromosome 7, in which a contiguous set of markers, ss715598269, ss715598270, ss715598271, and ss715598272, are highly significant, revealing the importance of this genomic location to EGR and EPH. This locus also colocalize with a known QTL, plant height 19-5 , and is e GmCHX1 . FurtherGlyma.07G055800.1 and Glyma.07G055900.1 on chromosome 7, were identified as significantly related to EPH and EGR. Significant markers are located within the introns of these genes and the untranslated 3′ region of Glyma.07G055800.1. Glyma.07G055800.1 encodes a Cytochrome b561 transmembrane protein, or CYB561 in Arabidopsis, a transmembrane protein involved in electron transport [Glyma.07G055900.1, encodes a Tetratricopeptide repeat-like super family protein, homologous to Reduced Chloroplast Coverage 1 (REC1) in Arabidopsis. The Tetratrichopeptide (TPR) domain protein has been shown to be involved in plant height-related phenotypes in Maize and Arabidopsis [REC1 is involved in establishing and maintaining chloroplast coverage in Arabidopsis and could be manipulated in order to influence energy intake and yield [G. soja-type REC1, Glyma.07G055900.1, is likely involved in similar chloroplast coverage and plant hormone signaling pathways to those found in Maize and Arabidopsis, with a direct relationship to photosynthesis efficiency and growth rate, and therefore is a promising candidate gene to further investigate for crop improvement.Two candidate genes, ransport . Glyma.0bidopsis ,52 and ibidopsis ,54. It iGlyma.07G055800.1 and Glyma.07G055900.1, related to early vigor traits, EGR and EPH. These traits are highly beneficial to agriculture and might have been artificially selected for in breeding practices within cultivated soybean G. max. However, the extent of adaptation by selection in the cultivated soybean population is limited by the small gene pool. We explored the genetic architecture of these traits in the more diverse wild soybean G. soja to further improve our cultivation practices beyond the limited genotype of G. max. Further investigation, such as function validation of these candidate genes, will shed light on understanding the molecular mechanisms of these agriculturally and ecologically important traits. Meanwhile, it will provide a foundation for soybean trait improvement by traditional breeding, biotechnology, or genome editing. The long-term goal is to make full use of the wild genetic resources to meet the global challenges of agriculture sustainability and food security.This study identified two candidate genes, G. soja accessions obtained from the USDA Soybean Germplasm Collection were used for measurements and analysis. The original geographic distribution of these accessions includes areas in China, Japan, Russia, and South Korea  [Previously identified markers, single nucleotide polymorphisms (SNPs), for all 225 ase.org) . All marase.org) . All marase.org) ,58,59.Pair-wise correlations among the four traits were evaluated with Spearman’s analysis due to non-normal distributions to determine the relationship between traits . It has been suggested that normalization is not necessary for genome-wide association analysis when the data size is relatively large to avoid error, such as false positives . Thus, tp-value  for each marker [p < 0.05 or q < 0.05 cutoff.A PCA was conducted using the GAPIT package . A Mixedh marker . Genome-h marker ,66, wereG. soja. The annotated soybean reference genome, Wm82.a2.v1 , was used to determine these genes along with further investigation into the function using Phytozome [All genes within 50 kb of significant SNPs were evaluated for potential association with each phenotype. The interval was used based on the average linkage disequilibrium reported in hytozome , TAIR [6hytozome , and BLAhytozome . Known Qhytozome  in each hytozome .


Bayesian regression methods that incorporate different mixture priors for marker effects are used in multi-trait genomic prediction. These methods can also be extended to genome-wide association studies (GWAS). In multiple-trait GWAS, incorporating the underlying causal structures among traits is essential for comprehensively understanding the relationship between genotypes and traits of interest. Therefore, we develop a GWAS methodology, SEM-Bayesian alphabet, which, by applying the structural equation model (SEM), can be used to incorporate causal structures into multi-trait Bayesian regression methods. SEM-Bayesian alphabet provides a more comprehensive understanding of the genotype-phenotype mapping than multi-trait GWAS by performing GWAS based on indirect, direct and overall marker effects. The superior performance of SEM-Bayesian alphabet was demonstrated by comparing its GWAS results with other similar multi-trait GWAS methods on real and simulated data. The software tool JWAS offers open-source routines to perform these analyses. The fixed effects are assigned flat priors. The residuals, Assuming that individuals have all traits measured with a general mean as the only fixed effect, we write the multi-trait model for individual e.g., multi-trait BayesCj can be written as j for trait k is zero or not, and i” and Allowing each locus to affect any combination of traits, in a multiple-trait Bayesian variable selection method, i, q × 1 vectors of residuals. The details of parameter estimation are discussed in The linear SEM is composed of two parts: the measurement equation analyzing the relationship between the observable variables and latent variables, and the structural equation capturing the connections among latent variables . These ti.e., phenotypes, are fitted in the SEM model  as:yi=Λi.e., i results in a j. Given the causal structure above, the To illustrate, we assume that the phenotypes of three traits for each individual .The genetic value that is attributed to genomic window Oryza sativa individual accessions was used in the analysis. Three traits were considered, including plant height (PH), flowering time in Arkansas (FTA), and panicle number per plant (PN) in our GWAS. After removing the records with missing data for these three traits and genotype with minor allele frequency http://www.ricediversity.org/. It has been shown that using a threshold of WPPA The Rice Diversity Panel with 413 γ): fewer QTL with large effects   were used for comparing both the pAUC5 mean across all scenarios  and the pAUC5 mean for each level of γ .The performances of SEM-BayesCe.g., e.g., The GWAS results based on overall, direct and indirect effect were shown in e.g., IC1 is used to demonstrate the performance of SEM-BayesCThe causal structure among three traits is inferred by the IC algorithm from the estimated posterior distribution of the residual covariance matrix in the multi-trait BayesCDirect, indirect, and overall SNP effects for all markers are estimated from SEM-BayesCThe results of GWAS from SEM-BayesCe.g., the overall effect of SNP “id1024159”, as shown in For the overall effects, in the SEM-GWAS, window D achieved -log 14.21; in the SEM-BayesCAs shown in The complex causal relationships among multiple traits are usually not considered in conventional multi-trait GWAS. Here we propose the SEM-Bayesian alphabet method to incorporate pre-inferred causal structures among multiple traits into multi-trait Bayesian regression methods. SEM-Bayesian alphabet accounts for causal structures among traits, and has the potential advantage of estimating causal effects, providing genomic window-based inference, as well as providing a comprehensive understanding of the underlying biological mechanism.γ) and different numbers of QTL. The level of gene pleiotropy, e.g., proportion of markers affecting different combinations of traits as shown in SEM-Bayesian alphabet provides more interpretation into biological mechanisms than Bayesian regression methods by decomposing the overall SNP effects into direct and indirect SNP effects. In SEM-Bayesian alphabet, posterior distributions of the overall, direct, and indirect SNP effects, as well as causal structure coefficients, are obtained, which are used to make inferences about these parameters. Compared to the typical GWAS method incorporating causal structure among multiple traits, such as SEM-GWAS, SEM-Bayesian alphabet obtains the posterior distributions for the proportion of variance attributed to a genomic region to detect causal loci (


Detection of Identical-By-Descent (IBD) segments provides a fundamental measure of genetic relatedness and plays a key role in a wide range of analyses. We develop FastSMC, an IBD detection algorithm that combines a fast heuristic search with accurate coalescent-based likelihood calculations. FastSMC enables biobank-scale detection and dating of IBD segments within several thousands of years in the past. We apply FastSMC to 487,409 UK Biobank samples and detect ~214 billion IBD segments transmitted by shared ancestors within the past 1500 years, obtaining a fine-grained picture of genetic relatedness in the UK. Sharing of common ancestors strongly correlates with geographic distance, enabling the use of genomic data to localize a sample’s birth coordinates with a median error of 45 km. We seek evidence of recent positive selection by identifying loci with unusually strong shared ancestry and detect 12 genome-wide significant signals. We devise an IBD-based test for association between phenotype and ultra-rare loss-of-function variation, identifying 29 association signals in 7 blood-related traits. Accurately measuring genetic relatedness by Identical-By-Descent (IBD) segments is challenging in biobank-level genome data. The authors present IBD method FastSMC, which when applied to the UK Biobank gives a detailed picture of genetic relatedness and evolutionary history in the UK over the past 2000 years. Utilizing such datasets to understand disease and health outcomes requires understanding the fine-scale genetic relationships between individuals. These relationships can be characterized using short segments (less than 10 centimorgans [cM] in length) that are inherited identical by descent (IBD) from a common ancestor between purportedly unrelated pairs of individuals in a dataset5. Accurate detection of shared IBD segments has a number of downstream applications, which include reconstructing the fine-scale demographic history of a population9, detecting signatures of recent adaptation11, discovering phenotypic association13, estimating haplotype phase15, and imputing missing genotype data17, a key step in genome-wide association studies (GWAS)18. Detection of IBD segments in millions of individuals within modern biobanks poses a number of computational challenges. Although several IBD detection methods have been published21, few scale to analyses comprising more than several thousand samples. However, scalable methods that do exist trade modeling accuracy for computational speed. As a result, current IBD detection algorithms are either scalable but heuristic, solely relying on genotypic similarity to detect shared ancestry and not providing calibrated estimates of uncertainty, or too slow to be applied to modern biobanks. Here, we introduce an IBD detection algorithm, called fast sequentially Markovian coalescent (FastSMC), which is both fast, enabling IBD analysis of modern biobank datasets, and accurate, relying on coalescence modeling to detect short IBD segments (down to 0.1 cM). FastSMC quantifies uncertainty and estimates the time to most recent common ancestor (TMRCA) for individuals that share IBD segments. It does so by efficiently leveraging information provided by allele sharing, genotype frequencies, and demographic history, which results in a cost-effective boost in accuracy.Large-scale genomic collection, through efforts like the NIH All of Us research programWe validate the scalability, accuracy, and robustness of the FastSMC algorithm in detecting IBD sharing within recent millennia using extensive coalescent simulation. Leveraging the speed and accuracy of FastSMC, we analyze IBD sharing in 487, 409 phased individuals from the UK Biobank dataset, identifying and characterizing  ~214 billion IBD segments transmitted by shared ancestors within the past 50 generations. This network of shared ancestry enables us to reconstruct a fine-grained picture of time-dependent genomic relatedness in the UK. Analysis of the distribution of recent sharing within specific genomic regions reveals evidence of recent positive selection at 12 loci. We find the sharing of IBD to be highly correlated with geographic distance and the sharing of rare variants. Leveraging this correlation, we detect 20 associations to genomic loci harboring loss-of-function (LoF) variants with seven blood-related phenotypes. These results underscore the importance of modeling distant relatedness to reveal subtle population structure, recent evolutionary history, and rare pathogenic variation.19 speed and memory requirements and thus enables us to very efficiently detect IBD candidate regions in millions of genotyped samples. GERMLINE2 utilizes hash functions to identify pairs of individuals whose genomes are identical in small genomic regions, thus being Identical-By-State (IBS). The presence of these short identical segments triggers a local search for longer segments that are likely to reflect recent TMRCA and thus IBD sharing in the region. Although the original GERMLINE algorithm utilizes a similar strategy, GERMLINE2 offers two key improvements, which result in faster computation and lower memory consumption. First, the GERMLINE algorithm can become inefficient in regions where certain short haplotypes can be extremely common in the population (e.g. due to high linkage disequilibrium), which results in hash collisions across a large fraction of samples, effectively reverting back to a nearly all-pairs analysis and monopolizing computation time. GERMLINE2 avoids this issue by introducing recursive hash tables, which require haplotypes to be sufficiently diverse before they are explored for pairwise analysis and significantly decrease downstream computation  TMRCA along the segment. FastSMC can be parallelized to efficiently scale up to biobank datasets. The FastSMC software implements both the GERMLINE2 and ASMC algorithms, and is freely available.The algorithm we developed, called FastSMC, detects IBD segments using a two-step procedure. In the first step (identification), FastSMC uses genotype hashing to rapidly identify IBD candidate segments, which enables us to scale to very large datasets. In the second step (verification), each candidate segment is tested using a coalescent hidden Markov model (HMM), which enables us to improve accuracy, compute the posterior probability that the segment is IBD , and provide an estimate for the TMRCA in the genomic region. The identification step leverages the GERMLINE2 algorithm that we developed and present here, which improves over GERMLINE’s2. We benchmarked IBD detection for FastSMC in addition to three other widely used or recently published IBD detection methods: GERMLINE19, RefinedIBD20, and RaPID21. Parameters for all methods were optimized to maximize accuracy and evaluated on the detection of IBD segments within the past 25, 50, 100, 150, or 200 generations on simulated populations with a European ancestry  to produce an improved estimate of IBD segment age. We found FastSMC’s segment age estimates to be more accurate than a length-based estimator . For instance, within the past  ~300 years, two individuals born in North London share on average 0.0092 common ancestors and two individuals born in Birmingham share on average 0.0043 common ancestors. In contrast, and despite the relative geographic proximity, an individual born in North London shares on average a substantially lower 0.00059 ancestors with one born in Birmingham. We observed similar trends when we restricted this analysis to samples of self-reported and inferred non-White British ancestry2, as shown in Supplementary Fig. Next, we analyzed the network of recent genetic relatedness for 432,968 samples for whom birth coordinates are available. As observed in previous studies of fine-scale genetic structure30. We computed the fraction of individuals who find at least one close genetic relative within the UK Biobank dataset . However, by conditioning on the presence of recent shared ancestors, the IBD matrix is better suited to capture genomic relationships that are recent but would not result in large outlier entries in the GRM. To compare the performance of our IBD-based approach with an approach based on allele sharing in the absence of extremely close relatives, we removed individuals with very recent genetic ties  and used a simple machine learning approach (K Nearest Neighbors) to perform the prediction of birth coordinates. Prediction of birth coordinates using the IBD matrix was 44% more accurate than prediction based on allele sharing , substantially higher than the correlation achieved using allele sharing .As expected, entries of the IBD matrix within the past 10 generations are highly correlated to corresponding allele sharing entries of the genetic relatedness matrix (GRM) that is widely used in applications such as principal component analysisr = 0.28, 95% CI =  by bootstrap using postcodes) with present-day population density  statistic23, capturing the density of recent coalescence events along the genome within the past 50 generations  with the DRC150 statistic that was computed using fewer samples from a previous UK Biobank data release by Palamara et al.23, the DRC50 statistic reflects more recent coalescence events than the DRC150 statistic, and thus more specifically reflects natural selection occurring within recent centuries.We analyzed locus-specific patterns of recent shared ancestry, seeking evidence for recent positive selection by identifying loci with unusually high density of recent coalescence times in the UK Biobank dataset. We computed the DRC50 p < 0.05/52, 003 = 9.6 × 10−7; Fig. NBPF137, HLA38), nutrition , and mucus production (MUC223). We also identified 7 other loci, harboring genes related to immune response , mucus production , tumor growth , as well as genetic disorders . We checked that these regions are not extreme in recombination rate or marker density , which tend to be very recent in origin and are usually co-inherited through recent ancestors who carried such variants. We verified this by testing for correlation between the sharing of IBD segments at various time scales and the sharing of rare variants for the  ~50k individuals included in the UK Biobank’s initial exome sequencing data release49 , which we refer to as FN mutations51. We compared the sharing of FN mutations to the sharing of IBD segments in the past 10 generations within all postcodes in the UK . The correlation between IBD sharing and FN variant sharing decreases as N increases, with slightly higher correlation for more recent IBD segments, while deeper IBD sharing (within 50 generations) tends to provide better tagging of ultra-rare variants of slightly higher frequency  and any IBD segments they shared with individuals in the non-sequenced cohort . As expected due to the effects of natural selection54, the LoF variants belonging to a small subset for which an age estimate has recently been computed55 are slightly younger than other exome-sequenced variants  non-sequenced cohort, we tested for association between carrying a LoF-segment (the LoF-segment burden) and the phenotype known to be associated with that gene. This approach would be optimal when IBD individuals carry a LoF variant that arose prior to the TMRCA of their shared segment. We thus tested 10 transformations of the LoF-segment metric for association with phenotype to model uncertainty about the age distribution of the underlying causal variants.Based on this correlation between sharing of mutations and sharing of IBD segments, we hypothesized that IBD sharing of disease causing mutations would be predictive of disease. In particular, individuals who share an IBD segment with a pathogenic rare variant carrier in a known gene have a higher probability of carrying the pathogenic variant (by inheriting it from the shared ancestor) than the general population, and would thus be at increased risk for the phenotypic effect. The UK Biobank exome pilot49 associations with seven blood-related traits at p < 0.05/10 = 0.005 , reflecting 14,249 genes tested using 10 transformations; Fig. 49. The ratio of these variances was 19.64% on average, corresponding to the decrease in effect-size (in units of variance) due to estimation error and inclusion of segments sharing the non-LoF haplotype. We note that, due to phase uncertainty, we expect LoF-segment burden to explain at most 50% of the variance explained by direct sequencing. Assuming the ratio of variances corresponds to the squared correlation between the LoF-segment burden estimate and the true exome burden, the LoF-segment burden estimator has statistical power equivalent to a direct exome sequencing study of 19.64% of the 303, 125, or  ~60k samples57 – effectively doubling the size of the exome study. This demonstrates FastSMC’s accuracy and, more broadly, the utility of leveraging distant relatedness in identifying disease associations.Using our LoF-segment burden, we replicated 11 out of 14 previously reportedp < 0.05/) spanning 33 genomic loci in the non-sequenced cohort by only leveraging LoF-segments  spannts Table –25.TableMPL (two-sided t-test p = 1.99 × 10−7), which encodes the thrombopoietin receptor that acts as a primary regulator of megakaryopoiesis and platelet production and has not been previously implicated by genome-wide scans of either rare or common variants. We also detect several associations in genes that were not detected using exome sequencing but have been previously implicated in genome-wide scans for common variants, including associations between eosinophil count, GFI1B (two-sided t-test p = 1.92 × 10−7) and RPH3A (two-sided t-test p = 7.63 × 10−14)59, and associations between platelet count, IQGAP2 (two-sided t-test p = 6.52 × 10−8) and GP1BA (two-sided t-test p = 1.43 × 10−7)60. We also identify genes that were previously associated with other blood-related phenotypes in other populations, including the association between platelet distribution width and APOA5 (two-sided t-test p = 1.94 × 10−8), a gene that encodes proteins regulating the plasma triglyceride levels; common variants linked to this gene have been linked to platelet count in individuals of Japanese descent61. We detect association between red blood cell distribution width and APOC3 (two-sided t-test p = 3.67 × 10−11), a gene encoding a protein that interacts with proteins encoded by other genes  associated with the same trait. The association between APOC3 and platelet count was also detected with our WES-LoF burden analysis (two-sided t-test p = 2.13 × 10−7) and by previous studies based on common SNPs59. We also found an association between CHEK2 and both mean corpuscular hemoglobin (two-sided t-test p = 1.43 × 10−7) and mean platelet volume (two-sided t-test p = 1.93 × 10−7). This gene plays an important role in tumor suppression and was found to be associated with other blood traits, such as platelet crit, using both exome sequencing49 and common GWAS SNPs59, and red blood cell distribution width58. Overall, this analysis highlights the utility of applying FastSMC on a hybrid sequenced/genotyped cohort to identify novel, rare variant associations and/or characterize known signals in larger cohorts.Our exome-wide significant signals include the association between platelet count and We developed FastSMC, an algorithm for IBD detection that scales well in analyses of very large biobank datasets, is more accurate than existing methods, enables estimating the time to most recent common ancestor for IBD individuals, and provides an estimate of uncertainty for detected IBD regions. We leveraged FastSMC to analyze 487,409 British samples from the UK Biobank dataset, detecting  ~214 billion IBD segments transmitted by shared common ancestors in the past  ~1500 years. This enabled us to obtain high-resolution insight into recent population structure and natural selection in British genomes. Lastly, we used IBD sharing between exome sequenced and non-sequenced samples to infer the presence of LoF variants, successfully replicating known burden associations with seven blood-related complex traits and revealing novel gene-based associations.15, haplotype-based associations13, as well as in the estimation of evolutionary parameters such as recombination rates63, or mutation and gene conversion rates64. More broadly, the observed geographic heterogeneity in IBD sharing and fine-scale structure is a reminder that human populations substantially deviate from random mating, even within small geographic regions. In particular, efforts to generate optimal sequenced reference panels for imputation65 may be greatly improved by directly sampling based on distant relatedness. Our findings also provide empirical support to recent hypotheses that relatedness within available genomic databases is sufficiently pervasive to enable recovering the genotypes of target individuals31, or to re-identify individuals through familial searches32. As demonstrated by our analysis, leveraging IBD to impute ultra-rare variant burden from small sequenced reference panels can be an effective approach to reveal gene associations in complex traits and diseases. Although our analysis only considered association to individual genes, in principle genome-wide IBD sharing could also be leveraged to enhance common SNP-based risk prediction, which is particularly relevant for non-European cohorts where sequencing is limited.The level of geographic granularity that could be captured by the IBD networks emerging from our analysis underscores the importance of modeling distant relationships in genetic studies. Indeed, detecting IBD segments among close and distant relatives is a key step in many analyses, such as genotype imputation or haplotype phase inference14. This is particularly true in regions that harbor IBD segments, which are of interest in our analysis. Nevertheless, our analysis has shown the presence of substantial regional heterogeneity in the extent to which individual genomes are spanned by IBD segments, which is likely reflected in a heterogeneous quality of phasing, as well as other downstream analyses, such as imputation, that rely on the presence of IBD segments. Second, FastSMC requires the input of a demographic model and allele frequencies as a prior in order to accurately estimate the age of IBD segments, and is thus subject to biases whenever the demographic model is misspecified. Although we have verified that these biases are not substantial, future work may enable us to simultaneously estimate IBD sharing and demographic history. Like ASMC, FastSMC may tolerate reasonable levels of model misspecification, but a user should be aware that issues such as substantial inaccuracies in the genetic map or strong heterogeneity of genotyping density or quality may lead to biases. Third, FastSMC currently does not enable analysis of imputed data, a limitation that is shared by other IBD detection methods. Finally, the accurate identification of extremely short IBD segments (<1 cM) spanning hundreds of generations remains a challenge, both computationally (as the number of such segments increases very rapidly) and methodologically . This underscores the importance of quantifying uncertainty through estimates such as IBD segment quality, precision, and recall, which are affected by parameter choices for FastSMC and other IBD detection methods. Our analysis detected an average of 1.8 IBD segments per pair in the UK Biobank dataset within the past 50 generations. This is consistent with a previous study focusing on longer and more recent segments (average of 0.1 segments  >2.9 cM per pair66), but less than another recent study in a similar length range (average 1.96 segments  >2 cM per pair67). Taking uncertainty of the detected IBD segments into account may reconcile these estimates.FastSMC inherits some of the limitations and caveats of the GERMLINE and ASMC algorithms. First, as with most IBD detection methods, FastSMC requires the availability of phased data. We note, however, that when very large cohorts are analyzed, long-range computational phasing results in high-quality haplotype estimation with switch errors rates as low as one every several tens of centimorgans66), or methods that rely on the positional Burrows-Wheeler transform (PBWT) data structure68. Several methods now exist to reconstruct gene genealogies in large samples72. Two recent methods substantially improved the scalability of this type of analysis, but they either focus on data compression, relying on fast heuristics to achieve scalability at the cost of deteriorating accuracy in sparse array data71, or employ further modeling that requires sequencing data72, with a computational cost that is quadratic in sample size . It is of continued interest to identify synergies between fast heuristic and accurate probabilistic approaches, which can lead to computationally efficient methods that remain robust to real world data heterogeneity. Although in this work we focused on large modern biobanks comprising SNP array data, sequencing datasets are quickly becoming available. FastSMC may be tuned to enable the analysis of sequencing data as well. Finally, looking at downstream applications, a direction of future work will be to leverage FastSMC to better control for subtle population stratification for both rare and common variants in association studies. Our results show that geographic coordinates can be effectively inferred from recent IBD sharing, and suggest that this may be a path towards capturing subtle environmental covariates30 that are missed by genome-wide IBS-based approaches. FastSMC’s output could thus account for subtle stratification even when the non-genetic confounder has a small and sharp distribution, where methods such as genomic control, PCA, or mixed models have limited efficacy73.In addition to algorithmic improvements to address the limitations above, we believe there are a number of interesting future extensions and interactions with other existing methods in this area. FastSMC’s identification step currently relies on the GERMLINE2 genotype hashing strategy. It will be interesting to test other heuristic strategies for rapidly identifying identical segments, such as the locality-sensitive hashing strategy recently implemented in the iLASH algorithm  all haplotypes are converted to binary sequences and efficiently hashed into bins of identical segments; (3) for each bin that contains more individuals than a fixed threshold (i.e. a low complexity bin) step 2 is recursively performed for window w + 1 until no more low complexity bins are found; (4) all pairs of individuals sharing within a bin are then recorded in a separate hash table that stores putative segments; (5) pairs of individuals sharing contiguous windows that are sufficiently long are reported for validation. The primary computation speed-up comes from the recursive hashing step, which requires haplotypes to be sufficiently diverse before they are explored for pairwise analysis and stored . GERMLINE2 thus does not require any backtracking and only a small number of physical windows need to be stored in memory at any time (only enough to perform the recursion), allowing the method to run on input data of unlimited length.FastSMC’s identification step leverages genotype hashing, a strategy that was introduced by the GERMLINE algorithm23 once the buffer is full. ASMC is a coalescent-based HMM74 that estimates the posterior of the coalescence time, or TMRCA, for a pair of individuals at each site along the genome using either sequencing or SNP array platforms. It leverages a demographic model as prior on the TMRCA, which increases accuracy in detecting regions of low TMRCA26, but would be infeasible to apply to the analysis of all pairs of genomes, and is thus only applied with the goal of validating previously identified candidate IBD regions. The hidden states of the HMM are discretized intervals, corresponding to a user-specified set of TMRCA intervals. The HMM emissions probabilities correspond to the probabilities of observing both the genotypes of the pair of analyzed individuals and the frequencies of mutations along the sequence, given the pair’s TMRCA at each site, and the frequency of the allele27. The HMM transitions between hidden states correspond to changes in TMRCA along the genome due to recombination events, based on the conditional Simonsen-Churchill model76. The demographic history of the analyzed haplotypes is first estimated using other methods27 and provided in input, so that the initial state distribution, the transition, and the emission probabilities can be computed. The most likely posterior sequence of TMRCAs along the genome is inferred using a dynamic programming approach that requires computing time linear in the number of hidden states, leading to a substantial speed-up over an HMM’s standard forward-backward algorithm, which scales quadratically in the number of hidden states. When decoding the buffer of candidate segments, ASMC computes the posterior of the coalescence time for each candidate segment and each site from the minimum starting position to the maximum ending position in the buffer. At each site, if the posterior of coalescence time being between present time and the user-specified time threshold is higher than its prior, the site is considered to be IBD and the IBD segment is extended to the next site if the same condition is still satisfied, obtaining multiple IBD segments, all shorter than the original IBD candidate segments. The average probability of the TMRCA being between present time and the user-specified time threshold is computed over all sites until the segment breaks. This average probability corresponds to an IBD quality score: the higher it is, the more likely the segment is IBD. Each segment is also associated with an age estimate corresponding to the average MAP along the segment. FastSMC finally outputs each IBD segment with its corresponding IBD quality score and age estimate.Every segment detected by GERMLINE2 in the identification step is added to a buffer of candidate segments. These segments are immediately decoded by the ascertained sequentially Markovian coalescent (ASMC) algorithm23. This enabled us to efficiently parallelize analyses on the UK Biobank dataset, and prevented issues due to low marker density in centromeres. In addition, FastSMC enables a user to parallelize the analysis by specifying the total number of computing jobs to be run in parallel. If the user requests to run K independent parallel jobs, the total number of K groups of approximately equal number of pairs. More in detail, the samples are divided into K is such that S is an integer. Each parallel job then processes a unique pair of sets {i, j} for 1 ≤ i ≤ j and 1 ≤ j ≤ S. Note that only samples in sets i and j are loaded in memory, which leads to substantially lower memory footprint when large data sets are processed. IBD detection is then only performed for the Ni × Nj pairs across sets i and j if i ≠ j, or for the i if i = j. We leveraged this approach to extensively parallelize the analysis of the UK Biobank dataset.We divided the genome in 39 autosomal regions from different chromosomes or separated by centromeres23, which is described in this section. We used the ARGON simulator (v.0.1.160615)77, incorporating recombination rates from a human chromosome 2 and a recent demographic model for European individuals (Northern European [CEU] population27). For each dataset, we simulated 300 haploid individuals and a region of 30 Mb. To simulate SNP array data, we subsampled polymorphic variants to match the genotype density and allele frequency spectrum observed in the UK Biobank dataset. We used recombination rates from the first 30 Mb of chromosome 2 (average rate of 1.66 cM per Mb). No genotyping or phasing error was introduced in our simulations. We simulated one dataset following this setup to fine-tune parameters, and 10 other datasets  for accuracy benchmarking. The demographic model and genetic map used to simulate the data were used when running FastSMC, unless otherwise specified. When testing FastSMC’s robustness to demographic model misspecification, we simulated data under a constant population size of 10,000 diploid individuals, but ran FastSMC assuming a European demographic model.Unless otherwise specified, all simulations use the setup of Palamara et al.22. This is often due to the fact that current IBD detection algorithms cannot effectively estimate the TMRCA of a putative IBD segment. Downstream analyses of shared segments (e.g. refs. 9) thus often resort to using the length of detected segments as a proxy for its age, since a segment’s length is expected to be inversely proportional to its TMRCA. We benchmarked all methods using several such time thresholds , testing all polymorphic sites for all pairs of genomes in the simulated data, across 10 coalescent simulations. Accuracy was quantified using the area under the precision-recall curve (auPRC), which effectively addresses issues with class imbalance that are expected in this analysis due to the low prevalence of IBD sites compared to non-IBD sites. Precision represents the fraction of identified sites that are indeed IBD (following the TMRCA-based definition of IBD), and recall represents the fraction of true IBD sites that are successfully identified. Particularly, for a given IBD time threshold, a site inferred to be IBD by one of the methods was considered correct (true positive) if the true TRMCA at this site was indeed below the specified IBD time threshold, and incorrect  if the true TRMCA at this site was above the IBD time threshold. Similarly, a site that was not reported to be IBD by the tested method was considered correct/incorrect  if the true TMRCA at the site was found to be below/above the IBD time threshold. We used these definitions to compute the precision and recall values for all methods. Each method presents different parameters, which can be used to tune precision and recall, e.g. by allowing a more or less permissive detection of IBD segments. String-matching methods (GERMLINE and RaPID) report long, approximately IBS regions and do not produce calibrated estimates of segment quality. A commonly used proxy for the likelihood of a detected IBS segment being IBD is its length, with longer IBS segments being more likely to be IBD than shorter ones. In lack of an interpretable measure of accuracy, precision and recall for the output of GERMLINE and RaPID was thus tuned by using different segment length cutoffs. RefinedIBD and FastSMC, on the other hand, both provide an explicit quantification of segment quality. RefinedIBD outputs a LOD score for each segment, while FastSMC computes a segment’s IBD quality score, which is the posterior of the TMRCA being between present time and the user-specified time threshold. We thus used LOD score and IBD quality score to tune precision and recall of RefinedIBD and FastSMC, respectively. Each method presents a number of additional parameters, which we further optimized using a grid-search, so that each method can be run with a set of parameters that is as close to optimal as possible. Despite the extensive tuning, not all accuracy values could be explored by all methods. Namely, some recall values cannot be achieved using realistic parameters, due to factors such as the minimum allowed LOD parameter for RefinedIBD, the time discretisation introduced in FastSMC and the minimum length parameter for all methods. We thus evaluated all algorithms by restricting the comparison to the range of recall values that could be achieved by all methods, which we refer to as common recall range. Furthermore, some of these parameters affect the speed of each algorithm. The parameters we chose for comparing methods are optimized for maximum accuracy, although we avoided parameters that would result in degeneracies .We compared FastSMC to the most recent published software version available for existing methods at the time we conducted this analysis: germline-1-5-2, refined-ibd.23Apr18.249 and RaPID_v.1.2. Throughout this work, we define a genomic site to be shared IBD by a pair of phased haploid individuals if their TMRCA at the site is lower than a specified time threshold (e.g. 50 generations). This is a natural definition for IBD sharing, as it is closely related to several other quantities that are of interest in downstream analyses, such as genealogical relatedness or the probability of sharing rare genomic variants. We note, however, that a number of other definitions can be found in the literature19, RefinedIBD20, and RaPID21) and each IBD time threshold , we performed a grid-search over possible parameter values to optimize the accuracy on one simulated dataset and select the best set of parameters. For each method, we then explored the obtained set of parameters to make the algorithm faster while negligibly compromising the accuracy . We finally used 10 independent simulated datasets to validate the accuracy and the UK Biobank dataset to measure running time and memory usage  were computed by bootstrap using 39 genomic regions as resampling unit. The use of genomic regions as resampling unit, rather than individuals, ensures that approximately independent bootstrap replicates are utilized. These 39 genomic regions were obtained by dividing the genome  in regions from different chromosomes or separated by centromeres.g to the most recent common ancestor is known, the total length of a randomly chosen shared IBD segment follows an exponential distribution with rate 1/2g per Morgan6. The likelihood function is thus given by l denotes the segments length in Morgans. As A common way to estimate the age of an IBD segment is to use its length to obtain a maximum likelihood estimator (MLE). When the time in generations Ne, the probability of finding a common ancestor at a given site for a pair of individuals is exponentially distributed with mean Ne. The probability of finding a common ancestor before any time threshold T is thus given by Ne → ∞ i.e T > 0. We estimate this probability using the fraction of genome shared by IBD segments denoted by fT. Let Γ denote the set of sites along the genome and θ the demographic model. Ne using T > 0, where fT. Note that, for simplicity, we infer a single aggregate effective population size across the past T generations rather than comparing more complex demographic models.Assuming a constant effective size 2 contains 487,409 samples, which were phased at a total of 678,956 autosomal biallelic SNPs using Eagle215. In all, 49,960 of these individuals were also exome-sequenced resulting in  ~4 million polymorphic variants, 98.4% of which have frequency <1%49. We used the same sets of unrelated individuals  and individuals of self-reported and inferred White British ancestry  as defined by Bycroft et al.2. Related individuals refer here to ≤3rd degree relatives, e.g. first degree cousins, estimated using the software KING78. The UK Biobank cohort predominantly contains samples of White British ancestry2 and the inclusion of non-White British samples did not result in substantial biases for analyses of population structure and natural selection. We thus decided not to exclude samples based on ancestry, unless otherwise specified, so that results are representative of the average UK Biobank participant. FastSMC was run on the UK Biobank data set using the optimal set of parameters for IBD detection within the past 50 generations, using the demographic model for CEU individuals inferred by Terhorst et al.27. We note that several candidate demographic models could be adopted9 and that simultaneous estimation of IBD sharing and demographic model are an attractive direction of future investigation.The UK Biobank cohortBirth coordinates  were available for 432,968 individuals in the cohort in the Ordnance Survey Great Britain 1936 (OSGB36) Eastings and Northings system. We refer to these coordinates as X and Y coordinates, which can be converted into longitude and latitude. Home addresses at assessment were available for 482,832 samples in the OSGB36 Eastings and Northings system. We refer to these coordinates as home addresses. We analyzed population structure using 120 postcodes in the UK, only looking at the first one or two letters indicating the city or region. Postcodes BT, BF, BN, and CR were not included due to lack of samples.i, j) corresponds to the fraction of genome shared by common ancestry in the past 10 generations between individuals i and j. We computed the largest connected component of this matrix, which comprised all but 102 individuals, which we excluded from further analysis. We then applied an Agglomerative Hierarchical Clustering algorithm for Sparse Similarity Matrices using average linkage with the sparseAHC library. We obtained a dendrogram with 432,866 leaves (one for each sample) and a single root. Each node is annotated with a distance from the root, ranging from 0 (the root itself) to 1 (the leaves). A node’s distance from the root corresponds to the fraction of genome shared by individuals whose TMRCA is such a node. To visualize clustering of individuals in Fig. X-axis and 126 lines along the Y-axis). In each cell, we computed the most represented cluster  and individuals from that cluster are shown in the corresponding color. The transparency of all points within a cell (ranging from 0 to 1) was set to the fraction of individuals from that cell corresponding to the most represented cluster. All light gray dots correspond to individuals that are either in clusters containing <500 samples or part of a cluster different from the one represented in the grid cell. Including/excluding individuals of non-White British ancestry has a negligible impact on this analysis, as most of these samples belong to smaller clusters not represented in Fig.  We constructed a similarity matrix for all individuals with birth coordinates in the UK Biobank dataset  using the sharing of IBD segments within the past 10 generations. This resulted in a sparse 432,968 × 432,968 matrix, where entry , standardized to have mean 0 and variance 1 for each column. Sharing of very close relatives is highly informative of geographic proximity. We thus excluded ≤3rd degree relatives2 from the dataset to bypass this source of information and test the generality of this approach. Prior to the exclusion of close relatives, the IBD-based predictor obtained an average error of 86 km , while the allele sharing distance predictor obtained an average mean error of 118 km . After removing close relatives (which brought sample size down to 8226), the IBD-based predictor obtained an average error of 95 km, 95% CI = , optimal K = 5 compared to 137 km, 95% CI = , optimal K = 5 for allele sharing. Note that this analysis focused on mean error, which is larger than median error  birth coordinates on the predicted X (resp. Y) birth coordinates using either IBD sharing in the past 20 generations allele sharing, for the set of 8226 random samples we obtained after excluding 3rd degree relatives2. The estimated coefficient for the IBD-based predictor was 0.91, 95% CI = , , substantially larger than the estimated coefficient for the allele sharing predictor . Finally, after excluding close relatives, we computed the correlation between true and predicted coordinates for both methods, obtaining a stronger correlation when using IBD sharing (r = 0.6 for X coordinate and r = 0.74 for Y coordinate) than when using allele sharing . Correlation for IBD sharing was also stronger without removing close relatives . We did not exclude individuals from these analyses based on their inferred or reported ancestry, so that these results are reflective of the average UK Biobank participant. Prediction accuracy for non-White British individuals will be lower due to a smaller sample size. We thus expect that restricting these analyses to White British samples will lead to slightly improved accuracy.We regressed the true T) statistic within the past T generations23. FastSMC does not output the posterior of the TMRCA but provides an IBD quality score, corresponding to the sum of posterior probabilities between generations 0 and T, where T is the user-specified threshold. As the UK Biobank dataset was analyzed for T = 50, the DRC50 statistic at a given site along the genome was estimated by averaging all IBD quality scores obtained from all analyzed pairs of samples (assuming a score of 0 if no segment is present for a pair). The DRC50 statistic reflects the probability that a random pair of individuals coalesced at a given genomic site during the past 50 generations. We averaged it within windows of 0.05 cM along the genome. Results are presented in Fig. In order to identify genomic regions with an usually high density of coalescence times, we computed the Density of Recent Coalescence  to the estimated DRC50 values within putative neutral regions (after excluding the regions of known positive selection and 500 kb windows around them), and used this model to obtain approximate one-sided p-values throughout the genome. We analyzed 52,003 windows, using a Bonferroni significance threshold of 0.05/52,003 = 9.6 × 10−7. When multiple candidate genes were found, we only retained the one nearest to the top SNP . Three of the genome-wide significant signals we detected  fell within the putative neutral regions of the genome. We thus iterated this procedure, excluding these loci from the set of putative neutral loci. Once again, one of the genome-wide significant loci  overlapped with the putative neutral regions. We excluded this locus and iterated the procedure again. Results from the empirical null model fitting are presented in Supplementary Fig. Given 50 statistic using this approach relies on several simplifying assumptions. Specifically, we assume that all pairs of individuals coalesce independently within the past 50 generations, which is not conservative and may be violated in practice. On the other hand, we fit the null model using real data, which likely contains regions under weak selection, and neglect the correlation across DRC estimates in different bins, applying a Bonferroni correction; both are conservative choices. Overall, using this approach to assess significance for the DRC statistic within small time windows was observed to not lead to significant inflation23  of all LoF-segments involving that individual, under the assumption that increased IBD probability and incidence corresponds to increased probability of sharing the LoF variant. Finally, this burden is tested for association with each target phenotype  in a linear regression with covariates for age, sex, BMI, smoking status, and four principal components (two-sided test), similarly to the study from Van Hout et al.p-value after adjusting significance thresholds by conservatively assuming independence for all tests. Not all genes contained shared LoF-segments for testing, which reduced the total number of tested genes to 14,249. This resulted in a Bonferroni-corrected exome-wide significance threshold of 0.05/ for our LoF-segment burden analysis. We note that this approach does not rely on phasing information and that the IBD segment shared with a carrier is equally likely to involve or not the haplotype that harbors the LoF variant. In principle it may be possible to leverage phasing information to increase the accuracy of this approach. Phasing of rare exome sequencing variants is however challenging80 and we do not attempt that in this work.Although this test captures uncertainty about the sharing of IBD segments through the use of IBD quality scores, it makes use of all LoF-segments, regardless of their age. As a result, it may be suboptimal in cases where the LoF arose after the TMRCA, for which a LoF-segment is independent of underlying LoF sharing, and thus do not contribute signal to the burden test. We thus augmented the LoF burden test by separately considering only LoF-segments older than a specified threshold. For each gene, we divided all LoF-segments into deciles based on IBD quality score. For instance, segments with IBD quality scores in the tenth decile , strongly suggest the sharing of common ancestors that lived recently and have therefore transmitted extremely recent variation. We then constructed 10 separate LoF-segment burdens, with increasingly more stringent quality score cutoffs , and performed 10 association tests for each gene, taking the test that resulted in the lowest 81. In particular, these common variants may provide better tagging of the underlying true causal variation than our LoF-segment burden score, and would thus remove or significantly reduce the association signal if included as covariates in the test. Based on this principle, for each gene and each trait, we selected up to three genotyped SNPs that were in proximity (±1 Mb from the gene), which were significantly (p < 1 × 10−8) associated by Loh et al.82, and used them as covariates. We observed that this approach often improves the association signal  dataset , which we however believe did not introduce any significant biases in our analyses.Both LoF-segment burden and WES LoF burden analyses were restricted to unrelated individuals of White British ancestry, as defined by Bycroft et al.49. We also detected three additional associations that were not reported by Van Hout et al.49: MAPK8 and APOC3 with red blood cell distribution width (two-sided t-test p = 1.33 × 10−6 and p = 2.13 × 10−7 respectively), and TET2 with eosinophil count (two-sided t-test p = 1.79 × 10−8). Results are summarized in Fig. 73 but addressing this issue goes beyond the scope of the current study.Applying our WES-LoF burden analysis, we detected 10 out of 14 exome-wide significant associations also reported by Van Hout et al.Further information on research design is available in the Supplementary InformationReporting Summary